I have a graduate degree in mathematics, and I think this is a fascinating question. Here's my take on this. Mathematical objects are, fascinatingly, both *objective* and *abstract*. That is an exceedingly rare pair of properties for a thing to have. Everyone (including mathematicians like myself) will agree that mathematical objects are *abstract* (that is, they do not have a "physical" or "material" existence). And for many people (especially anti-realists) the conversations ends there. But if you want to know why mathematicians tend to be mathematical realists, it is because we become deeply familiar with the *objectiveness* of mathematics. You see, unlike most other abstract things, mathematical objects do not bend *one iota* to a thinker's will. They may exist entirely in our mind, but they are not subjective objects. We cannot shape or carve them. They do not bend to our opinions or preferences. Prime numbers, for example, have certain properties that arise from their definition itself. Any mind that springs into existence anywhere in any universe will (if they are fortunate enough to “discover” or “invent” prime numbers to begin with) would agree on the properties of the primes. The properties are *inherent* in the objects themselves, and these properties are the same for all observers. Indeed, any mind that ever comes into existence in any universe would agree on *every* property of prime numbers, circles, squares, etc. It is this property of objectivity that imparts on the mathematician the feeling that these objects exist "on their own". It is from this position that the mathematical realist argues that mathematical objects "actually exist" - even while readily admitting that they have no physical or material substance. It is why mathematicians describe the action as “discovery” rather than “creation”. People *without* that deep direct experience of the objectiveness of mathematical objects (most of my students, for example) often have the sense that the "rules" of mathematics are somehow arbitrary. As if things are the way things are because a bunch of professors decided it was going to be that way -- as if they could have just as easily decided it was going to be some other way instead. But such is not the case. These objects are they way they are with complete indifference to the way we feel about them. Does this objectivity imply that mathematical objects “exist”? Well that depends entirely on how we define the word “exist”. The way the word is commonly defined is not strict enough for us to decide either way. The anti-realist would say “the abstractness implies it doesn’t exist”. The realist would say “the objectiveness implies it does exist”. I say “mathematics is abstract and objective”, and I ask myself “what does it mean for thing to exist?”.
I used to think the rules of math were arbitrary until I began attending university. I am happy I got the opportunity to finally learn enough to properly appreciate the nature and beauty of math.
The way I think about it math is the study of abstractions and the patterns that rise from those abstractions. So those patterns exist regardless of who's observing them. I think you're right, the problem is trying to define exist to an abstract thing in this case. Do thoughts exist? And if they don't then how do we know that we exist? If they do exist then we must exist as the source of those thoughts. since those thoughts are an abstraction then they must have something similar such as we can only think about stuff we know. Even imagined things are based off of things we know. As to the videos argument about it boiling down to faith, all physical sciences do as well. Human knowledge is limited and will always be. It is like asking what was before the Big Bang or how large is the universe outside the observable universe, it's impossible to know and at a certain point you have to accept the limitations.
Aren't you assuming that another mind would use the same logic as we do though? What if using the same axioms it would arrive at different conclusions? Hence, to describe it's objects it would have a different set of axioms and it's system of axioms would appear inconsistent to us but perfectly consistent in their logical system?
Math is "real" in the same sense that language is "real". When you say the word "tree", there is no actual tree. The word is simply an abstract concept used to describe something real. It's the same with math. Math helps us accurately make sense of reality.
ism schism That's because "three" only implies three units OF something. It is simply another layer of abstraction. We don't see "love", yet it "exists" in the sense that we are able to distinguish a certain range of feelings from another range of feelings that make up "hate".
CampingforCool41 Just a "layer of abstraction." That's good to hear. I always wondered why someone might have some short used inferior-quality pencils while I have some new long, superior-quality pencils, but people say we each have three pencils. It seems to do no justice to reality!
+CampingforCool41 You might have missed the point of the video then. Of course math is cognitively consistent. Or else we'd throw it out. The main question is whether math is something out there to be discovered (like a new fossil), or whether it's something that humans create that is really good at describing things in reality.
I think the INSPIRATION for math exists in real life. Angles, shapes, values, they can be observed throughout the universe. But we as humans decided they were angles, shapes, and values in the first place. Before humans existed, things didn't really have "value". They were just there. Humans, in an attempt to organize what they observed, decided that an apple and another apple were two apples.
agree but in some case we not been able to invent tangible value, like why 1/3 is 0.333333..... to infinite!?? or Pi is 3.1415....... to infinite!?? we couldnt complete it? math is full of flaw but still usefull
They exist, but is an angle that occurs in nature inherently an angle, or is it an angle because that's what we call it? Before the word "angle" existed, were they angles? Or were they simply natural occurrences that meet the criteria for what we consider an angle?
Math is the extrapolation of logical reasoning, founded in axioms and relationships. It's a study of how far can you push logic and still produce useful results.
What is thinking? What are thoughts? Do plants & animals have thoughts? Can they think? What about an amoeba, neuron or virus? Can they think & have thoughts? Can a computer/calculator/abacus think too?
Well then math is a way that we think as humans with minds in a certain way, meaning it is a fiction of the mind. But if it is a real as thoughts are it is a thing that exists in the universe objectively, so you have an opinion that is neither one of the original answers. Congratulations, you advanced the discussion.
i think what he meant was that, wew all have thoughts, know what they are and consider them real, yet a thought is not a physical thing you can point at and say "that's a thought"
Thoughts don't exist as objects, at most they are being experienced, that doesnt make them real. Otherwise dreams and optical illusions would also ''exist''.
When I was 16 I asked my Maths teacher "Is Maths something inherent in reality or just something we impose on the world?". He looked at me and said "Get back to work Beach". I ended up doing a degree in Philosophy while my Maths declined :)
I remember asking my math teacher who decided that 2+2=4? What if I suddenly decide to say that 2+2 really equals 5, how could anyone prove me wrong? What if 5 is really 4 and 4 is really 5? How could we truly know?
the memes and jokes in these videos are hilarious because everything about mikes ideas are but everything else about the videos have aged so much hahaha
Let's be clear, in math we have mainly two things: -Definitions -Theorems We invent definitions with abstract logical rules. We discover the theorems, that are logical consequences of the rules we invented. So, one part of the math is an invention and a language(the definitions) and other one is a discovery(the theorems). Many things in the real world follow our definitions up to certain point in consequence they follow our theorems up to certain point. The fact is that with math we can discover universally valid facts that can explain things that had happened and predict things that still don't happen. Does math really "exists"? I think that question doesn't have any sense, the concept of existence is not well defined and should not be used for this purpose.
Math is both a feature of the Universe and a Human Creation, because we humans are part of the universe and even we create it with our conscience (and this conscience is, of course, part of the universe).
The main problem with this discussion is that most people don't have any clue what math is based on. In mathematics we call this basis our "axioms". Axioms are facts we accept/assume to be true and use to deduce more mathematical facts. The axioms for the average person are usually what they learned at school or, for those who actually listened that one time the teacher proved Pythagoras' theorem, what they learned at primary school. Namely stuff like "1+1=2" or "The square root of two has infinite decimal places". In practice mathematicians aren't that different, but in theory, all math is based on some very abstract but basic principles. Something like "1+1 = 2" might seem like good candidate for an axiom: Everybody would accept that it's true and it seems very basic. But for an axiom to be viable as a basis for *all* math, it has to have more to it than just being accepted by everyone. For example: If you accept addition, you can easily establish multiplication as repeated addition, or subtraction as reversed addition, but if you try to prove something about for example set theory, you will find it to be impossible to do so with this assumption ("Addition"). So after thousands of years of mathematical progress without a well defined basis, in the early 20th century mathematicians decided to clean the whole system up by defining these very basic axioms and actually proving trivial stuff like addition to "be true". They are like the wooden blocks kids played with before smartphones were invented: You can do a lot with them, but after a while all possibilities are exhausted. You could build an even higher tower or an even longer bridge, but you can't build anything actually new out of them like for example a bowl. To come back to the original question, continuing this analogy: When a kid plays with its blocks, it might discover that it can place one block on two others and thereby build a bridge. Of course this kid weren't the first to build a bridge, but it _discovered_, without ever seeing one before, that it can create what we call a bridge out of its toys. Mathematicians do essentially the same thing: They use mathematical building blocks and play around with them until they find some new combination. The question is: Does the constellation of the bricks, the "bridge", already exist as an abstract concept, or does a child have to exist and create it for the "One block on two others" concept to exist? If for example in absence of any conscious being one block happens to fall onto two others, thereby forming what our kid _invented_, we still get the same result *without* anybody inventing it. There isn't anybody there to call it "Bridge", but it exists the same way an undiscovered species or unknown chemical element exists. The same way you can ask whether multiplication exists in a universe of addition. Maybe nobody thought about actually giving it a name (yet), but still, when repeatedly adding e.g. dinosaurs to a population, you are doing the same thing as we are when we are multiplying numbers. So far it might seem like mathematical facts "exist" and are there to be discovered, since even without anybody there to think about them, they still apply. Here is where the problem lies: Where do the wooden blocks come from? The bridge is made out of blocks, but what are the blocks made of? You can break the block down into molecules, the molecules into atoms, the atoms into protons, neutrons and electrons, those into quantum particles, the quantum particles into ???. Based on our current understanding of physics, quantum particles are the absolute basic building blocks of our universe and *everything* is made out of there. Applying this concept to mathematics we can break down every theory, all formulas and any mathematical concept into the concepts they are based on, and in turn break those down, and so on until we reach our absolute basic building blocks, our axioms. So in the end, mathematical concepts exist in our mathematical universe, which is defined by our mathematical capabilities / axioms, the same way that objects exist in our physical universe. When a scientist discovers an unnatural chemical element by *producing* it via combining existing chemicals or when a physicist lets particles collide to produce new ones, did they really discover something or did they invent it? How can you draw a distinction between those "discoveries" and supposed "inventions" in mathematics? You combine existing objects to produce something new. Thereby, the real question is: What is the difference between invention and discovery? You would call finding out that rubbing a balloon on your hair produces electricity a discovery, but creating an iPhone an invention. When Edison observed that letting current flow through a wire produces light, did he invent or discover the light bulb? It is hard to draw a line between invention and discovery. Thereby this whole discussion is interesting, but it is impossible to give a definitive answer, making it a slightly pointless endeavour.
+Garbaz great comment... and just brainstorming aloud here... but in the example about scientists producing an unnatural element or physicist producing particles by collision... I'd say, if these elements didn't occur by themselves in nature (without human intervention), then these scientists have invented the new element/particles. If they could be produced naturally, then they are discovering. (Humans are arguably "natural" too [existing in nature], but lets say we are not.) So, yes - rubbing balloon on hair causes static is discovery and creating iPhone invention. And Edison observing current through wire producing light is discovery, but building the mechanism in which to channel that light (the light bulb) is an invention. I actually don't think you can invent anything in mathematics... we may have invented the language to describe the concepts... but we discovered the mathematical facts / concepts.
Euler's identity, e^i*pi + 1 = 0, absolutely blows my mind, even though I understand its derivation. These constants are completely unrelated constants which are simply INHERENT to the nature of things which are just a part of the universe, such as circles, compound interest, etc. The fact that they are all so beautifully and elegantly related, whether or not we like it, is probably the most compelling demonstration of realism.
I think this is the best comparison. I'm sure if we used a different system like base 12 a lot of our equations would look different, but still be true nonetheless. Thus our math isn't a fact of the universe but our way of conveying the facts.
@@KEvronista But what if we were not attempting to describe Quantum Mechanics. The real question is whether or not the properties of what we call "Quantum Mechanics" existed before it was observed. It is the same argument of whether or not a tree falling somewhere, and not a single living organism was there to observe it, did it even fall. For, until it is discovered, it does not exist. The same would go for Schrodinger's Cat and so many other problems. The main problem here is that there is no way of knowing anything exists before it has been observed since just knowing that it exists is observation in and of itself.
@@arthurianpaladarian9531 *"But what if we were not attempting to describe Quantum Mechanics."* huh?! i said qm describes. i didn't say anything about describing the descriptions. KEvron
@@KEvronista “Observer” in quantum mechanics is a bit of a misnomer. An observation is just a measurement or interaction. It doesn’t require a physical entity “observing” it. Stars would still star without a living entity in the universe there to see them. The physics of quantum mechanics would still exist. Quantum fluctuations would still occur. Quarks would still come in pairs and quantum tunneling would still be a thing. Black holes would still evaporate as virtual particles became real at the event horizon. The universe would behave exactly as it always has if life did not exist. Because an “observation” is any interaction, not the physical act of “looking” or “measuring” something.
DronePunkGAME Sure you can. Your teacher will then probably say that your math grade doesn't exist. And the school will say your diploma doesn't exist. But I digress ;-)
DronePunkGAME "Math doesn't exist" is only interesting as a semantic question. If math has nothing with reality to do, it exist at least as a notion, an idea, a fantasy, and as a very sophisticated artificial cathegory. It is not even very interesting as a semantic discussion.
DronePunkGAME If I was your math teacher, i would say. "Yes, I agree, math may be a creation of the human mind, but it is how we organize the world and interact with it and understand it, therefore you must still take your math test."
Gordon Chin a bunch of channels doesn't realize these truth, a smart editing or an outside reference at the right moment may make the explanation more lively but to drown the video on this things, just bores.
I've always said I've had a hard time rationalizing math. Every teacher thinks it's because I'm not putting effort into it, but I know I put a ton of effort in. I think I have a bad time following math because it's not base in actuality. I know math is the language of the universe, but it's like Chinese to me. This video gets a 10/10 from me.
Same! With Biology and Chemistry it was almost like I could anticipate the next lesson, every concept built logically and intuitively upon the last that felt so… natural. But with math, I could understand it, but it seemed very rote, and I often got lost in the abstract concepts within it trying to understand them more concretely.
@@isidoreaerys8745 that's often a product of the public education system :( proofs and logical mathematical reasoning should be taught earlier in education so students aren't confused and understand the foundations of maths
Only if you combined those two lumps of sand. If they remain seperated they are 2 different lumps of sand. 1 kg lump + 1 kg lump = 2 kg lump regardless of seperation.
@@balasubramanians7932 one particle + one particle = zero particles. A virtual electron + a virtual positron will annihilate and leave nothing. So addition does not work in Quantum mechanics. Also take empty space and wait. Eventually you will get two particles created from the void. So zero = two. Math fails, it is flawed and based on Classical physics.
@@jeffbguarino I don't know what is "virtual" here. But Wikipedia says, for that, " At low energies, the result of the collision is the annihilation of the electron and positron, and the creation of energetic photons .... At high energies, other particles, such as B mesons or the W and Z bosons, can be created." Hence, annihilation of an electron and a positron does not leave out nothing, a photon is not zero. On the other hand, these are just fluctuations in fields without very well defined position, so we should not count if we can not count. Math was developed before physics. Physics uses a lots of maths. But none are based on the other. One is science and the other is not. Quantum mechanics is physics which uses a lot of maths, so if addition(or math) is invalid none of those formulas are valid.
Math is a human invention, but it is not "made up." It is our way of explaining the already existing things around us, which is pretty much the definition of spoken language. Essentially, math is a language. On a side note, religion is not the opposite of science, in fact, it's not even related to science. Science is the explanation of the existence while religion is the belief, or disbelief, that a higher power created existence, simply the belief in higher powers or the supernatural, or an interest that is held and pursued at a supreme importance. By this definition, science can even be a religion if a person holds it to be important enough.
err, no, belief in a creator power is not religion, nor even A region. At best, it is part of some religions, and more often than not an after thought, nowhere near central point of the religion that a believed power or powers created the universe. It is, I agree, a central part of the most popular religions, but that fact does not define the idea of religion itself.
Louis Victor Correct, religion is much more diverse and complex than that, but a five paragraph essay about the definition of religion is not necessary to make my point. Additionally, a majority of people only know about the most popular religions, to which my explanation relates, so it is fruitless to go deeper when the possibility of somebody not grasping the point and recognizing the difference is so small.
S.M. grimbldoo It is not fruitless, it bears negative fruit. Using the expression "popularly" and with a meaning that is false is, at best and most innocently, keeping alive and helping to disseminate the falsehood. If it is incorrect, incomplete, and misleading, why state it in the first place? Not that what the vast majority of people think/know makes it a valid argument or a "so small" chance of getting it wrong - people are already broadly ignorant, they don't need any help with that. Now, if you really just wanted to say the Abrahamic religions (and perhaps Hinduism), or "the most popular religions are..." rather than reduce religion to just the most popularly known, you could have easily said just that with those few words. Doesn't require making an essay, doesn't reinforce a false concept, and is still 100% accurate....
Louis Victor There you are mistaken, the definition I used is not false and neither was my statement.Too specific, but not incorrect. Here's my question, are you really going to try to tell me that science is the opposite of religion when science is the observation and explanation of nature while religion is the belief or disbelief that a higher power created the universe, the belief in higher powers, or an interest held in supreme importance? By this defenition, science could even be a religion. Thank you for pointing that out, however. I was struggling a bit to grasp that my statement was too vague. I knew what message I was trying to convey so I didn't really see where the delivery fell short.
S.M. grimbldoo I didn't opine regarding the original point about science vs religion, so I am not saying Science is or isnt opposite to religion. I was just focusing on the meaning of the word religion (which can contain your first definition, but is not the same since it is much broader - i.e. some vegetables are food, but food isn't (just nor always contain) some vegetables).
If you define something into existence, does it actually exist? If you define a concept by giving it a few properties, then it is a mathematical object. You can then use the laws of logic-identity, non-contradiction, excluded middle-to find out all statements about your newly defined object, as well as if it is logically possible. If that is good enough criteria for something to exist, then math exists. On the other hand, if something has to physically interact with physical reality to be real, then it doesn't exist. But real things must obey the laws of logic, and so must mathematical things, so in that sense, they are alike.
Ultimately all of language is arbitrary, relying on the pattern recognition encoded in our DNA. So we talk and hope that the people we're talking to perceive the world in a way somewhat like we do.
Actually, by the way you phrased your sentence, it has to exist: If we gave something a name, there has to be something that we have just named. Otherwise we would not have succeeded in giving a name to anything at all.
I have always wondered this! I have always wondered how math can be, "real" but I've always in my head thought it was our way of understanding and explaining things.
Math is one of the intelligent creatures' tools for linking with reality. By practicing math this link grows, and it gets easier to implement new ideas.
