I love that at the very end the interviewer has the giant cheesy smile saying “we are now far more confused than when we started” as I now have a lot more questions and wonder if the original question even makes total sense
The richest answers to a question ARE those which leave us with more questions than when we started. An "open and shut" slam-dunk of an answer, leaving no ambiguity, might feel more satisfying at first, but ultimately the most dramatic effect it has had is to take the wonder you felt peering through an open door -- and slammed it shut. How much more wondrous it would be to lead you to that door, and in the space beyond, find five MORE doors beckoning with mystery!
Tegmark essentially answered the entire question in the first sentence. Mathematical language is an invention, a way of describing mathematical principles, confined to our known universe, which are "self-consistent" as Tegmark notes.
There are no mathematical principles confined to our universe. The physical world is not inherently mathematical even though we use mathematics to describe that world.
Jamaal Richardson Michael Beer Interesting and thx for the reply.. I find it rather amazing that our self proclaimed “intelligence” has literally been halted at a fork in the road.. A point wherein we are left with one unanswerable question... ..was mathematics discovered or invented? Surely in the quantum realm mathematics, physics, standard model and all theories dissolve.. Equations that are flawless in predicting the macro are rendered completely useless in the micro! Ironically, within such micro it seems scientific explanation is just as ridiculous as all religious explanations!
What do you mean "confined to our known universe"? Tegmark believes in a sort of multiverse, whereby all structures that exist mathematically also exist physically.
Yes, but later they both seemed to say that math was platonic "Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. Just as electrons and planets exist independently of us, so do numbers and sets" To me this implies that math is discovered and not invented since it was there all the time waiting to be discovered. I don't know though, this question seems like a very complicated one and I'm not making a strong stand either way.
"For every single physical entity, that we can think of something we can touch or measure with a detector, there is corresponding mathematical entity there in the mathematical structure."
I very much enjoy reading books by Tegmark as a physicist. This question, however, in its deepest sense, is best answered by not talking so much about physics. As someone else here commented, Tegmark answers the question in the best way in his first sentences where he distinguishes between our mathematical language (which we invent) and mathematics as such (which we discover). After that, I think the interview loses track in the hunt for the sought answer and deeper understanding of it.
I 100% agree with this. The realization that physics was not "equations that nature gives us" but rather mathematical models that model what we discover in nature really shook me and led me to this video. It's exactly what science is mostly: just humans trying to model our information about the world in an organized way that works for us.
Numbers have emerged in our history as a simple tool for counting units around us. We could never imagine how many things these numbers would still show us.
The problem with insanely intelligent people is their ability to put their thoughts into a clear statement. The easiest answer to this question isn't explaining how math is real because of some multiverse theory but rather by giving an easily understood analogy. Say you have 1 marble in your left hand and 1 marble in your right hand. Now when you put both of those marbles in your right hand, you now have 2 marbles in your right hand. This proves math to be real. The word "two" is used to describe how many marbles (or whatever you're counting) you have. One + One = Two. So let's just say instead of the word "two" mathematicians decided the word should be "owt." So in this case One + One = Owt. So you can see that no matter how you describe how many marbles you have. You will always have a set answer that is manufactured by a predetermined set of laws in our universe. The language of math is invented. The laws of math are universal and discovered.
@@thomashooper9148dude... that is literally what we are saying... this is what I'm trying to explain. People are too focused on the vocabulary of a subject when in reality it can be explained much simpler without all the added nonsense. Arithmetic is like getting from point A to point B and math is a like car. Getting from point A to point B is the same distance no matter how you decide to get there but we invented a system to get us there faster and easier even though the distance stays the same. So we can keep inventing new ways to get to point B faster but the distance is always the same. THE DISTANCE IS UNIVERSAL, THE CAR IS HUMAN MADE.
GreenEarthers Business , then we do disagree. Take infinity as an example, this is clearly a man made concept. One that has no real bearing on reality. Yet a mathematical reality!
@@thomashooper9148 space is infinite. words invented to describe things that people see or measure doesn't discredit the concept? If I see a blue flower it doesn't matter if I call it indigo, sky blue, baby blue. The flower is blue. We invented the word blue to describe the color we see, just as we invented addition to describe how many things there are when you put things together. This + that = those. It's been this way since the dawn of time and it will continue to be this way until the end. Math is all around us but how we choose to perceive it and measure it is up to you
To me, mathematics has always been a language used to describe the physical world and the intrinsic laws of nature. But all I have is first year college math to back that assertion.
I really like the attitude and passion Max has in his interviews as much as I enjoyed his first book. Nonetheless I have to say that in this interview he really dodged the question several times, whereby the interviewer was clearly concerned about the cardinality of the platonic realm (or level 4 multiverse in Max's terminology).
The mathematical multiverse contains only Gödel-complete structures, in fact all computable functions, and we know that there is a relation between complexity and decidability, all mathematical formulas more complex than d(E)=K(E)-lenght(E) are indecidable, where K stands for Kolmogorov complexity and E is a mathematical statement. There is a deep relation between formal systems and computability. His hypothesis makes sense and is probably true, reality has to be necessary in order to exist, math is the only answer I can imagine.
@@omega82718 It could be the world is indeed a multiverse where everything than can exist, exists. But that doesn't mean that the world is necessarily such a multiverse.
@@cube2fox Unless mathematics is a metaphysically necessary being. I don't see how a tautology could fails to exist, and math is just a bunch of tautologies.
@@omega82718 It's quite a jump from "all mathematical statements are necessarily true" to "all non-contradictory statements are necessarily true (in some sub-universe)".
That's precisely the problem. All axioms are subject to choice. A different axiom could've been chosen. For example A != A. Formally and computationally speaking, such a Mathematical universe can exist. Like so: repl.it/repls/EnchantingMindlessSource
Lol no it fucking isn’t. Please tell me where you’ve observed 21 dimensional shapes? What senses did you use when you ‘observed’ the power set of the set of real numbers? I’m sticking to very basic mathematical objects here.
@@massecl A definition can also be axiomatic. Can you attempt to disprove A=A without relying on that in your argument? That's what makes it axiomatic.
Thing about math being discovered is: we would first have to agree on an ontology of math to meaningfully discuss this question. Otherwise we can’t tell if math pre-exists or is created by us, because we didn’t even specify what existence means for math. The ontology of math has been highly controversial for centuries though.
i think mathematics is the language in which the physical approximations are described in, but mathematics itself is not an approximation as it can exists independently. Even if that means that it would be pointless without a physical world. But i guess everything would be pointless then.
That was not the question. The question was: Is Mathematics invented or discovered? How does your statement relate to this question in *any* way? Mathematics does not "depend" on physics.Mathematics is a world perfect and eternal. If you want to express a relationship between Mathematics and Physics, then it is our physical world that is a crude approximation to the perfection of the mathematical one.
“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” - Albert Einstein
In some cases yes, for example there are certain mathematical statements that are only true for a base 10 number system. Or structures that depend on a particular orthonormal base we choose in a vector space. Those statements that are true regardless of these arbitrary choices are truly fundamental.
What's the most important thing to understand is that there are 2 things we call mathematics. There is the mathematics with small m, our human invention which some of us hate for understandable reasons. The other kind of math, is Mathematics with capital M. Our human made mathematics was invented to help us understand the order and properties of Mathematics. Mathematics is just pure logical relationships which have to exist between certain matehamtical structures. They just exist. They're timeless. They have to, otherwise reality would contradict itself. Once you really understand "Mathematics", everything else will start making sense.
So this goes further than Platonism in asserting that not only do all mathematical objects exist, but nothing else does. All structures that exist mathematically also exist physically.
Anonymous - Lately, I’m kind of leaning towards mathematical structures being literally identical to physical structures-but maybe these structures are only “actualized” when they produce conscious observers (whatever “conscious observers” even are). Sounds kind of “woo”, but it feels like a reasonable possibility to me. The thing is, mathematical notation may be a human invention, but what is it actually describing? There really seems to be a deep significance to math. I think mathematical truth _is_ base reality. No. I don’t have a shred of empirical evidence to back this conjecture up... 🤷🏻♂️
@@BugRib Hi again. So after more thought, I think that perhaps the "unreasonable effectiveness" of mathematics is explained by a relation between the nature of consciousness (and thus its mathematical intuition) and the nature of physical reality (from which the conscious mind comes from).
Mathematical universe is such an underrated idea and hypothesis .so much umdeserved criticism. No one can disprove it and no one can prove its existence either.
When he said they discovered the five shapes but cannot discover NOR INVENT the sixth... that was compelling. Sounds so simple, even basic, in retrospect - but Ive listened to a lot of these without hearing such clarity. From there his identification of what exists vs doesnt exist platonically (spaces but not each number etc) needs a lot of working out.
I find Max Tegmark the most fascinating mathematician physicist in cosmology. He really is one of a kind. I admire him but also regard him as 'too much'. Not even I, a Mathematical Realist (commonly known as a Platonist) can call myself a super-Platonist like Max Tegmark. For him, every modal potentiality is actual, e.g. every possible (i.e. self-consistent) universe exists physically. He literally fuses mathematical reality with physical reality. All possibilities, in this precise sense of the word, are real, and actual. Real means that it’s possible to find a physical structure that matches it, and actual means that it’s not only possible but already existing. Thus, his multiverse is the set of all possible mathematical and physical realities. Not surprisingly, this is a tautological statement in itself, since, for Tegmark, possible = actual = real. Or, in his own words: “all structures that exist mathematically exist also physically". In summary, Max Tegmark is a genius, perhaps too intelligent to be restrained by mere common sense.
I think he's saying the opposite. That for every physical phenomenon there is a corresponding mathematical object. Which is a pretty much just that the world is intelligible, not super platonism.
@@blakemcalevey-scurr1454 I read the Mathematical Universe several times, and I think @jit1881 understands it correctly, that is why this is such a rare idea. The level 4 multiverse is actually the proposal that the existence of a mathematical structure that is complex enough to describe a dynamical system (not sure, which universe corresponds to just the integers with addition) is equivalent with the existence of that universe. For our universe this of course needs to be a very complex structure, for example a pseudo-Riemannian manifold Tegmark talks about in the video describes a curved spacetime, but with nothing in it, so definitely not our universe.
The way I explained it to the pupils I tutored was that relationships between parts of material reality pre exist mathematical expression . There is an internal logic to material reality and maths also has internal logic which is potentially capable of expressing possibly all material reality in mathematical form. Platonic Idealists would say the opposite ! As a keen follower of science and philosophy I know that at the extreme opposite ends of reality the subatomic and the infinity of the whole universe uncertainty prevails ! That is challenging for those that expect universal certainty and consistency ! But not for a dialectical materialist for whom all reality is in dynamic and contradictory movement ! But only very curious and in-dependant minded pupils think and ask questions that cross discipline boundaries ! Which I encourage them in, mostly by defying their expectation that I give them solutions rather then posing puzzles ! In school they get trained to mechanically perform to produce ‘correct’ answers ! That kills curiosity and limits meaningful thought. Computers calculate, minds should do far more !
