Full podcast episode: ua-cam.com/video/Osh0-J3T2nY/v-deo.html Lex Fridman podcast channel: ua-cam.com/users/lexfridman Guest bio: Edward Frenkel is a mathematician at UC Berkeley working on the interface of mathematics and quantum physics. He is the author of Love and Math: The Heart of Hidden Reality.
Before I watched this video I was confident that we discovered math as it seems like a fundamental law of the universe. But after reading the comments, I am blown away by how many great discussions and explanations you have provided. I feel more confused and undecided on the question than ever lol. Thank you.
We discover phenomenon, and describe it the best we can as humans. This debate between whether math is discovered or invented is semantics, a farce really. It’s both.
@@DanielAnderssson "I think pure math is geometrical forms." That's absolutely not true in any way. There are pre-geometrical mathematical structures. "Without knowing anything, but that’s what the LSD told me." No you brain on LSD made you come up with this idea based on the information you had gathered before hand. LSD modifies the way our brain processes information. It doesnt gives you new information.
Math is a tool using rational principles. One of any given unit added to another of the same unit creates a sum of 2 units. This fundamental principle replicates itself in many different directions. Math is not so much a "truth" to be discovered or created, but a language to explain quantity and it's applications.
In some other part of this podcast Frenkel states that at the beginning of mathematics there's a choice and this is the set of axioms. He was very correct about that. After this choice the mathematics of this system can be discovered, but what is very important to notice is the order in which mathematics was developed and this order isn't some mathematician set up ZFC and then all the results were step by step derived. No. Often we get inspired by nature, some pattern which seem interessting, some problem we want to solve. So mathematicians formalized those and build mathematical tools to aid the solution. Building upon that the results are generalized and a theory build around it from which new results are derived. Only after that some first principle axioms are chosen to build a (hopefully) contradiction free and complete math-universe. This happened in the 20th century with ZFC and others. In general (like with learning) the mathematical development process is recursive swinging between invention and discovery. The choice of axioms was depent on the before made inventions and these inventions were often motivated by problems or patterns arising in the natural world thus indirectly discovered. Important tho is that the basis of all of this is how human brains process information. This is the basis of logic and also patterns - patterns are a part of the cognitive process. They are the interpretation of information that our brains make. This information process must be somewhat accurate as it has evolved to be, but even if it is absolutely accurate the brain process - or lets say the idealized brain process as we certainly arent perfectly logical - must not be confused with the structure of the natural world itself. World and image aren't the same even in case of 100% accuracy. The question "Is math discovered or invented?" is interessting, but terribly misunderstood. It isnt or shouldnt be about if mathematics is literally the structure of the universe. Even if logic truly is something fundamental (impossible to proof) and not just how our neural network process information between the logic and the mathematics there still is the mathematician, whos neural network is being feed with information that is then related, recombined and conceptionalized (and what else is invention if not that?). Thus when pressed i would answer the question with "invented", but it is much more difficult.
Have we? Maybe, but what is the distiction between that and being able to catch an object thrown towards us, or rightly suspecting an event to occur; things we already could before the energence of math.
@wolfgang-franzkranek6146 how did anyone "invent" the Mandlrbrot set? Are you insane? Lol the plots you get from it where 100% discovered..sure you can assemble your own mathematical objects ALSO but no one will consider that new math unless it leads to some *discovery* - some otherwise unknowable or unconstructable structures or objects or relationships.
@@Calligraphybooster Did you even read the comment? Clearly he stated "we invented uses for it" Just like how language is created, we invented uses for our language, sure you can interact with just hand signs or grunts before language was even invented but that doesn't take away the fact that we invented uses for it.
I’ve always thought about this in grade school but couldn’t articulate it. Are we noticing patterns and giving it meaning or are we finding meaning from patterns?
Yeah, Math is to big of a concept to answer the question directly, if you ask me if the universe creates patterns symmetry, efficiency, etc then the answer is obvious, if you ask me if calculus is an invention, it feels more of a tool based on some truth that is useful, but we know calculus in the edge is not 100% accurate.
Math is insanity. There are infinite numbers 1.2.3 etc., but there is also infinity inbetween each number also. What amazes me about it is everything is in there we just have to find it and when I say everything, I mean everything. Want a particle to be only a particle and not a wave function, its in there, but at the same time if you want a particle to be only a wave and not a particle, its in there also. Insanity at its finest.
@@DnVFMVs I think that is the true nature of life as they were saying in the video its full of paradoxes. Even ancient eastern philosophies understood this idea that life isn't black or white, it's non-dual. Just look at the Yin-Yang both the black and white exist simultaneously connected to each other.
Not sure if we live in a world of paradoxes when there is no consistent semantic system of language. More like we fail to explain what appear to be paradoxes. Wave particle duality is a misnomer since an electron can appear as a wave, a particle, both, or neither, depending on the semantic system we use to measure and describe it. The underlying info doesnt seem to be paradoxical, just our explanations of it. Not sure why anyone would be surprised that we dont understand anything at a fundamental level, but I wouldnt assume we live in a world of paradoxes, just a world where we fail to communicate perfectly.
I think if it is invented we would have control to manipulate mathematics in many ways as we wish, but actually we don't have such a freedom , so for me is more discovered. Like lows of physics - we can discover and use them but can't change them. My humble opinion.
It's much more abstract than that. The generalization of patterns, how they relate to each other, their properties and categories. It's not just about solving an equation, and more about understanding what it represents. Take a look at AI and machine learning for example, it's about building models of cognition, pattern recognition and more.
If maths is an expression of our understanding of how to describe what is not only physical, but our shared imaginations as conceptual realities, then as part of that lingual technology it is only natural it evolves into more complex forms. It feels like a space where we can both invent and discover at the same time, as the function of that lingual technology has not simply evolved to help us share ideas and concepts, thus describing the outer edges of our reality, but to provide insight into the depths of complexity and dimensionality our imaginations are able to wander confidently.
Hard disagree. We try using language to make sense of our preexisting understanding of math, not the other way around. Math exists independent of communication. A single, simple consciousness instantaneously performs advanced calculus without outside influence/education. E.g. a dung beetle will automatically calculate which area has more pieces of shit (mathematics) & calculating which pile of shit has more mass based on limited dimensional information. They do this (whether they know it or not) using geometry/volumetrics, and calculus formulas that the majority of humans also use, but couldn’t explain if their lives depended on it.
@@jessereeves3120 language can describe concepts over time. Animals are also understanding concepts and making decisions overtime. Your argument would still hold true for language just as it does for maths. The maths could be used to describe the thought process of the beetle as well as the language that we use i.e I am hungry, I am going to eat skmething
@@jessereeves3120also, the math that we use may be "true" I ky because we set rules saying it is i.e 1+1=2. Now, maths is very effective, however we aren't really accessing complete truth when we use it, it is simply used for its utility. This is because the world is infinity divisible, and we may use maths to figure things out and get a good enough answer where we don't realise/care that it's not precise. But we never use maths in the real world completely correctly. We make these concepts and structures with both language and maths for our use to survive. I love maths though and I think on a spectrum it is more objective than language.
In a romantized sense, creation is the discovery of the unknown. Personally I think as humans, every moment is a discovery because the future is unknown.
I always think of this thought experiment: if you'd have multiple people/machines in a isolated room for an infinite amount of time and have them discover/invent new math. Language aside (notation used etc.), they are all going to come up with the same. It just seems way more intuitive to see as a discovery because math is already always present, we just have to find a way to understand articulate it.