Math does not exist "out in the universe". At the same time, it does not simply "exist in our brain". It is actually in a layer that is beyond the universe. Math is not in the universe, the universe is in Math. This may sound strange, awfully philosophical, or perhaps even meaningless, until you understand model theory. The idea behind model theory is that mathematical rules can "map" into real-world concepts. Like, similar to the example already given, 2+2=4 can map into the real-world take 2 cats, add 2 more cats, get 4 cats. But the main premise of model theory is that you can map the same mathematical concept into several different elements. For example, 2+2 doesn't have to be about cats. In fact, it doesn't even have to be about physical objects. If you've waited 2 seconds, and immediately after you've waited 2 more seconds, then you've waited for 4 seconds. In the eyes of model theory, then, math is about finding out what's common to different models. It starts by trying to find a minimal list of observable facts that a certain model has to fulfill in order to be "sufficiently similar" to other models. For example, in the case of addition, we require that we don't care about the order of the objects. For instance, if you put 2 black cats right of 2 white cats, then while you have 4 cats, this doesn't represent the fact that you have, right to left, black-black-white-white cats. Only if you decide this latter detail is unimportant, does the model fit. On the other hand, if color does matter, than taking the black cats first, and then putting the white cats right of them, changes the group of cats. The next step is then to figure out what can be inferred based only on these observable facts, without relying on the observations themselves. For instance, 2+2=4 is actually a direct result of 1+1=2, 2+1=3, 3+1=4 and order of operations not mattering. The first 3 can be seen simply as definitions of 2, 3 and 4 (As what happens to the group when you add one more of the smallest group). They are giving names to concepts. The last one is the thing that must be true for a model to fit. Any aspect of this universe, or any other, that fits this requirement, would also fulfill 2+2=4. The ultimate result of model theory lies in Godel's completeness theorem. It states that: 1. If something is true in a purely mathematical sense, then it is true for all models that satisfy the basic required observations. This means that math can be used to reason about the real universe. Another way to look at it, is that math can be used to show that certain types of things cannot exist, in any universe, simply because, in mathematical form, they would result in a contradiction. A good example is that the laws of thermodynamics (conservation of energy) can't be violated without first violating one of the basic laws of mechanics (e.g. every action has an equal and opposite reaction) that mathematically cause them. So long as the basic observations hold, the conclusions must also hold. Conversely, if an observation shows that the conclusion was violated, it implies that one of the basic rules on which it was based was violated as well. 2. If something is true for all models, then there is a finite mathematical proof for it. Or, conversely, if there is no finite mathematical proof for something, then there is a theoretical model in which it is not true. While this fact may not directly relate to this universe, as the "model in which it is not true" may simply be a theoretical universe that doesn't actually exist, it does give us a way to limit the things that must be absolutely true for all possible universes. All of those must have FINITE proof, that is, the proof can be written using mathematical symbols on a finite number of pages. At the same time, every time mathematicians think they've found a model that could only exist in theory, the universe has shown that if it's mathematically possible, then there's some aspect of the universe in which it physically exists. That's not to say that this is always the case, simply that mathematicians are still in search of the case in which it isn't.
1 cat plus 1 cat doesn't equal 2 cats. They are not identical units. Both cats are infinitely different and can't be added or subtracted to an exact degree. Math isn't true, it's simply a tool of observation, navigation, and creation.
Marcus It depends on how you define "cat". If you get too metaphysical, one never feels pain, and one never sees anything. It's all nerve impulses, which also don't exist, as it is field movements, which are actually vibrations of strings, which are actually a hologram on the surface of an inverse black hole spanning the exterior of the universe. All of this metaphysics is very interesting, until you get punched in the face, and then it actually very really hurts.
Math is something we use, its a tool, that we created to help convey and understand patterns, and other situations in nature, and to define nature in a sense Math is a Language
When I saw this for the first time 5 years ago, I was so certain math is objective entity of the universe. Now I am inclined to the opposite, but see how both could be true. Beautiful how one's perspective changes over time :)
Math is like a language. It is a tool that we describe things with. But there are possibilities for a new rule to exist, like other languages. This is studied in abstract algebra, where new sets of rules are made and observed. A new mathematical language, if you will. But just like a language, it isn't a part of an entity, or an entity itself.
Good thing I found this video. I've been telling this to people for a long time. Math is not proven empirically, but logically, it's proven in itself. Therefore it's not science, it's philosophy.
***** It's not the only one though. There's a number of philosophical tools constantly used in science. They're just not as complicated and most people use them without thinking about them.
I mean, you're right, but saying that it's philosophy oversimplifies the argument a lot. All things are philosophy in the same sense, ie the sense that they can be deconstructed to a simple tautology. The only way we gather information is via senses (or a layer of abstraction from our senses), and we do this without being able to tell if our senses are correct. Following this line of reasoning down, we can conclude that all information is based on a tautology, and becomes philosophy. So we are left with taking as an assumption at least one thing that is likely "unknowable," or becoming solipsistic. What math, and by extension science, takes as that assumption is orcam's razor. Why I feel that calling math philosophy is an oversimplification is that it doesn't convey the idea that, as opposed to most modern branches of philosophy, we made a key assumption for the sole value of utility.
There's 3 types of formal knowledge: Science, which is corroborated empirically, Philosophy, which is corroborated in itself, and theology, which is corroborated in the scriptures. It's not an oversimplification because math is by definition part of philosophy. There's no room for interpretation, it's just what it is. People just vastly underestimate how useful and how widelly used philosophy is because they only think of it as people thinking about existence.
Altrantis I completely agree about the last part. I was a philosophy major before switching to engineering. The first part, though, I'm having issues with. We both accept that everything is philosophy, right? If so, it puts the word in a precarious position of being redundant. Further clarification is needed to draw a distinction, which is quite simply, math/logic. Calling math/logic anything other than what it is runs the risk of being either too broad a term, or too narrow.
Not everything is phylosophy. Just because you need phylosophy to establish a link between science and your own understanding doesn't mean that science is phylosophy. It doesn't prove itself on itself, it proves itself on the non-self. Math and logic do not enjoy that distinction. Regardless of the fact you manipulate science using philosophy, like if it was a mechanical arm, what you're working with has a given result that does not necesarilly follow logic. That's when you realize something's wrong and have to change your hypothesis. Science is always wrong. Philosophy on the other hand, is neither right nor wrong, since it's what defines what is right and wrong (not morally). And that distinction is most likelly eminently human and not out there in the universe. There's a reason logic as a class in the education system is taught both in math classes and philosophy classes. Math is to logic is to philosophy what biology is to chemistry is to physics. Sure, they're conceptually too different for the human brain to work math as part of philosophy, same as we can't work the intricate workings of biology from a physics point of view, but that doesn't mean it's part of it. Biology is a specific branch of chemistry that studies the specific types of chemical phenomenon called life, and chemisrty is a specific branch of physics that works with a specific type of matter arrangement, which is when atoms unite to form molecules. Logic is to math and philosophy like what atomic physics are to physics and chemistry. Or geomorphology is to geography and geology.
Mathematics is real and exists independent of the human mind. Anyone who thinks otherwise doesn't understand math, and is likely getting confused by the human symbols, terms (names), and definitions that we invent in order to comprehend math.
Math is more like a tool for modeling the universe than something that fundamentally exists. It is a way to define physics; an abstraction to help people understand. There is purely logic based math, but all logic is actually just defined by people to fit things that make sense to them. It is proven because it has been applied and models real things, otherwise it is just logical system, even if it fits in its own framework. An idea that can be rigorously proven within its own accepted rules is still an idea and not a universal truth. If even the numbers themselves are just abstractions than there is no way the rest of math isn't one.
When you say "is a tool" that tells me you're doing exactly what I said. Confusing the symbols, terms, definitions, etc. to be what math IS. That is not what math is. Those are the tools we use to understand math. It's like the question of whether a tree makes a sound if there's no one around to hear it. Energy from the fall of the tree causes waves in the atmosphere, which is what sound is - it does make a sound. If someone were around that could perceive it, they would hear those sounds. 1+1=2 independently of whether there is anyone around to perceive it. Those perceptions are uniquely human. The existence of the math itself is not. It's been shown that other animals can do rudimentary math. If we encounter alien species, surely they will understand math. Their definitions, their terms, and concepts will undoubtedly be different than ours, and have different implications - for example, what it means for a function to be continuous. HOWEVER, we will agree on the implications of their definitions, and they will agree on the implications of the definitions we've chosen. They and we will have different perceptions, different perspectives, different views of the math, but the math itself exists independent of our minds and perceptions of it.
My point is that 1+1 itself is not even a universal truth but a defined and abstract truth. It is a way to model things that we categorize with our brains, not something that fundamentally exists. The most important "discoveries" in math were simply ways to model things that existed in the world and tools for more people to be able to understand how those things worked, they didn't invent the math and then use the math to figure out what to do.
How can 1+1 not be a universal truth? The symbols used are human ones (specifically the symbols of our particular human culture - Sumerians, Egyptians, etc. used different symbols), but the existence of a singleton and the process of combining singletons that we call addition is not something that only existed after we thought of it. 1+1 (in whatever guise) exists independently of the human mind (or any mind). If the universe consisted entirely of two atoms, then the one atom, combined with the other atom, would make two atoms. That's an extremely universal truth. Even if the universe consisted of no particles and was just empty space, even if the universe didn't exist, you'd still have the existence of 1+1=2, and all the rest of mathematics including that which hasn't been figured out yet and math that will never be figured out. Math is not just "models" that we come up with. Models are just our way to conceptualize and understand the universal truth of math.
Dagobah 359 So what you are saying is that math exists as a concept but does not fundamentally exist. Math needs an additional understanding to make any sense, it requires human grouping. Using the addition example, a person actually requires a scope and a definition of an atom for 1 + 1 = 2, atoms are actually not atoms but a group of other things that we call atoms. Same with everything else; the fact that addition is possible is only down to categorization, which is not universal at all. (Yes, math is possible without categorization using only numbers, but the end result has no meaning at all. It would be like language without nouns.)
I don't understand the question. The human brain is in the universe, part of the universe. To ask if math comes from the universe or the brain is to give no choice in answers...
hm maybe think of it this way: your brain is just cells connected with electricity and thinking is nothing more than your cells "talking" to each other. soo there is no math in your head. not a "real" thing you could call math. so the question is, is math just our way of thinking and analysing or is there a natural math, like, if there were no humans with brains, would there be 1,2, pi and this stuff
ViperblueHD Simplistically speaking, rocket ships don't grow out of the ground. We take natural materials and natural processes and combine them in ways nature never would to make unnatural things.
Math must be the symbolic shadow of concrete realities MC Escher has some great art depicting the fuzzy barrier between reality and our contrived symbols of it
Realism and platonism is one of the biggest disservices to students of mathematics ever. Mathematicians understand that they're just working with a formal system of axioms and rules of inference. Thinking of numbers as platonic objects that exist was a great impediment for me in exploring mathematics at the horizons, for example, in researchinig hyperreals of model theory and the history of transfinites. PLEASE, educate your math students about what math really is: a human language. Mathematics, unlike spoken languages like English, admits only precise statements in meaning while employing a small set of primitive nouns and even smaller set of primitive relationships among those nouns. Actually, a great deal of effort has been made to reduce the primitives of mathematics to its bare essentials (Zermelo-Fraenkel Set Theory and First Order Logic are the best examples of this), and then use these to build the entirety of nouns and relationships in mathematics like numbers, arithmetic operators, functions, vectors, tensors, manifolds, theorems, advanced operators, and on and on. This is quite different from English for which syntax is arbitrary, nouns emerge, and meaning is vague and evolving. Mathematics and Logic are languages created by philosophers of old to think, communicate, and record ideas precisely and no ambiguity. That language has allowed rigor of thought and method first in business, geometry (literally measuring the earth), and natural science. Programming languages are in between mathematics and spoken languages. Those likely provide the best analogy to think about mathematics. You can prove things about programming languages, but obviously they are man made. Now, all forms of human activity are adopting precise languages, like chemistry, psychology, finance, art, you name it.
+oarevalo21 What if we contacted aliens that also used the same mathematics? Is it then a "sentient language" all thinking beings understand? Is mathematics part of being sentient or aware?
+octavio echeverria Is it impossible to independently invent similar things? And even if math is some language invented by us, it isn't arbitrary. It's main purpose is to "talk" about the external world and we share that world with those aliens. This limits the freedom a lot. And of course, we don't know, how some hypothetical aliens think about the world. Until we find some, this line of thinking doesn't help with this question at all. I was convinced by one think. Imagine, that you are counting apples. Now try to precisely define, what apple is and isn't. What atoms are part of it, etc. You aren't counting real apples but abstract ones. Math isn't the first layer of abstraction of the real world. You can count meters or kilograms using math. But math itself can't tell you anything about what those meters or kilograms really mean.
+oscar i think a helpful term for you might be "ontological mathematics" which is commonly used to differentiate mathematics-itself from humans' interpretation of mathematics, which would be the language subset you speak of.
I miss this channel. I can’t believe this video came out 10 years ago. I remembered a conversation at a family function recently where I argued with someone that math doesn’t actually exist, it’s another form of language that we use to describe the universe, so it’s “real” the same way English and Mandarin Chinese are real, but is also constructed by humans and exists only in our minds when we think it into being. And my family member was like “no.” Lol anyway, I’m sure I got that argument from this video and I just love the number of ideas I have taken with me from this entire channel… truly ingrained in me.
Yeah, he does but I see Hank as the progenitor of that kind of over-emphasised speech pattern. I know what they're going for but when it's exaggerated so that it stands out it comes across as patronising. Now I'm just bitching and moaning.
it's the standard cool teacher speech pattern. I see myself falling into it all the time in class. somehow it's the go-to option when you're trying to get teenagers to follow you thru the boring parts into the (hopefully) exciting ones.
Math is just a model of the universe like anything else. Nothing in the world is objectively true, everything we know about the world is filtered through our senses. It is consistent with observation in a vast variety of settings and that is all we can say about anything. Also its not so much a separate science as a useful extension of existing sciences. It is literally useless without applications. I think however that it is as "real" as physics and chemistry for the reasons I have stated. Btw this is from a mathematician, so I am not saying math is useless only that its existence relies on its applications.
i've never met and single mathematician or engineer that thinks math "exists" in any kind of objective state. most mathematicians will probably tell you that math has very little to do with the external world, and it's effectiveness in describing said world is more of a side effect of the real goal of math. that being to produce as few contradictions as possible.
I've met lots of mathematicians that subscribe to mathematical realism or platonism in various disguises. Can't say anything about engineers though - they are probably busy computing integrals to think about this stuff
Math is obviously a system created to describe numerical operations that already existed. Before "math" was "developed" people could still have 2 apples and eat 1, leaving 1 remaining apple. Math accidentally came about through the discovery of language. This is the reason why every country has different words for the operations. In English we say: 2 plus 2 equals 4 In Japanese it would be: 2 tasu 2 ha 4 The concepts always existed, we just created variables (words) to describe them.
Try telling a hardcore pious type that. They attempt to discredit mathematics saying it can't exist because it isn't physical yet we know it exists therefore the same principal can be applied to God. This theory that mathematics doesn't exist is just another Creationist attempt to "prove" God. They fail to understand it is a descriptive part of language to describe quantity of something which evolved to advanced equations to make larger sums easier to equate... Basically the idiots who claim this have no real understanding of the history of human language and its impact on society.
I would say those 2 things are mutually exclusive. I could see both religious and nonreligious people choosing either side. You are injecting your own antireligious views into a topic that has nothing to do with religion.
Guys, you are simply awsome at explaining things ! Being of a limited brain like everybody else, I have a limited answer for the limited conjectures we make and this applies to math and all other sciences, I wish it were otherwise !!
I think it's time I brought out Dumbledore for this one: "Of course it is happening inside your head, Harry, but why on earth should that mean that it is not real?"
Because Harry is not schizophrenic? The belief that one's thoughts are reality is usually seen as a sign of insanity, even though I can find no logical reason not to believe it. What is reality?
People tend to base reality on popular vote. If everyone thinks it's real, then it "must" be real...which is technically fallacious reasoning. You're right. What *is* reality?
Gibran Mahmud And that's the key word: "believe", not "know." And, "pointless philosophizing"? Not sure if you've noticed, but that's kind of what this (awesome) Internet show is. If "pointless philosophizing" doesn't benefit anyone, then neither does this Internet show. And if that's the case, why are you watching it? Assuming, of course, you did actually watch the video and didn't simply go down to the comments.
You are wrong. Simple as that. So how can math be perfect and the processes it describes not? How can exponential decay describe something more accurately than reality can? Math explains half life infinitely but reality will eventually run out of particles. It can't keep up with math and it's pure logic. And that's why so many people don't get it. Because they can't think logically.
lutascheier The problem there is the model we use to apply math to reality, not math in and of itself. (Simplified) mathematical models are often used in physics where we basically try to understand the universe with the assistance of math in conjunction with observation, no wonder themodel doesn't match perfectly if we can't observe perfectly.
The idea math helps us describe geometry is certainly true, but an odd point, since geometry is a field of math. Math is used to describe math. True enough, just as astronomy is used to describe astronomy, tennis is used to describe tennis, and language is used to describe language. Navel gazing anyone?
no, math is pretty easy actually. My problem with math in school is that we have to use tools that were built in some way by someone as is convention, rather than create logical tools by ourselves.
How did language come to be? Letters are essentially shapes, yet our brain recognizes these shapes and when these shapes are sequenced they form sentences. Our mouths, tongue and jaw moves in unison with vocal chords creating sounds with just vibrations calling it "speech" is just as amazing as math in my opinion.