Mathematics at it's core has nothing to do with our universe. To quote Roger Penrose loosely, the mathematical fact that there are infinitely many prime numbers holds forever and everywhere, even if there was only nowhere. It is entirely inadequate to refer to physics to give an answer to the question if mathematics is discovered or invented. The fact thatour universe is that seamlessly described by Mathematics - from the mathematical perspective - is a mere coincidence, and honestly has no meaning for Mathematics itself. Thus the fact that our uinverse contains uncertainties and flaws does not allow for any deductions about mathematics. The existence of the mathematical entities is absolute and not dependent of the existence of a universe or even a mind to think about.
As a platonic idealist I would think that mathematics help us to uncover a reality which is ultimately identical to the physical reality. Mathematics are a window into the fundamental structures of the universe. But we, as limited and sentient beings we will never be able to cross the divide between intellectual forms and matter.
I can see and sense Robert’s frustration with Max’s responses..Max explains what he’s been taught and has learned but has great difficulty explaining exactly why something is..Reminds me of the kid that knows math well and you ask him/her how they arrived to the right answer and they say “hell, I don’t know, I just know that when you apply such and such it just works out”...lol lol lol
The rules of math are invented. The ways the rules play out are discovered. It's the same with chess. The rules of chess were invented, but the strategies for winning were discovered.
@Adam Southworth I could say the rules of chess existed in some other realm before we invented them, but that doesn't change the fact that we invented them, unless these men are suggesting that we gained our rules of math from this other realm and didn't invent them?
@@everything777 We may have gotten the inspiration for mathematics from nature, but the idea of mathematics is a human invention. Counting, arithmetic, geometry and so forth may have started out as ways to represent nature, but much of the mathematics derived from those starting points have no representation in nature. They exist only hypothetically. It's safe to say that mathematics extends far past only nature and as far as we know, only a subset of nature follows mathematical law. There is no proof that all of nature follows mathematical law. We press on with math not because it will work, but because it has worked. It's the best we got right now.
@@momentary_ I don't think you've understood his answer very well or at least your answer differs from his. Also your original point is somewhat nonsensical. You say the rules are invented but how they play out is discovered, this seems incompatible. How the rules play out ARE the rules. What name you give them is irrelevant.
@@momentary_ That's a poor analogy that doesn't work well with mathematics. You've chosen an artificial human law which can be broken at any time as opposed to a law or rule in the mathematical sense which describes reality and cannot be broken. What he is saying is that in a certain mathematical structure for example vectors, addition is commutative. The property of being commutative is the rule, we could have called it any name we wanted but that property exists for that structure. Physical phenomena that are described by vectors follow that rule whether we know about it or not or what name we have for it. To go back to your analogy it would be like going to strange country where nobody drinks and discovering that prohibition was in effect there but people didn't even have the concept of breaking it.
As I understand him: In the mathemathical world the system of integers exists as system without further details, and when we understand that system we can, if we want or need for some reason, calculate/infer individual integers that are like signs/representations FOR US of a virtually/potentially implied relation within that system. In the physical world (or in any specific one of the multiple physical worlds) not all but some of these relations are/have become "real" as a kind of physical double of the counterrelation in the mathematical world. So in the physical world these specific realized integers have come to exist. - My question here is: What then is the difference between the mathematical and the physical world, what is the specific physical or actual about it? - In one interview Texmark seems to say, it is the being perceived or at least has some connection with its being perceived by a perceiver (that, as he sais there, could be an animal as well). I guess we won't get around reading his book.
No, I don't think he did. He sort of referred to the concept that the integers exist. I would describe it by saying "Oh, look at that!" That eureka moment means you've found a _thing_ . Then, five minutes later, you surprise everyone by saying, "Look! There's another one!" which means you've invented the concept of "two". That kind of implies that the concept of "the same as" is required to go from "one" to "two", and subsequently from "two" to "three". This is verging dangerously close to the idea of "the set of things which look like that." You can't count things unless you've chosen _which_ things you want to count.
@@rjd53 This explanation is not self consistent How much detail already exists and how much is "created" when for eg humans want to calculate Who decides and what is the level of detail ? Do real numbers exist already ? Rationals ? Irrationals ? Complex numbers ? Does zero exist?
@@abhir7823 In the meantime I have read his book "The Mathematical Universe". Now I know that what I've written in the comment above is wrong. What he means is: reality is not described by, reality IS the various mathematical structures. Different kinds of such structures exist, that is one of the reasons why different kinds of universes exist. Math'l structures do not consist of numbers at all, they consist of pure relations. Numbers do not exist. Numbers are just the way WE represent these relations for us. So, the relation pi exists, but not the number we come up with, when we calculate the relation as division. That the number cannot be calculated, even by best computers, is OUR problem, but not a real aspect of the universe itself. - By the way Stephen Wolfram would not regard this as just our problem, but he also thinks, that numbers are not necessary to do math.
Mel Gross he could just say what he said from 1:50 to 2:05 in so many words, the things we discovery about the physical world are same as we discover in mathematics. Which came first chicken or egg. Obviously the egg.
numbers are a tool for mapping an underlying mathematical structure. the structure has some characteristic symmetries. the structures are discovered. the tools are a mental construct.
Mathematics is neither invented by us nor discovered by us, strictly speaking. The only view that doesn’t generate paradoxes upon closer inspection is essentially a version of the Kantian one: mathematical concepts, along with space and time, are the forms of intuition and rationality; that is, they are the necessary conditions for a mind to have conscious experience. There is simply no way around the fact that not a single person can make any claims about the nature of reality abstracted from a conscious subject. There are no objective facts (and I’m using this term in a different and more contemporary way than Kant did) because all knowledge is subjective. When asked to give a description of a world in which there are no subjects, one cannot accomplish the task without smuggling in a subject, which is in fact not accomplishing the task at all. So mathematics is neither out there in the world independent of us or our minds because strictly speaking such a world doesn’t exist. Here’s where Hegel comes into play. He said “the real is rational and the rational is real”. He took Kant’s idealism and purified it of any mind-independent world. For Hegel, there is only the world of ideas, and these are what constitute reality. Really, the philosophical question of whether we invented or discovered mathematics comes from a failure of our language, as do most philosophical problems. Languages developed as means to navigate complex social hierarchies for the most part-not to solve philosophical problems. But I digress. For mathematics to have been invented by us would entail its non-existence prior to our inventing it, but since mathematics is one of the forms of knowledge and thus necessarily prior to any thinking, we could not have invented it. Also, for mathematics to have been discovered, we would have had to be completely ignorant to it prior to its discovery. However, once again, as it is the ground of our experience, we could not have been ignorant to it. We would have been using it already in order to discover it. In my view, the most precise way to answer this question faithfully is to say the scholastic discipline that we call mathematics represents a gradual refinement of our understanding of the forms that ground our experience. Even primitive people without formal learning have systems of counting that reach about five or so. Is this mathematics? Of course. Sequences are one of the foundations of mathematics. Numbers represent an aspect of our conscious experience because in order to have experiences there must be many distinguishable objects of experience. This applies to all mathematical concepts-even imaginary numbers, which are real in so far as they describe our experience of things such as electrical currents. So, to reiterate, mathematics is neither discovered nor invented. We simply experience the world through mathematics so it cannot be something we invent and it is not something external to us so we cannot discover it.
I'm getting the impression that we construct theories and we make sense to ourselves within the limits of these theories, but outside of them we are talking gibberish. Which is why no one can agree on very much at all.
@Lucas Fabisiak, this is where you're getting confused my friend: "For mathematics to have been invented by us would entail its non-existence prior to our inventing it, but since mathematics is one of the forms of knowledge and thus necessarily prior to any thinking, we could not have invented it". You are confusing mathematics with patterns which, do exist independent of our existence and subjective interpretation. Mathematics on the other hand is a highly abstract language, invented by men, which is meant to describe those patterns in nature and the objects around us, by abstracting them and creating mathematical object and relations as a meta information of the world.
spring You didn’t understand my comment. Try reading it again. Edit: And just to be clear, the reason I know you didn’t understand it is because you failed to address my argument. You simply beg the question by stating without any sort of reasoning that the patterns represented in mathematics are mind-independent and objective entities. Also, I addressed this distinction between mathematics as an abstract language and the form of intellect and experience. Maybe you didn’t read that far?
@@lucasfabisiak9586 I went through your poem. all of it. the idea you convey the most, is confusion. the answer is simple, math is an abstract language INVENTED by men, meant to describe, predict and communicate patterns in nature. Patterns are objective representations of the world, regardless of our presence. You are confusing mathematics with the patterns in the world which is meant to describe. The concept of language and communication is a very broad one, not fix, neither unique and it is intrinsic to a species and particular to the message. To summarize, once again, Math is Invented.