Both, it's a question of categorization or classification. It's like asking if something is a chemical or physical process. I think the question is misleading, but I would classify it as invented, because we would also say that language is invented and with language we can also describe abstract situations and stories that are not really there, although they are of course physically exist in our neurons, so it's a matter of classification.
The reason we ask this question is because we don't like chaos, it could be dangerous, so it leads people into error, they want to organize it so it won't cause problems in the future, but they forget that the question is more important than the answer.
In order for math to have been discovered, it had to have been there before it's discovery in some shape or form. Since we have invented it it now appears to us to be "there", and that gives us the illusion that it was always there. But it really was not until we invented it.
I think the more appropriate contrast here would be "constructed" rather than "invented". As in "Is math discovered or constructed?". The answer is that it is both: "Discovered and constructed". Or rather in the reverse order: "Constructed and discovered". First, we conceptually construct, then we explore and discover. We explore and discover the extent of local specifities included in the conceptual space that we have constructed from abstract general construction principles, which is sometimes so vast and breathtaking that our mind can barely grasp it. And then we get kickass videos like this: ua-cam.com/video/LhOSM6uCWxk/v-deo.html.
It really doesn't make sense to me to say that math is invented. Math is the discovery of universal truths. Sure our representation of mathematical entities is invented, but the concepts described by them are discovered.
Then it seems our pictoral or axiomatic representation of the mathematical truths that seem to exist are invented, with that underlying "thing" being natural and thus discoverable.
His reflection that belief in Platonism is connected with the feeling of uncertainty and injustice in the (messy, material, changing) world, is profound and speaks of a great capacity for self-insight.
These guy recently learned Pythagoreans saw profound meaning in numbers and is amazed by it. Meanwhile, 90% of mathematicians have known this their whole lives. I think there is an unbroken line of true masters of the art and their apprentices from the time of the Pythagoreans to us, and even further back. 10,000 years of legacy, only known to a few, apparently, despite our best efforts to convey it to others.
@@Milark obviously, the first ones barely knew how to add and subtract and other minor stuff, but quite rapidly they discovered fractions, knew something about patterns, discovered some geometrical truths. About 6000 years ago they already knew quite a bit.
Here's my answer, and why, via an example: There are an infinite number of theorems in math. The vast majority of them are useless and/or boring. Mathematicians search for the ones that are useful and interesting. The fact that there are so many theorems of that type is explained by math as well. If we number all possible theorems as n= 1, 2, 3, etc. then there will be some that exhibit symmetries and structure and broad application, despite being very short, just as we encounter patterns in random numbers, 1234, 3333, etc. The powerful theorems exhibit the same behavior as these compressible numbers in terms of prevalence. There are an infinite number of them, however they are sparse, and their sparseness increases with n. If there were no powerful theorems (or an extreme lack thereof), this in itself would imply something special at work, since it is incredibly hard to avoid symmetries and patterns in even random sequences, so to not stumble upon them would be highly unlikely. On the other hand, if theorems were as common as the even numbers (as an extreme example), then they would hardly be of any note. So, what we have is a clustering of useful theorems, which are manageable in size and then a few less that are a bit larger, and a few less that are even larger, and so forth. So there's no upper limit on how many useful theorems that are "shorter than x" for example, and it certainly can't be zero - it's somewhere in between, and even if the usability of any particular theorem were to correlate with the compressibility of a sequence of random numbers (i.e. pure chance), which is just about the worst case scenario that I can imagine in the universe, there's still going to be plenty of them - a lot of shorter ones, and fewer longer ones, but every so often, you'll encounter one that is an absolute banger.
We observe nature, then invent math to describe it. Then we test that math which yields new observations. It’s a never ending feedback loop that we’re all addicted to.
@Bob Nah. First need of math will be for early man to communicate amongst each other about how much to trade of something, generally food in this case. So inventing a counting system (math) to observe/measure fruit (nature).
@@jarrodfodemski1018what about the case of people "discovering/inventing" maths purely for maths sake. Then 100s of years later it gets applicated to the "real world"?. I guess you could still say that there is plenty of pure maths that doesn't get used so it doesn't really prove either way idk. It seems like tho if maths was invented you could treat it like making a song or a dress and do whatever TF you want it seems like there are set rules that make you obey. Are these the laws of the universe or just axioms pre set idk tbh
The way we create in this world is using language, and with numbers, we create mathematics. We use more mathematics now to let computers solve the language we can't understand, but numbers allow us to understand better because we rely on technology to solve the language of what we want to create. In our imagination, it's our home in a way that we don't need to understand bc we are creating things by thought... imagination is our own way to create in our own world but in the real world it's with language and now numbers but now with ai I fear we will end up giving a language to the ai which can transition the sense of now but it's either gonna be a great thing or bad but I hope for good... keep the imagination alive it's our art our way of bringing it to here!
The paradox of questions like these make the meme answer of "yes", the most true statement to ever be uttered. Is math created or discovered? Yes. Is a photon a particle or a wave? Yes. Do we have free will or is life deterministic? Yes. That one being based upon the laws of physics and the quantum state of superposition(s). Do you want to drink tonight or do you have work in the morning? Yes. Am I an alcoholic or do I just enjoy drinking more than the average person? I'm an alcoholic lmao
I’ve argued both sides of aPriori math/geometry ad nauseam in epistemologically based philosophy courses. IMHO, it is as simple as instinctively understanding two berries are more nutritious than one. It’s also intuitive that walking a straight line to those berries is more efficient than a long, non-direct track-line. Even for a rat isolated from any any schema influence. That doesn’t mean math/geometry is an epistemological truth, it just means our experiential epistemological truths are readily apparent without outside agent influence. So either math & geometry are intrinsically true, or our entire experience is false.
Seems like a fallacy of composition to suggest that if any part of our experienced truth is incorrect it all must be false. Isn't all of science built on the rejection of this mode of thinking -- a demand for consensus over individual lived experience? Point in case - the world is curved, so the fastest way from point a to b is also a curve (though often too slight to matter). 1 toxic berry might not be enough to harm you, and you can consume its calories; 2 and you throw up, resulting in a loss of calories.
I think the correct answer is it always existed. However, the way we interpret math, so much as, the symbols we use in our equations are a creation of our minds as humans in order to begin to comprehend "Mathematics".
I think having a "response" to something like this, its like stop experiencing. There is no unidirectional or unique response, it's weird to grasp but the "answer" is both imo...
The question is not if it is invented or discovered...the question is if it exists independently of us. The answer to that is an unequivocal affirmative. IOW...something exists out of which we create this thing called mathematics. That 'something' exists independently of our discovery of it. Whether mathematics exists in the exact form within which we comprehend it ...independently of us...is a different question. It almost certainly does...and as the understanding of consciousness advances this will be confirmed. The reasoning is not that complex. Mathematics is a function of advanced consciousness. As Don Hoffman says...consciousness is everywhere...and there are almost certainly varieties of it (what Don calls 'conscious agents') that are far more advanced than our own...therefore their 'experience' of math will incorporate our rudimentary comprehension of it...as well as an equivalently advanced understanding. No big deal really.
When I have to answer this question I just say that it's both, which is a like a different version of the answer, it's more complicated than that, and I think that's the essence of what Edward Frenkel is suggesting as far as how we should try to understand this question.
Mathematics is a generalisation of numerical properties. Much like electricity is discovered and the light bulb is invented to generate light mathematics is an invention that enables us to transform numerical properties and discover new numerical properties. That's one way of looking at.
It’s a false contrast - invention is a form of discovery. It’s discovering how to combine and integrate existing knowledge and objects in order to make something useful.