It’s crazy because a while ago I had this weird thesis about math and physics that I wrote about. I suggested that half - if not all, physics and math was abstract and could very well be not true universally and only to US since we created it for US to understand things better. Little did I know this was an actual thing that geniuses have already came up with.. 🤔
As a mother myself, I can assure you that we are indeed all hamsters. Every one of us. Have you watched us eat the food our kids tried to make? We nibble. We are hamsters. Also, and we didn't want our kids to know this, but your fathers all smelled of elderberries. Sorry to tell you this, but now that you know it: you're an adult. Now go find your own hamster or man who smells of elderberries and make babies with them! 😁
Math to me is a concept of measurement created by humans to attempt consistency. Like time it was a creation born out of our need to have things organized or placed in an order so we can record it and go back and say "This is when and this is how." If you go back to the invention of the wheel, I wonder if our ancient ancestors figured out that a wheel works best or did they just find a oval stone with a hole in it, carved it down to be symmetrical because our brains wanted it that way, and figured out if you rolled it, it moved more easy? No math involved? It just made sense and we happen to have reached that cognitive ability to make use of it. I also wonder if ancient man maybe used woven material or even animal skin to put things on and then drag all his stuff behind him. Maybe a vine worked as a rope and he tied it to his torso so his arms where free while dragging it. Later the wheel came about through necessity or just made sense rather than dragging it. For all we know the wheel was a couple of coconut halves with holes for an axle. Math had nothing to do with it. We probably only started math when we had to represent how many let's say bananas we were willing to trade for tool or female. We probably used our fingers and thought. "One fruit for each finger I have and I will trade you one spear." But as things became more valuable like better spears or animal meat, they had to say "I want all my fingers worth of fruit plus another half of my fingers worth. So they held up their hand and made a ten gesture then a five. Eventually grunts represented a finger and we took off from there. Of course maybe we started with fives. Since it was easy. and then came up with single digit numbers for each finger. " Hey, ill give you one hand and two fingers worth for your warm fur coat." Maybe a small community came up with the simple add and subtract and names for numbers out of a sort of natural communication. They started by pointing and showing symbols for what meant what then made noise to what each one sounded like. I would bet that about the same time we began trading and representing how many with our fingers, we started growing our language skills and even developed a sort of mini economy in a group of people all interested in trading and communicating. Probably made it easier than roaming around and finding new, less educated cave men that they would then have to teach. So maybe they would bring them to the community if they had something good and would teach them the trade and noises. Over say a few years or even decades they probably expanded very quickly once the idea of trade and communication solidified a group of our cave man ancestors. They began to realize trade was far more beneficial than trying to take it and maybe getting killed in the process. Maybe they learned the value of having someone return with more goods to trade then just getting a one time reward of killing them and taking it. Now they have a year around supply they can trade back and forth for. Of course it probably wasn't too long after that disagreements occurred and escalation led to waring groups. So to conclude, Man invented stuff, people traded for it. People assigned symbols and sounds to amounts and society was born out of the economy it created. Math was born of that system and then disagreements led to war. So Math is to blame for war. Thanks Math. :D
Like i said the better question we should all be asking is that - not whether math exists or not...but if its the universal construct, that is actual for EVERYTHING in our reality or its just something we completely made out in our heads?! Because if its not just something in our heads, then the next question arises - where does that come from?! Is there some sort of alternate reality with its own "laws of physics", where things like letters and numbers re actual physical constructs?! If it is so, then it could explain all our habbits, like why we have this funny idea we should measure things, name things etc...
I wonder how the first human, who invented math itself as a method of measuring things in life found out that is how you should approach things?! Something, somewhere and someone should have "hinted" and "pointed" that person towards it, so that concept would be born! Its the only logical thing to assume!
I agree It’s a model of regularities. It’s kind of both. There’s the objective underlying regularities, but there’s also the imperfect abstraction we created to describe those regularities.
math isn't an actual thing. one, for example, is merely an idea, same as language. it is merely because we call it one that it exists. what we call one and what we call two could be mixed around and we would have just developed things differently (as in, instead of 1+1=2, 2+2=4, it would be 2+2=1, 1+1=4), and things wouldn't change, in the same way that if we had originally called the sun "the hort", it wouldn't have made any difference in anything except language. it would still be what it is. numbers themselves, same with mathematical functions and equations, are not real things. we cannot sense them in any way, we just use them more as labels. however, since they do label things, they do exist in a sense. using the James Bond reference as an example, merely saying "shaken, not stirred" is nothing special, however, it is linked to James Bond, what makes it special or better than other sentences is the label, that it is a James Bond quote. if you went to an alternate universe where James Bond didn't exist in any form, the sentence would lose it's special meaning, the fact that it's a James Bond quote, and would be about as interesting as saying "shake it". however, it does still have the meaning that James Bond used it for, that you want it "shaken, not stirred". go to an alternate universe in which math doesn't exist, and saying 1+1=2 is meaningless. however, what it labels (a cookie and a cookie is a couple of cookies) still does
I think your explaination is too focused on naming of concepts. The relations between numbers and the like are the interesting part. For example we came up with the definition of natural numbers as that there exists a first natural number(regardless of what it is called) and that the successor of a natural number is also a natural number (regardless of what the successor functions is called). That such a concept exists may be inherent in the universe, since it is for instance closely related to counting. We can rename things in the way you described it, but if we rename everything consistently, the relations, consequences of axioms, theorems stay the same. Not really the exactly the same, but mathematically it is the same and I think this would be called an isomorphism (may be this renaming is something that also arises naturally, hence we have some mathematical concept for it). There is actually also a theory that says that language is not a mere idea, but that certain concepts are encoded in our (?) before we are born. I think I read that all languages have some grammatical structures in common (observed on a very abstract level).
Martin Tappler that's all very interesting and included a few things I didn't know however, maybe a slightly simpler, and summarized, version of how I see it might be a good idea: Math is a concept, like language. it is not tangible and there is no way to show it exists without more math. everything else is either tangible, or can be proven with something other than itself. some examples would be dogs, which we can prove the existence of using our senses, gravity, which we cannot prove the existence of using our senses, but can prove exists using the fact that something keeps us from flying off the Earth (among other explanations), books, which we can, again, prove exist using our senses, and any force, which we can sort of feel when strong enough, but which can also be shown to exist by the fact that they make things move. on the other hand, we can't show math as existing. there is nothing tangible, nothing our senses can actually perceive, nor can we prove it exists except with math. we cannot prove one plus one equals two because a cookie is not "one", it is a cookie. "one" cookie, sure, but not "one" itself, or is it "two" itself. language has the same problem, as we cannot prove language exists using our senses, as speech is really just fancy sound and is only meaningful because we make it so, which is how words can sound the same and be mistaken for others, and letters themselves are concepts created by us. however, at the same time, because they are concepts and are found everywhere, they are real in their own way. similarly, any story is real in its own way, not being true, but being a real product of one's imagination. you cannot deny the existence of a story, nor can you deny the existence of math and language, however their existences are really only concepts
Hey, I'm replying to this after 8y. Hope you are good. I respect your viewpoint on this topic and it's like we are thinking alike. You made a lot of sense here.
Math is not the story explaining the reality, that is science. Math is a set of tools, guidelines and a language, which you can write the story with. It is not the very esthetics, just like how the letters, words, grammar and all the generalized theory behind how to write a good story isn't the book it self. All they do is to help explaining the story and maybe help with the making of a story. They just form a tool box for Shakespeare to use when he expresses his ideas.
I agree. The question at stake though is whether these tools were created, like, say, a hammer, or discovered (maybe like a rock? I'm trying to think of an example). In my opinion, just like language, math was created.
Luís Frederico Dornelas Conti It doesn't matter if you find the rock. A rock is only a tool when you invent a way to use a rock like that. The world around us doesn't work by human concepts like rocks for example. We humans can never actuaualy understand the infinitly complex reality. So instead we order the what we observe in to concepts like rocks or hammers, just for our simple minded to be able to handle reality. The irony is that humans are genetically coded to think of concepts like rocks or trees as part of the actual reality and not as a construc of our own mind. But this is probebly just an instinct that exist for the purpouse of our own survival.
Electro-Cute except it's a fact that one apple plus one apple is two apples. You're clearly describing a function that actually exists with math. So math very evidently exists. But it is also an abstraction so we can use it to talk about things that don't exist like hyperspheres.
+Matt Bacon Apples "one apple plus one apple is two apples" is not the reality it self. It is the use of human thought processes, like concepts and mlogic, to understand observations. Mathematically it is not a fact, it is perfect truth because math is defined by humans and therefor can be perfect in its own definition. What we call reality in the other could be an ilusion for all we know.
Math is real because two intelligent beings in far apart places yet members of the same universe can come up with the same logical realization that 1+1 = 2 Math is a phenomenon of time and space. If there was no time we couldn't count passing events, if there was no space there wouldn't be two of anything, maybe not even one.
I can see what you're trying to say but it's a clumsy way to say it. A better argument might be that since humans can apply the math they have to situations they haven't previously encountered and get a predictable outcome it must exist as an objective fact. Yes, you could use other units of measurement to measure it but the fact remains that there is something to measure and would be consistency in that measurement. I don't know enough about math to know how there even could be math we don't know about, since arguably I would think that more complex problems would only be made up of less complex problems. But the idea something doesn't exist simply because you require a little trust to believe in it is an utterly fallacious one. Many of us spend each day living in the assumption that what they see and feel is real when it's possible that it's just a hallucination. Many of us believe things we've never personally experienced on top of that. Yet, life goes on and the world hasn't imploded. Trust seems to work.
Shona McCarthy One could argue that math is the study of the relations objects have between each other, and that the symbols and blocks we use to define them are subjective. Just like our world is subjective... But just like Descartes pointed out "I think, therefore I am" our reality is still valid however it comes about.
***** Interesting. Well in that case, if 1=1 does not give an extra hint of how equal one thing is really to another we could say that there is really just an equivalence. It seems that things only exist in relation to other things, after all the only singularity we know of are black-holes where there are no two of anything and nothing we can think of has solved how they work; but math tells us that what was there is infinitely small and is stop in time. Therefore 1=1 can only exist because each number occupies just one place at one time, but when things do become truly equal then we get a singularity. Out of this realization we could say that mathematics happens as the order of things in the universe. Even if our thoughts can be abstract they must also happen during a given time at an specific place, thus also having the quality of being accountable.
Defining the Universe with Mathematics is like exploring a room by touch. You know the limits because you've pushed up against them. Sometimes you meet what appears to be a wall, but upon exploring in more detail, you discover is actually a door.
I think Math comes from the human mind but it is, of course, an exact science. It´s a system that grows on itself to describe everything that happens around us. It is abstract because it´s just a bunch of concepts but they are exact because they accurately describe what we see and a lot of times predict that will happen in the real world.
iPokerrr Ah, but math is also objective. Think about it. Putting one bed on top of another gives you a stack of 2 beds. Always. 5+5 is 10 and you cannot change that. An alien race would have the same mathematical concepts as we do, because unlike most abstracts, it is objective, and cannot be bent to your will
+Chaotic Fox How many beds can you stack on top of each other? Give 3 candies to a kid, then give him 3 more. How many does he have? None, he ate them all. You have to ignore many aspects of reality to fit it to math. You also have to ignore many aspects of math to fit it to reality. You used Natural numbers and some equivalent of Peano arithmetic, but why not some other arithmetic/algebra? In modular arithmetic, 5+5 could be 1, 2, 3 or whatever you want. If it's 16:00 hrs, you wait 24 hrs and it's 16:00 hrs again. Same for rotation and many other phenomena.
Math absolutely exists. The fact that we call this particular grouping "three" and that particular grouping "five" doesn't mean that, when combined, they don't classify as what we could call "eight." The fact that the people on Zebulon 9 call it "Theenor" or the people on Rylax Minor call it "Ik Thok" doesn't change that there are eight. The fact that we use the term geometric progression or some guy named Fibonacci discovered the Fibonacci sequence doesn't change the fact that bacteria cells would still grow at an exponential rate, very similar to the Fibonacci sequence. The idea that, if humans were not around, they would violate what we know call math is a level of arrogance (that humans are just *that* special) I can't even begin to comprehend. Some of math's concepts are constructs for things we can't see, feel, touch, or even conceive of. Negative numbers, for example, are often only a notation and can't exist in reality. A vector space of 41 dimensions isn't really conceivable by human standards, but we can still do math within the 41 dimensional vector space and be assured it works. An excellent example of this is quaternions. They are four dimensional vectors, and although humans are capable of thinking in four dimensions, it's not really what our brains do best. However, we can see and verify the effect that quaternions have on 3-dimensional elements by firing up just about any game made today. Things on the screen rotate, translate (move around), and scale (grow or shrink in size). In fact, just getting anything on the screen is impressed, since you're projecting 3D images onto a 2D surface using nothing but math. And electrons, silicon, phosphorous, boron, some copper...all that jazz.
+nychold It's interesting, because for me, the idea that we humans, a collective of survival machines that evolved in order to find fruit, not truth, have somehow been able to discover something objectively true about the universe is also incredibly arrogant (not meaning that in an insulting way in the same way that I'm sure you don't mean it in an insulting way!). I would imagine that, if there are aliens out there that are similar enough to us to have a concept of math (which is no guarantee), they would be just as trapped by the limits of their survival machines as we are. As for the advancing of technology, we know that technology advances even if a species doesn't have mathematics. Look at crows or chimps or other tool-making-and-modifying animals - there's no math, but there is technological advancement and modification of existing designs regardless. I don't see why another technologically advanced species wouldn't have developed in the same fashion.
+Nav Vandela Math is not about formulas. Math is more about defining a "something" and making observations based on it that hold "objectively", at the very least in a given context. If an alien designs a technology based on observing or conceiving (without observation) exponential acceleration of any kind after realizing that this indeed will re-occur, it would have used an instance of Math to create the technology. Physics is the Math of physically observable things, while allowing for more ambiguity due to the context, it's mostly a sub-branch of Statistics. Biology is then the sub-branch which only deals with organisms and cells (as far as I'm aware of), and so on. Whether or not Mathematics is the stem of the tree on which the rest of our knowledge and technology branches off from, is unclear and something that we may or may not be able to find out. Who knows, maybe the branches recombine into the stem and it becomes an obsolete question.
+nychold It doesn't matter if the intelligence inventing math is human or alien, they would invent the same math because they live in the same consistent universe. Math as a language describes and models these consistencies
Ali Jorani Aliens could have a vastly different brain and conscious experience of the universe, which would have an impact on their science and Math. Most of the patterns that we see in nature are patterns found in the brain. Basically, what you see outside is just a mirror of what you are inside.
***** I disagree, what you're saying is that there is not objective reality. The reason that science works is because there exists an objective reality independent of our brain patterns. Aliens will describe this objective reality using different models or theories but the ultimate abstraction of this reality which is math wont be that different from ours
I was pondering on this subject and I think we stumbled across the fundamental concepts which led to mathematical explanations. Then we did the foot work by crunching the numbers to show proofs for these concepts and thus came to answers that naturally fit our reality. Proofs are the beauty of math. I believe it is the only expression we can show that has a proof to back it up.
Math itself I believe is a tool, is a framework to describe things, the same thing as a language. But the the things which it describes are "real", some aliens would invent totally different language, but the things which their language would describe, would be the same "real" as our "real", otherwise their spaceships and whatever technological would not work.
i feel like maths is like Celsius its a measurement of temperature maths is the measurement of stuff and what it can do its a measurement of... everything
What about proofs? Like square root 2 is a irrational number. Or pi is a transcendent number. How are those kind of activities like a measurements? What are we measuring in those cases?
Mic Mule As you are aware, pi is the ratio of the circumference to the diameter of a specific circle. In this case, a perfect circle in the Euclidean space. In non-Euclidean space, the value of pi becomes different. Can we get the value of pi by measuring? If so you would need a perfect circle, a perfect ruler, and a perfect method done in a perfect non-changing Euclidean space. If non these are perfect, how can you hope to measure pi? In addition, since pi is a transcendent number, can you ever hope to get the "entire" value of pi in finite time?
I see math more like language fo physics. (and other sciences, but other sciences are just very specialized branches of physics, so still physics) It goes like this philosophy asks questions and physics answers them, often using math as a language to do so.
+iNezumi A language is for communication, but there's still the question of what is communicated. Math seems to communicate something that can be confirmed by other people. What do they confirm and how?
Math is a way to can calculate and understand things around us, to give things a name, caracteristics and make them easy to understand, if there is a guy and walk five meters timed, math is a way you can calculate the distance and speed in that case. Its like colors, we give them a name and caracteristics to make it easy to understand
+iNezumi But please tell me if math is a language how does a computer work ??? a language is fluid and meanings change.. a computers calculations do not... and because a computer is based on Math is should change from time to time if its a language... What i mean is not that 2+2 will equal 5 but that sometimes 2 and 2 banans can become 2 and 2 fruits with out losing its meaning in a context... because of this fluidity is disagree... (Darn i just made my self agree with you :( ) yes maths is a language... Creers..
+3dmoddeler Language is fluid when language is fluid, and that usually happens either because of the need of its users to account for some previously unexpressed idea or from sheer creativity. There is nothing about language itself that HAS to change over time. Computers have to contend with neither necessity nor creative sponteneity. They are programmed with whatever "language" they have; if a concept falls outside of that language's ability to deal with it, the computer simply doesn't do anything with that concept. And so far as I know, computer's rewriting their own code spontaneously is still the realm of science fiction. So no, we should not expect the language computer's use to change like a more fluid, human language, and so we can expect them to consistently work.
Math can describe many processes in the real world very beautifully. For instance there is a quite easy formula to describe organic growth or fractal structures in plants. Mandelbrot discovered some fascinating formulas describing processes in the financial market, distribution of stars etc. It seems that seemingly random events in the real world all follow a mathematical formula, we only have to find out which one. This can of course also be the fact because we are living in a matrix. :-)
Mathematics is not the study of math, but is the study data interactions. Data is real and math is the study of how data works, how I can transform, understand, read, collect and interact with it. All phenomena in the universe produces data and you need a way to work with it and this is math!
There are very interesting concepts here, but I have a question: Is there any part of math, which does not have an observable or measurable representation in the real world?! I personally find it absolutely amazing, that even the most outlandish and hard to graps concepts in math still find application in the real world: Imaginary numbers, irrational numbers, multi-dimensional calculations... all these (in math rather basic) counter-instinctive constructs find not only application, but even are the only way to model some processes in the real world.
Ramiel But is it? We created those concepts to make better conceptual models of phenomenon. Like how mathematicians throughout the time decided that 1 is not a prime number or astronomers no longer calling pluto a planet. All to have a better understanding of the universe. It doesn't mean that Pluto changed at all or that 1 of something have now a different set of properties. We were taught in school that if I have one apple and then get another one, I'll have two apples, but what if we wanted to be precise. How would you define a unique set of particles that conform a unique apple with another unique set of particles?
cuellartovar Don't forget that our Math is a language that describes events in the universe, but the phenomenon of math does happen everywhere in our universe. In other words: Suppose you have a wedding anniversary in two weeks, and at the time you are in Monday the first. But for some reason you have forgotten number 7 and now when you count days you go 1,2,3,4,5,6,8 and next week 9,10,11,12,13,14,15. Obviously you will be one day too late if you just remember your wrong math, however if you were to mark with an X in a calendar every passing day, you would clearly see that you have made a mistake. We all make math mistakes and nobody knows all math possible. However, we only know that we are wrong when our universe proves us wrong because quantifiable events happen in mathematical order whether we can count them or not.
Years after this, i recommend reading Wittgenstein regarding analoguous questions. I would posit, inspired by his tractatus logicophiosophicus, that the structure of languages mirror the structure of the world, and math is an extension of logic, the field that studies this kind of structures.
Math was discovered but it might could be that the system of math itself still might not bet applicable to everything that exists in the universe and so it eventually can't explain everything.
True. Math is extremely useful, but in range of observed phenomena and also useful to predict some phenomena by calculating outcomes of some existing interactions. But it always works with set of variables given by observation. What about things that are not available for observation and yet still existing ?
I mean you are very right, we have had to invent several different systems of math to describe the world. We just decided to lump them all together as math but we might as well have decided that X new field isn't math, it's fairly arbitrary what we decide to call math and what we don't. But given that we have things which cannot be described by classic systems of math you are right.