for those that are wondering about this, his ultimate argument is actually far beyond the ages-old argument of whether mathematics is real or just an impressionistic description of nature. his real proposal is that there isn't just a correspondence between a physical entity and its mathematical counterpart - they are one and the same. there is no physical structure we exist within, only a mathematical structure with sufficient complexity for it to evolve life with senses that can experience it. our whole perception of a distinction between "substance" and "concept" emerges from our senses. there isn't really anything distinct about the physical substance we perceive except that it exists outside us in a way that concepts don't. but that doesn't mean the universe itself isn't merely a smaller subset of that conceptual space. in a multiverse where every internally consistent mathematical/conceptual structure exists, its subsets will all perceive themselves as being all that there is, and everything else as being purely imaginary. more importantly, we can easily imagine creating a digital simulation, a world that we know to be purely mathematical, where we can create creatures that experience their math world the same way we perceive ours, i.e., as having substance and being qualitatively different from mere ideas or platonic objects. as you can see, this is quite similar to popular conjectures that we are living in a simulation rather than a "real" universe. where tegmark differs (and in my opinion excels beyond) these ideas is in the reason and the necessity of living in a mathematical structure. it's not that we could have lived in a real, "natural" universe, but just happen not to because intelligences create more simulations than "nature" creates real universes. it's that we fundamentally could not have existed in a substantial universe because there are no universes that are not purely mathematical structures. there aren't "real" universes that merely correspond to math... containing objects that merely behave according to mathematical laws. rather, the objects themselves are pure math. it's the relationships between those mathematical entities ("objects") in the structure and the consequent, emergent complexity that results in a world that can experience itself as something more "tangible" than a bunch of quanta flying around. such a universe does not require engineers to create it like neo's matrix did. it doesn't need a creator any more than the concept of a cube does... or indeed, the concepts of 2, 1, or zero. accepting this idea, you could suppose that there is no real gap between existence and nonexistence. in principle, intelligent beings could experience a mathematical universe without that universe existing the way we tend to think ours does. just like the concept of a cube doesn't cease to exist just because I stopped thinking about it. most physicists argue it's unfalsifiable. and I can't say I believe it since I just don't know. but I can tell you with absolute certainty that for me, it's the theory that comes closest to satisfying that fundamental, frustrating attempt to understand why anything exists at all, as opposed to nothing. theories that predict just one universe not only need to deal with fine-tuning challenges, they also need to somehow deal with the conundrum of existence itself. it's largely been relegated to philosophy, but there's no reason in principle physics/math should not be able to explain why existence (as we perceive it) itself exists. in most worldviews or physical frameworks, the concept of existence itself is incoherent. there really is no definition except in opposition to what *doesn't* exist. but just as we can't explain why the stuff in our experience does exist, nor can we explain why other stuff doesn't exist. it all seems completely arbitrary, unless you accept the idea that the whole concept of existence is fundamentally misguided. that nothing exists except those things which have to exist. and the only things which must exist in principle (i.e., must exist a priori, without needing further explanation) are the bare axioms of mathematics, of logic. the idea of quantity. even in a hypothetical scenario where truly, nothing exists, it seems that quantity would still exist to exactly the same degree and in exactly the same way as it exists in our universe. it would just be one big fat zero, but that still means zero exists. so it's not much of a leap to go from accepting that axioms must exist to accepting that all internally consistent mathematical structures of arbitrary size and complexity may exist. and there's nothing that proves that a purely mathematical, conceptual entity can't have intelligent life. if the relationships between bits in a computer system can produce what amounts to intelligence, then why not the relationships between quantities in a completely imaginary coordinate plane? if a completely imaginary coordinate plane (one that doesn't exist in any "physical" sense from the point of view outside of it) can, according to its own internal relationships, contain networks of quantities that aggregate, repel, exert influence on each other, and ultimately do all the things that matter and energy are known to do, why can't those quantities wind up organized in such a way that they experience consciousness? why do we act like being "physically real" is a prerequisite for life? everything that is believed to happen in our brain to result in thought could just as easily happen in a purely hypothetical model. it's all just relationships between tiny things, which are themselves relationships between tiny things, which are ultimately relationships between indivisible, dimensionless quantities like the color charge of a quark. so accepting that an entirely imaginary system could exist which is identical to our universe, does it not follow that our universe is in fact that imaginary system? what can we actually come up with that would distinguish our universe from an identical imaginary one? the only difference between the universe as we experience it, and an imaginary copy of it, is the simple fact that we experience it and we don't experience the imaginary copy. but since it's a copy of our universe, it necessarily contains identical copies of us. copies of us who are thinking exactly the same thing about our universe... supposing that we don't exist, because they don't experience our existence. in other words, the fact that we experience this universe and don't experience all the possible mathematical structures is not proof or even suggestion that they don't exist. because any mathematical structure with emergent intelligent life will perceive itself exactly the same way, as an exclusive existence. therefore, we have no way of knowing whether we're in a purely hypothetical universe. and the fact that we have no way of knowing it suggests that it must be hypothetical, because that was supposed to be the only distinction we could even THINK of. we can't think of anything else that separates our universe from an identical hypothetical copy of our universe. the list of differences is 1 item long: the fact that we experience this one. if every hypothetical universe experiences itself as fundamentally distinct from all the others, in terms of this abstract idea of "existence," then there really is no difference between the tangible and the intangible. it's all relative. any intangible intelligence will experience itself as tangible and experience everything outside its purview as intangible. if that distinction is entirely relative, then perhaps it's just as imaginary as the mathematical structures themselves.
again, this is obviously broadly considered unfalsifiable and more inside the realm of philosophy than science. I do agree that it's at least not falsifiable in a satisfying sense. max tegmark and others have claimed that it is falsfiable, and have made some steps toward executing their proposed tests. but the idea of falsification there is really just a statistical analysis. that's a whole other story in itself, basically assessing the likelihood of our world existing, given some variable constraints on which mathematical structures are legal or not. there's a lot more nuance to it though, and I don't want to butcher it. so if anyone is really curious about that, look into the Mathematical Universe Hypothesis (MUH) proposed by max tegmark. like I said before, I don't think the reality of this as a physical description of reality can be demonstrated to anyone's satisfaction any time soon. but the more I've thought about it, the more I find any other existing proposal for the origins of reality itself to seem totally incoherent. most theoretical physics, even at the grand scale, does not attempt an ultimate cause for existence. it might explain some physical constants, the relationships between things that seem fundamental like forces, e.g., in spontaneous symmetry breaking, or describe the very ancient, like the big bang. but it does absolutely nothing to explain why this stage upon which the universe plays out should exist in the first place. it might even someday explain why the laws of physics are as they are. but that still would not explain why laws of physics should exist at all. the only answer I've ever heard that truly makes sense (rather than locking up in infinite regress due to lack of a metaphysical cause, like the concept of god or the idea of an eternal universe with no beginning or end) is the mathematical universe hypothesis. of course there's still the question of why should math itself exist. but we can't imagine a reality where mathematical concepts do not exist in exactly the form we know them, e.g., we can't imagine a universe where the concept of the quantity of 1 doesn't exist, where you can't deduce from basic quantity that 2 plus 2 equals 4. yet you CAN imagine a reality where our physical, tangible universe doesn't exist. so it stands to reason that math/logic/whatever must exist in a way that our particular universe must not. as the only thing that MUST exist, perhaps the abstract/platonic is ALL that exists... and our idea of another category, the category of the "real," is simply an experience we have of the particular mathematical structure in which we exist. I've had a really hard time coming up with any other definition for the "real" that isn't predicated on experience and in opposition to those things that can't be experienced, i.e., holding a platonic solid. regarding hypothesized origins that circumvent these problems by positing the infinity of time, I have lots more to say but this is getting too long. I don't think time being a loop without a beginning solves things any more than time as a straight arrow does. either way you envision it, you can't describe something creating it, since creation as we know it is a causal relationship, so it requires time. I get the sense that people proposing a time loop think they're being really clever, but the argument "it has no beginning, therefore its existence doesn't need to be explained" could be applied just as easily to a straight arrow of time: "there was no 'time before' the arrow existed, therefore its existence doesn't need to be explained." for one, it presumes that our timeline is the only one. but even assuming it is the only one, this still doesn't explain why such a timeline exists. it makes sense for a purely conceptual universe to exist purely by its own force, since there IS no force. it exists for no reason in the same way a platonic solid exists for no reason. it is because it can't not be. but if you think there's some physical tangibility in our universe that isn't an illusion equally present in any arbitrary universe, you have to explain why it came about, if not how. saying time is eternal doesn't answer the question, it really just claims without evidence that the question itself can't be understood. why should a timeline exist at all, eternal or no, if not because it can't not exist? and if we accept that the universe exists because it must, we then need to explain why this one in particular. and when you push theoretical physicists in that direction, they often retreat to the anthropic principle. the idea that this isn't the only one, it's just the one we happen to be in. but that means they believe essentially the same thing max tegmark does. they just aren't ready to accept the premise that there is no such thing as a physical object, that is, an object that is something more than mathematical or conceptual. their worldview is basically the same as tegmark's except they're still attached to the idea of the universe as some kind of substance. even though they know from quantum mechanics that everything we think of as an object is almost certainly just a smattering of dimensionless wavefunctions. the EXPERIENCE of substance, this sensation we have that emerges from instinct, a sort of adaptation for interacting with the mathematical world around us, is extremely compelling. shedding it is probably similar to "overcoming" the need for food. coming to perceive a platonic sphere as just as real as a basketball is like trying to imagine an extra-dimensional object. we exist within this particular mathematical structure. our thought processes are completely built around it. we can't imagine life in 4 spatial dimensions because our brains are part of the 3-dimensional fabric of the mathematical structure. likewise, we can't imagine that fabric the way it is. we can't imagine a rock as just a conglomeration of quanta, as something akin to a matrix, because we ourselves are conglomerations of quanta.
Since we are living inside the mathematical structure, all we can do is describe what it is, to really know what it is, we would have to be the programmer.
amounts are values. values are a product of valuation, which is a reasoning process. patterns describe sets, and sets and their descriptions are products of the mind. KEvron
The word "discovered" implies "human" (the discoverer) The word "invented" implies "human" (the inventor). The human mind evolved within nature, and cannot be separated from it. If a system such as the brain evolved to accurately represent reality utilizing a specific type of language (math) then it is reasonable to state that to some degree mathematical language is natural.
When they say "Discovered" in this context, they mean (or should mean) that the mathematics already exists in the nature, we just identified it. So, yes, both verbs imply human activity, but that is not the issue. I would say that if nature behaves as if math is accurate, even when nobody is observing, then we "discovered" the math: we found something that existed. That seems to obviously be the case. The precise symbols, etc, of course are human inventions. But those symbols represent an underlying reality. (Edit: I just re-read the original post by Michael Cameron, and I agree with it more than I thought the first time. I think I was reading something into it that wasn’t there.)
We invent our myths and maths, and sometimes some of them, but by any means never all, find partitions of correspondence in reality. It's not a one-way road, it's a reciprocal circuit of creation/discovery moved by what is. Often, we do take our mental creations for the reality, as in those many forms of idealisms the history of philosophy is chock-full.
It doesn't say anywhere close to everything about the world. We are discovering parts of our own mind. That's most definitely negligible in the grand scheme of things.
Didn't understand much of it. Just restarting myself in this field after shitty school education. Hope to change some perspectives and try and learn something
Δωδεκα (dodeca) means twelve in Greek and Εικοσι (icosi) means twenty. Εδρα (hedra) means side (sort off). So the dodecahedron and icosaedron literally means the shape with 12 and 20 sides respectively. The name given by the Greeks was anything but random!
To answer this question, I think it helps to think of chess. Chess is a game that was invented by humans. Everything from there is discovered: all possible games, strategies, etc. Well, like chess, the foundations of mathematics were invented. We set the foundations, but all the theorems, proofs, etc were discovered thereafter.
Then how do you go about explaining the fact that the entirety of the universe is bound to the mathematical concepts invented by the human mind? That's what made the observation of the higgs boson particle so spectacular; it was proven mathematically to be in existence long before it was actually discovered. You would not be able to use math to predict with incredible accuracy such complex things about the universe if it was merely invented by the human mind.
jdm11060 mathematic models could very well just be good approximations for the physical world as opposed to the definitions of it. In that case they are just tools we have developed, and as the op pointed out we often start with a framework and then discover different manipulations within it
Thank you prof Max. Mathematics us not a single thing to decide whether it is invented or discovered. Prof's 8 mt lecture clarifies how to go about finding out what maths is already in nature and what we have invented.
Mathematics is the language by which we comprehend our reality. Or, by which the nature of our reality can be revealed. Sometimes we conceptualize the math first , and say it must be reality. sometimes we conceptualize the reality first, like Einstein’s thought experiments. Then That reality concept can be explored, maybe proven through mathematics. Math is the language of our universe. Good topic.
The mystery is whenever we look for the truth, we end up in mathematics. Reminds me of "word problems" in grade school -- the goal is always to reduce it to a mathematical statement, remove the obfuscatioins and get to the meat of the issue, and then solve. Now, that makes me think of the opposite -- suppose you took a word problem, and then added to the story, turning a two sentence word problem into a three paragraph story, adding all kinds of new, possibly irrelevant information -- wait -- that's policitics.