I believe that math is like the part of philosophy that deals with metaphysics. In ancient philosophy, physics was the study of the appearance and function of being, metaphysics was the study of being itself, stripped away of all fancy. In a similar way, mathematics is the study of quantity as it relates to reality. Wanna describe objects in numbers? Geometry. Wanna describe motion in numbers? Calculus. Math is simply the description of reality through numbers. Language is the description of reality through words.
@@havenbastion Even the names are discovered. I know it seems like we're inventing things, but we're not. Think of the name or use of word for anything and you cannot account for why we chose that exact term. That's because we didn't choose it, we discovered it out of the ether or the whole of consciousness, which is already complete if not in form or function, then in potential.
It wasnt the Love at first sight experience that made me feel an overwhelming Soul connection, .. it was the eventual recognition, of the enormity, of that momentary minutiae chance in infinity, a coherent weaving of pattern, of complexity, time and space.
It would be interesting if you could take the current universe then replay it via a new simulation in a computer and see how things pan out... probably in a different way albeit with the same fundamentals... The question of discovery and invention merely depends from which direction you're referencing: They are both present.
I'm mystified why anyone would believe human math is anything other than a language our brain needs to extend ( into 'difference'). The idea an alien would necessarily have something similar seems preposterous. On myth AND OR logic Bertrand Russell wrote a fantastic essay.
We are drawn to art/music because it's a very efficient, direct, and adequate way of communicating with each other about the ineffable but true. And art involves the WHOLE person, including their emotions. The 'real world' is the ENGINE that drives the NEED to discover the invented mathematics which faithfully describes it. Humans don't fundamentally invent mathematics in a vacuum, nor do we settle for mathematics that's completely divorced from the 'real world' itself. The scribbles on the chalkboard are NEVER meaningless, and we can sooner or later TELL that they are right or wrong, and WHY. The 'elegance factor' involved with our invention of mathematics is tied to our need to understand the universe LOGICALLY, and the fact that LOGICAL mathematics 'does the job' with respect to codifying how the real world actually functions indicates two things: (1) The universe DOES function along logical lines. (2) The Mind ultimately responsible for this logical functioning is akin to ours since our minds are readily enough able to decode and quantify that logic.
Some of it is invented. For example, Lebesgue integrals were invented to include a larger set of integrable functions than the Riemann integrables. But the content of number theory is discovered.
@queerdo Well, by your usage of "discover" every thing is "discovered," as in Edison "discovered" how to make an electric light emitting device. The Lebesgue integral isn't the only way to enlarge the class of integrable functions.
Paradoxes are a product on incomplete understanding, and is the perfect mirror for humans to reflect on our miniscule perspective. Our current sense of logic is flawed, but all we can ask is that it's less erroneous than its previous iteration. The interesting question is: is there a limit to understanding? Is there such a thing as "knowing it all"?
Fair point…. yet mathematicians have ‘played’ with ideas that resulted in what we thought were illogical conclusions… only to find out later described aspects of nature. That, being true, suggests math is discovered, not invented.
Any life form intelligent enough to build any type of mechanical devices would have a symbol or figure which represents Pi. The circumference of any circle is a ratio involving Pi and it's diameter, whether or not someone understands this or realizes it, is of little consequence, it is a maxim, it was long ago proven. I personally have used it for a growth formula to calculate the number of feet of paper wrapped around a given core diameter and a given overall diameter with a given paper thickness.13" OD core Roll 72" overall diameter paper thickness .004" - calculate ft.
I fully believe mathematics is invented as a description of the patterns in the universe we’ve discovered. Just as human languages are invented as a means to convey our ideas. The evidence of this to me is in how mathematics can seem to breakdown at points (true of any imperfect model of something more complex) and then we can adjust it or expand it to work again in a more generalized way. The fact that humans can change mathematics demonstrates that we “own” it. It is descriptive, not prescriptive. It is our best idea we’ve come up with to describe the patterns of the universe, but that doesn’t mean it _is_ the universe itself, or there isn’t another way that is even better out there.
math is independent of the universe, and infinitely more complex. math doesn't break down. our models of reality (which is physics, not math) break down and are inperfect. we then change and adjust the theory (which again is physics). We dont change math.
I respectfully disagree. Math has changed a ton over the last few millennia. The origins of algebra, geometry, calculus, etc. all have quite well documented histories. I.e, there is a time in human history prior to the existence of these forms of mathematics, therefore it isn’t static or preexisting but rather invented and extended by humans as a tool/language to describe the world. There are plenty of examples of similar concepts having been represented by different nomenclatures in the past. E.g., not all societies have even used base-10 arithmetic.
For billions of years, there existed...a slab of marble. Inside that slab of marble, for all those years, there existed...the statue of David. Did Michelangelo invent the statue....or discover it?
The collective unconscious can direct our passions to memetics that enrich our confidence on a matter that has already been considered. I think this could be a form of morphic resonance, but I am plagiarizing here. Objects with invariant contexts can be systematically manipulated in predictable ways. But a lot of functions only correlate to target models and are more useful than fundamental. I think as we try things our "memory" promotes what is most useful. This is some pretty big talk.
i always thought that math is probably invented. fundamentally, there are quanta, which to me can be very similar to numbers: discrete units of energy or any value. it makes sense then that we make sense of the world by using numbers and variables as quanta. then its all about relationships to one another which i think integrates equations and so forth
You could say that about every invention. an iPhone for example.. we discovered that if we put all these things together, it becomes an iPhone. The difference between discovery and invention is subjective.
@@Defort-jd8xe Not at all. 2 and 2 make 4. It just is. It doesn’t have be designed or made. Just observed and it exist weather we observe it or not. Math exist independently of of human beings. Even an animals can keep track of how many babies it has. An iPhone is a thing.
@@Nochancet.v That’s an entirely different equation. How many atoms can four cats be broken down too, has nothing at all to do with… two cats plus two cats gives you four cats. Atoms are not cats. And 2 atoms plus’s two atoms gives you four Atoms.
A certain design of the incandescent light bulb has the predictable physical properties that it has, from the dawn of the universe, long before Edison found that that design solved a certain problem for his customers. Nonetheless, the light bulb is the quintessential invention (light bulbs were invented if anything was invented). Similarly, for, say, probability theory. The theorems of probability were entailed by its axioms before the dawn of man, but when we discovered that those axioms and theorems could be used in a certain way to solve certain classes of material problems, we invented probability theory (if light bulbs were invented, and indeed if there is such a thing as invention).
“There is a tide in the affairs of men. Which, taken at the flood , leads on to fortune; Omitted, all the voyage of their life, is bound in shallows and in miseries. On such a full sea are we now afloat. And we must take the current when it serves, or lose our ventures.” - William Shakespeare, Julius Caesar -- here we are , again.
Not to get religious, but this is how I feel about the idea of God too. Either there is some-thing or no-thing and that something is what we call "God" and then we started inventing characteristics and an identity to God. But the idea of a Creator seems to be universal, intuitive, and a logical possibility. But a "flying spaghetti monster" isn't a universal discovery...if that makes sense.
It is the preexisting logical relationships reflected in nature that guide and mold development of math's notations, with proofs. It's the logical relationships that are discovered. Math is a back feeding rigorously developed notation used to describe and facilitate discovery of those logical relationships.