Personally, I think that Mathematical relationships, concepts, and properties are inherent properties of the universe itself. They exist in the same way that gravitation or the strong nuclear force exists. There can be individual circumstances where such properties are "called" and manifested in a particular region, but those properties exist as features of the universe itself. Think of it like a computer program. You can more or less divide everything into Objects and Functions. Objects are particular entities that exist and can be manipulated and interacted with, such as planets, stars, cats, trees, waffle irons, photons of light, etc. Functions are rules for manipulating those objects within the context of the program and are called when their influence is required, for example, relativity, gravity, nuclear forces, and yes, mathematics. What we mean by "exist" between those two groups of universal features is different. Functions are unquantifiable and intangible, but still exist as properties of the universe itself. Not outside it, not within it, but manifested AS the framework itself. If you think of the universe as a box, the Objects are the things inside the box and the Functions are the traits of the box itself (wood, metal, empty, full, square, round, big, small, etc.). To that end, there are a few clarifications that I'd like to make as well. For one, our representation of maths is not inherent. It is a language that is used to describe mathematical properties that do exist. But it is still representative of mathematical truth. Also, numbers themselves are not Functions of the universe. There is no mathematical truth of "threeness" or "twelveness" or whatnot. Quantities and groupings ARE a human construction developed so that the universe is comprehensible to us clusters of matter. Numbers themselves are arbitrary units of measurement, but what they measure is still real. (this bit is the weirder bit that is harder to explain within the bounds of language and logic) However, there is still a definite difference between 0, 1, and 2 (other larger numbers are just groupings of 1's and 2's). 0 would be non-existence, or a null value, for example, there are 0 parrots within a defined radius of me. 1 would represent solitary particles, for example, a photon traveling through space. And 2 would represent particle interaction, for example, said photon interacting with an atom that it collided with. A case could potentially be made for the inherent existence of "3" by taking into account the structure of a baryon, as they are composed of three quarks interacting with one another equally, however, they interact by exchanging photons, rather than by directly interacting, thus, even this relationship doesn't make a strong case for the existence of "3".
ok half way into this video first thought was...I never stopped to think if math was a feature of the universe or if we just made it all up. So far the suggestion made me think about us as people and that we love to create tools to either manipulate the world around us or to describe the world around us...so far your video sir has my attention. Please continue.......
Prove math doesn't exist. Since you have chosen observation, could you prove it empirically? Please consider the relationship between information and energy. Also remember energy and matter are interchangeable. I speculate matter is information is mathematics. Anything observable is math. (This could be wrong, but I doubt anyone has shown it empirically.)
People have proved that mass is the same as energy. From my understanding, this means that the observable universe is made of energy. It is my belief that math is a human representation of energy that is recorded so that we can understand the observable universe. Any input is always appreciated so thank you :)
It has not been demonstrated that math is exclusive to human brains. Math is likely a form of information though. Since information is energy which is in turn matter, it is a stretch to claim math cannot be observed. While that could be true, it could also be false.
there is no true way of knowing the answer to this. we can only make educated guesses. math probably can be used by many different organisms if not all. we only see what the brain is showing us at the end of the day.
I've been wondering if there will be a time when we realize that all the math we use now for describing the universe, being based on counting our fingers, suddenly becomes really beautiful and simple when we base ist on $whatever (like strings).
It would be interesting it we could catch a glimpse of what math would look like from an outsider of our human history. I think it would be as foreign to them as their math is to us.
Human creation. Math is a consistent system with which to measure something, the same with any other system. It's like asking if English is a feature of the universe or of human creation.
+Kevin Cobb He didn't say it exists _because_ we invented a way to describe it, he said that it exists, and what we invented was the way to describe it :-P
You can only watch 9 of the videos in the super collaboration as of July 25, 2017. The video on the Spengler Effect seems to have gone private. I'm binging the colllab right now. This is one of many great videos.
Not quite. Basic math is indeed observable, however I have never heard of someone observing any complex numbers, no one have ever found √-1 of anything. Even negative numbers are pretty hard to observe, aren't they?
When going this deep one must define what one actually means by the term "existence". A good start is: An abstract concept "exists" if it has relations to other concepts. But does one include relations over time linking to concepts that are not yet discovered? "Existence" seems to get blurry. ... On an other note if I understand correctly cunstructivists/intuitionists say everything that cannot yet be constructed may not "exist".
Math is as "real" as sarcasm, and this is coming from a mathematician by trade. It's a series of useful predictive and modelling concepts which do describe real phenomena with varying degrees of accuracy, but the idea of "purely mathematical truths" is fiction in the extreme. The properties of a thing are not themselves a thing.
This falls into Austin's description of "the abstractness implies it doesn't exist." What does it mean to exist? Can't something be both abstract and objective?
@@ac4740 Unfortunately Austin just begs the question against platonism, if existence is defined only for causal entities then numbers have been out defined from the debate not proven to not exist. In that case, the question really hinges on platonists finding a reasonable response to the epistemic access problem since platonism is much nicer than nominalism. They have a hell of a time coming up with rephrasings that arent utter hell.
they will use the same math there is just one math... they will use diferent symbols.. i mean i call a dog (perro) and some other lenguages call it any other way but the dug still a dug no matter what way you call it ... do you get my point?
is like saying do other aliens have any other type of gravity? well they might experience depending on the mass of their planet more or less gravity than us but gravity is not diferent here than it is there... is the atraction between two bodies with mass.
i think math is fairly man made. Math is made to analyze and find solution to problems. The problems is the same and the answers is the same, but the method to get there is different. For instance, the rules of trigonometry is the same everywhere, but subjects as algebra and calculus is most likely different...
You have overlooked one crucial thing. Science is faith as well, People used to think that the earth is the center of the universe. Most people had faith in it thus it was science. We all think that the Sun is the center now but that may not really be the case. Science may also be a creation of the human mind. In fact, if you think about it, nothing can be really said to be of the universe
Lindle Lee You're referring to scientific theories. Science itself, doesn't require faith. Definition of faith I'm using (in this context): _"complete trust or confidence in someone or something."_ Nobody should ever have complete trust or confidence in anything. Sure you may believe it to be true, but that doesn't mean you should believe it blindly. Have some scepticism. Science isn't about finding a theory and then blindly believing it. If you can find evidence which contradicts theories/claim and come up with a better theory, then your theory will be what is considered true for the moment. Science is ever changing. No scientific theory will ever be proven to be 100%. However, that doesn't mean we should ignore all scientific theories either. If you think it make sense and logically explains whatever it's supposed to explain, then believe it. However, if you're sceptical, don't believe it and try and find better evidence/contradictory evidence to prove it false.
645akz I think you are forgetting that ~100% of people have faith in gravity. Much like any other religion, there are principles within science that must be accepted. And much like science, many religions are striving to explain the reality of the world. The only real difference between the two (that I see) is the amount of scrutiny that it takes to be accepted. Which only means that we are trading in a (possible) personal delusion, for a (possible) mass delusion. :P Math (as an extension of philosophy), has the unique position to show what is real while still reflecting how the world is. But like philosophy, sometimes it is hard to determine where reality ends (the irrationality of pi for example).
noah schaefferkoetter _"I think you are forgetting that ~100% of people have faith in gravity."_ The scientific theory of gravity is very complicated. Most people don't even know about the effect gravity has on other planets. Sure everybody understands a portion of it, but most of it, most people probably don't have a clue about. For instance, how gravity links with general relativity. I don't quite understand everything about it as well. So no, they don't have faith in the scientific theory of gravity. As for their own pseudo believes about what the theory of gravity does, they personally observe it's effects. That alone, separates gravity from being completely faith based. _"Fact" in a scientific context is a generally accepted reality (but still open to scientific inquiry, as opposed to an absolute truth, which is not, and hence not a part of science)"_ _"Much like any other religion, there are principles within science that must be accepted."_ Such as? Nothing, absolutely nothing has be accepted. If you find evidence to the contrary to what is stated in a scientific theory, bring that up. It may put a hole in the scientific theory. It's when you stop thinking and blindly accepting (faith), that's when you stop finding any major breakthroughs in science.
You say "absolutely nothing has to be accepted". I disagree. For example: the idea that "reality is what I am experiencing" is taken for granted. Without that, science (and religion for that matter) can't even begin. Please understand that I think that science is necessary to understand our experienced environment, but to say "it requires no faith" is like saying "religion requires no faith because my experiences have lead me to this".
My thoughts on this is that our interpretation of math and how we represent it, is just that. A representation or description of real concepts such as movement, mass, shape, etc... That are then (as you mentioned) applied practically. We do discover how things act and then invent ways to represent the systems and connections (Or in reverse, suggest then test theories). At it's core (Actions, reactions, happenings and otherwise) I do agree that math is something discovered. Similar to how pioneering doctors and such assign terms to processes in the body (to greatly simplify it) Though, without the same level of versatility throughout the sciences math has.
Why can't math be both real and a story? I think the debate is more about how we define reality than about Math. That doesn't mean the question isn't fundamental or important, but the concepts being dealt with are at least as important as the concept of "reality". Some people believe reality is a story. some people believe reality is Math or Truth or something. Some people believe Math just describes what is real. I don't think we have an agreed upon definition of reality fine enough to answer the question. Personally I speculate that matter is made from information. Electrons are made from information. Matter is a story. Further it is a mathematical story spun out by some super being called "God" of whom we know little. I could be wrong though.
I think if math is real then it can be a story, but I personally believe math is just an adjective we use to describe thing(s). Things math describes do not require the math to do what they do, but they simply can do what they do because it is possible and math explains how. If the definition of reality is physically being then math must be not be real and is simply a thought used to describe things that are real.
I think Either-Or questions are anti-reality. Embrace the tension! Be a Both-And believer! Math is not either a reality or an anti-reality. Math can be both reality and anti-reality. I.E. Math god is out there, but we can choose to understand our world mathematically without him with our (maybe) god-given minds? At least that is one way to address and embrace both worldviews.
Scientists have converted information to energy and energy to matter. They are the same thing. Reality is information. Some stories are real and some are fake, but dismissing all ideas as insubstantial is clearly incorrect.
1 is 1 because we say it is; we define these terms. We say 2 is 1 more than 1, 3 is 1 more than 2, and so on. With these definitions, there are logical identities we can deduce. If 3 is 1 more than 2, then 3 - 1 = 2 is true necessarily. We create the definitions, we discover what's true using those definitions. 1 + 1 = 2.2x10^-5 is true if we DEFINE the first term as centimeters, the second as inches, and the third as miles. Definitions are important. So obviously, we created math. But if our definitions are consistent with physical reality, we will also discover information about the world and the relationship between objects within it.
Strongly disagree. There is a set of possible whole numbers (or natural numbers, or whatever you want to call them). You can have 1 of a discreet object (let’s say, an electron, for simplicity’s sake) or you can have 2 of a discreet object, or 3, and so on, but you can’t have 1.5 of a discreet object. There can be no whole number between 1 and 2, even if we wanted to make one up. The reality IMO is that we create the symbols used to *represent* numbers, but the sets of possible numbers and the numbers themselves that constitute those sets are just an objective reality. If intelligent aliens discovered math somewhere else in this universe, they’d still have to have a number for 1, for 2, for 3, etc., but they still couldn’t create an arbitrary whole number between 1 and 2. They would still have to have addition, subtraction, etc., if they were to have a complete knowledge of algebra. Their symbol/character for “1” or “2” or “+” or “-“ would almost certainly be completely different- as far as I can deduce there is no reason to suspect that there’s any universality to the symbols we create to represent universals- that’s the same reason why diffferent languages use different alphabets and different words, even though their words are describing the same concrete objective realities (i.e. trees exist in the world, whether you call them “trees” or “des arbres” or you represent them with a little symbol of a tree or with some other symbol altogether). But numbers and operations themselves are not arbitrary or fabricated. They are objective and we discover them. To take a slightly more tangible example, the Pythagorean Theorem was *true* before we discovered it. It is simply a reality about the form of right triangles (three-sided shapes with a 90 degree angle). You can call triangles something else (as you do in other languages), you can call the theorem something else, you can change out the individual symbols in the theorem (“a,” “^,” “2,” “+,” and so on)... But those symbols assembled in that equation describe an objectively true, universal fact about triangles within our universe. It was true that a^2+b^2=c^2 before we discovered that fact, and in fact it was true before a single physical triangle existed in our universe, because it is a fact about the nature of triangles themselves, not any particular triangle. It is a universal which is applied to particular cases. At this point many physicists believe that *information* (e.g. the sort that is encoded to the surface of black holes) is more fundamental than matter, energy, or spacetime, so by now I don’t think it should be such a shock that non-physical phenomena can be objectively real. But setting that aside, it seems very certain to me that mathematics is discovered. We do invent symbols to describe it, but when we, for instance, create formal logics to describe the relationship between 1 and 2, what we are creating is the explanation, not the phenomenon. Numbers already were manifest in the world in all kinds of ways (shapes could have 3 sides or 4 sides, but only whole numbers of sides; you could have a family of 2 people or 3 people but not 2.5 people; there was already one constant value that was the ratio of every circle’s circumference to its diameter, even before we’d measured it- we may call it “pi” or we could call it “circle-number-“ you can call it whatever you want, but it is an objective constant- it’s value is what it is no matter what symbols you use to represent it).
My take as an anti-realist: For me, math is seemingly created. We invented math as a way for us to be more concise about measurements, designs, ratios, and so forth. Mathematics does not happen naturally in tje universe, and unlike biochemistry, biology, and any life science, we cannot see it happen without our intervention. I do, however, love math now, and I consider it one of the sole best inventions, ever.
Colby Jack Well math it is real & it is natural... in chemistry for example in atoms theres electrons & protons & they have to complete negatives & positive particles to interact & make a new element, but always thay have to make together a specific number of particles in set... & then theres Fibonacci, all nature comes in Fibonacci numbers, from u to the entire galaxy...
Juan Lopez While that may be true, it is still, currently because we do not have contact with any other worlds using math, a human made field used for abstract ideas, additions, subtractions, etc. And Brock, yes that is true, but we can know atoms exist without the idea that Chemistry. If we observe enough and theorize, we can conclude that there are smaller units of matter besides us, the macromatter.
Ted Chiang, author of ''Story of your life'', the story that the movie Arrival is based on, wrote a short story on this very subject called ''Division by Zero''. It's excellent, available online (link on his wikipedia page) and you should be reading it right now. After finishing this video.
I have a graduate degree in mathematics, and I think this is a fascinating question. Here's my take on this.
Mathematical objects are, fascinatingly, both *objective* and *abstract*. That is an exceedingly rare pair of properties for a thing to have.
Everyone (including mathematicians like myself) will agree that mathematical objects are *abstract* (that is, they do not have a "physical" or "material" existence). And for many people (especially anti-realists) the conversations ends there.
But if you want to know why mathematicians tend to be mathematical realists, it is because we become deeply familiar with the *objectiveness* of mathematics. You see, unlike most other abstract things, mathematical objects do not bend *one iota* to a thinker's will. They may exist entirely in our mind, but they are not subjective objects. We cannot shape or carve them. They do not bend to our opinions or preferences.
Prime numbers, for example, have certain properties that arise from their definition itself. Any mind that springs into existence anywhere in any universe will (if they are fortunate enough to “discover” or “invent” prime numbers to begin with) would agree on the properties of the primes. The properties are *inherent* in the objects themselves, and these properties are the same for all observers.
Indeed, any mind that ever comes into existence in any universe would agree on *every* property of prime numbers, circles, squares, etc.
It is this property of objectivity that imparts on the mathematician the feeling that these objects exist "on their own". It is from this position that the mathematical realist argues that mathematical objects "actually exist" - even while readily admitting that they have no physical or material substance. It is why mathematicians describe the action as “discovery” rather than “creation”.
People *without* that deep direct experience of the objectiveness of mathematical objects (most of my students, for example) often have the sense that the "rules" of mathematics are somehow arbitrary. As if things are the way things are because a bunch of professors decided it was going to be that way -- as if they could have just as easily decided it was going to be some other way instead.
But such is not the case. These objects are they way they are with complete indifference to the way we feel about them.
Does this objectivity imply that mathematical objects “exist”? Well that depends entirely on how we define the word “exist”. The way the word is commonly defined is not strict enough for us to decide either way.
The anti-realist would say “the abstractness implies it doesn’t exist”.
The realist would say “the objectiveness implies it does exist”.
I say “mathematics is abstract and objective”, and I ask myself “what does it mean for thing to exist?”.
Beautifully put.
I used to think the rules of math were arbitrary until I began attending university. I am happy I got the opportunity to finally learn enough to properly appreciate the nature and beauty of math.
The way I think about it math is the study of abstractions and the patterns that rise from those abstractions. So those patterns exist regardless of who's observing them. I think you're right, the problem is trying to define exist to an abstract thing in this case. Do thoughts exist? And if they don't then how do we know that we exist? If they do exist then we must exist as the source of those thoughts. since those thoughts are an abstraction then they must have something similar such as we can only think about stuff we know. Even imagined things are based off of things we know. As to the videos argument about it boiling down to faith, all physical sciences do as well. Human knowledge is limited and will always be. It is like asking what was before the Big Bang or how large is the universe outside the observable universe, it's impossible to know and at a certain point you have to accept the limitations.
I really enjoyed this answer. I do not agree with everything, but it was a very well worded explanation of how mathematicians view math as objective.
Aren't you assuming that another mind would use the same logic as we do though? What if using the same axioms it would arrive at different conclusions? Hence, to describe it's objects it would have a different set of axioms and it's system of axioms would appear inconsistent to us but perfectly consistent in their logical system?
Math is "real" in the same sense that language is "real". When you say the word "tree", there is no actual tree. The word is simply an abstract concept used to describe something real. It's the same with math. Math helps us accurately make sense of reality.
+CampingforCool41 I agree about the "tree," but I see no "three."
ism schism
That's because "three" only implies three units OF something. It is simply another layer of abstraction. We don't see "love", yet it "exists" in the sense that we are able to distinguish a certain range of feelings from another range of feelings that make up "hate".
CampingforCool41
Just a "layer of abstraction." That's good to hear. I always wondered why someone might have some short used inferior-quality pencils while I have some new long, superior-quality pencils, but people say we each have three pencils. It seems to do no justice to reality!
+CampingforCool41 You might have missed the point of the video then. Of course math is cognitively consistent. Or else we'd throw it out. The main question is whether math is something out there to be discovered (like a new fossil), or whether it's something that humans create that is really good at describing things in reality.
....what?Larry Weru
I think the INSPIRATION for math exists in real life. Angles, shapes, values, they can be observed throughout the universe. But we as humans decided they were angles, shapes, and values in the first place. Before humans existed, things didn't really have "value". They were just there. Humans, in an attempt to organize what they observed, decided that an apple and another apple were two apples.
exactly human just happen to name those things is a mathematical way
agree but in some case we not been able to invent tangible value, like why 1/3 is 0.333333..... to infinite!?? or Pi is 3.1415....... to infinite!?? we couldnt complete it? math is full of flaw but still usefull
no, we made names, those things still exist.
