Mathematics, like Language, in its infinite manifestations is constantly being discovered. Mathematics, like Language, is the expression of an Intelligence that permeates all that Is, all that Was, and all that Will Be, in this and any other universe of existence. This expression facilitates self discovery of Intelligence with Itself within the 'physical' universe through the filter of us All.
@@Z-Diode If you have 1 coin and another coin, then you have 2 coins. Whether you call it 1 or 2, or purple or whatever. The value is universal, the name for it is man-made. 2 plus 2 equals 4. No matter where in the universe you are.
Math is like the finest poetry. Something so enlightening that dazzles us sometimes. But, as poetry, is only language, a language that we invented to describe the Universe.
In the last 200 years alone, science has made so many discoveries. The revelations or findings by observation, trail and error, show the answers were always there; just not yet understood or proven.
So wonderful what this series tells and although it does not bring you any closer to the truth, it does bring you closer to the people who are so passionate and full of knowledge. What a beautiful journey in itself. Thanks.
Dear Robert, I'm a math professor who follows your channel and especially this series about mathematics. I am very surprised that when you interviewed specialists about the nature of mathematics, you actually avoided speaking to any pure mathematician! You have certainly interviewed some outstanding and renowned experts whose work can be described as mathematical, but whose main research activity is actually not on core mathematics (i.e., algebra/analysis/geometry/number theory/combinatorics etc.) and belong to certain other research communities such as theoretical physics/theoretical computer science/logic-foundations etc. The lack of any pure mathematician in your interviews about the nature of mathematics is so striking that it cannot be accidental, and I find it very regrettable. It gives a skewed picture, because it is well known that the further from core math somebody is, the less likely they are to be a platonist, as can be seen from your interviews with Balaguer and Wolfram, for example (similarly Chaitin was the most purely mathematical of your interviewees and also the most platonist). It is true that most pure mathematicians are not very interested in the philosophy of mathematics (unlike theoretical physicists and logico-foundational people who tend to have a relatively strong interest in philosophy), but surely you could have found somebody.
I've noticed that as well. Most devoted mathematicians have a platonic view of math, and consider it an objective abstract reality that can apply to physical reality, but is not dependent on it.
Platonic reality was mentioned by Roger Penrose as most likely the case in Robert’s interview with him. Please reply as I’m very interested in this subject but not a mathematician.
I think it seems like a valid complaint. But he phrased the question as a philosophical one. It sounds a little like: if you want to know about the daytime ask the sun. But what does the sun know about daytime? That being said yes I would have liked to hear from a mathematician myself.
A good thought provoking discussion. Penrose said it is not us that that imposes math on the world, it's out there. In other words, a controlling intelligence = G-D. So from time to time, we humans discover a fundamental law following mathematical principles. There are however other mathematical edifices such as String Theory that have no basis in reality at all. So we could describe it as a mathematical game. In other words mathematics is a non physical construct, which can be applied to the real world when circumstances require it. However you need to bear in mind that both Newton and Einstein employed their own mathematical theories to describe the same thing. e.g. Gravity. Both were correct, but Einstein's theory proved to be a more accurate representation of reality, but that does not mean that is the end of the story.
If you ascribe to the many worlds model of reality that allows for infinite dimensions of infinite variance from our own, then every tangent of reality already exists simultaneously within that multidimensional fabric of ulterior reality. In effect that would mean everything is deterministic in their own regard to their own reality/plane, lending to the philosophy that everything is preset and is only being discovered rather than originating spontaneously.
A good way of visualizing it, is like a fractal pattern, similar to how a tree branches off. From root timeline, or ultimate moment of potentiality fractaling/branching off from every other ensuing potentiality, explored to the degree of their potential. The same visual phenomenon can be seen intrinsically across almost all fields, scales and spectrums of our material reality. Which like a snake eating its own tail, brings it back to the conversation to begin with. Its through this observation of these various patterns repeated across reality that we can begin to understand the greater and greater nature of reality
@Mr Right - the iPhone is comprised of electronic components such as the transistor and other devices, these devices were developed using mathematical derivatives associated with current flow (electricity), which was discovered.
I found this discussion very interesting because I Am a Numerologist & student of Astrology - Which has been confused as different sciences (What Ever That Word Means)... I can fully understand why most folks get loss in their discussions, because they are talking about complicated theories. And Einstein was absolutely Correct, that Everything is Connected. The Simple version to understand, Represents how We All Are Connected to the Circle (The Universe as Planets within us. When you study your Birth chart as to the meaning of Each House on the Zodiac, you will learn that each Planet in Your Chart - Represents your entire Personality as Players Upon the Stage .... Shakespeare once revealed that Earth represents a Stage and We All Are But Bit Players Upon it” Then the Queen who lost her own head - after Shakespeare did a live show of the characters from the Village ... the thief lost his head for stealing something to Eat. Kings & Queens Created Words to keep their subjects Confused.. So in closing - Numbers are the Language of the Universe - In the Biblical studies of Satan, he had to reverse engineer Everything that GOD CREATED. Each Letter is Matched & Connected to two sets of Numbers reduced to their lowest common denominators. Because the Numbers Represents Portals leading to other Universes as follows: A= 1 - 10 - 19 B= 2 - 11 - 20 C= 3 - 12 - 21 represents the number of the Adult Universe - 12 also represents Zodiac D= 4 - 22 represents the second Master Number - 13 Transformation & O Karma reborn E= 5 - Education & Learning & Teaching (Creativity & Art) 5th House/Home of Leo etc F= 6 G= 7 H= 8 I= 9 K= (10 = 1)Graduation or Wheel of Fortune - start over if failed back to 1 or 19= Sun Energy has been learned to proceed to (22). As this applies to the year like 2020 ... the end of the Zodiac Chart 12th House 2+2 = 13 or the New Zodiac begins the New House or moving into the 4th Dimension #4 13 also Represents the ending of an Era of 2020 years for the time period of each House as the Universe keeps Traveling as WE Do. This is the simple outline to understand about Yourself - because we all are made with Atoms/Adams who was cast out of Heaven and Eve represents the light of Day as in New births. Science is Theory & Numbers Are the Reality of Who We Are... The first number after each Number Represents the First Set of Numbers It’s like when you turn 10 years old to complete your first cycle in this life time (1-9) if You Are The Universe When Born as anew Star 💫
Well ..... I guess it all depends on the definition you choose for mathematics for you to consider it invented or discovered, platonic or fictional. I’m no mathematician but I think it’s a more of a methodology or a technique we use creating the axiom, quantify the world accordingly to predict , operate and make sense of the physical world ( or at least how it started ) , therefore it can not be a platonic object nor fictional.
In this world there was wood and stone, a man put them together to form a hammer to build his house.After 20 years someone came and asked "was hammer invented or dicovered?" So everyone do you need to know the answer?
@@suntzu7727 "Electricity at the beginning was used for magic show now it's used to power up our current world." You can learn from the use of something evolve(at first maths was not used to calculate the physical reality) and the other is that just like the magician"we don't need to question the existence(electricity,maths) to make use of it unless it prevent further research."
Watched this twice now, and will probably watch and refer back to it again in the future, but I can't seem to shake that old metaphor attributed to several musicians ... 'Talking about music is like dancing about architecture.' 🤣
If we all agreed with that, it would be very difficult to explain music theory or write a song with other musicians. If a musician said that, they were probably high.
9:11 Mark Balaguer outlines 4 different views of the origin of Mathematics: (1) A _mentalist_ view - It exists only subjectively, in the mind (2) A _physical_ view - It exists objectively, in the universe (3) A _Platonic_ view - It has an abstract, yet real, existence of its own, independent of both of the above (4) An _anti-realist_ view - It's an abstract, but fictional, human invention, with no existence of its own. Indeed, the idea that it "exists" at all is nonsense. 2 & 3 differ about how they define reality, whereas 1 & 4 seem complimentary. What do you think of his classification into these 4 views and which of them, if any, do you think are correct?
i agree: 1 & 3 seem most complimentary. both are consistent with a determinist pov. 2 & 3 would seem to bear a greater burden of proof, but then again, mind-dependent cases are beyond proof, except maybe to the bearer. KEvron
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.
@@ascensionunlimited4182 This is obviously a oversimplification, each step would’ve been repeated/stolen, lost and invented an uncountably different number of ways by even more cultures. First a culture was trying to show the difference between quantities of things and counting was invented A culture took their invention of counting and introduced subtraction, eventually another culture ran into negative numbers and the another culture invented 0. Then another culture tried simplifying some questions and invented multiplication then later division. From that another culture invented powers and roots. After that a another culture was thinking more abstractly and tried to create a consistent set of rules. That collective decentralised work is what we call number theory Another culture started thinking more abstractly about number theory then created algebra. Another culture was trying to simplify some questions from algebra and a 14 year old created abstract algebra. Then our culture found some questions abstract algebra couldn’t answer and created calculus from there Today all of mathematics (from typology to derivatives) is a combination of number theory with either calculus and or abstract algebra.