To help the interviewer see why "5" is not a mathematical structure but "the integers" is, the words words "set", "operations" and "axioms" would have been far more useful than the words "Pseudo-Riemannian manifold"...
This is the classic error of redefining something and thinking you've discovered something new. In this case they have refined what it is to exist. This definition is different from the way the word is used in everyday speech. And it leads to a contradiction. We usually say that given a thing that exists, we can think of it not existing. For example, we can think of an apple existing on a table and we can think of an apple not existing on a table. But can we think of a "two" (the abstract object in the Platonic realm) NOT existing? If a "two that does not exist" is meaningless, then this "two" is a tautology. It is just a concept. You can, of course, expand the idea of "existence" to say that concepts exist, but by doing so you are changing the meaning of the word. This will only cause arguments where none need to be when you start talking to people who use the usual meaning of the word. The question is what is the utility of this new definition? What does it help you explain that the usual definition does not. In this case, as in many cases, this only thing this redefinition does is blow your mind. But it is meaningful to talk about mathematics being discovered...in the sense that new chess strategies can be discovered. Does that mean we need to consider that chess moves "exist" in a sort of game realm? Whoa. I think I just blew my own mind.
People often discuss about existence of different things, but they rarely think about what existence is. If they look close enough, they will notice that existence is a construct of consciousness, which enabled grasping phenomena. Existence is not an inherent nature of things, it's a mode of perception.
@@NeoShaman But what is a perception. We perceive things in dreams and do not believe they exist - for logical reasons that determine what counts as existing. But does that logic "exist"?
Texmark sais that we discover the SYSTEMS. The details we infer from it might be just our conceptions, ways WE conceive of the systems. So, in analogy, what exists are the rules of the game. That makes sense, because they do not depend on you, you did not make them up, you have to understand and obey them, or you don't play the game. The concrete moves in a specific game exist as well, but in a different way, in another realm of existence. They do depend on you, your decicions, your action.
I get it. The author of physics and math is the same dude and the author of the bangs! Take out the author and it becomes a really interesting conversation, for me at least. Forgive me. I'm a literature major. But I'm often compelled to investigate all things related to the origin of mathematics. I simply don't have a vocation for it, so these videos help immensely. Y'all's comments are helpful as well.
It cannot be abstract if it has real world predictive, replicative structure. Look at the detection of the Higgs Boson particle, for example. It was mathematically shown to exist before it was ever observed or discovered. Why on earth would the entirety of the universe subject itself to the subjective abstracts of human mind? Rather, the universe is bound to certain rules and laws, the objective nature of math being a substructure of it. That's kind of the point being made in this video.
@@jdm11060 let us not confuse the nature of physics to mathematical tools . You can predict the arrival time of a moving matter according its speed and distance. The last sentence above is true not because of mathematics but because it abide by the law of physics. Don't get too hung up on the word "abstract". Cheers
@@Thinker14264 Differential Geometry explained Relativity decades before Einstein, Statistical Mechanics was before Quantum Mechanics...yet the former could easily explain the later. And this doesn't go into the appearances of the Golden Ratio, Fibonacci Sequence, etc...which were found in nature later than discovered in math. The physical world imitates math, rather than the other way around. If math was used to explain the physical world, then Euler's number would have been discovered after compounding interest...not before. The evidence points the other way.
I think the way we try to understand the things we use to make sense of things is created. But, we don’t necessarily create how we think. We just do. And math is the embodiment of thinking. It’s like looking in the mirror asking why your reflection shows every time. They do because you know it makes sense that they do. So I guess it’s more of the language of abstraction that you discover as universal since all people think.
the math discovered by other aliens could start with postulates different from ours and so the definition of what is considered a simple concept such as integers maybe something that is only apparent after complex derivations in their system. but the overall idea that they would be just exploring different parts of the same larger mathematical universe is completely valid and I agree with him
How do we really know that that overall idea is 'valid'? Isn't it more plausible that it has to do with explanatory power (cf. S. Weinberg)? So we do discover things, but we can so far only say that we are discovering things about our own way of describing things. That is to say, we are discovering "ourselves". I am not sure, but it seems to me to go a step too far to say that mathematics is the only 'valid' way of describing the world. Seems that we simply don't really know.
"It's very important to not conflate the language of mathematics, which we do invent, with the structures of mathematics, which we discover." In 10 seconds Max sums it up better than most every other person that answers this question. The languages of maths could take most any form that we choose, it's the relationships they describe that are truly fascinating.
@@surfinmuso37 I find it amazing that where ever one could travel in the universe maths would be a universal language. "They" will know about Pi of course, not in 3.142 terms but as a fraction of a circle and that could form the initial contact with any being.
Maxwell, in his equations, "discovered" radio-magnetic waves, before Hertz made his famous experiment. Mathematics somehow "sees" nature before we can.
Lots of the universe appears to be predictable to humans especially when we use the tools we’ve derived. Sometimes the universe can be codified and communicated between humans to create human value. Mathematics is a combination of tools we know work for us and seeking new tools we want to work for us.
Maths is form without content: all that matters is the relationship between its elements, not the actual elements themselves. Physics is form with content: not only do the elements of the model satisfy certain relations, but they also matter in their own right, and furthermore, they correspond by some consistent dictionary to elements of reality. The word that professor Tegmark is searching for is “model” : physicists use mathematics to model the physical world, and the success of the model depends on how closely its properties imitate the properties of the real world.
Mathematics is necessary to be able to do physics at all, how will you do physics if you don't first assume the existence of numbers (quantity and difference), mathematical truths such as 2+2=4 and the like, so it can't just be things that they do not exist; Tegmark is very smart and realizes how ridiculous the materialist paradigm is that mathematical entities are just a fiction even though I may not agree that all reality is just mathematical.
People discover things that the universe has always understood if we resist that that we devised to enslave and stick with that that the universe gave use and can’t be destroyed -love
surfinmuso no....the ratio of the circumference of a circle to its diameter will always be π. 2+2 will always equal 4. Those structures will always be true no matter what, and we discovered them. However the symbols and languages we use to describe them is invented.
To me the answer to the question is tritely obvious: mathematics is a reality awaiting discovery. What interests me more, though, is how it comes to pass that there is often more than one way to describe what is essentially the same mathematical reality. The most obvious example that springs to my mind is Newton's fluxions. Those fluxions, which provide a way of expressing the same notion as calculus, were cumbersome to work with. Coming from a different angle, though, Leibniz conceived of a language of mathematics that looks much more like modern calculus. Both geniuses saw the same essential problem (how to address change over time), but from two distinctly separate viewpoints. Reality, then, can be conceived in different, though yet compatible ways. Is this distinction merely semantic - a matter of nomenclature - or does it of itself reveal some further mystery about the nature of mathematics? That is to say, do mathematic truths cast out from them the shadow of perspectives of meaning, expressed in different, though arguably identical, ways? And are those shadows of meaning mathematical in nature? If not, what are they?
That which is, exists, whether we know of it and can describe it or not. Since Pythagoras, we have developing our knowledge of what is, and the language that we use to describe it is mathematics. Today we are a point whereby we discover things by observing the physical reality, but will not accept as reality unless we can describe it mathematically. It begs the question, which came first the chicken or the egg; the math or the universe?
a dumb agreement of a dumb statement. literally fuck all about the observed universe is simple. the fact that after some 200+ years of life even the brightest minds still remain utterly ignorant of fundamental principles of the universe stands testament to that.
But why does the physical world behave in a way such that it remains in lock step with our creation of symbols and expressions of quantity? What dictates this obvious symmetry that allows us the use of mathematics?
I don't have an answer for why or how it is, but reality seems very fractal to me. And so a description of something on one scale tends to have an analogy on another.
Because our universe appears to obey laws (recurring behavior). It would be hard to imagine a physical reality which contains stuff but has no repeated behavior, and even more difficult to imagine intelligence developing there.
jakejakeboom yes and thus this “recurring behavior” can be thought of as a fundamental fingerprint of the universe which can be mathematically quantified. But the question remains if there exists a substrate for what we may regard as fundamental or could our consciousness perception of the symmetry of the universe be a mirage? Where we have placed order and meaning onto that which is inherently devoid of such a truth.
We don't know how the physical world behaves. We only extract information that is pertinent to us, by projecting mathematical structures upon it. We have no mathematical formalism that describe the world in full details and in a consistent way. We must use patches that work for particular domains, according to the type of information we are interested in. The set of all these patches is not the description of a behaviour.
Nature prefers simplicity like a builder prefers simplicity. These things build themselves first and in an infinite universe are going to be most common.
Certainly if the magnetic field is real (and all quantum fields for that matter) then the gravitational field would be objectively real as well. The current trouble in physics is that we cannot characterize or describe the gravitational field using the same mathematical language that we describe quantum fields. Therein lies the challenge of quantizing gravity, which most physicists believe is a difficult but ultimately solvable problem. This would mean the gravitational field is as "real" as any other.
Math was created, built into the very creation. We are composed of it,part of it. When you discover this, you discover a part of yourself, who you are. So yes, in a sense math, which is part of YOU is a discovery.
Kind of fun when he talks on a metalevel that the other guy cant grasp. Because the argument aginst it would be like: - we set the rules and without them there would be nothing to discover. Tegmark is moore like: - there are infinit rule sets that could give you some kind of math, and sometimes we discover one simple form that we like.
Mathematics are human invention, just like a PC or an abacus (which in itself uses properties that we didn't invent, just learned to control), it's a tool we use to simplify things and predict, etc. The properties that Math and Physicists try to predict/understand are what we didn't invent.
I think the is finite and isnt infinity...i thin all the math structure is what is called the string landscape ..its 1 and 500 zers next to it...its huge but finite....
Max is, like, a really cool guy. My cat can count. She is a counting cat and sometimes I hold her accountable for how many mice she brings into the house.
Mathematics is its own world, totally disparate from our physical one. The fact that aspects of the physical world might be described in terms of Mathematics does not feed back to the Mathematical one. If we found our universe to be contradictory to Mathematics, Mathematics would still be the same. You cannot "bend" Mathematics to adapt to our world, you cannot influence the appearance of the Mathematical world - there is no way for creativity in Mathematics - everything is already fixed, all you can do is stumble upon.
@@w1darr Math isn't in it's own world. No floating triangles in extra-dimensional space. We didn't discover circles, but the fact we can invent circles and they seem to contain consistent properties, suggests they reflect something metaphysical beyond our physical world. But unlike delusional Neo-Platonist, we don't have direct access to truths.
I love that at the very end the interviewer has the giant cheesy smile saying “we are now far more confused than when we started” as I now have a lot more questions and wonder if the original question even makes total sense
The richest answers to a question ARE those which leave us with more questions than when we started.
An "open and shut" slam-dunk of an answer, leaving no ambiguity, might feel more satisfying at first, but ultimately the most dramatic effect it has had is to take the wonder you felt peering through an open door -- and slammed it shut.