They exist, but is an angle that occurs in nature inherently an angle, or is it an angle because that's what we call it? Before the word "angle" existed, were they angles? Or were they simply natural occurrences that meet the criteria for what we consider an angle?
CerberusKnox they are angles, we make names, they have definitions. That is how the universe works.
Math is the extrapolation of logical reasoning, founded in axioms and relationships. It's a study of how far can you push logic and still produce useful results.
Math is a method of thinking. It's as real as thoughts are.
What is thinking? What are thoughts? Do plants & animals have thoughts? Can they think? What about an amoeba, neuron or virus? Can they think & have thoughts? Can a computer/calculator/abacus think too?
Well then math is a way that we think as humans with minds in a certain way, meaning it is a fiction of the mind. But if it is a real as thoughts are it is a thing that exists in the universe objectively, so you have an opinion that is neither one of the original answers. Congratulations, you advanced the discussion.
i think what he meant was that, wew all have thoughts, know what they are and consider them real, yet a thought is not a physical thing you can point at and say "that's a thought"
Thoughts don't exist as objects, at most they are being experienced, that doesnt make them real. Otherwise dreams and optical illusions would also ''exist''.
Dsc yingyue But if thoughts aren't real Dsc then you couldn't have wrote that comment.
When I was 16 I asked my Maths teacher "Is Maths something inherent in reality or just something we impose on the world?". He looked at me and said "Get back to work Beach". I ended up doing a degree in Philosophy while my Maths declined :)
How’s that going for ya?
You rock!!!
You're so cool 😅😅😂
I remember asking my math teacher who decided that 2+2=4? What if I suddenly decide to say that 2+2 really equals 5, how could anyone prove me wrong? What if 5 is really 4 and 4 is really 5? How could we truly know?
@@dizzy4423because the math has a direct reflection onto reality
It's so nostalgic watching a video with old memes
Most sincere, genuine, and important comment in this thread.
can i haz cheezburger memes were already old by 2013.
the memes and jokes in these videos are hilarious because everything about mikes ideas are but everything else about the videos have aged so much hahaha
It’s 2022 and I’m still hoping this channel makes a comeback…
Since you can't even prove that the Universe exists independent of your own perception of it, how could you ever prove that any piece of it does?
Not being able to prove the external world is a feature of the nature of proof and not of humans being incapable of knowing the existence around them.
Math is human logic in its purest form, and numbers are the language we use to convey math.
Let's be clear, in math we have mainly two things:
-Definitions
-Theorems
We invent definitions with abstract logical rules.
We discover the theorems, that are logical consequences of the rules we invented.
So, one part of the math is an invention and a language(the definitions) and other one is a discovery(the theorems).
Many things in the real world follow our definitions up to certain point in consequence they follow our theorems up to certain point. The fact is that with math we can discover universally valid facts that can explain things that had happened and predict things that still don't happen.
Does math really "exists"? I think that question doesn't have any sense, the concept of existence is not well defined and should not be used for this purpose.
great comment!
Brilliant.
The reason it comes up about whether math "exists" is because of "materialism", which I don't know enough about to give any justice to.
"the concept of existence is not well defined" so good! That cracked me up :)
Math is both a feature of the Universe and a Human Creation, because we humans are part of the universe and even we create it with our conscience (and this conscience is, of course, part of the universe).
The main problem with this discussion is that most people don't have any clue what math is based on.
In mathematics we call this basis our "axioms". Axioms are facts we accept/assume to be true and use to deduce more mathematical facts.
The axioms for the average person are usually what they learned at school or, for those who actually listened that one time the teacher proved Pythagoras' theorem, what they learned at primary school. Namely stuff like "1+1=2" or "The square root of two has infinite decimal places".
In practice mathematicians aren't that different, but in theory, all math is based on some very abstract but basic principles.
Something like "1+1 = 2" might seem like good candidate for an axiom: Everybody would accept that it's true and it seems very basic. But for an axiom to be viable as a basis for *all* math, it has to have more to it than just being accepted by everyone. For example: If you accept addition, you can easily establish multiplication as repeated addition, or subtraction as reversed addition, but if you try to prove something about for example set theory, you will find it to be impossible to do so with this assumption ("Addition").
So after thousands of years of mathematical progress without a well defined basis, in the early 20th century mathematicians decided to clean the whole system up by defining these very basic axioms and actually proving trivial stuff like addition to "be true".
They are like the wooden blocks kids played with before smartphones were invented: You can do a lot with them, but after a while all possibilities are exhausted. You could build an even higher tower or an even longer bridge, but you can't build anything actually new out of them like for example a bowl.
To come back to the original question, continuing this analogy:
When a kid plays with its blocks, it might discover that it can place one block on two others and thereby build a bridge. Of course this kid weren't the first to build a bridge, but it _discovered_, without ever seeing one before, that it can create what we call a bridge out of its toys.
Mathematicians do essentially the same thing: They use mathematical building blocks and play around with them until they find some new combination.
The question is: Does the constellation of the bricks, the "bridge", already exist as an abstract concept, or does a child have to exist and create it for the "One block on two others" concept to exist?
If for example in absence of any conscious being one block happens to fall onto two others, thereby forming what our kid _invented_, we still get the same result *without* anybody inventing it. There isn't anybody there to call it "Bridge", but it exists the same way an undiscovered species or unknown chemical element exists.
The same way you can ask whether multiplication exists in a universe of addition. Maybe nobody thought about actually giving it a name (yet), but still, when repeatedly adding e.g. dinosaurs to a population, you are doing the same thing as we are when we are multiplying numbers.
So far it might seem like mathematical facts "exist" and are there to be discovered, since even without anybody there to think about them, they still apply.
Here is where the problem lies: Where do the wooden blocks come from? The bridge is made out of blocks, but what are the blocks made of?
You can break the block down into molecules, the molecules into atoms, the atoms into protons, neutrons and electrons, those into quantum particles, the quantum particles into ???.
Based on our current understanding of physics, quantum particles are the absolute basic building blocks of our universe and *everything* is made out of there.
Applying this concept to mathematics we can break down every theory, all formulas and any mathematical concept into the concepts they are based on, and in turn break those down, and so on until we reach our absolute basic building blocks, our axioms.
So in the end, mathematical concepts exist in our mathematical universe, which is defined by our mathematical capabilities / axioms, the same way that objects exist in our physical universe.
When a scientist discovers an unnatural chemical element by *producing* it via combining existing chemicals or when a physicist lets particles collide to produce new ones, did they really discover something or did they invent it?
How can you draw a distinction between those "discoveries" and supposed "inventions" in mathematics? You combine existing objects to produce something new.
Thereby, the real question is: What is the difference between invention and discovery?
You would call finding out that rubbing a balloon on your hair produces electricity a discovery, but creating an iPhone an invention. When Edison observed that letting current flow through a wire produces light, did he invent or discover the light bulb?
It is hard to draw a line between invention and discovery.
Thereby this whole discussion is interesting, but it is impossible to give a definitive answer, making it a slightly pointless endeavour.
+Garbaz great comment... and just brainstorming aloud here... but in the example about scientists producing an unnatural element or physicist producing particles by collision... I'd say, if these elements didn't occur by themselves in nature (without human intervention), then these scientists have invented the new element/particles. If they could be produced naturally, then they are discovering.
(Humans are arguably "natural" too [existing in nature], but lets say we are not.)
So, yes - rubbing balloon on hair causes static is discovery and creating iPhone invention.
And Edison observing current through wire producing light is discovery, but building the mechanism in which to channel that light (the light bulb) is an invention.
I actually don't think you can invent anything in mathematics... we may have invented the language to describe the concepts... but we discovered the mathematical facts / concepts.
and when they TRIED to break math down into rigorously provable units they found it could not be done, see Bertrand Russel et al.
props for writing all that, good read
Bertrand Russel et al. and what else? Year, title ... I'm sure the guy has more than one piece out there.
Actually, sqrt(2) having infinite decimals _isn't_ just an axiom, it has been proven :-P
Euler's identity, e^i*pi + 1 = 0, absolutely blows my mind, even though I understand its derivation. These constants are completely unrelated constants which are simply INHERENT to the nature of things which are just a part of the universe, such as circles, compound interest, etc. The fact that they are all so beautifully and elegantly related, whether or not we like it, is probably the most compelling demonstration of realism.
+1F1i2b3o5n8n1a3c2i1 I much prefer saying e^Pi*i = -1, just so you can wear a T-Shirt with "I'm the e^Pi*i" on it.
+TheDeadlyPianist I think "I'm the e^tau*i" would be more accurate in this case.
+Lucas Cottica Silveira tau is the worst thing that ever happened
Leo Simmel I wouldn't say it's the worst thing even. It's just completely bloody useless.
+1F1i2b3o5n8n1a3c2i1 That's like saying God exists because the Heavens and the Earth are beautiful. Totally irrational. My position is anti-realist.
Math is just a language. Asking "is math real" is like asking "is spanish real"
I think this is the best comparison. I'm sure if we used a different system like base 12 a lot of our equations would look different, but still be true nonetheless. Thus our math isn't a fact of the universe but our way of conveying the facts.
Maokai Hecarim mind you changing from a decimal system to a 12-base is still math - just different math.
Maokai Hecarim
Switching bases would change... no equations.
You didn't understand the video.
I can guarented you, that to a blue whale Spanish Is not real.
"Did quantum mechanics exist before we observed it?" My brain just broke.
the science of quantum mechanics describes reality, and no description of reality existed prior to the existence of observers.
KEvron
@@KEvronista But what if we were not attempting to describe Quantum Mechanics. The real question is whether or not the properties of what we call "Quantum Mechanics" existed before it was observed. It is the same argument of whether or not a tree falling somewhere, and not a single living organism was there to observe it, did it even fall. For, until it is discovered, it does not exist. The same would go for Schrodinger's Cat and so many other problems. The main problem here is that there is no way of knowing anything exists before it has been observed since just knowing that it exists is observation in and of itself.
@@arthurianpaladarian9531
*"But what if we were not attempting to describe Quantum Mechanics."*
huh?! i said qm describes. i didn't say anything about describing the descriptions.
KEvron
@@KEvronista Ok ok, sorry. I thought that is what you were talking about. Just pointing things out.
@@KEvronista “Observer” in quantum mechanics is a bit of a misnomer. An observation is just a measurement or interaction. It doesn’t require a physical entity “observing” it.
Stars would still star without a living entity in the universe there to see them. The physics of quantum mechanics would still exist. Quantum fluctuations would still occur. Quarks would still come in pairs and quantum tunneling would still be a thing. Black holes would still evaporate as virtual particles became real at the event horizon.
The universe would behave exactly as it always has if life did not exist. Because an “observation” is any interaction, not the physical act of “looking” or “measuring” something.
If I say math doesn't exist to my math teacher, does that mean I can get out of tests?
DronePunkGAME Sure you can. Your teacher will then probably say that your math grade doesn't exist. And the school will say your diploma doesn't exist. But I digress ;-)
DronePunkGAME If you say that if English doesn't exist, does that mean you can get out of grade school grammar?
DronePunkGAME "Math doesn't exist" is only interesting as a semantic question. If math has nothing with reality to do, it exist at least as a notion, an idea, a fantasy, and as a very sophisticated artificial cathegory. It is not even very interesting as a semantic discussion.
Stroheim333 Math doesn't exist. The way in which we use an artificial construct to organize, orchestrate and explain our lives and existence, does.
DronePunkGAME If I was your math teacher, i would say. "Yes, I agree, math may be a creation of the human mind, but it is how we organize the world and interact with it and understand it, therefore you must still take your math test."
the constant meme references is too distracting.
Gordon Chin a bunch of channels doesn't realize these truth, a smart editing or an outside reference at the right moment may make the explanation more lively but to drown the video on this things, just bores.
Exactly, I couldn't watch the whole video without having a migraine
memes were the hot thing in mid 2013, the date the Vid was published.
HappyFluegel Wrong, memes never die
I've always said I've had a hard time rationalizing math. Every teacher thinks it's because I'm not putting effort into it, but I know I put a ton of effort in. I think I have a bad time following math because it's not base in actuality. I know math is the language of the universe, but it's like Chinese to me. This video gets a 10/10 from me.
Same! With Biology and Chemistry it was almost like I could anticipate the next lesson, every concept built logically and intuitively upon the last that felt so… natural. But with math, I could understand it, but it seemed very rote, and I often got lost in the abstract concepts within it trying to understand them more concretely.
@@isidoreaerys8745 that's often a product of the public education system :( proofs and logical mathematical reasoning should be taught earlier in education so students aren't confused and understand the foundations of maths
same
Math is fantastic!
carrot + carrot = 2 carrots
lump of sand + lump of sand → 1 large lump of sand
sorites paradox
Only if you combined those two lumps of sand. If they remain seperated they are 2 different lumps of sand. 1 kg lump + 1 kg lump = 2 kg lump regardless of seperation.
@@balasubramanians7932 one particle + one particle = zero particles. A virtual electron + a virtual positron will annihilate and leave nothing. So addition does not work in Quantum mechanics.
Also take empty space and wait. Eventually you will get two particles created from the void. So zero = two. Math fails, it is flawed and based on Classical physics.
@@jeffbguarino I don't know what is "virtual" here.
But Wikipedia says, for that, " At low energies, the result of the collision is the annihilation of the electron and positron, and the creation of energetic photons .... At high energies, other particles, such as B mesons or the W and Z bosons, can be created." Hence, annihilation of an electron and a positron does not leave out nothing, a photon is not zero.
On the other hand, these are just fluctuations in fields without very well defined position, so we should not count if we can not count.
Math was developed before physics. Physics uses a lots of maths. But none are based on the other. One is science and the other is not.
Quantum mechanics is physics which uses a lot of maths, so if addition(or math) is invalid none of those formulas are valid.
Math is a human invention, but it is not "made up." It is our way of explaining the already existing things around us, which is pretty much the definition of spoken language. Essentially, math is a language.
On a side note, religion is not the opposite of science, in fact, it's not even related to science. Science is the explanation of the existence while religion is the belief, or disbelief, that a higher power created existence, simply the belief in higher powers or the supernatural, or an interest that is held and pursued at a supreme importance. By this definition, science can even be a religion if a person holds it to be important enough.
err, no, belief in a creator power is not religion, nor even A region. At best, it is part of some religions, and more often than not an after thought, nowhere near central point of the religion that a believed power or powers created the universe. It is, I agree, a central part of the most popular religions, but that fact does not define the idea of religion itself.
Louis Victor
Correct, religion is much more diverse and complex than that, but a five paragraph essay about the definition of religion is not necessary to make my point. Additionally, a majority of people only know about the most popular religions, to which my explanation relates, so it is fruitless to go deeper when the possibility of somebody not grasping the point and recognizing the difference is so small.
S.M. grimbldoo It is not fruitless, it bears negative fruit. Using the expression "popularly" and with a meaning that is false is, at best and most innocently, keeping alive and helping to disseminate the falsehood. If it is incorrect, incomplete, and misleading, why state it in the first place? Not that what the vast majority of people think/know makes it a valid argument or a "so small" chance of getting it wrong - people are already broadly ignorant, they don't need any help with that.
Now, if you really just wanted to say the Abrahamic religions (and perhaps Hinduism), or "the most popular religions are..." rather than reduce religion to just the most popularly known, you could have easily said just that with those few words. Doesn't require making an essay, doesn't reinforce a false concept, and is still 100% accurate....
Louis Victor
There you are mistaken, the definition I used is not false and neither was my statement.Too specific, but not incorrect.
Here's my question, are you really going to try to tell me that science is the opposite of religion when science is the observation and explanation of nature while religion is the belief or disbelief that a higher power created the universe, the belief in higher powers, or an interest held in supreme importance? By this defenition, science could even be a religion.
Thank you for pointing that out, however. I was struggling a bit to grasp that my statement was too vague. I knew what message I was trying to convey so I didn't really see where the delivery fell short.
S.M. grimbldoo I didn't opine regarding the original point about science vs religion, so I am not saying Science is or isnt opposite to religion. I was just focusing on the meaning of the word religion (which can contain your first definition, but is not the same since it is much broader - i.e. some vegetables are food, but food isn't (just nor always contain) some vegetables).
If you define something into existence, does it actually exist? If you define a concept by giving it a few properties, then it is a mathematical object. You can then use the laws of logic-identity, non-contradiction, excluded middle-to find out all statements about your newly defined object, as well as if it is logically possible. If that is good enough criteria for something to exist, then math exists. On the other hand, if something has to physically interact with physical reality to be real, then it doesn't exist. But real things must obey the laws of logic, and so must mathematical things, so in that sense, they are alike.
What does it mean to "exist?" This whole Reality and everything about it is just whacky as hell.
Ultimately all of language is arbitrary, relying on the pattern recognition encoded in our DNA. So we talk and hope that the people we're talking to perceive the world in a way somewhat like we do.
This notion of "existence" is Platonism. And, I'm sorry, but the notion is idiotic, IMHO.
I didn't say math exists. I said it is like reality in that it follows logical laws.
Actually, by the way you phrased your sentence, it has to exist: If we gave something a name, there has to be something that we have just named. Otherwise we would not have succeeded in giving a name to anything at all.
I have always wondered this! I have always wondered how math can be, "real" but I've always in my head thought it was our way of understanding and explaining things.
Math is one of the intelligent creatures' tools for linking with reality. By practicing math this link grows, and it gets easier to implement new ideas.
Math does not exist "out in the universe". At the same time, it does not simply "exist in our brain". It is actually in a layer that is beyond the universe. Math is not in the universe, the universe is in Math.
This may sound strange, awfully philosophical, or perhaps even meaningless, until you understand model theory.
The idea behind model theory is that mathematical rules can "map" into real-world concepts. Like, similar to the example already given, 2+2=4 can map into the real-world take 2 cats, add 2 more cats, get 4 cats. But the main premise of model theory is that you can map the same mathematical concept into several different elements. For example, 2+2 doesn't have to be about cats. In fact, it doesn't even have to be about physical objects. If you've waited 2 seconds, and immediately after you've waited 2 more seconds, then you've waited for 4 seconds.
In the eyes of model theory, then, math is about finding out what's common to different models. It starts by trying to find a minimal list of observable facts that a certain model has to fulfill in order to be "sufficiently similar" to other models. For example, in the case of addition, we require that we don't care about the order of the objects. For instance, if you put 2 black cats right of 2 white cats, then while you have 4 cats, this doesn't represent the fact that you have, right to left, black-black-white-white cats. Only if you decide this latter detail is unimportant, does the model fit. On the other hand, if color does matter, than taking the black cats first, and then putting the white cats right of them, changes the group of cats.