@@ascensionunlimited4182 math is a tool; it arises out of need. it needn't travel from culture to culture in order to see its use across cultures. new world peoples invented their systems independently of old-world cultures, and some current cultures are entirely anumeric, and have no maths at all. KEvron
Yes I understand, your saying it's truth is independent of human minds or any other kind of consciousness! In other words the mathematical concepts have just has much right to be treated has objective reality has the things we perceive with our senses! Very profound!
Mathematics is clearly more than an abstract object, it is the underlying fabric of reality. It transcends human ideas like emotions, civilization and processes, to name a few examples of abstract objects. For example, no matter what universe or reality, no matter what type of particles and physical structures exist, no matter how many amount of dimensions an existence has, 2 plus 2 is always 4. There is no reality where 2+2=5, because one such a contradiction implies a contradiction of the entire system. One can argue that the concept of mathematics is a human invention, but it transcends humanity and thought. Even many species without brains or sentience have some form of counting and calculation. Any life with sufficient intelligence would come to the exact same conclusions in mathematics as we would.
*"There is no reality where 2+2=5"* in this reality, there is no proposition that may exist absent a proposing agent. if the proposition "2+2=5" may exist absent such an agent, then the proposition "this sentence is nether true nor false" may exist absent one, and reality then incurs a genuine paradox. the existence of concepts absent the process of conceptualization results in paradox. KEvron
Math, as is commonly known, is an expression of the "reality" as we perceive it.. Whether our perceived "reality" is the only "reality"? I think, we don't have any formal way to know it for sure... We may apply empiricism or theoretical explanation. But all these will be limited by our understanding or perceptions of "reality". So we arrive at kind of circular arguments only, I think. Any way, a beautiful video raising these quests.. Thanks RLK..
The laws of the universe will never change. It is simply up to humanity to create the right formulae to accurately describe the experience. Breakthroughs don't actually mean new physics, but we as a species are simply catching up to what already *is.*
Godel already answered it in his incompleteness theorem. My take is you can be more and more precise but you will never arrive at exactness because the physical universe isn’t exact.
Gödel gave a hint by explaining that a set of rules and laws in mathematical systems cannot be described nor explained from within that system. You need an external standpoint or viewpoint. But that is impossible as you would need to exit from your own reality or the material world. So again you are thrown back to merely imagine that it is discovered as it exists on a higher level of reality or a different dimension of mind space and time. It's transcendental like e is!
Balaguer: Do black holes exist, do Higgs bosons exist, does Bitcoin exist? If so, in what sense do they exist? Do you need a village in Nepal you can go to and find them? To understand Platonism one has to have a broader understanding of the notion of existence. There are precise senses in which mathematical objects exist, for example that they form an indispensable part of successful/useful scientific theories about the world (Quine).
It’s analytical a-posteriori. People are still struggling with arriving at the a-posteriori though. Deriving complex analytical truths requires a lot of experience, you need to know what to look for. Which is why often in statically typed programming languages, you do need type annotations even if there is type inference. Those type systems can easily go undecidable and need a human guide.
Mathematics is discovered. It has always existed but took we are slowly discovering how to express it. Not all the math we know today is correct, therefore from time to time there is a refining and getting closer to the correct mathematics, closer to the truth.
Math is logical, so is nature. The difference is that nature exists by itself; math, not so. Philosophers, not nature, invented logic. So, mathematics is a human invention. Nature is logical simply because it works. What doesn't work can't exist in the first place! There is no intention anywhere. Logic happens by itself. It has rules, but nature doesn't know that. The AND operation occurs with a chain: all links have to work for the chain to work. A river flowing down will split in two streams when an obstacle is hit. That's the OR operation. If it doesn't rain for a long time, the grass will turn yellow. That's the IMPLICATION operation. Logic just happens in nature. Math doesn't just happen.
@@jeancorriveau8686 Math does just happen in nature in very similar ways as you mentioned per logic. What other than mathematics could explain the logic of how a flower grows and changes?
Mathematics, like Language, in its infinite manifestations is constantly being discovered. Mathematics, like Language, is the expression of an Intelligence that permeates all the Is, all that Was, and all that Will Be, in this and any other universe of existence.
Encouraged at every turn to "think outside the box" perhaps it's time for a closer look at what got us into boxes in the first place. If you proceed, keep in mind, ahead are precise scale models of existing structures designed and assembled in prehistory, before the catastrophe that drove humanity mad by amnesia fell upon us: brainelevator.org
Maths can't be wrong. Axioms of today may describe something else, not the same thing that some entity in the future might want to describe, but all things that are proven from the axioms today are absolutely correct in this system of axioms. No god can piss on that.
I was thinking the same thing, also why are we restricted to choosing any of them at all? Math is really just a description, and does a description fit perfectly into one of those options? Not really.
Urantia: 15:14.9 Your planet is a member of an enormous cosmos; you belong to a well-nigh infinite family of worlds, but your sphere is just as precisely administered and just as lovingly fostered as if it were the only inhabited world in all existence.
I'm not convinced that the fact maths are derived from roughly the same set of axioms constitutes evidence that it is discovered. Does an author 'discover' the sequel to her or his novel by deriving some set of logical consequences? See, when the author adds new variables, these variables that the author invents are still designed to obey the initial set of axioms that the author has set of the world of his or her story. The next chapter 'feels' right because it follows the same principles and is made to stem smoothly from the earlier part of the story, as though it was all there from start, only unveiled one step at a time. But in reality, the author just thought of a working framework, imagined an outline, then planned and/or pantsed the rest via some kind of intuitive (or non intuitive) inference reasoning. It seems that this appearance that the structure is being uncovered is the byproduct of a commitment to self-consistency, not some kind of unknown realm that is being unveiled one area at a time.
It's a matter of perspective. Inventing a steam engine is also a form of discovery - you discover that if you turn water into steam it expands, so if you combine mechanical elements in such and such way, you can convert thermal energy into kinetic energy etc. You could write your reasoning down on a piece of paper, never constructing a physical steam engine, only proving the validity of the concept in theory. Have you invented it? Or have you only discovered certain possibilities that have always been part of the fabric of reality? It's only a matter of convention which word you decide to use.
Animals sense quantity, eg, a cat sensing his power to jump onto a fence. There is no counting, which requires units, eg, a five-foot high fence. Man counts by abstracting, ie, selectively focusing (on quantity, here, the length of a ruler relative to to the length of a fence). There are many ruler-lengths to one fence, each one having a name, eg, five ruler-lengths,ie, counting. Intro. To Objectivist Epistemology-Ayn Rand Leap Of Logic-David Harriman
@@TeaParty1776 If you think concerning predicting a thing that does not exist in front of you at that exact moment , but can predict it will soon happen at a certain time and place your doing math at least counting. Migration patterns show this these things must be learned to be performed.
what i find interesting is that mathematicians and scientists seem to see maths as perfect and ideal, and physical reality as an approximation to that. when it should be thought of the other way round: mathematics is a simplified model of reality. mathematics is a system of pure logic, extending from some basic principles; we are fortunate to live in a reality which is logically consistent, and we have chosen the basic principles of mathematics to describe what we observe in the universe - so its no surprise that mathematics describes the universe so well
I think you've got the idea of what math really is. It's the three laws of logic: identity, excluded middle, and non-contradiction expressed symbolically. From these simple rules all mathematics are derived. So logic and math are the same. They're non-material. I'm not certain what physical reality is and it's most basic form. Most mathematical laws are approximations of physical relationships. Which tells me that the rules of logic are somehow more fundamental than physical or conceptual reality. The implementation of mathematics is sometimes wrong but that doesn't mean that the logical rules themselves are. Sometimes people do math wrong doesn't make math wrong.
Maths is the perfect tool to do research on the physical reality.That's why scientist and mathematicians give it so much importance."It is in human nature to value what is of use to them."
@@levipack3835 identity and excluded middle are just different flavors of non-contradiction. Mathematics and logic both answer to physical reality as the former two are human inventions about the latter.
Mathematics, like Language, in its infinite manifestations is constantly being discovered. Mathematics, like Language, is the expression of an Intelligence that permeates all that Is, all that Was, and all that Will Be, in this and any other universe of existence. This expression facilitates self discovery of Intelligence with Itself within the 'physical' universe through the filter of us All.