How much more wondrous it would be to lead you to that door, and in the space beyond, find five MORE doors beckoning with mystery!
Indeed. A very Socratic statement, the more I know, the less I know. :)
Read the wikipedia page on 'Philosophy of mathematics'
@@ASLUHLUHC3 Thank you for that. I got mind fucked when the article kept using the phrase "mathematical entity".
Tegmark essentially answered the entire question in the first sentence. Mathematical language is an invention, a way of describing mathematical principles, confined to our known universe, which are "self-consistent" as Tegmark notes.
There are no mathematical principles confined to our universe. The physical world is not inherently mathematical even though we use mathematics to describe that world.
Jamaal Richardson Michael Beer Interesting and thx for the reply.. I find it rather amazing that our self proclaimed “intelligence” has literally been halted at a fork in the road.. A point wherein we are left with one unanswerable question... ..was mathematics discovered or invented? Surely in the quantum realm mathematics, physics, standard model and all theories dissolve.. Equations that are flawless in predicting the macro are rendered completely useless in the micro! Ironically, within such micro it seems scientific explanation is just as ridiculous as all religious explanations!
What do you mean "confined to our known universe"? Tegmark believes in a sort of multiverse, whereby all structures that exist mathematically also exist physically.
Yes, but later they both seemed to say that math was platonic "Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. Just as electrons and planets exist independently of us, so do numbers and sets" To me this implies that math is discovered and not invented since it was there all the time waiting to be discovered. I don't know though, this question seems like a very complicated one and I'm not making a strong stand either way.
@@BladeRunner-td8be You are right that's his pedantic point. He's the new Plato, the enlightened mathematician that will unveil the truth for us.
"For every single physical entity, that we can think of something we can touch or measure with a detector, there is corresponding mathematical entity there in the mathematical structure."
I very much enjoy reading books by Tegmark as a physicist. This question, however, in its deepest sense, is best answered by not talking so much about physics. As someone else here commented, Tegmark answers the question in the best way in his first sentences where he distinguishes between our mathematical language (which we invent) and mathematics as such (which we discover). After that, I think the interview loses track in the hunt for the sought answer and deeper understanding of it.
I concur
I 100% agree with this. The realization that physics was not "equations that nature gives us" but rather mathematical models that model what we discover in nature really shook me and led me to this video. It's exactly what science is mostly: just humans trying to model our information about the world in an organized way that works for us.
I've always enjoyed when Max says: "We physicists..." he loves saying that in all his interviews haha
More than Michio Kaku?
@@RunnerBrain lol
Numbers have emerged in our history as a simple tool for counting units around us. We could never imagine how many things these numbers would still show us.
The problem with insanely intelligent people is their ability to put their thoughts into a clear statement. The easiest answer to this question isn't explaining how math is real because of some multiverse theory but rather by giving an easily understood analogy. Say you have 1 marble in your left hand and 1 marble in your right hand. Now when you put both of those marbles in your right hand, you now have 2 marbles in your right hand. This proves math to be real. The word "two" is used to describe how many marbles (or whatever you're counting) you have. One + One = Two. So let's just say instead of the word "two" mathematicians decided the word should be "owt." So in this case One + One = Owt. So you can see that no matter how you describe how many marbles you have. You will always have a set answer that is manufactured by a predetermined set of laws in our universe. The language of math is invented. The laws of math are universal and discovered.
Arithmetic and mathematics are not the same thing!
@@unlockwithjsr , mathematics is the cognition, arithmetic is the calculation.
@@thomashooper9148dude... that is literally what we are saying... this is what I'm trying to explain. People are too focused on the vocabulary of a subject when in reality it can be explained much simpler without all the added nonsense. Arithmetic is like getting from point A to point B and math is a like car. Getting from point A to point B is the same distance no matter how you decide to get there but we invented a system to get us there faster and easier even though the distance stays the same. So we can keep inventing new ways to get to point B faster but the distance is always the same. THE DISTANCE IS UNIVERSAL, THE CAR IS HUMAN MADE.
GreenEarthers Business , then we do disagree. Take infinity as an example, this is clearly a man made concept. One that has no real bearing on reality. Yet a mathematical reality!
@@thomashooper9148 space is infinite. words invented to describe things that people see or measure doesn't discredit the concept? If I see a blue flower it doesn't matter if I call it indigo, sky blue, baby blue. The flower is blue. We invented the word blue to describe the color we see, just as we invented addition to describe how many things there are when you put things together. This + that = those. It's been this way since the dawn of time and it will continue to be this way until the end. Math is all around us but how we choose to perceive it and measure it is up to you
Max is a hero. Love his attitude and intelligence.
My fav archdolt😊
@@ligayabarlow5077 🤓
It must be a true struggle for somebody like MT to dumb this stuff down for the common man to try and grasp….that alone makes him a hero!
'Nature prefers simplicity....this is a deep mystery' My favourites are E=mC^2, Euler's Identity ad the beauty and complexity of a simple fractal.
To me, mathematics has always been a language used to describe the physical world and the intrinsic laws of nature. But all I have is first year college math to back that assertion.
We discover mathematical truths and invent our ways of understanding them.
I really like the attitude and passion Max has in his interviews as much as I enjoyed his first book. Nonetheless I have to say that in this interview he really dodged the question several times, whereby the interviewer was clearly concerned about the cardinality of the platonic realm (or level 4 multiverse in Max's terminology).
Why do you say he dodged the question?
The mathematical multiverse contains only Gödel-complete structures, in fact all computable functions, and we know that there is a relation between complexity and decidability, all mathematical formulas more complex than d(E)=K(E)-lenght(E) are indecidable, where K stands for Kolmogorov complexity and E is a mathematical statement.
There is a deep relation between formal systems and computability.
His hypothesis makes sense and is probably true, reality has to be necessary in order to exist, math is the only answer I can imagine.
@@omega82718 It could be the world is indeed a multiverse where everything than can exist, exists. But that doesn't mean that the world is necessarily such a multiverse.
@@cube2fox Unless mathematics is a metaphysically necessary being. I don't see how a tautology could fails to exist, and math is just a bunch of tautologies.
@@omega82718 It's quite a jump from "all mathematical statements are necessarily true" to "all non-contradictory statements are necessarily true (in some sub-universe)".
A=A is an axiom, and mathematics is a system of restating that in more complex ways in order to describe and leverage what we observe with our senses.
Action = Equal and opposite reaction.
That's precisely the problem. All axioms are subject to choice. A different axiom could've been chosen. For example A != A.
Formally and computationally speaking, such a Mathematical universe can exist. Like so: repl.it/repls/EnchantingMindlessSource
It is but a definition, not even an axiom.
Lol no it fucking isn’t. Please tell me where you’ve observed 21 dimensional shapes? What senses did you use when you ‘observed’ the power set of the set of real numbers? I’m sticking to very basic mathematical objects here.
@@massecl A definition can also be axiomatic. Can you attempt to disprove A=A without relying on that in your argument? That's what makes it axiomatic.
Thing about math being discovered is: we would first have to agree on an ontology of math to meaningfully discuss this question. Otherwise we can’t tell if math pre-exists or is created by us, because we didn’t even specify what existence means for math. The ontology of math has been highly controversial for centuries though.
The fact that the 20 or so so called universal“constants” are not in fact constant, the best our mathematics is is an approximation.
i think mathematics is the language in which the physical approximations are described in, but mathematics itself is not an approximation as it can exists independently. Even if that means that it would be pointless without a physical world. But i guess everything would be pointless then.
That was not the question.
The question was: Is Mathematics invented or discovered?
How does your statement relate to this question in *any* way?
Mathematics does not "depend" on physics.Mathematics is a world perfect and eternal.
If you want to express a relationship between Mathematics and Physics, then it is our physical world that is a crude approximation to the perfection of the mathematical one.
the hosts confused smile and nod at the end says it all
If a mathematician says: "The symmetry of mathematics is beautiful", I immediately have to think of observers bias - Still, I agree :-)
What a perfect idea, Jeff Goldblumb cosplaying Steve Jobs just WORKS FOR ME
“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” - Albert Einstein
I prefer the question: are the truth-conditions for mathematical statements dependant on our naming them as such?
That's a pretty interesting question
In some cases yes, for example there are certain mathematical statements that are only true for a base 10 number system. Or structures that depend on a particular orthonormal base we choose in a vector space. Those statements that are true regardless of these arbitrary choices are truly fundamental.
Don't over complicate mathematics> It is a system for human beings that helps them under their existence. It is nothing more.
This channel is for all mankind and will be viewed by people centuries to come!
What's the most important thing to understand is that there are 2 things we call mathematics. There is the mathematics with small m, our human invention which some of us hate for understandable reasons. The other kind of math, is Mathematics with capital M. Our human made mathematics was invented to help us understand the order and properties of Mathematics. Mathematics is just pure logical relationships which have to exist between certain matehamtical structures. They just exist. They're timeless. They have to, otherwise reality would contradict itself. Once you really understand "Mathematics", everything else will start making sense.
So this goes further than Platonism in asserting that not only do all mathematical objects exist, but nothing else does. All structures that exist mathematically also exist physically.
The physical is identical to the mathematical structure.
@@BugRib Personally, I wouldn't say that the universe is literally maths, but just that mathematics describes aspects of the universe
Anonymous - Lately, I’m kind of leaning towards mathematical structures being literally identical to physical structures-but maybe these structures are only “actualized” when they produce conscious observers (whatever “conscious observers” even are).
Sounds kind of “woo”, but it feels like a reasonable possibility to me.
The thing is, mathematical notation may be a human invention, but what is it actually describing? There really seems to be a deep significance to math. I think mathematical truth _is_ base reality.
No. I don’t have a shred of empirical evidence to back this conjecture up... 🤷🏻♂️
@@BugRib Hi again. So after more thought, I think that perhaps the "unreasonable effectiveness" of mathematics is explained by a relation between the nature of consciousness (and thus its mathematical intuition) and the nature of physical reality (from which the conscious mind comes from).
@@BugRib Hi again. So now a year later, I completely disagree with what I wrote above
Mathematical universe is such an underrated idea and hypothesis .so much umdeserved criticism.
No one can disprove it and no one can prove its existence either.
No one can prove the existence of your brain, either. Where do you get this shit?
I love Max...but everytime I see him, I hear in my head, "Say hey-low tu mah lit-tel freh!"
When he said they discovered the five shapes but cannot discover NOR INVENT the sixth... that was compelling. Sounds so simple, even basic, in retrospect - but Ive listened to a lot of these without hearing such clarity. From there his identification of what exists vs doesnt exist platonically (spaces but not each number etc) needs a lot of working out.