The question of whether math is discovered or invented is a topic of much debate among philosophers, mathematicians, and scientists. Some argue that math is discovered because its laws and principles exist independently of human thought and are waiting to be uncovered. Others believe that math is invented because humans create mathematical concepts and systems to describe the world and solve problems. One argument in favor of math being discovered is that mathematical principles, such as the Pythagorean theorem or the laws of calculus, exist independently of human beings and were waiting to be discovered by mathematicians. Additionally, some argue that mathematical concepts, like the number pi, exist independently of human beings and are simply waiting to be discovered. On the other hand, some argue that math is invented because mathematical concepts are created by humans to describe the world and solve problems. For example, the concept of negative numbers was invented to solve problems that arose in mathematics, but negative numbers don't exist in the physical world. Ultimately, whether math is discovered or invented depends on one's philosophical viewpoint. Some believe that math is a human creation, while others argue that math exists independently of human beings and is simply waiting to be discovered.
I would say, the application is an invention of a sort; however, "math" and the measurements themselves TO BE MEASURED by math...that is all a constant. It's simply an idea we captured...but then again some could say EVERYTHING, is just an idea waiting to come to life. To be embodied.
We discover the entity "my imagination" is not in the brain and so math is a discovery. Proof: Let "my imagination" be a space in which mathematical explanations can be drawn. In the space is a large box labeled the universe, and inside the universe is a smaller box labeled "my brain", and inside the smaller box is labeled "my imagination", which is a contradiction.
We invented mathematics as a language to interpret and communicate the reality that surrounds us. Just like we do with languages. A language is only symbols and signs that represent "whatever" That "whatever" is discovered and not invented.
You contradict yourself. It is a discovery. 'language to interpret and communicate the reality that surrounds us'. The reality that surrounds us is described by maths. We didn't invent anything except our way of describing that reality. The reality is a discovery not an invention.
Very clearly it is invented, the rules are put forth. Now the elaborations of that those rules end up implying, needs to be calculated, which you can consider a discovery if you want. Yet the idea that there are these mathematical domains beyond us is patently unnecessary.
I've always felt that math has been invented, we have created this language to help us describe things of the real world, this is me saying that as a 3rd year math student in uni, maybe I will change my opinion though!
Math as a language is invented but the things math study is already present to be discovered other cognitive things could use a different notion to describe the same pattern that we observe 🤷🤷
Math is the invention that was created to describe everything that we discovered. I guess it all boils down to the fact that everything is a ratio. Like a room that is twice as long as it is wide, and you're installing trim, we use numbers and units to describe exactly what we need to fit it, but without all that it would just be a ratio of whatever stick we used to nail down as footer trim, the other wall is going to be twice as long so that we know that we need twice as much. We can take that stick and Market on another stick, and the move that stick down and Mark again and now we have a marking from end-to-end that is twice as long as that original stick. It's a ratio. Everything is a ratio.
I'm really looking forward to the moment when Mathematicians realize that base twelve math is different than base ten math, and that base ten Pi is wrong. The DISCOVERY of base twelve geometry, base twelve math, the base twelve dodecagon - THAT will be a big deal discovery. (coming soon)
I would say invented, math is just a way to describe things in the universe. Descriptions can only be made or understood by minds. If minds didn’t exist math wouldn’t exist.
If you thought about it, Humans, aren't the only animals that count. The knowledge of geometry for a perfect ambush, the solo chaser that leads the prey to the ambush. I think some animals may get the concept of the number 0 as well.
mathematics is our interpretation of the universe. I’m sure if we found another advanced civilization their math might look vastly different but describes the same thing.
6:18 You don't do bad things because God watching, you don't do because you know it is bad. Same way you don't steal in stores because the security camera is on but because you know it is bad.
Mathematics that's discovered most of the time is a representation of nature. However, mathematics that's invented usually leads to abstractions that do not represent nature. A case in point is string theory.
I would argue that math is invented because it is a descriptive reality but not the reality itself. This is because you may use it as a tool to predict reality but it isn’t unto itself the phenomenon, just a description of one.
Life is Eternal, the Structure is mirrored in the Rainbow, in naked form. the Six Colors symbolizes our Basic-Life-Abilities. Green is Intelligence, and stand for Logic and Order. Yellow is Feeling, the Perspective-Principle and the Contrast-Principle, makes Feeling into Sensing. so, Logic/Order + Perspective-Principle = Mathematic. this is the Mathematic of the Eternal Mathematic. Rainbow is actually the picture of a circuit, (Circuit-Principle) A Developing-Circuit holds Six Developing-Zones, Red/Plant-Kingdom, - Orange/Animal-Kingdom, - Yellow/RealHuman. > (Intelligence-Intuition-Memory) If Life didn have the Ability to Re-New it Self, there would Never have been any Life-Performance at all. So, for every new Developing-Circuit, the Life-Unit's create a whole new Language and Consciousness. The first Spoken Language, mostly specific Warnings, is in the last part of the animal-kingdom, (Campell-monkeys) Our developing from baby, mirror that of mankind, first one word, then two, and then 'one, two, many', (perspective) so, Mathematic is Eternal, and re-discovered,, re-invented, or re-developed. Circuit after Circuit, in the Developing-Spiral.
we dont get Quantum-Physics really but we can manage to make it work via Mathematics only and before 1900 we didnt even know of Q-Physics to exist so you could argue pro invention here...
Full podcast episode: ua-cam.com/video/Osh0-J3T2nY/v-deo.html
Lex Fridman podcast channel: ua-cam.com/users/lexfridman
Guest bio: Edward Frenkel is a mathematician at UC Berkeley working on the interface of mathematics and quantum physics. He is the author of Love and Math: The Heart of Hidden Reality.
I want to be that person that is called on by others when a nuclear war erupts.
Why was this interview not in Russian or a combination of English and Russian and then traslated/transcribed?
Before I watched this video I was confident that we discovered math as it seems like a fundamental law of the universe. But after reading the comments, I am blown away by how many great discussions and explanations you have provided. I feel more confused and undecided on the question than ever lol. Thank you.
Lol I thought the same, first UA-cam comment section that hasn't made me lose brain cells.
We discover phenomenon, and describe it the best we can as humans. This debate between whether math is discovered or invented is semantics, a farce really. It’s both.
It is discovered and the language used to describe and interpret it is invented
Good take
Agreed. Seems kind of obvious. The scientific method was invented but it allows us to discover.
The syntex we use for math is invented. I think pure math is geometrical forms. Without knowing anything, but that’s what the LSD told me
@@DanielAnderssson "I think pure math is geometrical forms." That's absolutely not true in any way. There are pre-geometrical mathematical structures. "Without knowing anything, but that’s what the LSD told me." No you brain on LSD made you come up with this idea based on the information you had gathered before hand. LSD modifies the way our brain processes information. It doesnt gives you new information.
This is the right answer. It’s so obvious idk how this is even a debate.
Math is a tool using rational principles. One of any given unit added to another of the same unit creates a sum of 2 units. This fundamental principle replicates itself in many different directions. Math is not so much a "truth" to be discovered or created, but a language to explain quantity and it's applications.
In some other part of this podcast Frenkel states that at the beginning of mathematics there's a choice and this is the set of axioms. He was very correct about that. After this choice the mathematics of this system can be discovered, but what is very important to notice is the order in which mathematics was developed and this order isn't some mathematician set up ZFC and then all the results were step by step derived. No. Often we get inspired by nature, some pattern which seem interessting, some problem we want to solve. So mathematicians formalized those and build mathematical tools to aid the solution. Building upon that the results are generalized and a theory build around it from which new results are derived. Only after that some first principle axioms are chosen to build a (hopefully) contradiction free and complete math-universe. This happened in the 20th century with ZFC and others. In general (like with learning) the mathematical development process is recursive swinging between invention and discovery. The choice of axioms was depent on the before made inventions and these inventions were often motivated by problems or patterns arising in the natural world thus indirectly discovered. Important tho is that the basis of all of this is how human brains process information. This is the basis of logic and also patterns - patterns are a part of the cognitive process. They are the interpretation of information that our brains make. This information process must be somewhat accurate as it has evolved to be, but even if it is absolutely accurate the brain process - or lets say the idealized brain process as we certainly arent perfectly logical - must not be confused with the structure of the natural world itself. World and image aren't the same even in case of 100% accuracy.