Math is fundamental. It exists, even without conscious entities. Pi describes a circle. Pythagoras' rule applies to Euclidean geometry even if no-one is there to measure it. Math is fundamental to the universe. QED...
Whole questions arises from confusion with surface appearance of language as if the question meant the same thing to everyone. Mathematical structures have risen from the need to represent relationships in the real world via attempts to generalize, simplify and get to get into the essence of the internal logic these representations. For example, it is extremely easy to invent scenarios how a smart carpenter working on wheels would end up formulating the axioms for the theory of finite groups. One can formulate an infinite amount of axiomatic systems and structures that are consistent with each other. Thus, is does not make any sense to state that structures such as groups or real numbers are the unique thing that represents nature. They just have risen representations via the human process of generalization and simplifcation.
Beautiful episode. Can't really still make out if it is discovered or invented. However, if there exist other intelligent civilizations in Universe, then, they ought to do so by use of complex maths.
It's both. The fundamental axioms of current mathematics were discovered. That they should be extended to infinite sets is more or less an invention. It is only becoming somewhat clearer now what that invention actually yields (if it yields anything at the end).
It is even more worrying that mathematics appears to have no content. As all proofs can ultimately be broken down into a sequence of syllogisms, however lengthy, theorems are essentially tautological or analytic and amount to no more than restatement of the axioms in other words, i.e. the assertion that A is A.
Sometimes the answer is way closer than you think: mathematics comes from the latin root: to learn, to study. Therefore it is an invention. Physics is also an invention, the study of nature at the physical level. The only reason, i believe, that mathematics and physics are able to sync with the Universe, and describe it to high accuracies, is that the Universe is very very ancient and very very big, which means some or more order eventually arises from chaos, through different interactions, repetitions, or other simple mechanisms, which can be captured by our mental tools. Another way to see this is that many mathematical theorems can be proven not to apply to physics, and many physical phenomena have yet any scientific explanation at all, therefore, a healthy mix between invention and discovery is the more rational, correct, and even humble solution
A policeman sees a drunk man searching for something under a streetlight and asks what the drunk has lost. He says he lost his keys and they both look under the streetlight together. After a few minutes the policeman asks if he is sure he lost them here, and the drunk replies, no, and that he lost them in the park. The policeman asks why he is searching here, and the drunk replies, "this is where the light is”. I think that mathematics is the light in this joke. But why mathematics? Because is the only thing we know. At least for now.
i agree totally. It just seems to work and that's all we really know. Whether math is "real"(or whatever) is an nonsensical question almost. We don't even know what we mean when we say, well is math platonic or not or real or whatever. In a certain sense math can't not exist, then in the other math can't exist. We don't even know what we're talking about so what's the point.
@@BLUEGENE13 One could argue that math couldn't exist without objects to describe, eg count figures. ie, math is an emergent property of the Universe...no?
Epistemologically, mathematics is primarily based on rationalism or one can also say it's axiomatic. Hence mathematics is both discovered and invented. At the same time it explains the empirical world as well as rationalize the abstract
In one sense, I think it's a bit of both; In a second, it seems to be invented. It's discovered in the sense that psychology discovered the mechanics of sensation and perception, not to mention other subconscious complexes that presumably existed throughout the entirety of human existence (that is to say, prior to the science itself). It is invented in the sense that glasses and binoculars are inventions we use when we need to see the phenomenal world more accurately. I didn't think I would get closer to truth so soon. After that first interview, I instantly knew that no one could actually prove whether math was invented or discovered. The idea that it was discovered seems to me to be nothing less than unwarranted speculation.
Excellent! I choose the Platonic view of mathematical information functioning on the boundaries of our spacetime limits molding our reality simulation according to its invisible prototype
I think physicists saying that math is foundational is a circular argument. Of course they’ll say it is, as science is based on math! And as scientists they willfully ignore/dismiss all things that can’t be explained by physics and math (e.g. consciousness, “the observer”, the measurement problem, Godel/Tarskis theorems, etc.). I love science, but I also realize it is foundationless... as is math. Foundationaless doesn’t mean useless, but it does mean it’s incomplete and will always be such. It’s just a tool, not the whole toolbox.
@@hckytwn3192 I'm not trying to prove anything, I'm asking you- do you know any tool for searching for truth which works better than science? I'm fully aware that it's not perfect, it's made up of people trying to seperate their own biases from their results (that's literally what science does, it's a method designed to counter bias) but its still being used by people who make mistakes. Unfortunately, we haven't found any better way to reliably learn about the world, so we'll just have to tentatively put our trust in this method, while understanding that anything we think we know could be wrong, until someone comes up with a better method of investigating the universe
@@trybunt Right, but that's exactly the point. You made the statement that science is the "best" tool we have, but we only judge that tool by using that tool (i.e. proving out science only using science). I am saying that is a logical fallacy. If we present any other possible tool--introspection/meditation, metaphysics, mysticism, religion, etc.--our first inkling would be to dismiss them using the scientific method, right? However, we know for a fact we can't use science to validate scientific truth, so how can it possibly be used to determine the truth of another tool? Really think about that. It's pure circular reasoning and very hypocritical. Also, if that weren't enough, the scientific method is deeply flawed. Science is based on observation and measurement, and yet it can't explain what those are really. So, if science can't even explain it's own internal processes, how can we assign words like better/best to it? I would expect a process to have internal consistency and completeness before we do that--but science doesn't have that, nor will it ever.
The discovery of invention is the truth of your words and feelings put in to action or made into an object(ive) The distance from earth to the moon can be calculated, measured, viewed, adjusted. Its a way to conclude, not something that yields any kind of monopoly. It just is. As is for simple questions being presented as complicated. "Be carefull seeking meaning, where there is none."
Discovered, however there is certain order in things that seem to rely upon mathematical principals. What we have for measuring is the result of motion of all things. This motion IS matter, and it's origin so to speak is metaphysical intent for lack of a better term. The intent was the reconciliation of the inability for nothing to exist.
The universe can only work randomly or by rules. If the universe works by rules, we can observe and read them. If we read the rules of the universe well, we can elaborate/perfect a language to describe how to read the universe. (math) If our math proves to be true - if it makes assumptions for future real-life events, then it means we got the language of reading the universe - well. Could we have created a different language to read the universe? Most likely. What is with the prime numbers? Most likely, the universe has rules which require their existence and we were able to read the situation. I did not see a single argument yet, of math existing which cannot be explained by the fact that this is how the universe works and we are reading it with math. Math is not how the universe works - they are 2 different things. How the universe works - the rules - that is the reality that does not care if someone reads it. Math is what we invented to transmit to each other how the universe works. It is like someone sees a house and he needs to tell someone else how the house is so he draws a picture.
What a question. Equivalent questions: - Is language invented or discovered? - Is logics invented or discovered? - Is music invented or discovered? - Is philosophy invented or discovered? All questions have the same fault: They are wrong.
@@mindofmayhem. That's a moronic statement. Life is not just matter forced to exchange energy, everybody knows that. Are your emotions just matter forced to exchange energy? How about conscienceness? How about thoughts and ideas? How about choices? How about skepticism, determinism, and realism... So many -ism's in life. Life can be as simple as possible, yet can be so complex at the same time. Well that's just a tiny fraction of life for you buddy, something that the most intelligent species in the universe is still trying to fathom. Alright buddy.
@@ultrainstinctgoku2509 Are your emotions just matter forced to exchange energy? Yes, they are complex chemistry common to all mammals. How about thoughts and ideas? Artifacts or neural networks that can be simulated in algorithms. How about choices? Illusions. There is only observable behaviour that can be simulated by algorithms. Ask social media companies. How about skepticism, determinism, and realism...? These are just thoughts and ideas.
In a way, a block of marble contains all possible sculptures but really it contain none, except that it is a block. You create the sculpture than you look at it to find the different meanings that can fit that creation.
When Wolfram talks about 'other mathematicses' is he talking about p-adic numbers and similar wildly different number systems? Or is he talking about different axioms rather than ZF? Thanks
There is an infinite number of possible axioms in mathematics. In a way mathematics is like chess that way... mathematicians are obsessed with the opening library. The problem here is that this chess board extends all the way to infinity. One can never get past the opening. I shouldn't say never. Most games are open. Some of the most beautiful ones, like the classification of all simple groups, are winnable and have been won. ;-)
Both. While the more practical parts are discovered as provable representations of elements of the real world, in usage today, particularly in astrophysics, key elements can be invented, or perhaps more to the point, concocted out of thin air. In common practice, assumptions are made that are both unprovable and logically fallacious. A very clear example of this is contained in the alleged four kinds of black holes, for instance. Einstein didn't believe any of them could exist, but most people nowadays think Einstein was wrong on that point.