The next step is then to figure out what can be inferred based only on these observable facts, without relying on the observations themselves. For instance, 2+2=4 is actually a direct result of 1+1=2, 2+1=3, 3+1=4 and order of operations not mattering. The first 3 can be seen simply as definitions of 2, 3 and 4 (As what happens to the group when you add one more of the smallest group). They are giving names to concepts. The last one is the thing that must be true for a model to fit. Any aspect of this universe, or any other, that fits this requirement, would also fulfill 2+2=4.
The ultimate result of model theory lies in Godel's completeness theorem. It states that:
1. If something is true in a purely mathematical sense, then it is true for all models that satisfy the basic required observations. This means that math can be used to reason about the real universe. Another way to look at it, is that math can be used to show that certain types of things cannot exist, in any universe, simply because, in mathematical form, they would result in a contradiction.
A good example is that the laws of thermodynamics (conservation of energy) can't be violated without first violating one of the basic laws of mechanics (e.g. every action has an equal and opposite reaction) that mathematically cause them. So long as the basic observations hold, the conclusions must also hold. Conversely, if an observation shows that the conclusion was violated, it implies that one of the basic rules on which it was based was violated as well.
2. If something is true for all models, then there is a finite mathematical proof for it. Or, conversely, if there is no finite mathematical proof for something, then there is a theoretical model in which it is not true. While this fact may not directly relate to this universe, as the "model in which it is not true" may simply be a theoretical universe that doesn't actually exist, it does give us a way to limit the things that must be absolutely true for all possible universes. All of those must have FINITE proof, that is, the proof can be written using mathematical symbols on a finite number of pages.
At the same time, every time mathematicians think they've found a model that could only exist in theory, the universe has shown that if it's mathematically possible, then there's some aspect of the universe in which it physically exists. That's not to say that this is always the case, simply that mathematicians are still in search of the case in which it isn't.
Finally, someone gets it
1 cat plus 1 cat doesn't equal 2 cats. They are not identical units. Both cats are infinitely different and can't be added or subtracted to an exact degree. Math isn't true, it's simply a tool of observation, navigation, and creation.
Marcus
It depends on how you define "cat". If you get too metaphysical, one never feels pain, and one never sees anything. It's all nerve impulses, which also don't exist, as it is field movements, which are actually vibrations of strings, which are actually a hologram on the surface of an inverse black hole spanning the exterior of the universe.
All of this metaphysics is very interesting, until you get punched in the face, and then it actually very really hurts.
I like your response! The hologram works. Let's put it that way. We are getting our money's worth.
***** Marcus I'm sorry there is nothing more "meta-physical" than the notion that math is "in a layer that is beyond the universe."
"In the Math we currently there is - More Mathe" Oooh no and I thought I could get rid of it. But now I know better.
Math is something we use, its a tool, that we created to help convey and understand patterns, and other situations in nature, and to define nature
in a sense Math is a Language
Math is like a Slap Chop, it can be yours for 3 easy payments of .999...
When I saw this for the first time 5 years ago, I was so certain math is objective entity of the universe. Now I am inclined to the opposite, but see how both could be true. Beautiful how one's perspective changes over time :)
very cool
Math is like a language. It is a tool that we describe things with. But there are possibilities for a new rule to exist, like other languages. This is studied in abstract algebra, where new sets of rules are made and observed. A new mathematical language, if you will. But just like a language, it isn't a part of an entity, or an entity itself.
Order, system, language, criteria, parameters, norma (castellano)
Good thing I found this video. I've been telling this to people for a long time. Math is not proven empirically, but logically, it's proven in itself. Therefore it's not science, it's philosophy.
*****
It's not the only one though. There's a number of philosophical tools constantly used in science. They're just not as complicated and most people use them without thinking about them.
I mean, you're right, but saying that it's philosophy oversimplifies the argument a lot. All things are philosophy in the same sense, ie the sense that they can be deconstructed to a simple tautology. The only way we gather information is via senses (or a layer of abstraction from our senses), and we do this without being able to tell if our senses are correct. Following this line of reasoning down, we can conclude that all information is based on a tautology, and becomes philosophy.
So we are left with taking as an assumption at least one thing that is likely "unknowable," or becoming solipsistic. What math, and by extension science, takes as that assumption is orcam's razor.
Why I feel that calling math philosophy is an oversimplification is that it doesn't convey the idea that, as opposed to most modern branches of philosophy, we made a key assumption for the sole value of utility.
There's 3 types of formal knowledge: Science, which is corroborated empirically, Philosophy, which is corroborated in itself, and theology, which is corroborated in the scriptures. It's not an oversimplification because math is by definition part of philosophy. There's no room for interpretation, it's just what it is. People just vastly underestimate how useful and how widelly used philosophy is because they only think of it as people thinking about existence.
Altrantis I completely agree about the last part. I was a philosophy major before switching to engineering.
The first part, though, I'm having issues with. We both accept that everything is philosophy, right? If so, it puts the word in a precarious position of being redundant. Further clarification is needed to draw a distinction, which is quite simply, math/logic. Calling math/logic anything other than what it is runs the risk of being either too broad a term, or too narrow.
Not everything is phylosophy. Just because you need phylosophy to establish a link between science and your own understanding doesn't mean that science is phylosophy. It doesn't prove itself on itself, it proves itself on the non-self. Math and logic do not enjoy that distinction.
Regardless of the fact you manipulate science using philosophy, like if it was a mechanical arm, what you're working with has a given result that does not necesarilly follow logic. That's when you realize something's wrong and have to change your hypothesis. Science is always wrong. Philosophy on the other hand, is neither right nor wrong, since it's what defines what is right and wrong (not morally). And that distinction is most likelly eminently human and not out there in the universe.
There's a reason logic as a class in the education system is taught both in math classes and philosophy classes. Math is to logic is to philosophy what biology is to chemistry is to physics. Sure, they're conceptually too different for the human brain to work math as part of philosophy, same as we can't work the intricate workings of biology from a physics point of view, but that doesn't mean it's part of it. Biology is a specific branch of chemistry that studies the specific types of chemical phenomenon called life, and chemisrty is a specific branch of physics that works with a specific type of matter arrangement, which is when atoms unite to form molecules.
Logic is to math and philosophy like what atomic physics are to physics and chemistry. Or geomorphology is to geography and geology.
Mathematics is real and exists independent of the human mind. Anyone who thinks otherwise doesn't understand math, and is likely getting confused by the human symbols, terms (names), and definitions that we invent in order to comprehend math.
Math is more like a tool for modeling the universe than something that fundamentally exists. It is a way to define physics; an abstraction to help people understand. There is purely logic based math, but all logic is actually just defined by people to fit things that make sense to them. It is proven because it has been applied and models real things, otherwise it is just logical system, even if it fits in its own framework. An idea that can be rigorously proven within its own accepted rules is still an idea and not a universal truth. If even the numbers themselves are just abstractions than there is no way the rest of math isn't one.
When you say "is a tool" that tells me you're doing exactly what I said. Confusing the symbols, terms, definitions, etc. to be what math IS. That is not what math is. Those are the tools we use to understand math.
It's like the question of whether a tree makes a sound if there's no one around to hear it. Energy from the fall of the tree causes waves in the atmosphere, which is what sound is - it does make a sound. If someone were around that could perceive it, they would hear those sounds.
1+1=2 independently of whether there is anyone around to perceive it. Those perceptions are uniquely human. The existence of the math itself is not.
It's been shown that other animals can do rudimentary math. If we encounter alien species, surely they will understand math. Their definitions, their terms, and concepts will undoubtedly be different than ours, and have different implications - for example, what it means for a function to be continuous. HOWEVER, we will agree on the implications of their definitions, and they will agree on the implications of the definitions we've chosen. They and we will have different perceptions, different perspectives, different views of the math, but the math itself exists independent of our minds and perceptions of it.
My point is that 1+1 itself is not even a universal truth but a defined and abstract truth. It is a way to model things that we categorize with our brains, not something that fundamentally exists. The most important "discoveries" in math were simply ways to model things that existed in the world and tools for more people to be able to understand how those things worked, they didn't invent the math and then use the math to figure out what to do.
How can 1+1 not be a universal truth? The symbols used are human ones (specifically the symbols of our particular human culture - Sumerians, Egyptians, etc. used different symbols), but the existence of a singleton and the process of combining singletons that we call addition is not something that only existed after we thought of it. 1+1 (in whatever guise) exists independently of the human mind (or any mind). If the universe consisted entirely of two atoms, then the one atom, combined with the other atom, would make two atoms. That's an extremely universal truth. Even if the universe consisted of no particles and was just empty space, even if the universe didn't exist, you'd still have the existence of 1+1=2, and all the rest of mathematics including that which hasn't been figured out yet and math that will never be figured out. Math is not just "models" that we come up with. Models are just our way to conceptualize and understand the universal truth of math.
Dagobah 359
So what you are saying is that math exists as a concept but does not fundamentally exist. Math needs an additional understanding to make any sense, it requires human grouping. Using the addition example, a person actually requires a scope and a definition of an atom for 1 + 1 = 2, atoms are actually not atoms but a group of other things that we call atoms. Same with everything else; the fact that addition is possible is only down to categorization, which is not universal at all. (Yes, math is possible without categorization using only numbers, but the end result has no meaning at all. It would be like language without nouns.)
I hate how much I love your show. In fact, I also enjoyed your Crash Course Playlist on Mythology.
I don't understand the question. The human brain is in the universe, part of the universe. To ask if math comes from the universe or the brain is to give no choice in answers...
think of it like this politness does not come the world around us it just something humans made up until not a real feature of the world.
The human brain may exist in the universe, but it creates things that are unnatural. So, our brains are sort of a contradiction in that sense.
How do you define unnatural
hm maybe think of it this way: your brain is just cells connected with electricity and thinking is nothing more than your cells "talking" to each other. soo there is no math in your head. not a "real" thing you could call math. so the question is, is math just our way of thinking and analysing or is there a natural math, like, if there were no humans with brains, would there be 1,2, pi and this stuff
ViperblueHD
Simplistically speaking, rocket ships don't grow out of the ground. We take natural materials and natural processes and combine them in ways nature never would to make unnatural things.
Math must be the symbolic shadow of concrete realities
MC Escher has some great art depicting the fuzzy barrier between reality and our contrived symbols of it
Realism and platonism is one of the biggest disservices to students of mathematics ever. Mathematicians understand that they're just working with a formal system of axioms and rules of inference. Thinking of numbers as platonic objects that exist was a great impediment for me in exploring mathematics at the horizons, for example, in researchinig hyperreals of model theory and the history of transfinites. PLEASE, educate your math students about what math really is: a human language. Mathematics, unlike spoken languages like English, admits only precise statements in meaning while employing a small set of primitive nouns and even smaller set of primitive relationships among those nouns. Actually, a great deal of effort has been made to reduce the primitives of mathematics to its bare essentials (Zermelo-Fraenkel Set Theory and First Order Logic are the best examples of this), and then use these to build the entirety of nouns and relationships in mathematics like numbers, arithmetic operators, functions, vectors, tensors, manifolds, theorems, advanced operators, and on and on. This is quite different from English for which syntax is arbitrary, nouns emerge, and meaning is vague and evolving. Mathematics and Logic are languages created by philosophers of old to think, communicate, and record ideas precisely and no ambiguity. That language has allowed rigor of thought and method first in business, geometry (literally measuring the earth), and natural science. Programming languages are in between mathematics and spoken languages. Those likely provide the best analogy to think about mathematics. You can prove things about programming languages, but obviously they are man made. Now, all forms of human activity are adopting precise languages, like chemistry, psychology, finance, art, you name it.
+oarevalo21 Well said. Math realism is irrational.
+oarevalo21 What if we contacted aliens that also used the same mathematics? Is it then a "sentient language" all thinking beings understand? Is mathematics part of being sentient or aware?
+octavio echeverria Is it impossible to independently invent similar things? And even if math is some language invented by us, it isn't arbitrary. It's main purpose is to "talk" about the external world and we share that world with those aliens. This limits the freedom a lot.
And of course, we don't know, how some hypothetical aliens think about the world. Until we find some, this line of thinking doesn't help with this question at all.
I was convinced by one think. Imagine, that you are counting apples. Now try to precisely define, what apple is and isn't. What atoms are part of it, etc. You aren't counting real apples but abstract ones. Math isn't the first layer of abstraction of the real world. You can count meters or kilograms using math. But math itself can't tell you anything about what those meters or kilograms really mean.
octavio echeverria
mathematics is a logical system of rules and definitions. therefore it requires sentience and intelligence.
+oscar i think a helpful term for you might be "ontological mathematics" which is commonly used to differentiate mathematics-itself from humans' interpretation of mathematics, which would be the language subset you speak of.
I miss this channel. I can’t believe this video came out 10 years ago. I remembered a conversation at a family function recently where I argued with someone that math doesn’t actually exist, it’s another form of language that we use to describe the universe, so it’s “real” the same way English and Mandarin Chinese are real, but is also constructed by humans and exists only in our minds when we think it into being. And my family member was like “no.” Lol anyway, I’m sure I got that argument from this video and I just love the number of ideas I have taken with me from this entire channel… truly ingrained in me.
The whole video:
Math is just an explanation
Why does everyone on youtube who talks about pop-intellectualism sound like a Hank Green impersonator?
Yeah, he does but I see Hank as the progenitor of that kind of over-emphasised speech pattern. I know what they're going for but when it's exaggerated so that it stands out it comes across as patronising. Now I'm just bitching and moaning.
it's the standard cool teacher speech pattern. I see myself falling into it all the time in class. somehow it's the go-to option when you're trying to get teenagers to follow you thru the boring parts into the (hopefully) exciting ones.
CowLunch
Wannabes
its a sign of underdeveloped testes
I think it's all the camera cuts. I remember that dude from =3 always doing it.
Maths is a translation of what we observe. Nothing more, nothing less.
I highly recommend reading Aristotle’s “Metaphysics”.
In response, I highly recommend reading Wittgenstein's "Philosophical Investigations".
Wonderful Alice I’m studying philosophy in a systematic way. Wittgenstein’s works are certainly held in the highest regard.
Math is just a model of the universe like anything else. Nothing in the world is objectively true, everything we know about the world is filtered through our senses. It is consistent with observation in a vast variety of settings and that is all we can say about anything.
Also its not so much a separate science as a useful extension of existing sciences. It is literally useless without applications. I think however that it is as "real" as physics and chemistry for the reasons I have stated.
Btw this is from a mathematician, so I am not saying math is useless only that its existence relies on its applications.
i've never met and single mathematician or engineer that thinks math "exists" in any kind of objective state. most mathematicians will probably tell you that math has very little to do with the external world, and it's effectiveness in describing said world is more of a side effect of the real goal of math. that being to produce as few contradictions as possible.
I've met lots of mathematicians that subscribe to mathematical realism or platonism in various disguises. Can't say anything about engineers though - they are probably busy computing integrals to think about this stuff
Math is obviously a system created to describe numerical operations that already existed. Before "math" was "developed" people could still have 2 apples and eat 1, leaving 1 remaining apple.
Math accidentally came about through the discovery of language. This is the reason why every country has different words for the operations.
In English we say:
2 plus 2 equals 4
In Japanese it would be:
2 tasu 2 ha 4
The concepts always existed, we just created variables (words) to describe them.
Try telling a hardcore pious type that. They attempt to discredit mathematics saying it can't exist because it isn't physical yet we know it exists therefore the same principal can be applied to God. This theory that mathematics doesn't exist is just another Creationist attempt to "prove" God. They fail to understand it is a descriptive part of language to describe quantity of something which evolved to advanced equations to make larger sums easier to equate... Basically the idiots who claim this have no real understanding of the history of human language and its impact on society.
I would say those 2 things are mutually exclusive. I could see both religious and nonreligious people choosing either side. You are injecting your own antireligious views into a topic that has nothing to do with religion.
終わり
I think the topic has much to do with religion. But I agree that he is injecting a lot of agenda into that comment.
Dauserofdasite There are numbers in the bible
SlightlyawkWard That could have been a hilarious pun. There's an entire book titled "Numbers" in the Bible.
Guys, you are simply awsome at explaining things ! Being of a limited brain like everybody else,
I have a limited answer for the limited conjectures we make and this applies to math and all other sciences, I wish it were otherwise !!
I think it's time I brought out Dumbledore for this one:
"Of course it is happening inside your head, Harry, but why on earth should that mean that it is not real?"
Because Harry is not schizophrenic?
The belief that one's thoughts are reality is usually seen as a sign of insanity, even though I can find no logical reason not to believe it.
What is reality?
People tend to base reality on popular vote. If everyone thinks it's real, then it "must" be real...which is technically fallacious reasoning.
You're right. What *is* reality?
Gibran Mahmud The question, then, is, what is true? How do we know for sure if something is true?
Gibran Mahmud
And how do we know for sure if those "indications" that something is true are true?
Gibran Mahmud And that's the key word: "believe", not "know."
And, "pointless philosophizing"? Not sure if you've noticed, but that's kind of what this (awesome) Internet show is. If "pointless philosophizing" doesn't benefit anyone, then neither does this Internet show. And if that's the case, why are you watching it?
Assuming, of course, you did actually watch the video and didn't simply go down to the comments.
I see math more as a meta language that helps us describe physics, geometry and other concepts. Somehow like XML?
You are wrong. Simple as that. So how can math be perfect and the processes it describes not? How can exponential decay describe something more accurately than reality can? Math explains half life infinitely but reality will eventually run out of particles. It can't keep up with math and it's pure logic. And that's why so many people don't get it. Because they can't think logically.
lutascheier The problem there is the model we use to apply math to reality, not math in and of itself. (Simplified) mathematical models are often used in physics where we basically try to understand the universe with the assistance of math in conjunction with observation, no wonder themodel doesn't match perfectly if we can't observe perfectly.
The idea math helps us describe geometry is certainly true, but an odd point, since geometry is a field of math. Math is used to describe math. True enough, just as astronomy is used to describe astronomy, tennis is used to describe tennis, and language is used to describe language. Navel gazing anyone?
Sandy Beach That's called demonstration, not explanation or describing. You did confound me momentarily however....
math is now a faith?
I guess I finally found a religion that make sense
ha!
Math is hard
+Cool cat saves the kids Fro crippling depression
Life is hard too.
no, math is pretty easy actually. My problem with math in school is that we have to use tools that were built in some way by someone as is convention, rather than create logical tools by ourselves.
math is a language, is as much of a religion as english is . . . .
How did language come to be? Letters are essentially shapes, yet our brain recognizes these shapes and when these shapes are sequenced they form sentences. Our mouths, tongue and jaw moves in unison with vocal chords creating sounds with just vibrations calling it "speech" is just as amazing as math in my opinion.