I find Max Tegmark the most fascinating mathematician physicist in cosmology. He really is one of a kind. I admire him but also regard him as 'too much'. Not even I, a Mathematical Realist (commonly known as a Platonist) can call myself a super-Platonist like Max Tegmark. For him, every modal potentiality is actual, e.g. every possible (i.e. self-consistent) universe exists physically. He literally fuses mathematical reality with physical reality. All possibilities, in this precise sense of the word, are real, and actual. Real means that it’s possible to find a physical structure that matches it, and actual means that it’s not only possible but already existing. Thus, his multiverse is the set of all possible mathematical and physical realities. Not surprisingly, this is a tautological statement in itself, since, for Tegmark, possible = actual = real. Or, in his own words: “all structures that exist mathematically exist also physically". In summary, Max Tegmark is a genius, perhaps too intelligent to be restrained by mere common sense.
I think he's saying the opposite. That for every physical phenomenon there is a corresponding mathematical object. Which is a pretty much just that the world is intelligible, not super platonism.
@@blakemcalevey-scurr1454 I read the Mathematical Universe several times, and I think @jit1881 understands it correctly, that is why this is such a rare idea. The level 4 multiverse is actually the proposal that the existence of a mathematical structure that is complex enough to describe a dynamical system (not sure, which universe corresponds to just the integers with addition) is equivalent with the existence of that universe. For our universe this of course needs to be a very complex structure, for example a pseudo-Riemannian manifold Tegmark talks about in the video describes a curved spacetime, but with nothing in it, so definitely not our universe.
There is NO platonic reality, there are just minds and language. Maths is just a special type of language to communicate ideas in an exact way.
The way I explained it to the pupils I tutored was that relationships between parts of material reality pre exist mathematical expression . There is an internal logic to material reality and maths also has internal logic which is potentially capable of expressing possibly all material reality in mathematical form. Platonic Idealists would say the opposite ! As a keen follower of science and philosophy I know that at the extreme opposite ends of reality the subatomic and the infinity of the whole universe uncertainty prevails ! That is challenging for those that expect universal certainty and consistency ! But not for a dialectical materialist for whom all reality is in dynamic and contradictory movement ! But only very curious and in-dependant minded pupils think and ask questions that cross discipline boundaries ! Which I encourage them in, mostly by defying their expectation that I give them solutions rather then posing puzzles ! In school they get trained to mechanically perform to produce ‘correct’ answers ! That kills curiosity and limits meaningful thought. Computers calculate, minds should do far more !
Mathematics at it's core has nothing to do with our universe.
To quote Roger Penrose loosely, the mathematical fact that there are infinitely many prime numbers holds forever and everywhere, even if there was only nowhere.
It is entirely inadequate to refer to physics to give an answer to the question if mathematics is discovered or invented.
The fact thatour universe is that seamlessly described by Mathematics - from the mathematical perspective - is a mere coincidence, and honestly has no meaning for Mathematics itself.
Thus the fact that our uinverse contains uncertainties and flaws does not allow for any deductions about mathematics.
The existence of the mathematical entities is absolute and not dependent of the existence of a universe or even a mind to think about.
As a platonic idealist I would think that mathematics help us to uncover a reality which is ultimately identical to the physical reality. Mathematics are a window into the fundamental structures of the universe. But we, as limited and sentient beings we will never be able to cross the divide between intellectual forms and matter.
There seemingly are strictures put on reality, which enable stuff to exist and we discover their limits.
Amazing..new sub👌
I can see and sense Robert’s frustration with Max’s responses..Max explains what he’s been taught and has learned but has great difficulty explaining exactly why something is..Reminds me of the kid that knows math well and you ask him/her how they arrived to the right answer and they say “hell, I don’t know, I just know that when you apply such and such it just works out”...lol lol lol
The rules of math are invented. The ways the rules play out are discovered. It's the same with chess. The rules of chess were invented, but the strategies for winning were discovered.
@Adam Southworth I could say the rules of chess existed in some other realm before we invented them, but that doesn't change the fact that we invented them, unless these men are suggesting that we gained our rules of math from this other realm and didn't invent them?
@@momentary_ that's exactly the point. Is math a construct of humans or a part of nature itself?
@@everything777 We may have gotten the inspiration for mathematics from nature, but the idea of mathematics is a human invention. Counting, arithmetic, geometry and so forth may have started out as ways to represent nature, but much of the mathematics derived from those starting points have no representation in nature. They exist only hypothetically. It's safe to say that mathematics extends far past only nature and as far as we know, only a subset of nature follows mathematical law. There is no proof that all of nature follows mathematical law. We press on with math not because it will work, but because it has worked. It's the best we got right now.
@@momentary_ I don't think you've understood his answer very well or at least your answer differs from his. Also your original point is somewhat nonsensical. You say the rules are invented but how they play out is discovered, this seems incompatible. How the rules play out ARE the rules. What name you give them is irrelevant.
@@momentary_ That's a poor analogy that doesn't work well with mathematics. You've chosen an artificial human law which can be broken at any time as opposed to a law or rule in the mathematical sense which describes reality and cannot be broken.
What he is saying is that in a certain mathematical structure for example vectors, addition is commutative. The property of being commutative is the rule, we could have called it any name we wanted but that property exists for that structure. Physical phenomena that are described by vectors follow that rule whether we know about it or not or what name we have for it.
To go back to your analogy it would be like going to strange country where nobody drinks and discovering that prohibition was in effect there but people didn't even have the concept of breaking it.
Max always looks intoxicated to me.
🤣🤣
Did he manage to answer the question on whether every individual integer exists in the mathematical world or the idea of integers exists?
As I understand him: In the mathemathical world the system of integers exists as system without further details, and when we understand that system we can, if we want or need for some reason, calculate/infer individual integers that are like signs/representations FOR US of a virtually/potentially implied relation within that system. In the physical world (or in any specific one of the multiple physical worlds) not all but some of these relations are/have become "real" as a kind of physical double of the counterrelation in the mathematical world. So in the physical world these specific realized integers have come to exist. - My question here is: What then is the difference between the mathematical and the physical world, what is the specific physical or actual about it? - In one interview Texmark seems to say, it is the being perceived or at least has some connection with its being perceived by a perceiver (that, as he sais there, could be an animal as well). I guess we won't get around reading his book.
No, I don't think he did. He sort of referred to the concept that the integers exist. I would describe it by saying "Oh, look at that!" That eureka moment means you've found a _thing_ . Then, five minutes later, you surprise everyone by saying, "Look! There's another one!" which means you've invented the concept of "two". That kind of implies that the concept of "the same as" is required to go from "one" to "two", and subsequently from "two" to "three". This is verging dangerously close to the idea of "the set of things which look like that." You can't count things unless you've chosen _which_ things you want to count.
He evaded the question
Could have just admitted that he hadn't thought about it
@@rjd53
This explanation is not self consistent
How much detail already exists
and how much is "created" when for eg humans want to calculate
Who decides and what is the level of detail ?
Do real numbers exist already ?
Rationals ? Irrationals ? Complex numbers ? Does zero exist?
@@abhir7823 In the meantime I have read his book "The Mathematical Universe". Now I know that what I've written in the comment above is wrong. What he means is: reality is not described by, reality IS the various mathematical structures. Different kinds of such structures exist, that is one of the reasons why different kinds of universes exist. Math'l structures do not consist of numbers at all, they consist of pure relations. Numbers do not exist. Numbers are just the way WE represent these relations for us. So, the relation pi exists, but not the number we come up with, when we calculate the relation as division. That the number cannot be calculated, even by best computers, is OUR problem, but not a real aspect of the universe itself. - By the way Stephen Wolfram would not regard this as just our problem, but he also thinks, that numbers are not necessary to do math.
2:24 what’s with the Beavis and Butthead impersonation?
Dark Matter i knew i heard that somewhere before lol
This is what your brain comes up with?
@@chrisw7347 Haha why not? Mike Judge is an engineer.
@@ungoyone Your answer being complete nonsense tells me that you're an AI
@@chrisw7347 Ha! Mike Judge is the creator and does voices for both B&BH. So AI that!
I think it’s a bit like Chess. The game itself is invented, but once you’re playing it every possible game that can be played is discovered.
Amazing!
Yes.
I was expecting some further explanation when it abruptly ended. I wasn’t watching it so I was surprised. I wasn’t satisfied at that point.
Mel Gross maybe set your expectations lower next time. Problem solved.
Mel Gross he could just say what he said from 1:50 to 2:05 in so many words, the things we discovery about the physical world are same as we discover in mathematics. Which came first chicken or egg. Obviously the egg.
Incredibly Interesting. Thank you.
numbers are a tool for mapping an underlying mathematical structure. the structure has some characteristic symmetries. the structures are discovered. the tools are a mental construct.
Mathematics is neither invented by us nor discovered by us, strictly speaking. The only view that doesn’t generate paradoxes upon closer inspection is essentially a version of the Kantian one: mathematical concepts, along with space and time, are the forms of intuition and rationality; that is, they are the necessary conditions for a mind to have conscious experience.
There is simply no way around the fact that not a single person can make any claims about the nature of reality abstracted from a conscious subject. There are no objective facts (and I’m using this term in a different and more contemporary way than Kant did) because all knowledge is subjective. When asked to give a description of a world in which there are no subjects, one cannot accomplish the task without smuggling in a subject, which is in fact not accomplishing the task at all. So mathematics is neither out there in the world independent of us or our minds because strictly speaking such a world doesn’t exist.
Here’s where Hegel comes into play. He said “the real is rational and the rational is real”. He took Kant’s idealism and purified it of any mind-independent world. For Hegel, there is only the world of ideas, and these are what constitute reality.
Really, the philosophical question of whether we invented or discovered mathematics comes from a failure of our language, as do most philosophical problems. Languages developed as means to navigate complex social hierarchies for the most part-not to solve philosophical problems. But I digress.
For mathematics to have been invented by us would entail its non-existence prior to our inventing it, but since mathematics is one of the forms of knowledge and thus necessarily prior to any thinking, we could not have invented it. Also, for mathematics to have been discovered, we would have had to be completely ignorant to it prior to its discovery. However, once again, as it is the ground of our experience, we could not have been ignorant to it. We would have been using it already in order to discover it.
In my view, the most precise way to answer this question faithfully is to say the scholastic discipline that we call mathematics represents a gradual refinement of our understanding of the forms that ground our experience. Even primitive people without formal learning have systems of counting that reach about five or so. Is this mathematics? Of course. Sequences are one of the foundations of mathematics. Numbers represent an aspect of our conscious experience because in order to have experiences there must be many distinguishable objects of experience. This applies to all mathematical concepts-even imaginary numbers, which are real in so far as they describe our experience of things such as electrical currents.
So, to reiterate, mathematics is neither discovered nor invented. We simply experience the world through mathematics so it cannot be something we invent and it is not something external to us so we cannot discover it.
I'm getting the impression that we construct theories and we make sense to ourselves within the limits of these theories, but outside of them we are talking gibberish. Which is why no one can agree on very much at all.
I still hate math.
@Lucas Fabisiak, this is where you're getting confused my friend: "For mathematics to have been invented by us would entail its non-existence prior to our inventing it, but since mathematics is one of the forms of knowledge and thus necessarily prior to any thinking, we could not have invented it".