Music, arts and literature do not precisely define reality like mathematical equations do. But yes it can be like that for instance the Euler equation.
Math is the expression of the objectively simplest things we can think of, with the goal of precise understanding. Art is an expression of the complicated mess of human emotion and experience, designed to affect other, equally complicated and messy human beings. I honestly don't see much in common, they seem more like the opposite ends of the spectrum.
@@AlexanderShamov well to me its like art is in the realm of the subjective to which the mathematics if there are any are still unknown. Its related to the unsolved question of consciousness and qualia. But look at the medium of any art its all things that are subject to the laws of physics which are mathematical. Also if you look at the technique of any artist they use mathematical concepts like rhythm, proportion, and tempo among others. So to me there is a connection but I see mathematics as objective while art in the realm of the subjective.
Mathematics, like Language, in its infinite manifestations is constantly being discovered. Mathematics, like Language, is the expression of an Intelligence that permeates all the Is, all that Was, and all that Will Be, in this and any other universe of existence.
Science is rigor. Logic is a subset of science that always replicates. Math is a subset of logic that deals with relationships of quantity. Quantity is recursive boundary conditions.
Even a block to carve the sculpture out of has to be discovered first and chiseled out of later, just so it LOOKS good. Number 0 does not exist in our word and number 1 seems to consist out smaller 1's infinitely... It is both invented and discovered, just like there is no 'yes', or 'no', only in between.
Mathematics is not needed for the nature to function. Nature works on a set of laws which create some regularities in the observable universe. We invented mathematics to describe such regularities of nature. In that way mathematics is not fundamental, it is an abstract object, a tool developed by the conscious mind to describe the regularities of nature.
I wished he'd have brought up things like how did Peter Higgs sit down with pencil and paper to figure out the Higgs' boson years ago or Gödel's Incompleteness Theorems one and two that shocked the math world and others beside. It basically states that you cannot prove the math by the math. Abstract world or not I have always been amazed at how Higgs did what he did or how a consistent system cannot prove itself. I studied engineering, but I had formulas I didn't need to understand to use. I then studied biology and the math changed, but it was doable though genetics was challenging and the math was there too. I'm like the host a bit confused, but I want to say invented yet it exists in the construction of how the Universe runs. Two dimensional.
I don't think these people made things up from the spot but rather had an intuition that these things should be true and then went about proving/modelling. I haven't studied particle physics properly but I'm pretty sure higgs modelled the higgs field in order to complete the set of objects that obey the symmetries of special relativity (so he took an aesthetic approach - striving for symmetry) and gödel probably (I'm completely guessing) noticed that certain examples of consistent axioms had unprovable statements and *then* tried to see if this was true in general. These guys were definitely smart, but it's not magic. Sorry if I'm misunderstanding what you're saying
Great episode and great discussions but I will criticize one thing : why there were no pure mathematician in the episode ? A pure mathematician (espacially an abstractionist) would have some interesting insight.
i'm not so sure. math and philosophy are fairly different disciplines, and the nature of existence is a philosophical pursuit. sure, there's some overlap, but the fundamentals are quite different. mathematicians seem to be overwhelmingly platonists on the matter in question, and it's the "overwhelmingly" - the lack of more diverse opinion in the field - that leads me to tend to think they're not so up on their philosophy, where platonism, while it still has its notable adherents, receives a good deal of pushback. KEvron
*Conditional Statement (Q)* "All languages were (invented or discovered) to describe the world" *Premise(P)* if "Mathmatics is the language of science" is true P1: If languages is (discovered) is true P2: If languages "describes the world" Q1: Then languages=world E1: "book describing outhouses"="actual outhouse" E2 Since "book describing outhouses" is not = "actual outhouses" Q2 then languages=(discovered) is false: P3: If languages = (discovered) is false Q3: then languages = (invented) *proof by controdiction mathmatics was not discovered* P1: If languages is (invented)=true P2: If "mathmatics is the language of science" Q1: Then mathmatics= (discovered) is false P3: If mathmatics is (discovered) is false: Q2: Then mathmatics is (invented) is true *direct proof mathmatics was invented* *Conclusion* ="mathmatics is the language of science and like all languages, it was invented to describe the world"
Does nyone recognise the shot at 07:00, just before the Oxford shots of Broad Street and the High? There's what looks like an Oxford tourist bus in the background but I'm pretty sure that's not Oxford!
a better question is why is september the 9th month october the 10th month and december the 12th month ,what difference does changing a system base from 12 to 10 do and why was it done ,answer that and then you have a starting point
Mathematics is all that exists. Everything is made out of it. Everything in all possible universes, in all possible multiverses (the cosmological multiverse, the many worlds of quantum mechanics) is made out of math objects, patterns and relations, but also math goes beyond all this. If you imagine all the possible physical worlds, that's an infinitely small part of mathematics.
Multiverse is an unscientific and unparsimonious hypothesis. It's a mental construct, a bad attempt at resisting the theological implications of the data from cosmic fine tuning.
Name one experience of math you've had outside consciousness or experience?... Every math equation you have ever looked at or read has been seen within conscious experience... it is comical to see you state the only something that exists is math which is something you have never experienced absent or outside consciousness... Find out who you are first before making claims about the universe, if you think you are a self or a personality... look harder... see if you truly are discrete like a number or if you are perfectly continuous... see if you have a name or a boundary or if that is a social convention... do this for 40,000 plus hours... keep asking "who am I?"... after you find out who you are... then we can trust you with the universe... but if you can't figure that out you should not to be trusted with the universe... just like a doctor who doesn't know who he is can't be trusted to do surgery..
Math is a tool, like a rock. We discover a rock can be used as a hammer tool, which is an invention. the invention of a hammer, is just the intentional use or a property of the physical world. Math is a tool used to describe truths, or properties of real or imagined realities
Mathematical relationships are discovered. The language describing them is invented.
Mathematics, like Language, in its infinite manifestations is constantly being discovered. Mathematics, like Language, is the expression of an Intelligence that permeates all that Is, all that Was, and all that Will Be, in this and any other universe of existence. This expression facilitates self discovery of Intelligence with Itself within the 'physical' universe through the filter of us All.
I was just thinking the exact same thing before i read this
The expression is physics the words are mathematics
Prove it.
@@Z-Diode If you have 1 coin and another coin, then you have 2 coins.
Whether you call it 1 or 2, or purple or whatever.
The value is universal, the name for it is man-made.
2 plus 2 equals 4. No matter where in the universe you are.
For those who has the same homework with me ....
2:15 Roger Penrose
7:20 Mark Balaguer
12:10 Gregory Chaitin
16:22 Stephen Wolfram
21:40 Frank Wilczek
Lmao you're a G for that. I don't have any homework, I just found this because I was interested in it
19:53
the most underrated show about our most fundamental questions.
My all time favorite episode of all that you’ve made. Thank you Dr. Kuhn, staff and production crew.
Math is like the finest poetry. Something so enlightening that dazzles us sometimes. But, as poetry, is only language, a language that we invented to describe the Universe.
In the last 200 years alone, science has made so many discoveries. The revelations or findings by observation, trail and error, show the answers were always there; just not yet understood or proven.
So wonderful what this series tells and although it does not bring you any closer to the truth, it does bring you closer to the people who are so passionate and full of knowledge. What a beautiful journey in itself. Thanks.
Dear Robert, I'm a math professor who follows your channel and especially this series about mathematics. I am very surprised that when you interviewed specialists about the nature of mathematics, you actually avoided speaking to any pure mathematician! You have certainly interviewed some outstanding and renowned experts whose work can be described as mathematical, but whose main research activity is actually not on core mathematics (i.e., algebra/analysis/geometry/number theory/combinatorics etc.) and belong to certain other research communities such as theoretical physics/theoretical computer science/logic-foundations etc. The lack of any pure mathematician in your interviews about the nature of mathematics is so striking that it cannot be accidental, and I find it very regrettable. It gives a skewed picture, because it is well known that the further from core math somebody is, the less likely they are to be a platonist, as can be seen from your interviews with Balaguer and Wolfram, for example (similarly Chaitin was the most purely mathematical of your interviewees and also the most platonist). It is true that most pure mathematicians are not very interested in the philosophy of mathematics (unlike theoretical physicists and logico-foundational people who tend to have a relatively strong interest in philosophy), but surely you could have found somebody.
I've noticed that as well. Most devoted mathematicians have a platonic view of math, and consider it an objective abstract reality that can apply to physical reality, but is not dependent on it.