The question "Is math discovered or invented?" is interessting, but terribly misunderstood. It isnt or shouldnt be about if mathematics is literally the structure of the universe. Even if logic truly is something fundamental (impossible to proof) and not just how our neural network process information between the logic and the mathematics there still is the mathematician, whos neural network is being feed with information that is then related, recombined and conceptionalized (and what else is invention if not that?). Thus when pressed i would answer the question with "invented", but it is much more difficult.
True lol
Math is like fire, we didn't invent it, but we invented uses for it, how to contain it, how to create it, how to keep it going...
We have invented a system that enables us to discover realities and possibilities that can be described with this system.
Have we? Maybe, but what is the distiction between that and being able to catch an object thrown towards us, or rightly suspecting an event to occur; things we already could before the energence of math.
@wolfgang-franzkranek6146 how did anyone "invent" the Mandlrbrot set? Are you insane? Lol the plots you get from it where 100% discovered..sure you can assemble your own mathematical objects ALSO but no one will consider that new math unless it leads to some *discovery* - some otherwise unknowable or unconstructable structures or objects or relationships.
We didn't invent it but we invented how to create it???
@@Calligraphybooster Did you even read the comment? Clearly he stated "we invented uses for it"
Just like how language is created, we invented uses for our language, sure you can interact with just hand signs or grunts before language was even invented but that doesn't take away the fact that we invented uses for it.
I’ve always thought about this in grade school but couldn’t articulate it. Are we noticing patterns and giving it meaning or are we finding meaning from patterns?
Yeah, Math is to big of a concept to answer the question directly, if you ask me if the universe creates patterns symmetry, efficiency, etc then the answer is obvious, if you ask me if calculus is an invention, it feels more of a tool based on some truth that is useful, but we know calculus in the edge is not 100% accurate.
@@wagmidaddy8766 whats the universe? another word for God but not God cause God is stupid? so just the say universe instead?
@@thisisSPARTAorsprite wow deep, whats another word for a priest, a pedophile so just say pedophile
@@wagmidaddy8766 you bring up humans and there disgusting sin as a rebuttal, weak
Meaning is the desire for things to be other than they are and has nothing to do with math per-se.
Math is insanity. There are infinite numbers 1.2.3 etc., but there is also infinity inbetween each number also. What amazes me about it is everything is in there we just have to find it and when I say everything, I mean everything. Want a particle to be only a particle and not a wave function, its in there, but at the same time if you want a particle to be only a wave and not a particle, its in there also. Insanity at its finest.
That's the part that's made up, and not really math.
@@havenbastion its all made up, its made up to prove concepts. Its literally a proving mechanism
That's quantum mechanics in nutshell, you just simplify an event horizon.
@@DnVFMVs I think that is the true nature of life as they were saying in the video its full of paradoxes. Even ancient eastern philosophies understood this idea that life isn't black or white, it's non-dual. Just look at the Yin-Yang both the black and white exist simultaneously connected to each other.
Not sure if we live in a world of paradoxes when there is no consistent semantic system of language. More like we fail to explain what appear to be paradoxes.
Wave particle duality is a misnomer since an electron can appear as a wave, a particle, both, or neither, depending on the semantic system we use to measure and describe it. The underlying info doesnt seem to be paradoxical, just our explanations of it. Not sure why anyone would be surprised that we dont understand anything at a fundamental level, but I wouldnt assume we live in a world of paradoxes, just a world where we fail to communicate perfectly.
I think if it is invented we would have control to manipulate mathematics in many ways as we wish, but actually we don't have such a freedom , so for me is more discovered. Like lows of physics - we can discover and use them but can't change them. My humble opinion.
Isn't maths just a measurement for something that exists already? The equation doesn't really matter if the results are the same
It's much more abstract than that. The generalization of patterns, how they relate to each other, their properties and categories. It's not just about solving an equation, and more about understanding what it represents. Take a look at AI and machine learning for example, it's about building models of cognition, pattern recognition and more.
If maths is an expression of our understanding of how to describe what is not only physical, but our shared imaginations as conceptual realities, then as part of that lingual technology it is only natural it evolves into more complex forms. It feels like a space where we can both invent and discover at the same time, as the function of that lingual technology has not simply evolved to help us share ideas and concepts, thus describing the outer edges of our reality, but to provide insight into the depths of complexity and dimensionality our imaginations are able to wander confidently.
Wow...thank you
Maths is a language and can be used to understand things our language couldn't do without.
Hard disagree. We try using language to make sense of our preexisting understanding of math, not the other way around. Math exists independent of communication.
A single, simple consciousness instantaneously performs advanced calculus without outside influence/education. E.g. a dung beetle will automatically calculate which area has more pieces of shit (mathematics) & calculating which pile of shit has more mass based on limited dimensional information.
They do this (whether they know it or not) using geometry/volumetrics, and calculus formulas that the majority of humans also use, but couldn’t explain if their lives depended on it.
@@jessereeves3120 language can describe concepts over time. Animals are also understanding concepts and making decisions overtime. Your argument would still hold true for language just as it does for maths. The maths could be used to describe the thought process of the beetle as well as the language that we use i.e I am hungry, I am going to eat skmething
@@jessereeves3120also, the math that we use may be "true" I ky because we set rules saying it is i.e 1+1=2. Now, maths is very effective, however we aren't really accessing complete truth when we use it, it is simply used for its utility. This is because the world is infinity divisible, and we may use maths to figure things out and get a good enough answer where we don't realise/care that it's not precise. But we never use maths in the real world completely correctly. We make these concepts and structures with both language and maths for our use to survive. I love maths though and I think on a spectrum it is more objective than language.
This is one of the best conversations I've listened to in years. It was deep and profound.
In a romantized sense, creation is the discovery of the unknown. Personally I think as humans, every moment is a discovery because the future is unknown.
Pass that blunt
I’ve never heard someone speak so passionately about their love for Mad Max
I always think of this thought experiment: if you'd have multiple people/machines in a isolated room for an infinite amount of time and have them discover/invent new math. Language aside (notation used etc.), they are all going to come up with the same. It just seems way more intuitive to see as a discovery because math is already always present, we just have to find a way to understand articulate it.
Both, it's a question of categorization or classification. It's like asking if something is a chemical or physical process. I think the question is misleading, but I would classify it as invented, because we would also say that language is invented and with language we can also describe abstract situations and stories that are not really there, although they are of course physically exist in our neurons, so it's a matter of classification.
The reason we ask this question is because we don't like chaos, it could be dangerous, so it leads people into error, they want to organize it so it won't cause problems in the future, but they forget that the question is more important than the answer.
Math is about solving problems.
In order for math to have been discovered, it had to have been there before it's discovery in some shape or form. Since we have invented it it now appears to us to be "there", and that gives us the illusion that it was always there. But it really was not until we invented it.