You are confusing mathematics with patterns which, do exist independent of our existence and subjective interpretation. Mathematics on the other hand is a highly abstract language, invented by men, which is meant to describe those patterns in nature and the objects around us, by abstracting them and creating mathematical object and relations as a meta information of the world.
spring You didn’t understand my comment. Try reading it again.
Edit: And just to be clear, the reason I know you didn’t understand it is because you failed to address my argument. You simply beg the question by stating without any sort of reasoning that the patterns represented in mathematics are mind-independent and objective entities. Also, I addressed this distinction between mathematics as an abstract language and the form of intellect and experience. Maybe you didn’t read that far?
@@lucasfabisiak9586 I went through your poem. all of it. the idea you convey the most, is confusion. the answer is simple, math is an abstract language INVENTED by men, meant to describe, predict and communicate patterns in nature. Patterns are objective representations of the world, regardless of our presence.
You are confusing mathematics with the patterns in the world which is meant to describe.
The concept of language and communication is a very broad one, not fix, neither unique and it is intrinsic to a species and particular to the message.
To summarize, once again, Math is Invented.
for those that are wondering about this, his ultimate argument is actually far beyond the ages-old argument of whether mathematics is real or just an impressionistic description of nature. his real proposal is that there isn't just a correspondence between a physical entity and its mathematical counterpart - they are one and the same. there is no physical structure we exist within, only a mathematical structure with sufficient complexity for it to evolve life with senses that can experience it. our whole perception of a distinction between "substance" and "concept" emerges from our senses. there isn't really anything distinct about the physical substance we perceive except that it exists outside us in a way that concepts don't. but that doesn't mean the universe itself isn't merely a smaller subset of that conceptual space. in a multiverse where every internally consistent mathematical/conceptual structure exists, its subsets will all perceive themselves as being all that there is, and everything else as being purely imaginary.
more importantly, we can easily imagine creating a digital simulation, a world that we know to be purely mathematical, where we can create creatures that experience their math world the same way we perceive ours, i.e., as having substance and being qualitatively different from mere ideas or platonic objects. as you can see, this is quite similar to popular conjectures that we are living in a simulation rather than a "real" universe. where tegmark differs (and in my opinion excels beyond) these ideas is in the reason and the necessity of living in a mathematical structure. it's not that we could have lived in a real, "natural" universe, but just happen not to because intelligences create more simulations than "nature" creates real universes. it's that we fundamentally could not have existed in a substantial universe because there are no universes that are not purely mathematical structures. there aren't "real" universes that merely correspond to math... containing objects that merely behave according to mathematical laws.
rather, the objects themselves are pure math. it's the relationships between those mathematical entities ("objects") in the structure and the consequent, emergent complexity that results in a world that can experience itself as something more "tangible" than a bunch of quanta flying around. such a universe does not require engineers to create it like neo's matrix did. it doesn't need a creator any more than the concept of a cube does... or indeed, the concepts of 2, 1, or zero. accepting this idea, you could suppose that there is no real gap between existence and nonexistence. in principle, intelligent beings could experience a mathematical universe without that universe existing the way we tend to think ours does. just like the concept of a cube doesn't cease to exist just because I stopped thinking about it.
most physicists argue it's unfalsifiable. and I can't say I believe it since I just don't know. but I can tell you with absolute certainty that for me, it's the theory that comes closest to satisfying that fundamental, frustrating attempt to understand why anything exists at all, as opposed to nothing. theories that predict just one universe not only need to deal with fine-tuning challenges, they also need to somehow deal with the conundrum of existence itself. it's largely been relegated to philosophy, but there's no reason in principle physics/math should not be able to explain why existence (as we perceive it) itself exists. in most worldviews or physical frameworks, the concept of existence itself is incoherent. there really is no definition except in opposition to what *doesn't* exist. but just as we can't explain why the stuff in our experience does exist, nor can we explain why other stuff doesn't exist. it all seems completely arbitrary, unless you accept the idea that the whole concept of existence is fundamentally misguided. that nothing exists except those things which have to exist. and the only things which must exist in principle (i.e., must exist a priori, without needing further explanation) are the bare axioms of mathematics, of logic. the idea of quantity.
even in a hypothetical scenario where truly, nothing exists, it seems that quantity would still exist to exactly the same degree and in exactly the same way as it exists in our universe. it would just be one big fat zero, but that still means zero exists. so it's not much of a leap to go from accepting that axioms must exist to accepting that all internally consistent mathematical structures of arbitrary size and complexity may exist. and there's nothing that proves that a purely mathematical, conceptual entity can't have intelligent life. if the relationships between bits in a computer system can produce what amounts to intelligence, then why not the relationships between quantities in a completely imaginary coordinate plane? if a completely imaginary coordinate plane (one that doesn't exist in any "physical" sense from the point of view outside of it) can, according to its own internal relationships, contain networks of quantities that aggregate, repel, exert influence on each other, and ultimately do all the things that matter and energy are known to do, why can't those quantities wind up organized in such a way that they experience consciousness? why do we act like being "physically real" is a prerequisite for life?
everything that is believed to happen in our brain to result in thought could just as easily happen in a purely hypothetical model. it's all just relationships between tiny things, which are themselves relationships between tiny things, which are ultimately relationships between indivisible, dimensionless quantities like the color charge of a quark. so accepting that an entirely imaginary system could exist which is identical to our universe, does it not follow that our universe is in fact that imaginary system? what can we actually come up with that would distinguish our universe from an identical imaginary one? the only difference between the universe as we experience it, and an imaginary copy of it, is the simple fact that we experience it and we don't experience the imaginary copy. but since it's a copy of our universe, it necessarily contains identical copies of us. copies of us who are thinking exactly the same thing about our universe... supposing that we don't exist, because they don't experience our existence.
in other words, the fact that we experience this universe and don't experience all the possible mathematical structures is not proof or even suggestion that they don't exist. because any mathematical structure with emergent intelligent life will perceive itself exactly the same way, as an exclusive existence. therefore, we have no way of knowing whether we're in a purely hypothetical universe. and the fact that we have no way of knowing it suggests that it must be hypothetical, because that was supposed to be the only distinction we could even THINK of. we can't think of anything else that separates our universe from an identical hypothetical copy of our universe. the list of differences is 1 item long: the fact that we experience this one. if every hypothetical universe experiences itself as fundamentally distinct from all the others, in terms of this abstract idea of "existence," then there really is no difference between the tangible and the intangible. it's all relative. any intangible intelligence will experience itself as tangible and experience everything outside its purview as intangible. if that distinction is entirely relative, then perhaps it's just as imaginary as the mathematical structures themselves.
again, this is obviously broadly considered unfalsifiable and more inside the realm of philosophy than science. I do agree that it's at least not falsifiable in a satisfying sense. max tegmark and others have claimed that it is falsfiable, and have made some steps toward executing their proposed tests. but the idea of falsification there is really just a statistical analysis. that's a whole other story in itself, basically assessing the likelihood of our world existing, given some variable constraints on which mathematical structures are legal or not. there's a lot more nuance to it though, and I don't want to butcher it. so if anyone is really curious about that, look into the Mathematical Universe Hypothesis (MUH) proposed by max tegmark. like I said before, I don't think the reality of this as a physical description of reality can be demonstrated to anyone's satisfaction any time soon. but the more I've thought about it, the more I find any other existing proposal for the origins of reality itself to seem totally incoherent.
most theoretical physics, even at the grand scale, does not attempt an ultimate cause for existence. it might explain some physical constants, the relationships between things that seem fundamental like forces, e.g., in spontaneous symmetry breaking, or describe the very ancient, like the big bang. but it does absolutely nothing to explain why this stage upon which the universe plays out should exist in the first place. it might even someday explain why the laws of physics are as they are. but that still would not explain why laws of physics should exist at all. the only answer I've ever heard that truly makes sense (rather than locking up in infinite regress due to lack of a metaphysical cause, like the concept of god or the idea of an eternal universe with no beginning or end) is the mathematical universe hypothesis.
of course there's still the question of why should math itself exist. but we can't imagine a reality where mathematical concepts do not exist in exactly the form we know them, e.g., we can't imagine a universe where the concept of the quantity of 1 doesn't exist, where you can't deduce from basic quantity that 2 plus 2 equals 4. yet you CAN imagine a reality where our physical, tangible universe doesn't exist. so it stands to reason that math/logic/whatever must exist in a way that our particular universe must not. as the only thing that MUST exist, perhaps the abstract/platonic is ALL that exists... and our idea of another category, the category of the "real," is simply an experience we have of the particular mathematical structure in which we exist. I've had a really hard time coming up with any other definition for the "real" that isn't predicated on experience and in opposition to those things that can't be experienced, i.e., holding a platonic solid.
regarding hypothesized origins that circumvent these problems by positing the infinity of time, I have lots more to say but this is getting too long. I don't think time being a loop without a beginning solves things any more than time as a straight arrow does. either way you envision it, you can't describe something creating it, since creation as we know it is a causal relationship, so it requires time. I get the sense that people proposing a time loop think they're being really clever, but the argument "it has no beginning, therefore its existence doesn't need to be explained" could be applied just as easily to a straight arrow of time: "there was no 'time before' the arrow existed, therefore its existence doesn't need to be explained." for one, it presumes that our timeline is the only one. but even assuming it is the only one, this still doesn't explain why such a timeline exists. it makes sense for a purely conceptual universe to exist purely by its own force, since there IS no force. it exists for no reason in the same way a platonic solid exists for no reason. it is because it can't not be. but if you think there's some physical tangibility in our universe that isn't an illusion equally present in any arbitrary universe, you have to explain why it came about, if not how. saying time is eternal doesn't answer the question, it really just claims without evidence that the question itself can't be understood. why should a timeline exist at all, eternal or no, if not because it can't not exist? and if we accept that the universe exists because it must, we then need to explain why this one in particular.
and when you push theoretical physicists in that direction, they often retreat to the anthropic principle. the idea that this isn't the only one, it's just the one we happen to be in. but that means they believe essentially the same thing max tegmark does. they just aren't ready to accept the premise that there is no such thing as a physical object, that is, an object that is something more than mathematical or conceptual. their worldview is basically the same as tegmark's except they're still attached to the idea of the universe as some kind of substance. even though they know from quantum mechanics that everything we think of as an object is almost certainly just a smattering of dimensionless wavefunctions. the EXPERIENCE of substance, this sensation we have that emerges from instinct, a sort of adaptation for interacting with the mathematical world around us, is extremely compelling. shedding it is probably similar to "overcoming" the need for food. coming to perceive a platonic sphere as just as real as a basketball is like trying to imagine an extra-dimensional object. we exist within this particular mathematical structure. our thought processes are completely built around it. we can't imagine life in 4 spatial dimensions because our brains are part of the 3-dimensional fabric of the mathematical structure. likewise, we can't imagine that fabric the way it is. we can't imagine a rock as just a conglomeration of quanta, as something akin to a matrix, because we ourselves are conglomerations of quanta.