Platonic reality was mentioned by Roger Penrose as most likely the case in Robert’s interview with him. Please reply as I’m very interested in this subject but not a mathematician.
@@bob9732 How can I help?
I think it seems like a valid complaint. But he phrased the question as a philosophical one. It sounds a little like: if you want to know about the daytime ask the sun. But what does the sun know about daytime? That being said yes I would have liked to hear from a mathematician myself.
omg what pleasure to be seen this doc , math always intriguing me about their origins
A good thought provoking discussion. Penrose said it is not us that that imposes math on the world, it's out there. In other words, a controlling intelligence = G-D. So from time to time, we humans discover a fundamental law following mathematical principles. There are however other mathematical edifices such as String Theory that have no basis in reality at all. So we could describe it as a mathematical game. In other words mathematics is a non physical construct, which can be applied to the real world when circumstances require it. However you need to bear in mind that both Newton and Einstein employed their own mathematical theories to describe the same thing. e.g. Gravity. Both were correct, but Einstein's theory proved to be a more accurate representation of reality, but that does not mean that is the end of the story.
It may sound philosophical..
But if we give a closer look to things.
"NOTHING IS INVENTED but DISCOVERED".
If you ascribe to the many worlds model of reality that allows for infinite dimensions of infinite variance from our own, then every tangent of reality already exists simultaneously within that multidimensional fabric of ulterior reality. In effect that would mean everything is deterministic in their own regard to their own reality/plane, lending to the philosophy that everything is preset and is only being discovered rather than originating spontaneously.
A good way of visualizing it, is like a fractal pattern, similar to how a tree branches off. From root timeline, or ultimate moment of potentiality fractaling/branching off from every other ensuing potentiality, explored to the degree of their potential. The same visual phenomenon can be seen intrinsically across almost all fields, scales and spectrums of our material reality. Which like a snake eating its own tail, brings it back to the conversation to begin with. Its through this observation of these various patterns repeated across reality that we can begin to understand the greater and greater nature of reality
@Mr Right - the iPhone is comprised of electronic components such as the transistor and other devices, these devices were developed using mathematical derivatives associated with current flow (electricity), which was discovered.
I found this discussion very interesting because I Am a Numerologist & student of Astrology - Which has been confused as different sciences (What Ever That Word Means)...
I can fully understand why most folks get loss in their discussions, because they are talking about complicated theories. And Einstein was absolutely Correct, that Everything is Connected.
The Simple version to understand, Represents how We All Are Connected to the Circle (The Universe as Planets within us.
When you study your Birth chart as to the meaning of Each House on the Zodiac, you will learn that each Planet in Your Chart - Represents your entire Personality as Players Upon the Stage .... Shakespeare once revealed that Earth represents a Stage and We All Are But Bit Players Upon it”
Then the Queen who lost her own head - after Shakespeare did a live show of the characters from the Village ... the thief lost his head for stealing something to Eat.
Kings & Queens Created Words to keep their subjects Confused.. So in closing - Numbers are the Language of the Universe - In the Biblical studies of Satan, he had to reverse engineer Everything that GOD CREATED.
Each Letter is Matched & Connected to two sets of Numbers reduced to their lowest common denominators. Because the Numbers Represents Portals leading to other Universes as follows:
A= 1 - 10 - 19
B= 2 - 11 - 20
C= 3 - 12 - 21 represents the number of the Adult Universe - 12 also represents Zodiac
D= 4 - 22 represents the second Master Number - 13 Transformation & O Karma reborn
E= 5 - Education & Learning & Teaching (Creativity & Art) 5th House/Home of Leo etc
F= 6
G= 7
H= 8
I= 9
K= (10 = 1)Graduation or Wheel of Fortune - start over if failed back to 1 or 19= Sun Energy has been learned to proceed to (22).
As this applies to the year like 2020 ... the end of the Zodiac Chart 12th House
2+2 = 13 or the New Zodiac begins the New House or moving into the 4th Dimension #4
13 also Represents the ending of an Era of 2020 years for the time period of each House as the Universe keeps Traveling as WE Do.
This is the simple outline to understand about Yourself - because we all are made with Atoms/Adams who was cast out of Heaven and Eve represents the light of Day as in New births.
Science is Theory & Numbers Are the Reality of Who We Are...
The first number after each Number Represents the First Set of Numbers
It’s like when you turn 10 years old to complete your first cycle in this life time (1-9)
if You Are The Universe When Born as anew Star 💫
We invent the axioms and discover the consequences
Interesting
This episode, like the rest, is a wonderful exploration of people -- even if ostensibly through their ideas.
Well ..... I guess it all depends on the definition you choose for mathematics for you to consider it invented or discovered, platonic or fictional. I’m no mathematician but I think it’s a more of a methodology or a technique we use creating the axiom, quantify the world accordingly to predict , operate and make sense of the physical world ( or at least how it started ) , therefore it can not be a platonic object nor fictional.
mathmatics is the proof of intelligent design and humans use of it proves our close relationship with the creator
Mathematics is the symbolic language that describes and explains reality to a conscious mind. It is to whom mathematics is useful
This unarguably has to be one of the best YT Channels that exist today.
In this world there was wood and stone, a man put them together to form a hammer to build his house.After 20 years someone came and asked "was hammer invented or dicovered?" So everyone do you need to know the answer?
yes.
If postulating the existence of some types of hammers allowed you to predict the workings of physical reality, your analogy would be a good one.
Why are you watching this?
@@suntzu7727
"Electricity at the beginning was used for magic show now it's used to power up our current world."
You can learn from the use of something evolve(at first maths was not used to calculate the physical reality) and the other is that just like the magician"we don't need to question the existence(electricity,maths) to make use of it unless it prevent further research."
@@cindyo6298
My answer is to be closer to the truth!
If you don't understand,you can ask.
Watched this twice now, and will probably watch and refer back to it again in the future, but I can't seem to shake that old metaphor attributed to several musicians ... 'Talking about music is like dancing about architecture.' 🤣
If we all agreed with that, it would be very difficult to explain music theory or write a song with other musicians. If a musician said that, they were probably high.
Roger Penrose seems to be his expert friend for all subjects
Penrose kinda acts like a dick. I still like the guy, but sheesh.
@@mindofmayhem. How does he "act like a dick"? Penrose is one of my favorite people on the planet.
Penrose is fake news
@@m3dia95 Except you saying some words is not an argument
@@Raptorel I don't argue with people determined to drag me down to their level.
9:11 Mark Balaguer outlines 4 different views of the origin of Mathematics:
(1) A _mentalist_ view - It exists only subjectively, in the mind
(2) A _physical_ view - It exists objectively, in the universe
(3) A _Platonic_ view - It has an abstract, yet real, existence of its own, independent of both of the above
(4) An _anti-realist_ view - It's an abstract, but fictional, human invention, with no existence of its own. Indeed, the idea that it "exists" at all is nonsense.
2 & 3 differ about how they define reality, whereas 1 & 4 seem complimentary.
What do you think of his classification into these 4 views and which of them, if any, do you think are correct?
i agree: 1 & 3 seem most complimentary. both are consistent with a determinist pov. 2 & 3 would seem to bear a greater burden of proof, but then again, mind-dependent cases are beyond proof, except maybe to the bearer.
KEvron
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.
Man's really just went on a world tour in the name of mathematics
Its so he can call his holiday a business expess and have it as a tax write off
Haven't we been doing that for the longest? How did knowledge of mathematics travel from culture to culture to begin with?
@@ascensionunlimited4182
This is obviously a oversimplification, each step would’ve been repeated/stolen, lost and invented an uncountably different number of ways by even more cultures.
First a culture was trying to show the difference between quantities of things and counting was invented
A culture took their invention of counting and introduced subtraction, eventually another culture ran into negative numbers and the another culture invented 0. Then another culture tried simplifying some questions and invented multiplication then later division. From that another culture invented powers and roots. After that a another culture was thinking more abstractly and tried to create a consistent set of rules. That collective decentralised work is what we call number theory
Another culture started thinking more abstractly about number theory then created algebra. Another culture was trying to simplify some questions from algebra and a 14 year old created abstract algebra. Then our culture found some questions abstract algebra couldn’t answer and created calculus from there
Today all of mathematics (from typology to derivatives) is a combination of number theory with either calculus and or abstract algebra.
@@ascensionunlimited4182
math is a tool; it arises out of need. it needn't travel from culture to culture in order to see its use across cultures. new world peoples invented their systems independently of old-world cultures, and some current cultures are entirely anumeric, and have no maths at all.
KEvron
Yes I understand, your saying it's truth is independent of human minds or any other kind of consciousness! In other words the mathematical concepts have just has much right to be treated has objective reality has the things we perceive with our senses! Very profound!