I think the more appropriate contrast here would be "constructed" rather than "invented". As in "Is math discovered or constructed?". The answer is that it is both: "Discovered and constructed". Or rather in the reverse order: "Constructed and discovered". First, we conceptually construct, then we explore and discover. We explore and discover the extent of local specifities included in the conceptual space that we have constructed from abstract general construction principles, which is sometimes so vast and breathtaking that our mind can barely grasp it. And then we get kickass videos like this: ua-cam.com/video/LhOSM6uCWxk/v-deo.html.
If math was invented then it would have been impossible for Ramanujan to have mastered mathematics at the level that he did in almost total isolation.
Jup!
It really doesn't make sense to me to say that math is invented. Math is the discovery of universal truths. Sure our representation of mathematical entities is invented, but the concepts described by them are discovered.
Then it seems our pictoral or axiomatic representation of the mathematical truths that seem to exist are invented, with that underlying "thing" being natural and thus discoverable.
His reflection that belief in Platonism is connected with the feeling of uncertainty and injustice in the (messy, material, changing) world, is profound and speaks of a great capacity for self-insight.
Makes you wonder what else we have yet to unlock.
These guy recently learned Pythagoreans saw profound meaning in numbers and is amazed by it. Meanwhile, 90% of mathematicians have known this their whole lives. I think there is an unbroken line of true masters of the art and their apprentices from the time of the Pythagoreans to us, and even further back. 10,000 years of legacy, only known to a few, apparently, despite our best efforts to convey it to others.
Math is truly quite profound. When you put it like that its crazy that there’s probably 10.000 year unbroken lineage of masters of it.
@@Milark obviously, the first ones barely knew how to add and subtract and other minor stuff, but quite rapidly they discovered fractions, knew something about patterns, discovered some geometrical truths. About 6000 years ago they already knew quite a bit.
Here's my answer, and why, via an example: There are an infinite number of theorems in math. The vast majority of them are useless and/or boring. Mathematicians search for the ones that are useful and interesting. The fact that there are so many theorems of that type is explained by math as well. If we number all possible theorems as n= 1, 2, 3, etc. then there will be some that exhibit symmetries and structure and broad application, despite being very short, just as we encounter patterns in random numbers, 1234, 3333, etc. The powerful theorems exhibit the same behavior as these compressible numbers in terms of prevalence. There are an infinite number of them, however they are sparse, and their sparseness increases with n. If there were no powerful theorems (or an extreme lack thereof), this in itself would imply something special at work, since it is incredibly hard to avoid symmetries and patterns in even random sequences, so to not stumble upon them would be highly unlikely. On the other hand, if theorems were as common as the even numbers (as an extreme example), then they would hardly be of any note. So, what we have is a clustering of useful theorems, which are manageable in size and then a few less that are a bit larger, and a few less that are even larger, and so forth. So there's no upper limit on how many useful theorems that are "shorter than x" for example, and it certainly can't be zero - it's somewhere in between, and even if the usability of any particular theorem were to correlate with the compressibility of a sequence of random numbers (i.e. pure chance), which is just about the worst case scenario that I can imagine in the universe, there's still going to be plenty of them - a lot of shorter ones, and fewer longer ones, but every so often, you'll encounter one that is an absolute banger.
We observe nature, then invent math to describe it. Then we test that math which yields new observations. It’s a never ending feedback loop that we’re all addicted to.
@Bob Nah. First need of math will be for early man to communicate amongst each other about how much to trade of something, generally food in this case. So inventing a counting system (math) to observe/measure fruit (nature).
@@jarrodfodemski1018what about the case of people "discovering/inventing" maths purely for maths sake. Then 100s of years later it gets applicated to the "real world"?. I guess you could still say that there is plenty of pure maths that doesn't get used so it doesn't really prove either way idk. It seems like tho if maths was invented you could treat it like making a song or a dress and do whatever TF you want it seems like there are set rules that make you obey. Are these the laws of the universe or just axioms pre set idk tbh
The way we create in this world is using language, and with numbers, we create mathematics. We use more mathematics now to let computers solve the language we can't understand, but numbers allow us to understand better because we rely on technology to solve the language of what we want to create. In our imagination, it's our home in a way that we don't need to understand bc we are creating things by thought... imagination is our own way to create in our own world but in the real world it's with language and now numbers but now with ai I fear we will end up giving a language to the ai which can transition the sense of now but it's either gonna be a great thing or bad but I hope for good... keep the imagination alive it's our art our way of bringing it to here!
The paradox of questions like these make the meme answer of "yes", the most true statement to ever be uttered. Is math created or discovered? Yes. Is a photon a particle or a wave? Yes. Do we have free will or is life deterministic? Yes. That one being based upon the laws of physics and the quantum state of superposition(s). Do you want to drink tonight or do you have work in the morning? Yes. Am I an alcoholic or do I just enjoy drinking more than the average person? I'm an alcoholic lmao
It is worth noting that a photon, singularly, does not have a wave function.
@@jackfox5738 A photon does not exist. There is no such thing a single photon.
I’ve argued both sides of aPriori math/geometry ad nauseam in epistemologically based philosophy courses. IMHO, it is as simple as instinctively understanding two berries are more nutritious than one. It’s also intuitive that walking a straight line to those berries is more efficient than a long, non-direct track-line. Even for a rat isolated from any any schema influence.
That doesn’t mean math/geometry is an epistemological truth, it just means our experiential epistemological truths are readily apparent without outside agent influence.
So either math & geometry are intrinsically true, or our entire experience is false.
Seems like a fallacy of composition to suggest that if any part of our experienced truth is incorrect it all must be false. Isn't all of science built on the rejection of this mode of thinking -- a demand for consensus over individual lived experience? Point in case - the world is curved, so the fastest way from point a to b is also a curve (though often too slight to matter). 1 toxic berry might not be enough to harm you, and you can consume its calories; 2 and you throw up, resulting in a loss of calories.
I think the correct answer is it always existed. However, the way we interpret math, so much as, the symbols we use in our equations are a creation of our minds as humans in order to begin to comprehend "Mathematics".
I think having a "response" to something like this, its like stop experiencing.
There is no unidirectional or unique response, it's weird to grasp but the "answer" is both imo...
The question is not if it is invented or discovered...the question is if it exists independently of us. The answer to that is an unequivocal affirmative. IOW...something exists out of which we create this thing called mathematics. That 'something' exists independently of our discovery of it. Whether mathematics exists in the exact form within which we comprehend it ...independently of us...is a different question. It almost certainly does...and as the understanding of consciousness advances this will be confirmed. The reasoning is not that complex. Mathematics is a function of advanced consciousness. As Don Hoffman says...consciousness is everywhere...and there are almost certainly varieties of it (what Don calls 'conscious agents') that are far more advanced than our own...therefore their 'experience' of math will incorporate our rudimentary comprehension of it...as well as an equivalently advanced understanding. No big deal really.
When I have to answer this question I just say that it's both, which is a like a different version of the answer, it's more complicated than that, and I think that's the essence of what Edward Frenkel is suggesting as far as how we should try to understand this question.
When I heard Frenkel say, "wouldn't it be nice," I thought Beach Boys.
Mathematics is a generalisation of numerical properties. Much like electricity is discovered and the light bulb is invented to generate light mathematics is an invention that enables us to transform numerical properties and discover new numerical properties. That's one way of looking at.
Really good conversation. it feels like it could be a longer comm unity .
It’s a false contrast - invention is a form of discovery. It’s discovering how to combine and integrate existing knowledge and objects in order to make something useful.
I think that mathematics was discovered first by the earliest of some of the cultivated humans and then contemplated as the generations evolved 🫡
I believe that math is like the part of philosophy that deals with metaphysics.