It’s crazy because a while ago I had this weird thesis about math and physics that I wrote about. I suggested that half - if not all, physics and math was abstract and could very well be not true universally and only to US since we created it for US to understand things better. Little did I know this was an actual thing that geniuses have already came up with.. 🤔
Hello, and you might be right. There's no wrong answer. What is wrong after all?
my mom was watching this with me
why u call her a hamster :(
As a mother myself, I can assure you that we are indeed all hamsters. Every one of us. Have you watched us eat the food our kids tried to make? We nibble. We are hamsters. Also, and we didn't want our kids to know this, but your fathers all smelled of elderberries. Sorry to tell you this, but now that you know it: you're an adult. Now go find your own hamster or man who smells of elderberries and make babies with them! 😁
Math to me is a concept of measurement created by humans to attempt consistency. Like time it was a creation born out of our need to have things organized or placed in an order so we can record it and go back and say "This is when and this is how." If you go back to the invention of the wheel, I wonder if our ancient ancestors figured out that a wheel works best or did they just find a oval stone with a hole in it, carved it down to be symmetrical because our brains wanted it that way, and figured out if you rolled it, it moved more easy? No math involved? It just made sense and we happen to have reached that cognitive ability to make use of it. I also wonder if ancient man maybe used woven material or even animal skin to put things on and then drag all his stuff behind him. Maybe a vine worked as a rope and he tied it to his torso so his arms where free while dragging it. Later the wheel came about through necessity or just made sense rather than dragging it. For all we know the wheel was a couple of coconut halves with holes for an axle. Math had nothing to do with it. We probably only started math when we had to represent how many let's say bananas we were willing to trade for tool or female. We probably used our fingers and thought. "One fruit for each finger I have and I will trade you one spear." But as things became more valuable like better spears or animal meat, they had to say "I want all my fingers worth of fruit plus another half of my fingers worth. So they held up their hand and made a ten gesture then a five. Eventually grunts represented a finger and we took off from there. Of course maybe we started with fives. Since it was easy. and then came up with single digit numbers for each finger. " Hey, ill give you one hand and two fingers worth for your warm fur coat." Maybe a small community came up with the simple add and subtract and names for numbers out of a sort of natural communication. They started by pointing and showing symbols for what meant what then made noise to what each one sounded like. I would bet that about the same time we began trading and representing how many with our fingers, we started growing our language skills and even developed a sort of mini economy in a group of people all interested in trading and communicating. Probably made it easier than roaming around and finding new, less educated cave men that they would then have to teach. So maybe they would bring them to the community if they had something good and would teach them the trade and noises. Over say a few years or even decades they probably expanded very quickly once the idea of trade and communication solidified a group of our cave man ancestors. They began to realize trade was far more beneficial than trying to take it and maybe getting killed in the process. Maybe they learned the value of having someone return with more goods to trade then just getting a one time reward of killing them and taking it. Now they have a year around supply they can trade back and forth for. Of course it probably wasn't too long after that disagreements occurred and escalation led to waring groups. So to conclude, Man invented stuff, people traded for it. People assigned symbols and sounds to amounts and society was born out of the economy it created. Math was born of that system and then disagreements led to war. So Math is to blame for war. Thanks Math. :D
Like i said the better question we should all be asking is that - not whether math exists or not...but if its the universal construct, that is actual for EVERYTHING in our reality or its just something we completely made out in our heads?! Because if its not just something in our heads, then the next question arises - where does that come from?! Is there some sort of alternate reality with its own "laws of physics", where things like letters and numbers re actual physical constructs?! If it is so, then it could explain all our habbits, like why we have this funny idea we should measure things, name things etc...
I wonder how the first human, who invented math itself as a method of measuring things in life found out that is how you should approach things?! Something, somewhere and someone should have "hinted" and "pointed" that person towards it, so that concept would be born! Its the only logical thing to assume!
I agree It’s a model of regularities. It’s kind of both. There’s the objective underlying regularities, but there’s also the imperfect abstraction we created to describe those regularities.
Having Dyscalculia, makes me happy learning this idea.
I remembered one interesting quote: "I was so smart and then education screwed me up".
math isn't an actual thing. one, for example, is merely an idea, same as language. it is merely because we call it one that it exists. what we call one and what we call two could be mixed around and we would have just developed things differently (as in, instead of 1+1=2, 2+2=4, it would be 2+2=1, 1+1=4), and things wouldn't change, in the same way that if we had originally called the sun "the hort", it wouldn't have made any difference in anything except language. it would still be what it is. numbers themselves, same with mathematical functions and equations, are not real things. we cannot sense them in any way, we just use them more as labels. however, since they do label things, they do exist in a sense. using the James Bond reference as an example, merely saying "shaken, not stirred" is nothing special, however, it is linked to James Bond, what makes it special or better than other sentences is the label, that it is a James Bond quote. if you went to an alternate universe where James Bond didn't exist in any form, the sentence would lose it's special meaning, the fact that it's a James Bond quote, and would be about as interesting as saying "shake it". however, it does still have the meaning that James Bond used it for, that you want it "shaken, not stirred". go to an alternate universe in which math doesn't exist, and saying 1+1=2 is meaningless. however, what it labels (a cookie and a cookie is a couple of cookies) still does
I think your explaination is too focused on naming of concepts. The relations between numbers and the like are the interesting part. For example we came up with the definition of natural numbers as that there exists a first natural number(regardless of what it is called) and that the successor of a natural number is also a natural number (regardless of what the successor functions is called). That such a concept exists may be inherent in the universe, since it is for instance closely related to counting.
We can rename things in the way you described it, but if we rename everything consistently, the relations, consequences of axioms, theorems stay the same. Not really the exactly the same, but mathematically it is the same and I think this would be called an isomorphism (may be this renaming is something that also arises naturally, hence we have some mathematical concept for it).
There is actually also a theory that says that language is not a mere idea, but that certain concepts are encoded in our (?) before we are born. I think I read that all languages have some grammatical structures in common (observed on a very abstract level).
Martin Tappler that's all very interesting and included a few things I didn't know
however, maybe a slightly simpler, and summarized, version of how I see it might be a good idea: Math is a concept, like language. it is not tangible and there is no way to show it exists without more math. everything else is either tangible, or can be proven with something other than itself. some examples would be dogs, which we can prove the existence of using our senses, gravity, which we cannot prove the existence of using our senses, but can prove exists using the fact that something keeps us from flying off the Earth (among other explanations), books, which we can, again, prove exist using our senses, and any force, which we can sort of feel when strong enough, but which can also be shown to exist by the fact that they make things move. on the other hand, we can't show math as existing. there is nothing tangible, nothing our senses can actually perceive, nor can we prove it exists except with math. we cannot prove one plus one equals two because a cookie is not "one", it is a cookie. "one" cookie, sure, but not "one" itself, or is it "two" itself. language has the same problem, as we cannot prove language exists using our senses, as speech is really just fancy sound and is only meaningful because we make it so, which is how words can sound the same and be mistaken for others, and letters themselves are concepts created by us. however, at the same time, because they are concepts and are found everywhere, they are real in their own way. similarly, any story is real in its own way, not being true, but being a real product of one's imagination. you cannot deny the existence of a story, nor can you deny the existence of math and language, however their existences are really only concepts
Hey, I'm replying to this after 8y. Hope you are good. I respect your viewpoint on this topic and it's like we are thinking alike. You made a lot of sense here.
PBS Idea Channel was an era of the internet unto itself, and I dearly miss it.
Like the english language, math is created by the human brain
Language (Math) is used to describe things, but the sentences (Physics) are the description, not the language itself.
Lukáš Fireš
And both are a bane of students around the world.
Math is not the story explaining the reality, that is science. Math is a set of tools, guidelines and a language, which you can write the story with. It is not the very esthetics, just like how the letters, words, grammar and all the generalized theory behind how to write a good story isn't the book it self. All they do is to help explaining the story and maybe help with the making of a story. They just form a tool box for Shakespeare to use when he expresses his ideas.
I agree. The question at stake though is whether these tools were created, like, say, a hammer, or discovered (maybe like a rock? I'm trying to think of an example). In my opinion, just like language, math was created.
Luís Frederico Dornelas Conti It doesn't matter if you find the rock. A rock is only a tool when you invent a way to use a rock like that.
The world around us doesn't work by human concepts like rocks for example. We humans can never actuaualy understand the infinitly complex reality. So instead we order the what we observe in to concepts like rocks or hammers, just for our simple minded to be able to handle reality.
The irony is that humans are genetically coded to think of concepts like rocks or trees as part of the actual reality and not as a construc of our own mind. But this is probebly just an instinct that exist for the purpouse of our own survival.
Electro-Cute except it's a fact that one apple plus one apple is two apples. You're clearly describing a function that actually exists with math. So math very evidently exists. But it is also an abstraction so we can use it to talk about things that don't exist like hyperspheres.
+Matt Bacon Apples "one apple plus one apple is two apples" is not the reality it self. It is the use of human thought processes, like concepts and mlogic, to understand observations. Mathematically it is not a fact, it is perfect truth because math is defined by humans and therefor can be perfect in its own definition. What we call reality in the other could be an ilusion for all we know.
Math is real because two intelligent beings in far apart places yet members of the same universe can come up with the same logical realization that 1+1 = 2
Math is a phenomenon of time and space. If there was no time we couldn't count passing events, if there was no space there wouldn't be two of anything, maybe not even one.
What you're saying makes sense.
rubbadingyrabids
Oh thanks, at least I know it didn't just made sense in my mind!
I can see what you're trying to say but it's a clumsy way to say it. A better argument might be that since humans can apply the math they have to situations they haven't previously encountered and get a predictable outcome it must exist as an objective fact.
Yes, you could use other units of measurement to measure it but the fact remains that there is something to measure and would be consistency in that measurement. I don't know enough about math to know how there even could be math we don't know about, since arguably I would think that more complex problems would only be made up of less complex problems. But the idea something doesn't exist simply because you require a little trust to believe in it is an utterly fallacious one.
Many of us spend each day living in the assumption that what they see and feel is real when it's possible that it's just a hallucination. Many of us believe things we've never personally experienced on top of that. Yet, life goes on and the world hasn't imploded. Trust seems to work.
Shona McCarthy
One could argue that math is the study of the relations objects have between each other, and that the symbols and blocks we use to define them are subjective. Just like our world is subjective... But just like Descartes pointed out "I think, therefore I am" our reality is still valid however it comes about.
*****
Interesting. Well in that case, if 1=1 does not give an extra hint of how equal one thing is really to another we could say that there is really just an equivalence. It seems that things only exist in relation to other things, after all the only singularity we know of are black-holes where there are no two of anything and nothing we can think of has solved how they work; but math tells us that what was there is infinitely small and is stop in time. Therefore 1=1 can only exist because each number occupies just one place at one time, but when things do become truly equal then we get a singularity.
Out of this realization we could say that mathematics happens as the order of things in the universe. Even if our thoughts can be abstract they must also happen during a given time at an specific place, thus also having the quality of being accountable.
Defining the Universe with Mathematics is like exploring a room by touch. You know the limits because you've pushed up against them. Sometimes you meet what appears to be a wall, but upon exploring in more detail, you discover is actually a door.
"The answer is don't think about it, Morty"
I think Math comes from the human mind but it is, of course, an exact science. It´s a system that grows on itself to describe everything that happens around us. It is abstract because it´s just a bunch of concepts but they are exact because they accurately describe what we see and a lot of times predict that will happen in the real world.
iPokerrr Ah, but math is also objective. Think about it. Putting one bed on top of another gives you a stack of 2 beds. Always. 5+5 is 10 and you cannot change that. An alien race would have the same mathematical concepts as we do, because unlike most abstracts, it is objective, and cannot be bent to your will
+Chaotic Fox
How many beds can you stack on top of each other?
Give 3 candies to a kid, then give him 3 more. How many does he have? None, he ate them all. You have to ignore many aspects of reality to fit it to math.
You also have to ignore many aspects of math to fit it to reality.
You used Natural numbers and some equivalent of Peano arithmetic, but why not some other arithmetic/algebra?
In modular arithmetic, 5+5 could be 1, 2, 3 or whatever you want. If it's 16:00 hrs, you wait 24 hrs and it's 16:00 hrs again. Same for rotation and many other phenomena.
Math absolutely exists. The fact that we call this particular grouping "three" and that particular grouping "five" doesn't mean that, when combined, they don't classify as what we could call "eight." The fact that the people on Zebulon 9 call it "Theenor" or the people on Rylax Minor call it "Ik Thok" doesn't change that there are eight. The fact that we use the term geometric progression or some guy named Fibonacci discovered the Fibonacci sequence doesn't change the fact that bacteria cells would still grow at an exponential rate, very similar to the Fibonacci sequence. The idea that, if humans were not around, they would violate what we know call math is a level of arrogance (that humans are just *that* special) I can't even begin to comprehend.
Some of math's concepts are constructs for things we can't see, feel, touch, or even conceive of. Negative numbers, for example, are often only a notation and can't exist in reality. A vector space of 41 dimensions isn't really conceivable by human standards, but we can still do math within the 41 dimensional vector space and be assured it works. An excellent example of this is quaternions. They are four dimensional vectors, and although humans are capable of thinking in four dimensions, it's not really what our brains do best. However, we can see and verify the effect that quaternions have on 3-dimensional elements by firing up just about any game made today. Things on the screen rotate, translate (move around), and scale (grow or shrink in size). In fact, just getting anything on the screen is impressed, since you're projecting 3D images onto a 2D surface using nothing but math. And electrons, silicon, phosphorous, boron, some copper...all that jazz.
+nychold It's interesting, because for me, the idea that we humans, a collective of survival machines that evolved in order to find fruit, not truth, have somehow been able to discover something objectively true about the universe is also incredibly arrogant (not meaning that in an insulting way in the same way that I'm sure you don't mean it in an insulting way!).
I would imagine that, if there are aliens out there that are similar enough to us to have a concept of math (which is no guarantee), they would be just as trapped by the limits of their survival machines as we are.
As for the advancing of technology, we know that technology advances even if a species doesn't have mathematics. Look at crows or chimps or other tool-making-and-modifying animals - there's no math, but there is technological advancement and modification of existing designs regardless. I don't see why another technologically advanced species wouldn't have developed in the same fashion.
+Nav Vandela Math is not about formulas. Math is more about defining a "something" and making observations based on it that hold "objectively", at the very least in a given context. If an alien designs a technology based on observing or conceiving (without observation) exponential acceleration of any kind after realizing that this indeed will re-occur, it would have used an instance of Math to create the technology.
Physics is the Math of physically observable things, while allowing for more ambiguity due to the context, it's mostly a sub-branch of Statistics. Biology is then the sub-branch which only deals with organisms and cells (as far as I'm aware of), and so on.
Whether or not Mathematics is the stem of the tree on which the rest of our knowledge and technology branches off from, is unclear and something that we may or may not be able to find out.
Who knows, maybe the branches recombine into the stem and it becomes an obsolete question.
+nychold It doesn't matter if the intelligence inventing math is human or alien, they would invent the same math because they live in the same consistent universe. Math as a language describes and models these consistencies
Ali Jorani
Aliens could have a vastly different brain and conscious experience of the universe, which would have an impact on their science and Math. Most of the patterns that we see in nature are patterns found in the brain.
Basically, what you see outside is just a mirror of what you are inside.
***** I disagree, what you're saying is that there is not objective reality. The reason that science works is because there exists an objective reality independent of our brain patterns. Aliens will describe this objective reality using different models or theories but the ultimate abstraction of this reality which is math wont be that different from ours
I was pondering on this subject and I think we stumbled across the fundamental concepts which led to mathematical explanations. Then we did the foot work by crunching the numbers to show proofs for these concepts and thus came to answers that naturally fit our reality. Proofs are the beauty of math. I believe it is the only expression we can show that has a proof to back it up.
It's all an illusion either way...
"There is no spoon."
Math itself I believe is a tool, is a framework to describe things, the same thing as a language. But the the things which it describes are "real", some aliens would invent totally different language, but the things which their language would describe, would be the same "real" as our "real", otherwise their spaceships and whatever technological would not work.
i feel like maths is like Celsius its a measurement of temperature
maths is the measurement of stuff and what it can do
its a measurement of... everything
So math is a measurement? We don't use math to calculate answers or solve problems?
Jet Chen the answer is a measurement
What about proofs? Like square root 2 is a irrational number. Or pi is a transcendent number. How are those kind of activities like a measurements? What are we measuring in those cases?
Jet Chen is pi not the measurement of the diameter of a circle
Mic Mule
As you are aware, pi is the ratio of the circumference to the diameter of a specific circle. In this case, a perfect circle in the Euclidean space. In non-Euclidean space, the value of pi becomes different. Can we get the value of pi by measuring? If so you would need a perfect circle, a perfect ruler, and a perfect method done in a perfect non-changing Euclidean space. If non these are perfect, how can you hope to measure pi? In addition, since pi is a transcendent number, can you ever hope to get the "entire" value of pi in finite time?
I see math more like language fo physics. (and other sciences, but other sciences are just very specialized branches of physics, so still physics) It goes like this philosophy asks questions and physics answers them, often using math as a language to do so.
I really like that wording, and completely agree!
+iNezumi A language is for communication, but there's still the question of what is communicated. Math seems to communicate something that can be confirmed by other people. What do they confirm and how?
Math is a way to can calculate and understand things around us, to give things a name, caracteristics and make them easy to understand, if there is a guy and walk five meters timed, math is a way you can calculate the distance and speed in that case. Its like colors, we give them a name and caracteristics to make it easy to understand
+iNezumi
But please tell me if math is a language how does a computer work ???
a language is fluid and meanings change.. a computers calculations do not...
and because a computer is based on Math is should change from time to time if its a language...
What i mean is not that 2+2 will equal 5 but that sometimes 2 and 2 banans can become 2 and 2 fruits with out losing its meaning in a context...
because of this fluidity is disagree...
(Darn i just made my self agree with you :( )
yes maths is a language... Creers..
+3dmoddeler Language is fluid when language is fluid, and that usually happens either because of the need of its users to account for some previously unexpressed idea or from sheer creativity. There is nothing about language itself that HAS to change over time. Computers have to contend with neither necessity nor creative sponteneity. They are programmed with whatever "language" they have; if a concept falls outside of that language's ability to deal with it, the computer simply doesn't do anything with that concept. And so far as I know, computer's rewriting their own code spontaneously is still the realm of science fiction. So no, we should not expect the language computer's use to change like a more fluid, human language, and so we can expect them to consistently work.
Math can describe many processes in the real world very beautifully. For instance there is a quite easy formula to describe organic growth or fractal structures in plants. Mandelbrot discovered some fascinating formulas describing processes in the financial market, distribution of stars etc. It seems that seemingly random events in the real world all follow a mathematical formula, we only have to find out which one.
This can of course also be the fact because we are living in a matrix. :-)
I think math is human made
Mathematics is not the study of math, but is the study data interactions. Data is real and math is the study of how data works, how I can transform, understand, read, collect and interact with it. All phenomena in the universe produces data and you need a way to work with it and this is math!
There are very interesting concepts here, but I have a question: Is there any part of math, which does not have an observable or measurable representation in the real world?!