Mathematics is clearly more than an abstract object, it is the underlying fabric of reality. It transcends human ideas like emotions, civilization and processes, to name a few examples of abstract objects. For example, no matter what universe or reality, no matter what type of particles and physical structures exist, no matter how many amount of dimensions an existence has, 2 plus 2 is always 4. There is no reality where 2+2=5, because one such a contradiction implies a contradiction of the entire system. One can argue that the concept of mathematics is a human invention, but it transcends humanity and thought. Even many species without brains or sentience have some form of counting and calculation. Any life with sufficient intelligence would come to the exact same conclusions in mathematics as we would.
*"There is no reality where 2+2=5"*
in this reality, there is no proposition that may exist absent a proposing agent. if the proposition "2+2=5" may exist absent such an agent, then the proposition "this sentence is nether true nor false" may exist absent one, and reality then incurs a genuine paradox.
the existence of concepts absent the process of conceptualization results in paradox.
KEvron
Math, as is commonly known, is an expression of the "reality" as we perceive it.. Whether our perceived "reality" is the only "reality"? I think, we don't have any formal way to know it for sure... We may apply empiricism or theoretical explanation. But all these will be limited by our understanding or perceptions of "reality". So we arrive at kind of circular arguments only, I think. Any way, a beautiful video raising these quests.. Thanks RLK..
Great episode.
The laws of the universe will never change. It is simply up to humanity to create the right formulae to accurately describe the experience.
Breakthroughs don't actually mean new physics, but we as a species are simply catching up to what already *is.*
again a wonderful video in this series.
I would wish to ask this question to Kurt Godel for a most memorable anwser !
Godel already answered it in his incompleteness theorem. My take is you can be more and more precise but you will never arrive at exactness because the physical universe isn’t exact.
Gödel gave a hint by explaining that a set of rules and laws in mathematical systems cannot be described nor explained from within that system. You need an external standpoint or viewpoint. But that is impossible as you would need to exit from your own reality or the material world. So again you are thrown back to merely imagine that it is discovered as it exists on a higher level of reality or a different dimension of mind space and time. It's transcendental like e is!
I just love the intro scoring, so enigmatic.
Fascinating! But needs WAY more commercials! 😃
Handy tip. Forward the video until the end then restart and the adds will be gone.
We have been trying to reach you about your car's extended warranty.😏
Balaguer: Do black holes exist, do Higgs bosons exist, does Bitcoin exist? If so, in what sense do they exist? Do you need a village in Nepal you can go to and find them? To understand Platonism one has to have a broader understanding of the notion of existence. There are precise senses in which mathematical objects exist, for example that they form an indispensable part of successful/useful scientific theories about the world (Quine).
It’s analytical a-posteriori. People are still struggling with arriving at the a-posteriori though. Deriving complex analytical truths requires a lot of experience, you need to know what to look for. Which is why often in statically typed programming languages, you do need type annotations even if there is type inference. Those type systems can easily go undecidable and need a human guide.
Mathematics is discovered. It has always existed but took we are slowly discovering how to express it. Not all the math we know today is correct, therefore from time to time there is a refining and getting closer to the correct mathematics, closer to the truth.
Math is logical, so is nature. The difference is that nature exists by itself; math, not so. Philosophers, not nature, invented logic. So, mathematics is a human invention. Nature is logical simply because it works. What doesn't work can't exist in the first place! There is no intention anywhere. Logic happens by itself. It has rules, but nature doesn't know that. The AND operation occurs with a chain: all links have to work for the chain to work. A river flowing down will split in two streams when an obstacle is hit. That's the OR operation. If it doesn't rain for a long time, the grass will turn yellow. That's the IMPLICATION operation. Logic just happens in nature. Math doesn't just happen.
@@jeancorriveau8686 Math does just happen in nature in very similar ways as you mentioned per logic. What other than mathematics could explain the logic of how a flower grows and changes?
Mathematics, like Language, in its infinite manifestations is constantly being discovered. Mathematics, like Language, is the expression of an Intelligence that permeates all the Is, all that Was, and all that Will Be, in this and any other universe of existence.
Encouraged at every turn to "think outside the box" perhaps it's time for a closer look at what got us into boxes in the first place. If you proceed, keep in mind, ahead are precise scale models of existing structures designed and assembled in prehistory, before the catastrophe that drove humanity mad by amnesia fell upon us: brainelevator.org
Maths can't be wrong. Axioms of today may describe something else, not the same thing that some entity in the future might want to describe, but all things that are proven from the axioms today are absolutely correct in this system of axioms. No god can piss on that.
(25:35) *"Math is either physical, or mental, or platonic, or fictional ... Choose only one."* ...Why are we restricted to only one choice?
I was thinking the same thing, also why are we restricted to choosing any of them at all? Math is really just a description, and does a description fit perfectly into one of those options? Not really.
This is a very well made, extremely interesting film.
Mathematics is a perception within your mind. The mind is describing the world through the medium of mathematics.
Urantia: 15:14.9 Your planet is a member of an enormous cosmos; you belong to a well-nigh infinite family of worlds, but your sphere is just as precisely administered and just as lovingly fostered as if it were the only inhabited world in all existence.
I'm not convinced that the fact maths are derived from roughly the same set of axioms constitutes evidence that it is discovered.
Does an author 'discover' the sequel to her or his novel by deriving some set of logical consequences? See, when the author adds new variables, these variables that the author invents are still designed to obey the initial set of axioms that the author has set of the world of his or her story. The next chapter 'feels' right because it follows the same principles and is made to stem smoothly from the earlier part of the story, as though it was all there from start, only unveiled one step at a time.
But in reality, the author just thought of a working framework, imagined an outline, then planned and/or pantsed the rest via some kind of intuitive (or non intuitive) inference reasoning.
It seems that this appearance that the structure is being uncovered is the byproduct of a commitment to self-consistency, not some kind of unknown realm that is being unveiled one area at a time.
It's a matter of perspective.
Inventing a steam engine is also a form of discovery - you discover that if you turn water into steam it expands, so if you combine mechanical elements in such and such way, you can convert thermal energy into kinetic energy etc.
You could write your reasoning down on a piece of paper, never constructing a physical steam engine, only proving the validity of the concept in theory.
Have you invented it? Or have you only discovered certain possibilities that have always been part of the fabric of reality?
It's only a matter of convention which word you decide to use.
Mathematics is a universal form of communication even animals can communicate counting.
Animals sense quantity, eg, a cat sensing his power to jump onto a fence. There is no counting, which requires units, eg, a five-foot high fence. Man counts by abstracting, ie, selectively focusing (on quantity, here, the length of a ruler relative to to the length of a fence). There are many ruler-lengths to one fence, each one having a name, eg, five ruler-lengths,ie, counting.
Intro. To Objectivist Epistemology-Ayn Rand
Leap Of Logic-David Harriman
@@TeaParty1776 If you think concerning predicting a thing that does not exist in front of you at that exact moment , but can predict it will soon happen at a certain time and place your doing math at least counting. Migration patterns show this these things must be learned to be performed.
There is a unique platonic space for the English alphabet, grammar and couple of dictionaries.
Why would this artificial garbage, called "natural" language by those who can't even appreciate the irony, have any place in the Platonic realm?
what i find interesting is that mathematicians and scientists seem to see maths as perfect and ideal, and physical reality as an approximation to that. when it should be thought of the other way round: mathematics is a simplified model of reality. mathematics is a system of pure logic, extending from some basic principles; we are fortunate to live in a reality which is logically consistent, and we have chosen the basic principles of mathematics to describe what we observe in the universe - so its no surprise that mathematics describes the universe so well
宇宙是用数学语言阅读和书写的。
I think you've got the idea of what math really is. It's the three laws of logic: identity, excluded middle, and non-contradiction expressed symbolically. From these simple rules all mathematics are derived. So logic and math are the same. They're non-material. I'm not certain what physical reality is and it's most basic form. Most mathematical laws are approximations of physical relationships. Which tells me that the rules of logic are somehow more fundamental than physical or conceptual reality. The implementation of mathematics is sometimes wrong but that doesn't mean that the logical rules themselves are. Sometimes people do math wrong doesn't make math wrong.
Maths is the perfect tool to do research on the physical reality.That's why scientist and mathematicians give it so much importance."It is in human nature to value what is of use to them."
@@levipack3835 identity and excluded middle are just different flavors of non-contradiction. Mathematics and logic both answer to physical reality as the former two are human inventions about the latter.
Mathematics, like Language, in its infinite manifestations is constantly being discovered. Mathematics, like Language, is the expression of an Intelligence that permeates all that Is, all that Was, and all that Will Be, in this and any other universe of existence. This expression facilitates self discovery of Intelligence with Itself within the 'physical' universe through the filter of us All.