In ancient philosophy, physics was the study of the appearance and function of being,
metaphysics was the study of being itself, stripped away of all fancy.
In a similar way, mathematics is the study of quantity as it relates to reality.
Wanna describe objects in numbers? Geometry.
Wanna describe motion in numbers? Calculus.
Math is simply the description of reality through numbers.
Language is the description of reality through words.
If it's a universal language.. It's discovered
True, but isn’t our translation of that language invented?
The relationships are discovered. The nomenclature is invented.
@@havenbastion Even the names are discovered. I know it seems like we're inventing things, but we're not. Think of the name or use of word for anything and you cannot account for why we chose that exact term. That's because we didn't choose it, we discovered it out of the ether or the whole of consciousness, which is already complete if not in form or function, then in potential.
Wrong, it's invented.
It wasnt the Love at first sight experience that made me feel an overwhelming Soul connection, .. it was the eventual recognition, of the enormity, of that momentary minutiae chance in infinity, a coherent weaving of pattern, of complexity, time and space.
I like the topics and fields Lex dude asks and is in trying to look beyond boundaries
It would be interesting if you could take the current universe then replay it via a new simulation in a computer and see how things pan out... probably in a different way albeit with the same fundamentals... The question of discovery and invention merely depends from which direction you're referencing: They are both present.
I'm mystified why anyone would believe human math is anything other than a language our brain needs to extend ( into 'difference'). The idea an alien would necessarily have something similar seems preposterous. On myth AND OR logic Bertrand Russell wrote a fantastic essay.
6:35 “I haven’t checked it in awhile” 😅
Everything that has ever been invented was discovered.
So true.
We are drawn to art/music because it's a very efficient, direct, and adequate way of communicating with each other about the ineffable but true. And art involves the WHOLE person, including their emotions.
The 'real world' is the ENGINE that drives the NEED to discover the invented mathematics which faithfully describes it. Humans don't fundamentally invent mathematics in a vacuum, nor do we settle for mathematics that's completely divorced from the 'real world' itself. The scribbles on the chalkboard are NEVER meaningless, and we can sooner or later TELL that they are right or wrong, and WHY. The 'elegance factor' involved with our invention of mathematics is tied to our need to understand the universe LOGICALLY, and the fact that LOGICAL mathematics 'does the job' with respect to codifying how the real world actually functions indicates two things:
(1) The universe DOES function along logical lines.
(2) The Mind ultimately responsible for this logical functioning is akin to ours since our minds are readily enough able to decode and quantify that logic.
Some of it is invented. For example, Lebesgue integrals were invented to include a larger set of integrable functions than the Riemann integrables. But the content of number theory is discovered.
@queerdo Well, by your usage of "discover" every thing is "discovered," as in Edison "discovered" how to make an electric light emitting device. The Lebesgue integral isn't the only way to enlarge the class of integrable functions.
Patterns and regularities are discovered but tools and techniques are invented.
Paradoxes are a product on incomplete understanding, and is the perfect mirror for humans to reflect on our miniscule perspective. Our current sense of logic is flawed, but all we can ask is that it's less erroneous than its previous iteration. The interesting question is: is there a limit to understanding? Is there such a thing as "knowing it all"?
It's totally invented. The world doesn't need "math" to exist, we created math to define and measure the relationships inherent in it.
Fair point…. yet mathematicians have ‘played’ with ideas that resulted in what we thought were illogical conclusions… only to find out later described aspects of nature. That, being true, suggests math is discovered, not invented.
Any life form intelligent enough to build any type of mechanical devices would have a symbol or figure which represents Pi. The circumference of any circle is a ratio involving Pi and it's diameter, whether or not someone understands this or realizes it, is of little consequence, it is a maxim, it was long ago proven. I personally have used it for a growth formula to calculate the number of feet of paper wrapped around a given core diameter and a given overall diameter with a given paper thickness.13" OD core Roll 72" overall diameter paper thickness .004" - calculate ft.
Pi is sloppy, so this is wrong. The reason pi never ends is because its a shit, but as good as we can, equation. Simple as.
I fully believe mathematics is invented as a description of the patterns in the universe we’ve discovered. Just as human languages are invented as a means to convey our ideas. The evidence of this to me is in how mathematics can seem to breakdown at points (true of any imperfect model of something more complex) and then we can adjust it or expand it to work again in a more generalized way. The fact that humans can change mathematics demonstrates that we “own” it. It is descriptive, not prescriptive. It is our best idea we’ve come up with to describe the patterns of the universe, but that doesn’t mean it _is_ the universe itself, or there isn’t another way that is even better out there.
math is independent of the universe, and infinitely more complex.
math doesn't break down. our models of reality (which is physics, not math) break down and are inperfect. we then change and adjust the theory (which again is physics). We dont change math.
I respectfully disagree. Math has changed a ton over the last few millennia. The origins of algebra, geometry, calculus, etc. all have quite well documented histories. I.e, there is a time in human history prior to the existence of these forms of mathematics, therefore it isn’t static or preexisting but rather invented and extended by humans as a tool/language to describe the world. There are plenty of examples of similar concepts having been represented by different nomenclatures in the past. E.g., not all societies have even used base-10 arithmetic.
For billions of years, there existed...a slab of marble.
Inside that slab of marble, for all those years, there existed...the statue of David.
Did Michelangelo invent the statue....or discover it?
I don't think we invented it per se but I imagine we defined it and gave it a name. Something that already exists which is then discovered.
The collective unconscious can direct our passions to memetics that enrich our confidence on a matter that has already been considered. I think this could be a form of morphic resonance, but I am plagiarizing here. Objects with invariant contexts can be systematically manipulated in predictable ways. But a lot of functions only correlate to target models and are more useful than fundamental. I think as we try things our "memory" promotes what is most useful. This is some pretty big talk.
i always thought that math is probably invented. fundamentally, there are quanta, which to me can be very similar to numbers: discrete units of energy or any value. it makes sense then that we make sense of the world by using numbers and variables as quanta. then its all about relationships to one another which i think integrates equations and so forth
Math is discovered. 2 + 2 equaled 4 long before human beings became aware of it.
You could say that about every invention.
an iPhone for example.. we discovered that if we put all these things together, it becomes an iPhone. The difference between discovery and invention is subjective.
But each "2" can be broken down into say millions of atoms so is it ever 2 plus 2
Nah. Math is just another language invented to describe the natural world.
@@Defort-jd8xe Not at all. 2 and 2 make 4. It just is. It doesn’t have be designed or made. Just observed and it exist weather we observe it or not. Math exist independently of of human beings. Even an animals can keep track of how many babies it has. An iPhone is a thing.
@@Nochancet.v That’s an entirely different equation. How many atoms can four cats be broken down too, has nothing at all to do with… two cats plus two cats gives you four cats. Atoms are not cats. And 2 atoms plus’s two atoms gives you four Atoms.
A certain design of the incandescent light bulb has the predictable physical properties that it has, from the dawn of the universe, long before Edison found that that design solved a certain problem for his customers. Nonetheless, the light bulb is the quintessential invention (light bulbs were invented if anything was invented). Similarly, for, say, probability theory. The theorems of probability were entailed by its axioms before the dawn of man, but when we discovered that those axioms and theorems could be used in a certain way to solve certain classes of material problems, we invented probability theory (if light bulbs were invented, and indeed if there is such a thing as invention).
Is 2 + 2 = 4 because your first grade teacher said so, or does 2 + 2 = 4 regardless of what anyone says?