I personally find it absolutely amazing, that even the most outlandish and hard to graps concepts in math still find application in the real world: Imaginary numbers, irrational numbers, multi-dimensional calculations... all these (in math rather basic) counter-instinctive constructs find not only application, but even are the only way to model some processes in the real world.
Than that is the answer, math is real.
Ramiel But is it? We created those concepts to make better conceptual models of phenomenon. Like how mathematicians throughout the time decided that 1 is not a prime number or astronomers no longer calling pluto a planet. All to have a better understanding of the universe. It doesn't mean that Pluto changed at all or that 1 of something have now a different set of properties. We were taught in school that if I have one apple and then get another one, I'll have two apples, but what if we wanted to be precise. How would you define a unique set of particles that conform a unique apple with another unique set of particles?
cuellartovar
Don't forget that our Math is a language that describes events in the universe, but the phenomenon of math does happen everywhere in our universe.
In other words: Suppose you have a wedding anniversary in two weeks, and at the time you are in Monday the first. But for some reason you have forgotten number 7 and now when you count days you go 1,2,3,4,5,6,8 and next week 9,10,11,12,13,14,15. Obviously you will be one day too late if you just remember your wrong math, however if you were to mark with an X in a calendar every passing day, you would clearly see that you have made a mistake.
We all make math mistakes and nobody knows all math possible. However, we only know that we are wrong when our universe proves us wrong because quantifiable events happen in mathematical order whether we can count them or not.
Years after this, i recommend reading Wittgenstein regarding analoguous questions.
I would posit, inspired by his tractatus logicophiosophicus, that the structure of languages mirror the structure of the world, and math is an extension of logic, the field that studies this kind of structures.
Math was discovered but it might could be that the system of math itself still might not bet applicable to everything that exists in the universe and so it eventually can't explain everything.
True. Math is extremely useful, but in range of observed phenomena and also useful to predict some phenomena by calculating outcomes of some existing interactions. But it always works with set of variables given by observation. What about things that are not available for observation and yet still existing ?
I mean you are very right, we have had to invent several different systems of math to describe the world. We just decided to lump them all together as math but we might as well have decided that X new field isn't math, it's fairly arbitrary what we decide to call math and what we don't. But given that we have things which cannot be described by classic systems of math you are right.
Personally, I think that Mathematical relationships, concepts, and properties are inherent properties of the universe itself. They exist in the same way that gravitation or the strong nuclear force exists. There can be individual circumstances where such properties are "called" and manifested in a particular region, but those properties exist as features of the universe itself. Think of it like a computer program. You can more or less divide everything into Objects and Functions. Objects are particular entities that exist and can be manipulated and interacted with, such as planets, stars, cats, trees, waffle irons, photons of light, etc. Functions are rules for manipulating those objects within the context of the program and are called when their influence is required, for example, relativity, gravity, nuclear forces, and yes, mathematics. What we mean by "exist" between those two groups of universal features is different. Functions are unquantifiable and intangible, but still exist as properties of the universe itself. Not outside it, not within it, but manifested AS the framework itself. If you think of the universe as a box, the Objects are the things inside the box and the Functions are the traits of the box itself (wood, metal, empty, full, square, round, big, small, etc.).
To that end, there are a few clarifications that I'd like to make as well. For one, our representation of maths is not inherent. It is a language that is used to describe mathematical properties that do exist. But it is still representative of mathematical truth. Also, numbers themselves are not Functions of the universe. There is no mathematical truth of "threeness" or "twelveness" or whatnot. Quantities and groupings ARE a human construction developed so that the universe is comprehensible to us clusters of matter. Numbers themselves are arbitrary units of measurement, but what they measure is still real.
(this bit is the weirder bit that is harder to explain within the bounds of language and logic)
However, there is still a definite difference between 0, 1, and 2 (other larger numbers are just groupings of 1's and 2's). 0 would be non-existence, or a null value, for example, there are 0 parrots within a defined radius of me. 1 would represent solitary particles, for example, a photon traveling through space. And 2 would represent particle interaction, for example, said photon interacting with an atom that it collided with. A case could potentially be made for the inherent existence of "3" by taking into account the structure of a baryon, as they are composed of three quarks interacting with one another equally, however, they interact by exchanging photons, rather than by directly interacting, thus, even this relationship doesn't make a strong case for the existence of "3".
Yeah, the last paragraph is mostly speculation on my part anyway. Feel free to ignore it.
too hard. gonna smoke a bowl.
Yea this video gets me hard too, but I don't get why you're immediate reaction is to do the marijuanas
ok half way into this video first thought was...I never stopped to think if math was a feature of the universe or if we just made it all up. So far the suggestion made me think about us as people and that we love to create tools to either manipulate the world around us or to describe the world around us...so far your video sir has my attention. Please continue.......
In the observable universe, there is no such thing as math. However, math can be employed by humans to understand how the universe behaves.
Well said. this is exactly what i think. best explanation.
Prove math doesn't exist. Since you have chosen observation, could you prove it empirically?
Please consider the relationship between information and energy. Also remember energy and matter are interchangeable.
I speculate matter is information is mathematics. Anything observable is math. (This could be wrong, but I doubt anyone has shown it empirically.)
People have proved that mass is the same as energy. From my understanding, this means that the observable universe is made of energy. It is my belief that math is a human representation of energy that is recorded so that we can understand the observable universe. Any input is always appreciated so thank you :)
It has not been demonstrated that math is exclusive to human brains. Math is likely a form of information though. Since information is energy which is in turn matter, it is a stretch to claim math cannot be observed. While that could be true, it could also be false.
there is no true way of knowing the answer to this. we can only make educated guesses. math probably can be used by many different organisms if not all. we only see what the brain is showing us at the end of the day.
I've been wondering if there will be a time when we realize that all the math we use now for describing the universe, being based on counting our fingers, suddenly becomes really beautiful and simple when we base ist on $whatever (like strings).
"5, 10, James Bond, and his martini don't actually real"
It would be interesting it we could catch a glimpse of what math would look like from an outsider of our human history. I think it would be as foreign to them as their math is to us.
Human creation. Math is a consistent system with which to measure something, the same with any other system. It's like asking if English is a feature of the universe or of human creation.
5+5=10 is true because of the way we have defined 5, the plus symbol, and 10.
It exists, we invented a way to describe it.
That means everything is an interpretation of what we observe (and call reallity). But math is the BEST interpretation :P
+Kevin Cobb
He didn't say it exists _because_ we invented a way to describe it, he said that it exists, and what we invented was the way to describe it :-P
You could say the same about God, but it doesn't mean God exists. Faulty logic
You can only watch 9 of the videos in the super collaboration as of July 25, 2017. The video on the Spengler Effect seems to have gone private. I'm binging the colllab right now. This is one of many great videos.
math is simply an explanation of our observations!
or the explanation of urselves
Not quite. Basic math is indeed observable, however I have never heard of someone observing any complex numbers, no one have ever found √-1 of anything. Even negative numbers are pretty hard to observe, aren't they?
2:44 Im a simple whovian: i see reference, i press like
I asked myself that question when I was a teenager.
When going this deep one must define what one actually means by the term "existence". A good start is: An abstract concept "exists" if it has relations to other concepts. But does one include relations over time linking to concepts that are not yet discovered? "Existence" seems to get blurry. ...
On an other note if I understand correctly cunstructivists/intuitionists say everything that cannot yet be constructed may not "exist".
Don't be afraid to question everything that you previously knew as truth ...
Don't be afraid to truth everything you previously knew as question...
Math is as "real" as sarcasm, and this is coming from a mathematician by trade. It's a series of useful predictive and modelling concepts which do describe real phenomena with varying degrees of accuracy, but the idea of "purely mathematical truths" is fiction in the extreme. The properties of a thing are not themselves a thing.
Very well put and succinctly, too.
This falls into Austin's description of "the abstractness implies it doesn't exist." What does it mean to exist? Can't something be both abstract and objective?
@@ac4740 Unfortunately Austin just begs the question against platonism, if existence is defined only for causal entities then numbers have been out defined from the debate not proven to not exist. In that case, the question really hinges on platonists finding a reasonable response to the epistemic access problem since platonism is much nicer than nominalism. They have a hell of a time coming up with rephrasings that arent utter hell.
So if intelligent aliens exist, would they use the same type of math as we do...?
just thinking how their math would be is sooo intricate
they will use the same math there is just one math... they will use diferent symbols.. i mean i call a dog (perro) and some other lenguages call it any other way but the dug still a dug no matter what way you call it ... do you get my point?
is like saying do other aliens have any other type of gravity? well they might experience depending on the mass of their planet more or less gravity than us but gravity is not diferent here than it is there... is the atraction between two bodies with mass.
no they won't. They will use something else
i think math is fairly man made. Math is made to analyze and find solution to problems. The problems is the same and the answers is the same, but the method to get there is different. For instance, the rules of trigonometry is the same everywhere, but subjects as algebra and calculus is most likely different...
So many years later, and I still come back to this video when I need to get outta my own head.
You have overlooked one crucial thing. Science is faith as well, People used to think that the earth is the center of the universe. Most people had faith in it thus it was science. We all think that the Sun is the center now but that may not really be the case. Science may also be a creation of the human mind. In fact, if you think about it, nothing can be really said to be of the universe
you are saying that we all think thesun is the center of the universe? or i misunderstood
Lindle Lee You're referring to scientific theories.
Science itself, doesn't require faith.
Definition of faith I'm using (in this context):
_"complete trust or confidence in someone or something."_
Nobody should ever have complete trust or confidence in anything.
Sure you may believe it to be true, but that doesn't mean you should believe it blindly.
Have some scepticism.
Science isn't about finding a theory and then blindly believing it. If you can find evidence which contradicts theories/claim and come up with a better theory, then your theory will be what is considered true for the moment.
Science is ever changing. No scientific theory will ever be proven to be 100%. However, that doesn't mean we should ignore all scientific theories either. If you think it make sense and logically explains whatever it's supposed to explain, then believe it. However, if you're sceptical, don't believe it and try and find better evidence/contradictory evidence to prove it false.
645akz I think you are forgetting that ~100% of people have faith in gravity. Much like any other religion, there are principles within science that must be accepted. And much like science, many religions are striving to explain the reality of the world. The only real difference between the two (that I see) is the amount of scrutiny that it takes to be accepted. Which only means that we are trading in a (possible) personal delusion, for a (possible) mass delusion. :P Math (as an extension of philosophy), has the unique position to show what is real while still reflecting how the world is. But like philosophy, sometimes it is hard to determine where reality ends (the irrationality of pi for example).
noah schaefferkoetter
_"I think you are forgetting that ~100% of people have faith in gravity."_
The scientific theory of gravity is very complicated.
Most people don't even know about the effect gravity has on other planets.
Sure everybody understands a portion of it, but most of it, most people probably don't have a clue about. For instance, how gravity links with general relativity. I don't quite understand everything about it as well.
So no, they don't have faith in the scientific theory of gravity.
As for their own pseudo believes about what the theory of gravity does, they personally observe it's effects. That alone, separates gravity from being completely faith based.
_"Fact" in a scientific context is a generally accepted reality (but still open to scientific inquiry, as opposed to an absolute truth, which is not, and hence not a part of science)"_
_"Much like any other religion, there are principles within science that must be accepted."_
Such as?
Nothing, absolutely nothing has be accepted. If you find evidence to the contrary to what is stated in a scientific theory, bring that up. It may put a hole in the scientific theory.
It's when you stop thinking and blindly accepting (faith), that's when you stop finding any major breakthroughs in science.
You say "absolutely nothing has to be accepted". I disagree. For example: the idea that "reality is what I am experiencing" is taken for granted. Without that, science (and religion for that matter) can't even begin.
Please understand that I think that science is necessary to understand our experienced environment, but to say "it requires no faith" is like saying "religion requires no faith because my experiences have lead me to this".
BANACH TARKSKI PARADOX BOOYAH
watch the vsauce vido on it
math describes the equation for which the universe runs on, basically math is god
I'm sorry but i must say, that is the most ridiculous thing I have ever heard. your saying that numbers created the universe? WOW!
Maytha Hussein no, equations do, some people call them laws, some people call them god
Maytha Hussein *you're! assuming he believes god made the universe.
Evan Cooper thanks for the correction i didn't know i hired an English tutor. cheers
*Thanks, *I, *Cheers. Beginnings of sentences have capitals. You're getting there Maytha.
My thoughts on this is that our interpretation of math and how we represent it, is just that. A representation or description of real concepts such as movement, mass, shape, etc... That are then (as you mentioned) applied practically. We do discover how things act and then invent ways to represent the systems and connections (Or in reverse, suggest then test theories). At it's core (Actions, reactions, happenings and otherwise) I do agree that math is something discovered. Similar to how pioneering doctors and such assign terms to processes in the body (to greatly simplify it) Though, without the same level of versatility throughout the sciences math has.
Why can't math be both real and a story? I think the debate is more about how we define reality than about Math. That doesn't mean the question isn't fundamental or important, but the concepts being dealt with are at least as important as the concept of "reality". Some people believe reality is a story. some people believe reality is Math or Truth or something. Some people believe Math just describes what is real. I don't think we have an agreed upon definition of reality fine enough to answer the question.
Personally I speculate that matter is made from information. Electrons are made from information. Matter is a story. Further it is a mathematical story spun out by some super being called "God" of whom we know little. I could be wrong though.
I think if math is real then it can be a story, but I personally believe math is just an adjective we use to describe thing(s). Things math describes do not require the math to do what they do, but they simply can do what they do because it is possible and math explains how. If the definition of reality is physically being then math must be not be real and is simply a thought used to describe things that are real.
ThatPsychicTrainerYo To sum all of that up math is a thought and is real, but only inside your mind.
I think Either-Or questions are anti-reality. Embrace the tension! Be a Both-And believer! Math is not either a reality or an anti-reality. Math can be both reality and anti-reality. I.E. Math god is out there, but we can choose to understand our world mathematically without him with our (maybe) god-given minds? At least that is one way to address and embrace both worldviews.
Tyler Sellhorn "Also, fake is the new real." -Kottke, et. al.
Scientists have converted information to energy and energy to matter. They are the same thing. Reality is information.
Some stories are real and some are fake, but dismissing all ideas as insubstantial is clearly incorrect.
1 is 1 because we say it is; we define these terms. We say 2 is 1 more than 1, 3 is 1 more than 2, and so on. With these definitions, there are logical identities we can deduce. If 3 is 1 more than 2, then 3 - 1 = 2 is true necessarily. We create the definitions, we discover what's true using those definitions. 1 + 1 = 2.2x10^-5 is true if we DEFINE the first term as centimeters, the second as inches, and the third as miles. Definitions are important. So obviously, we created math. But if our definitions are consistent with physical reality, we will also discover information about the world and the relationship between objects within it.
Strongly disagree. There is a set of possible whole numbers (or natural numbers, or whatever you want to call them). You can have 1 of a discreet object (let’s say, an electron, for simplicity’s sake) or you can have 2 of a discreet object, or 3, and so on, but you can’t have 1.5 of a discreet object. There can be no whole number between 1 and 2, even if we wanted to make one up. The reality IMO is that we create the symbols used to *represent* numbers, but the sets of possible numbers and the numbers themselves that constitute those sets are just an objective reality. If intelligent aliens discovered math somewhere else in this universe, they’d still have to have a number for 1, for 2, for 3, etc., but they still couldn’t create an arbitrary whole number between 1 and 2. They would still have to have addition, subtraction, etc., if they were to have a complete knowledge of algebra. Their symbol/character for “1” or “2” or “+” or “-“ would almost certainly be completely different- as far as I can deduce there is no reason to suspect that there’s any universality to the symbols we create to represent universals- that’s the same reason why diffferent languages use different alphabets and different words, even though their words are describing the same concrete objective realities (i.e. trees exist in the world, whether you call them “trees” or “des arbres” or you represent them with a little symbol of a tree or with some other symbol altogether). But numbers and operations themselves are not arbitrary or fabricated. They are objective and we discover them.
To take a slightly more tangible example, the Pythagorean Theorem was *true* before we discovered it. It is simply a reality about the form of right triangles (three-sided shapes with a 90 degree angle). You can call triangles something else (as you do in other languages), you can call the theorem something else, you can change out the individual symbols in the theorem (“a,” “^,” “2,” “+,” and so on)... But those symbols assembled in that equation describe an objectively true, universal fact about triangles within our universe. It was true that a^2+b^2=c^2 before we discovered that fact, and in fact it was true before a single physical triangle existed in our universe, because it is a fact about the nature of triangles themselves, not any particular triangle. It is a universal which is applied to particular cases.
At this point many physicists believe that *information* (e.g. the sort that is encoded to the surface of black holes) is more fundamental than matter, energy, or spacetime, so by now I don’t think it should be such a shock that non-physical phenomena can be objectively real. But setting that aside, it seems very certain to me that mathematics is discovered. We do invent symbols to describe it, but when we, for instance, create formal logics to describe the relationship between 1 and 2, what we are creating is the explanation, not the phenomenon. Numbers already were manifest in the world in all kinds of ways (shapes could have 3 sides or 4 sides, but only whole numbers of sides; you could have a family of 2 people or 3 people but not 2.5 people; there was already one constant value that was the ratio of every circle’s circumference to its diameter, even before we’d measured it- we may call it “pi” or we could call it “circle-number-“ you can call it whatever you want, but it is an objective constant- it’s value is what it is no matter what symbols you use to represent it).
My take as an anti-realist:
For me, math is seemingly created. We invented math as a way for us to be more concise about measurements, designs, ratios, and so forth. Mathematics does not happen naturally in tje universe, and unlike biochemistry, biology, and any life science, we cannot see it happen without our intervention. I do, however, love math now, and I consider it one of the sole best inventions, ever.
Colby Jack math was always there and not created as it was discovered as you will see it when taken complex analysis and differential equations.
Juan Lopez How has mathematics always been there? It's not at all natural phenomenon without human interaction.
Colby Jack Well math it is real & it is natural...
in chemistry for example in atoms theres electrons & protons & they have to complete negatives & positive particles to interact & make a new element, but always thay have to make together a specific number of particles in set...
& then theres Fibonacci, all nature comes in Fibonacci numbers, from u to the entire galaxy...
Colby Jack It may not be natural phenomenon but it always existed
Juan Lopez
While that may be true, it is still, currently because we do not have contact with any other worlds using math, a human made field used for abstract ideas, additions, subtractions, etc. And Brock, yes that is true, but we can know atoms exist without the idea that Chemistry. If we observe enough and theorize, we can conclude that there are smaller units of matter besides us, the macromatter.
Ted Chiang, author of ''Story of your life'', the story that the movie Arrival is based on, wrote a short story on this very subject called ''Division by Zero''. It's excellent, available online (link on his wikipedia page) and you should be reading it right now.
After finishing this video.