Math is fundamental. It exists, even without conscious entities. Pi describes a circle. Pythagoras' rule applies to Euclidean geometry even if no-one is there to measure it. Math is fundamental to the universe. QED...
Whole questions arises from confusion with surface appearance of language as if the question meant the same thing to everyone. Mathematical structures have risen from the need to represent relationships in the real world via attempts to generalize, simplify and get to get into the essence of the internal logic these representations. For example, it is extremely easy to invent scenarios how a smart carpenter working on wheels would end up formulating the axioms for the theory of finite groups.
One can formulate an infinite amount of axiomatic systems and structures that are consistent with each other. Thus, is does not make any sense to state that structures such as groups or real numbers are the unique thing that represents nature. They just have risen representations via the human process of generalization and simplifcation.
Beautiful episode. Can't really still make out if it is discovered or invented. However, if there exist other intelligent civilizations in Universe, then, they ought to do so by use of complex maths.
It's both. The fundamental axioms of current mathematics were discovered. That they should be extended to infinite sets is more or less an invention. It is only becoming somewhat clearer now what that invention actually yields (if it yields anything at the end).
It is even more worrying that mathematics appears to have no content. As all proofs can ultimately be broken down into a sequence of syllogisms, however lengthy, theorems are essentially tautological or analytic and amount to no more than restatement of the axioms in other words, i.e. the assertion that A is A.
Sometimes the answer is way closer than you think: mathematics comes from the latin root: to learn, to study. Therefore it is an invention. Physics is also an invention, the study of nature at the physical level. The only reason, i believe, that mathematics and physics are able to sync with the Universe, and describe it to high accuracies, is that the Universe is very very ancient and very very big, which means some or more order eventually arises from chaos, through different interactions, repetitions, or other simple mechanisms, which can be captured by our mental tools. Another way to see this is that many mathematical theorems can be proven not to apply to physics, and many physical phenomena have yet any scientific explanation at all, therefore, a healthy mix between invention and discovery is the more rational, correct, and even humble solution
A policeman sees a drunk man searching for something under a streetlight and asks what the drunk has lost. He says he lost his keys and they both look under the streetlight together. After a few minutes the policeman asks if he is sure he lost them here, and the drunk replies, no, and that he lost them in the park. The policeman asks why he is searching here, and the drunk replies, "this is where the light is”.
I think that mathematics is the light in this joke. But why mathematics? Because is the only thing we know. At least for now.
Walking in the dark hoping to stumble upon it, that's philosophy.
i agree totally. It just seems to work and that's all we really know. Whether math is "real"(or whatever) is an nonsensical question almost. We don't even know what we mean when we say, well is math platonic or not or real or whatever. In a certain sense math can't not exist, then in the other math can't exist. We don't even know what we're talking about so what's the point.
@@BLUEGENE13 One could argue that math couldn't exist without objects to describe, eg count figures.
ie, math is an emergent property of the Universe...no?
@-GinPi Gamma Relationship between diameter and the circle.
Safe to assume that pi wouldnt exist without circular objects in a physical universe, no?
@-GinPi Gamma 69
Epistemologically, mathematics is primarily based on rationalism or one can also say it's axiomatic. Hence mathematics is both discovered and invented. At the same time it explains the empirical world as well as rationalize the abstract
Roger Penrose. One cool dude.
In one sense, I think it's a bit of both; In a second, it seems to be invented. It's discovered in the sense that psychology discovered the mechanics of sensation and perception, not to mention other subconscious complexes that presumably existed throughout the entirety of human existence (that is to say, prior to the science itself). It is invented in the sense that glasses and binoculars are inventions we use when we need to see the phenomenal world more accurately. I didn't think I would get closer to truth so soon. After that first interview, I instantly knew that no one could actually prove whether math was invented or discovered. The idea that it was discovered seems to me to be nothing less than unwarranted speculation.
Excellent! I choose the Platonic view of mathematical information functioning on the boundaries of our spacetime limits molding our reality simulation according to its invisible prototype
Well, you can't conclude that Mathematics brings us closer to truth if we are not sure whether it was invented or discovered.
Developing new math seems less like "finding" something than comparing it with an established system to check for consistency.
I think physicists saying that math is foundational is a circular argument. Of course they’ll say it is, as science is based on math! And as scientists they willfully ignore/dismiss all things that can’t be explained by physics and math (e.g. consciousness, “the observer”, the measurement problem, Godel/Tarskis theorems, etc.). I love science, but I also realize it is foundationless... as is math. Foundationaless doesn’t mean useless, but it does mean it’s incomplete and will always be such. It’s just a tool, not the whole toolbox.
It's currently the best tool we have, I'd be happy to hear of any replacements you might know of
@@trybunt so how would you prove science is the “best tool we have”? With math? With even more science? 🤓
@@hckytwn3192 I'm not trying to prove anything, I'm asking you- do you know any tool for searching for truth which works better than science?
I'm fully aware that it's not perfect, it's made up of people trying to seperate their own biases from their results (that's literally what science does, it's a method designed to counter bias) but its still being used by people who make mistakes. Unfortunately, we haven't found any better way to reliably learn about the world, so we'll just have to tentatively put our trust in this method, while understanding that anything we think we know could be wrong, until someone comes up with a better method of investigating the universe
@@trybunt Right, but that's exactly the point. You made the statement that science is the "best" tool we have, but we only judge that tool by using that tool (i.e. proving out science only using science). I am saying that is a logical fallacy. If we present any other possible tool--introspection/meditation, metaphysics, mysticism, religion, etc.--our first inkling would be to dismiss them using the scientific method, right? However, we know for a fact we can't use science to validate scientific truth, so how can it possibly be used to determine the truth of another tool? Really think about that. It's pure circular reasoning and very hypocritical. Also, if that weren't enough, the scientific method is deeply flawed. Science is based on observation and measurement, and yet it can't explain what those are really. So, if science can't even explain it's own internal processes, how can we assign words like better/best to it? I would expect a process to have internal consistency and completeness before we do that--but science doesn't have that, nor will it ever.
The discovery of invention is the truth of your words and feelings put in to action or made into an object(ive)
The distance from earth to the moon can be calculated, measured, viewed, adjusted. Its a way to conclude, not something that yields any kind of monopoly. It just is. As is for simple questions being presented as complicated.
"Be carefull seeking meaning, where there is none."
Discovered, however there is certain order in things that seem to rely upon mathematical principals. What we have for measuring is the result of motion of all things. This motion IS matter, and it's origin so to speak is metaphysical intent for lack of a better term. The intent was the reconciliation of the inability for nothing to exist.
The universe can only work randomly or by rules.
If the universe works by rules, we can observe and read them.
If we read the rules of the universe well, we can elaborate/perfect a language to describe how to read the universe. (math)
If our math proves to be true - if it makes assumptions for future real-life events, then it means we got the language of reading the universe - well.
Could we have created a different language to read the universe? Most likely.
What is with the prime numbers? Most likely, the universe has rules which require their existence and we were able to read the situation.
I did not see a single argument yet, of math existing which cannot be explained by the fact that this is how the universe works and we are reading it with math.
Math is not how the universe works - they are 2 different things. How the universe works - the rules - that is the reality that does not care if someone reads it. Math is what we invented to transmit to each other how the universe works. It is like someone sees a house and he needs to tell someone else how the house is so he draws a picture.
0:57 exactly thankyou
Excellent.
What a question. Equivalent questions:
- Is language invented or discovered?
- Is logics invented or discovered?
- Is music invented or discovered?
- Is philosophy invented or discovered?
All questions have the same fault: They are wrong.
For real. I think the question itself is pointless and really just points out a flaw of our ability to describe how something came to be.
Lengages invented/developed.
Logcic, probably the same answer as math.
Music created.
Philosophy would depend on the branch of it.
Universe/ reality has patterns and math is just our translation of those patterns.
Life is just matter forced to exchange energy. :) Math is it's numerical expression.
@@mindofmayhem. dumb reductionism.
@@JustinHerchel More like adjective holism. {(-_-)}
@@mindofmayhem. That's a moronic statement. Life is not just matter forced to exchange energy, everybody knows that. Are your emotions just matter forced to exchange energy? How about conscienceness? How about thoughts and ideas? How about choices? How about skepticism, determinism, and realism... So many -ism's in life. Life can be as simple as possible, yet can be so complex at the same time. Well that's just a tiny fraction of life for you buddy, something that the most intelligent species in the universe is still trying to fathom. Alright buddy.