Is murder wrong because there are laws against it, or are there laws against it because it is wrong?
Do you and I both see 'green' grass and 'blue' sky, or do we just use the same words to describe what we are seeing?
Math is a language. We dont discover math, we discover math applications in other sciences.
Holy synchronicity batman. I just started reading the Birth of Tragedy yesterday.
“There is a tide in the affairs of men. Which, taken at the flood , leads on to fortune; Omitted, all the voyage of their life, is bound in shallows and in miseries. On such a full sea are we now afloat. And we must take the current when it serves, or lose our ventures.” - William Shakespeare, Julius Caesar -- here we are , again.
Not to get religious, but this is how I feel about the idea of God too. Either there is some-thing or no-thing and that something is what we call "God" and then we started inventing characteristics and an identity to God. But the idea of a Creator seems to be universal, intuitive, and a logical possibility. But a "flying spaghetti monster" isn't a universal discovery...if that makes sense.
The full precession cycle is 25000 years right?
It is the preexisting logical relationships reflected in nature that guide and mold development of math's notations, with proofs. It's the logical relationships that are discovered. Math is a back feeding rigorously developed notation used to describe and facilitate discovery of those logical relationships.
13:23 i am sorry..
The question of whether math is discovered or invented is a topic of much debate among philosophers, mathematicians, and scientists. Some argue that math is discovered because its laws and principles exist independently of human thought and are waiting to be uncovered. Others believe that math is invented because humans create mathematical concepts and systems to describe the world and solve problems.
One argument in favor of math being discovered is that mathematical principles, such as the Pythagorean theorem or the laws of calculus, exist independently of human beings and were waiting to be discovered by mathematicians. Additionally, some argue that mathematical concepts, like the number pi, exist independently of human beings and are simply waiting to be discovered.
On the other hand, some argue that math is invented because mathematical concepts are created by humans to describe the world and solve problems. For example, the concept of negative numbers was invented to solve problems that arose in mathematics, but negative numbers don't exist in the physical world.
Ultimately, whether math is discovered or invented depends on one's philosophical viewpoint. Some believe that math is a human creation, while others argue that math exists independently of human beings and is simply waiting to be discovered.
Math is not bounded to our limited understanding of it, especially when we try to encapsulate it within an inapt question.
There are NO paradoxes - there is only a misuse or misunderstanding of how language connects us to the objective world.
Vortex Mathematics explains the divine and the natural world. Very fascinating
I think of it like math was discovered but we invented a way to try and understand and communicate math.
What a great question
I would say, the application is an invention of a sort; however, "math" and the measurements themselves TO BE MEASURED by math...that is all a constant. It's simply an idea we captured...but then again some could say EVERYTHING, is just an idea waiting to come to life. To be embodied.
question is...what things do we capture, and what things do we let go? Because having some things could, itself, be a detriment...
I see a Lex video and I click.
Me too
We discover the entity "my imagination" is not in the brain and so math is a discovery. Proof: Let "my imagination" be a space in which mathematical explanations can be drawn. In the space is a large box labeled the universe, and inside the universe is a smaller box labeled "my brain", and inside the smaller box is labeled "my imagination", which is a contradiction.
We invented mathematics as a language to interpret and communicate the reality that surrounds us. Just like we do with languages.
A language is only symbols and signs that represent "whatever"
That "whatever" is discovered and not invented.
You contradict yourself. It is a discovery. 'language to interpret and communicate the reality that surrounds us'. The reality that surrounds us is described by maths. We didn't invent anything except our way of describing that reality. The reality is a discovery not an invention.
Very clearly it is invented, the rules are put forth. Now the elaborations of that those rules end up implying, needs to be calculated, which you can consider a discovery if you want. Yet the idea that there are these mathematical domains beyond us is patently unnecessary.
Why was this interview not in Russian or a combination of English and Russian and then traslated/transcribed?
I've always felt that math has been invented, we have created this language to help us describe things of the real world, this is me saying that as a 3rd year math student in uni, maybe I will change my opinion though!
The world of the paradoxes sounds nice
Correction... the Procession of the Equinoxes is ~ 26,000 years for one full cycle
Math as a language is invented but the things math study is already present to be discovered other cognitive things could use a different notion to describe the same pattern that we observe 🤷🤷
I was just talking to my brother about this
Math is the invention that was created to describe everything that we discovered. I guess it all boils down to the fact that everything is a ratio. Like a room that is twice as long as it is wide, and you're installing trim, we use numbers and units to describe exactly what we need to fit it, but without all that it would just be a ratio of whatever stick we used to nail down as footer trim, the other wall is going to be twice as long so that we know that we need twice as much. We can take that stick and Market on another stick, and the move that stick down and Mark again and now we have a marking from end-to-end that is twice as long as that original stick. It's a ratio. Everything is a ratio.
I'm really looking forward to the moment when Mathematicians realize that base twelve math is different than base ten math, and that base ten Pi is wrong. The DISCOVERY of base twelve geometry, base twelve math, the base twelve dodecagon - THAT will be a big deal discovery. (coming soon)
@LexClips I think Math was discovered by The magnetosome in which magnetotactic bacteria (MTB).
I would say invented, math is just a way to describe things in the universe. Descriptions can only be made or understood by minds. If minds didn’t exist math wouldn’t exist.
I’ve been on this for a couple years and I’m so fucking glad this has become a discussion
If you thought about it, Humans, aren't the only animals that count. The knowledge of geometry for a perfect ambush, the solo chaser that leads the prey to the ambush. I think some animals may get the concept of the number 0 as well.
Plato's form can be exhausting.
Life is a paradox wrapped in novelty
mathematics is our interpretation of the universe. I’m sure if we found another advanced civilization their math might look vastly different but describes the same thing.
It's observed and defined.
6:18 You don't do bad things because God watching, you don't do because you know it is bad. Same way you don't steal in stores because the security camera is on but because you know it is bad.
Mathematics that's discovered most of the time is a representation of nature. However, mathematics that's invented usually leads to abstractions that do not represent nature. A case in point is string theory.
I would argue that math is invented because it is a descriptive reality but not the reality itself. This is because you may use it as a tool to predict reality but it isn’t unto itself the phenomenon, just a description of one.
Life is Eternal, the Structure is mirrored in the Rainbow, in naked form.
the Six Colors symbolizes our Basic-Life-Abilities.
Green is Intelligence, and stand for Logic and Order.
Yellow is Feeling, the Perspective-Principle and the Contrast-Principle,
makes Feeling into Sensing.
so, Logic/Order + Perspective-Principle = Mathematic.
this is the Mathematic of the Eternal Mathematic.
Rainbow is actually the picture of a circuit, (Circuit-Principle)
A Developing-Circuit holds Six Developing-Zones,
Red/Plant-Kingdom, - Orange/Animal-Kingdom, - Yellow/RealHuman. > (Intelligence-Intuition-Memory)
If Life didn have the Ability to Re-New it Self, there would Never have been any Life-Performance at all.
So, for every new Developing-Circuit, the Life-Unit's create a whole new Language and Consciousness.
The first Spoken Language, mostly specific Warnings, is in the last part of the animal-kingdom, (Campell-monkeys)
Our developing from baby, mirror that of mankind, first one word, then two, and then 'one, two, many',
(perspective)
so, Mathematic is Eternal, and re-discovered,, re-invented, or re-developed.
Circuit after Circuit, in the Developing-Spiral.
we dont get Quantum-Physics really but we can manage to make it work via Mathematics only and before 1900 we didnt even know of Q-Physics to exist so you could argue pro invention here...