@@ultrainstinctgoku2509 Are your emotions just matter forced to exchange energy? Yes, they are complex chemistry common to all mammals. How about thoughts and ideas? Artifacts or neural networks that can be simulated in algorithms. How about choices? Illusions. There is only observable behaviour that can be simulated by algorithms. Ask social media companies. How about skepticism, determinism, and realism...? These are just thoughts and ideas.
Great topic
Please write a book about "Closer to truth: best interviews"
Math just describe the quantity of the Nature.
In a way, a block of marble contains all possible sculptures but really it contain none, except that it is a block. You create the sculpture than you look at it to find the different meanings that can fit that creation.
When Wolfram talks about 'other mathematicses' is he talking about p-adic numbers and similar wildly different number systems? Or is he talking about different axioms rather than ZF? Thanks
There is an infinite number of possible axioms in mathematics. In a way mathematics is like chess that way... mathematicians are obsessed with the opening library. The problem here is that this chess board extends all the way to infinity. One can never get past the opening. I shouldn't say never. Most games are open. Some of the most beautiful ones, like the classification of all simple groups, are winnable and have been won. ;-)
Thanks @@lepidoptera9337!
The invention of the automatic transmission still blows my mind.
Both. While the more practical parts are discovered as provable representations of elements of the real world, in usage today, particularly in astrophysics, key elements can be invented, or perhaps more to the point, concocted out of thin air. In common practice, assumptions are made that are both unprovable and logically fallacious. A very clear example of this is contained in the alleged four kinds of black holes, for instance. Einstein didn't believe any of them could exist, but most people nowadays think Einstein was wrong on that point.
It’s an expression like music, arts and literature.
Music, arts and literature do not precisely define reality like mathematical equations do. But yes it can be like that for instance the Euler equation.
Math is the expression of the objectively simplest things we can think of, with the goal of precise understanding.
Art is an expression of the complicated mess of human emotion and experience, designed to affect other, equally complicated and messy human beings.
I honestly don't see much in common, they seem more like the opposite ends of the spectrum.
@@AlexanderShamov the one who cannot transcend illusion of “Duality” does tend to complicate things.
@@AlexanderShamov well to me its like art is in the realm of the subjective to which the mathematics if there are any are still unknown. Its related to the unsolved question of consciousness and qualia.
But look at the medium of any art its all things that are subject to the laws of physics which are mathematical. Also if you look at the technique of any artist they use mathematical concepts like rhythm, proportion, and tempo among others. So to me there is a connection but I see mathematics as objective while art in the realm of the subjective.
Mathematics, like Language, in its infinite manifestations is constantly being discovered. Mathematics, like Language, is the expression of an Intelligence that permeates all the Is, all that Was, and all that Will Be, in this and any other universe of existence.
Science is rigor. Logic is a subset of science that always replicates. Math is a subset of logic that deals with relationships of quantity. Quantity is recursive boundary conditions.
Wonderful!
Even a block to carve the sculpture out of has to be discovered first and chiseled out of later, just so it LOOKS good.
Number 0 does not exist in our word and number 1 seems to consist out smaller 1's infinitely...
It is both invented and discovered, just like there is no 'yes', or 'no', only in between.
Mathematics is not needed for the nature to function. Nature works on a set of laws which create some regularities in the observable universe. We invented mathematics to describe such regularities of nature. In that way mathematics is not fundamental, it is an abstract object, a tool developed by the conscious mind to describe the regularities of nature.
bingo! the universe does not have to carry the one.
KEvron
Neither the answer, I'm still stuck of the question of why they made it so damn hard.
Because life is hard and so does the world , the universe
I wished he'd have brought up things like how did Peter Higgs sit down with pencil and paper to figure out the Higgs' boson years ago or Gödel's Incompleteness Theorems one and two that shocked the math world and others beside. It basically states that you cannot prove the math by the math. Abstract world or not I have always been amazed at how Higgs did what he did or how a consistent system cannot prove itself. I studied engineering, but I had formulas I didn't need to understand to use. I then studied biology and the math changed, but it was doable though genetics was challenging and the math was there too. I'm like the host a bit confused, but I want to say invented yet it exists in the construction of how the Universe runs. Two dimensional.
I don't think these people made things up from the spot but rather had an intuition that these things should be true and then went about proving/modelling. I haven't studied particle physics properly but I'm pretty sure higgs modelled the higgs field in order to complete the set of objects that obey the symmetries of special relativity (so he took an aesthetic approach - striving for symmetry) and gödel probably (I'm completely guessing) noticed that certain examples of consistent axioms had unprovable statements and *then* tried to see if this was true in general. These guys were definitely smart, but it's not magic. Sorry if I'm misunderstanding what you're saying
Wonderful👌
Genesis 2:18.
Learning: 5:30
Great conversations
Question - might the singularity at the center of a black hole be everywhere in the same place?
We invented the game, we are discovering the consequences...
Mathematics is a language
that evolved in human culture
in the same way and
for the same reasons
every other language did.
Great episode and great discussions but I will criticize one thing : why there were no pure mathematician in the episode ? A pure mathematician (espacially an abstractionist) would have some interesting insight.
i'm not so sure. math and philosophy are fairly different disciplines, and the nature of existence is a philosophical pursuit. sure, there's some overlap, but the fundamentals are quite different. mathematicians seem to be overwhelmingly platonists on the matter in question, and it's the "overwhelmingly" - the lack of more diverse opinion in the field - that leads me to tend to think they're not so up on their philosophy, where platonism, while it still has its notable adherents, receives a good deal of pushback.
KEvron
Art
*Conditional Statement (Q)* "All languages were (invented or discovered) to describe the world"
*Premise(P)* if "Mathmatics is the language of science" is true
P1: If languages is (discovered) is true
P2: If languages "describes the world"
Q1: Then languages=world
E1: "book describing outhouses"="actual outhouse"
E2 Since "book describing outhouses" is not = "actual outhouses"
Q2 then languages=(discovered) is false:
P3: If languages = (discovered) is false
Q3: then languages = (invented)
*proof by controdiction mathmatics was not discovered*
P1: If languages is (invented)=true
P2: If "mathmatics is the language of science"
Q1: Then mathmatics= (discovered) is false
P3: If mathmatics is (discovered) is false:
Q2: Then mathmatics is (invented) is true
*direct proof mathmatics was invented*
*Conclusion* ="mathmatics is the language of science and like all languages, it was invented to describe the world"
Does nyone recognise the shot at 07:00, just before the Oxford shots of Broad Street and the High? There's what looks like an Oxford tourist bus in the background but I'm pretty sure that's not Oxford!
a better question is why is september the 9th month october the 10th month and december the 12th month ,what difference does changing a system base from 12 to 10 do and why was it done ,answer that and then you have a starting point
I don’t like this guy’s answer, so I’m just gonna go and ask someone else.
If only we could understand Patterns....
It arrived with us
Mathematics is all that exists. Everything is made out of it. Everything in all possible universes, in all possible multiverses (the cosmological multiverse, the many worlds of quantum mechanics) is made out of math objects, patterns and relations, but also math goes beyond all this. If you imagine all the possible physical worlds, that's an infinitely small part of mathematics.
Multiverse is an unscientific and unparsimonious hypothesis. It's a mental construct, a bad attempt at resisting the theological implications of the data from cosmic fine tuning.
@@JustinHerchel Except, that world's top scientists think that it exists...
有限-无限的相互作用是人类思维的中心，从古代哲学家和数学家（齐诺，毕达哥拉斯），再到现代数学（康托尔，希尔伯特）和计算机科学（图灵，哥德尔）。
No. Concepts do not make anything
Name one experience of math you've had outside consciousness or experience?... Every math equation you have ever looked at or read has been seen within conscious experience... it is comical to see you state the only something that exists is math which is something you have never experienced absent or outside consciousness... Find out who you are first before making claims about the universe, if you think you are a self or a personality... look harder... see if you truly are discrete like a number or if you are perfectly continuous... see if you have a name or a boundary or if that is a social convention... do this for 40,000 plus hours... keep asking "who am I?"... after you find out who you are... then we can trust you with the universe... but if you can't figure that out you should not to be trusted with the universe... just like a doctor who doesn't know who he is can't be trusted to do surgery..
1.2 gpa... I never imagined myself of anything and never thought I'd be anything. I made it.... I can't believe it.
Superman is back...!!!🙂👍
Now thats a good question, best question i seen asked all day.
Math is a tool, like a rock. We discover a rock can be used as a hammer tool, which is an invention. the invention of a hammer, is just the intentional use or a property of the physical world. Math is a tool used to describe truths, or properties of real or imagined realities
through invention we discover and vice versa