Since we are living inside the mathematical structure, all we can do is describe what it is, to really know what it is, we would have to be the programmer.
You are...you just forgot 😉
Amounts & shapes are discovered. Math is a language used to approximate perceived patterns.
amounts are values. values are a product of valuation, which is a reasoning process. patterns describe sets, and sets and their descriptions are products of the mind.
KEvron
The word "discovered" implies "human" (the discoverer) The word "invented" implies "human" (the inventor). The human mind evolved within nature, and cannot be separated from it. If a system such as the brain evolved to accurately represent reality utilizing a specific type of language (math) then it is reasonable to state that to some degree mathematical language is natural.
When they say "Discovered" in this context, they mean (or should mean) that the mathematics already exists in the nature, we just identified it. So, yes, both verbs imply human activity, but that is not the issue. I would say that if nature behaves as if math is accurate, even when nobody is observing, then we "discovered" the math: we found something that existed. That seems to obviously be the case. The precise symbols, etc, of course are human inventions. But those symbols represent an underlying reality.
(Edit: I just re-read the original post by Michael Cameron, and I agree with it more than I thought the first time. I think I was reading something into it that wasn’t there.)
because the physics were invented through evolution. so like finding a new planet it's a discovery
discovery produces new knowledge, thus it's inductive. invention draws on existing knowledge, thus it's deductive.
KEvron
Thank you for this. Maybe the best comment
Fascinating
We invent our myths and maths, and sometimes some of them, but by any means never all, find partitions of correspondence in reality. It's not a one-way road, it's a reciprocal circuit of creation/discovery moved by what is. Often, we do take our mental creations for the reality, as in those many forms of idealisms the history of philosophy is chock-full.
It doesn't say anywhere close to everything about the world. We are discovering parts of our own mind. That's most definitely negligible in the grand scheme of things.
Oh no. You've employed that moving cameraman again. I'm dizzy.
Pussy
It is a little distracting and unnecessary
Lol
How about you wait to hear the full answer to your last question before you ask the next?
I didn't know Bruce Dickenson knew that much about mathematics.
Didn't understand much of it. Just restarting myself in this field after shitty school education. Hope to change some perspectives and try and learn something
Δωδεκα (dodeca) means twelve in Greek and Εικοσι (icosi) means twenty. Εδρα (hedra) means side (sort off). So the dodecahedron and icosaedron literally means the shape with 12 and 20 sides respectively. The name given by the Greeks was anything but random!
It’s not about the name being random, the point is that the name is arbitrary. The form exists irrespective of the name.
@@JD-cf4or yeah, you are right. But i wanted to clarify that and share the info...
why does dodeca mean 12 in greek?
you dont have to answer (because you can't) In fact the word is arbitrary
I like the dodecahedron. It’s fun to say too. I ordered a Rubik’s cube dodecahedron but it hasn’t arrived yet. I better check on it. Thanks 🙏🏻
To answer this question, I think it helps to think of chess. Chess is a game that was invented by humans. Everything from there is discovered: all possible games, strategies, etc.
Well, like chess, the foundations of mathematics were invented. We set the foundations, but all the theorems, proofs, etc were discovered thereafter.
Then how do you go about explaining the fact that the entirety of the universe is bound to the mathematical concepts invented by the human mind? That's what made the observation of the higgs boson particle so spectacular; it was proven mathematically to be in existence long before it was actually discovered. You would not be able to use math to predict with incredible accuracy such complex things about the universe if it was merely invented by the human mind.
jdm11060 mathematic models could very well just be good approximations for the physical world as opposed to the definitions of it. In that case they are just tools we have developed, and as the op pointed out we often start with a framework and then discover different manipulations within it
Thank you prof Max. Mathematics us not a single thing to decide whether it is invented or discovered. Prof's 8 mt lecture clarifies how to go about finding out what maths is already in nature and what we have invented.
Mathematics is the language by which we comprehend our reality. Or, by which the nature of our reality can be revealed. Sometimes we conceptualize the math first , and say it must be reality. sometimes we conceptualize the reality first, like Einstein’s thought experiments. Then That reality concept can be explored, maybe proven through mathematics. Math is the language of our universe. Good topic.
👌👌👌👌👌
The mystery is whenever we look for the truth, we end up in mathematics. Reminds me of "word problems" in grade school -- the goal is always to reduce it to a mathematical statement, remove the obfuscatioins and get to the meat of the issue, and then solve. Now, that makes me think of the opposite -- suppose you took a word problem, and then added to the story, turning a two sentence word problem into a three paragraph story, adding all kinds of new, possibly irrelevant information -- wait -- that's policitics.
To help the interviewer see why "5" is not a mathematical structure but "the integers" is, the words words "set", "operations" and "axioms" would have been far more useful than the words "Pseudo-Riemannian manifold"...
Great analogies.
This is the classic error of redefining something and thinking you've discovered something new. In this case they have refined what it is to exist. This definition is different from the way the word is used in everyday speech. And it leads to a contradiction. We usually say that given a thing that exists, we can think of it not existing. For example, we can think of an apple existing on a table and we can think of an apple not existing on a table. But can we think of a "two" (the abstract object in the Platonic realm) NOT existing? If a "two that does not exist" is meaningless, then this "two" is a tautology. It is just a concept. You can, of course, expand the idea of "existence" to say that concepts exist, but by doing so you are changing the meaning of the word. This will only cause arguments where none need to be when you start talking to people who use the usual meaning of the word.
The question is what is the utility of this new definition? What does it help you explain that the usual definition does not. In this case, as in many cases, this only thing this redefinition does is blow your mind.
But it is meaningful to talk about mathematics being discovered...in the sense that new chess strategies can be discovered. Does that mean we need to consider that chess moves "exist" in a sort of game realm?
Whoa. I think I just blew my own mind.
Jimmye Winburn Yes ,they exist and wait to be discovered.
I should very much like to hear your evidence for the "existence" of math instead of a simple refutation of my argument. :)
People often discuss about existence of different things, but they rarely think about what existence is. If they look close enough, they will notice that existence is a construct of consciousness, which enabled grasping phenomena. Existence is not an inherent nature of things, it's a mode of perception.
@@NeoShaman But what is a perception. We perceive things in dreams and do not believe they exist - for logical reasons that determine what counts as existing. But does that logic "exist"?
Texmark sais that we discover the SYSTEMS. The details we infer from it might be just our conceptions, ways WE conceive of the systems. So, in analogy, what exists are the rules of the game. That makes sense, because they do not depend on you, you did not make them up, you have to understand and obey them, or you don't play the game. The concrete moves in a specific game exist as well, but in a different way, in another realm of existence. They do depend on you, your decicions, your action.
Language vs structure. Answered the question 🙋
Now THIS is the kinda shit I'm interested in
What a fascinating interview between Einstein and Rob Lowe.
I get it. The author of physics and math is the same dude and the author of the bangs! Take out the author and it becomes a really interesting conversation, for me at least. Forgive me. I'm a literature major. But I'm often compelled to investigate all things related to the origin of mathematics. I simply don't have a vocation for it, so these videos help immensely. Y'all's comments are helpful as well.
Language is a tool of communication.
Mathematics is an abstract tool use to make sense of the physical world.
Are the proportions of your face abstract?
It cannot be abstract if it has real world predictive, replicative structure. Look at the detection of the Higgs Boson particle, for example. It was mathematically shown to exist before it was ever observed or discovered. Why on earth would the entirety of the universe subject itself to the subjective abstracts of human mind? Rather, the universe is bound to certain rules and laws, the objective nature of math being a substructure of it. That's kind of the point being made in this video.
@@jdm11060 let us not confuse the nature of physics to mathematical tools . You can predict the arrival time of a moving matter according its speed and distance.
The last sentence above is true not because of mathematics but because it abide by the law of physics.
Don't get too hung up on the word "abstract".
Cheers
@@Thinker14264 Differential Geometry explained Relativity decades before Einstein, Statistical Mechanics was before Quantum Mechanics...yet the former could easily explain the later. And this doesn't go into the appearances of the Golden Ratio, Fibonacci Sequence, etc...which were found in nature later than discovered in math. The physical world imitates math, rather than the other way around.
If math was used to explain the physical world, then Euler's number would have been discovered after compounding interest...not before. The evidence points the other way.
I think the way we try to understand the things we use to make sense of things is created. But, we don’t necessarily create how we think. We just do. And math is the embodiment of thinking. It’s like looking in the mirror asking why your reflection shows every time. They do because you know it makes sense that they do. So I guess it’s more of the language of abstraction that you discover as universal since all people think.
The host looks like the crazy Mayor from Sim City (Super Nintendo)
Mark Anthony , you mean Mr. Wright? He kinda does.
And he was designed to look like Albert Einstein.
the math discovered by other aliens could start with postulates different from ours and so the definition of what is considered a simple concept such as integers maybe something that is only apparent after complex derivations in their system. but the overall idea that they would be just exploring different parts of the same larger mathematical universe is completely valid and I agree with him
How do we really know that that overall idea is 'valid'? Isn't it more plausible that it has to do with explanatory power (cf. S. Weinberg)? So we do discover things, but we can so far only say that we are discovering things about our own way of describing things. That is to say, we are discovering "ourselves". I am not sure, but it seems to me to go a step too far to say that mathematics is the only 'valid' way of describing the world. Seems that we simply don't really know.
He didn't answer the question asked twicely: is every number in the platonic space or "just algortithm".
Can the camera man stand still?
"It's very important to not conflate the language of mathematics, which we do invent, with the structures of mathematics, which we discover." In 10 seconds Max sums it up better than most every other person that answers this question. The languages of maths could take most any form that we choose, it's the relationships they describe that are truly fascinating.
Exactly, but an important point must be made-without the invented language of mathematics there would be no structures of mathematics .
@@surfinmuso37 I find it amazing that where ever one could travel in the universe maths would be a universal language. "They" will know about Pi of course, not in 3.142 terms but as a fraction of a circle and that could form the initial contact with any being.
Maxwell, in his equations, "discovered" radio-magnetic waves, before Hertz made his famous experiment. Mathematics somehow "sees" nature before we can.
You are talking bullshit.
@@OjoRojo40 Just because you don't understand does not imply that it is bullshit.
Lots of the universe appears to be predictable to humans especially when we use the tools we’ve derived. Sometimes the universe can be codified and communicated between humans to create human value. Mathematics is a combination of tools we know work for us and seeking new tools we want to work for us.
@@w1darr No, I totally understand it's impossible for math to see nature's future.
@@OjoRojo40 It's not its future but its fundamental structure.
02:24 to 02:30 : My reaction while listening to this with no clue what Tegmark is talking about
Go back to sleep
Maths is form without content: all that matters is the relationship between its elements, not the actual elements themselves. Physics is form with content: not only do the elements of the model satisfy certain relations, but they also matter in their own right, and furthermore, they correspond by some consistent dictionary to elements of reality. The word that professor Tegmark is searching for is “model” : physicists use mathematics to model the physical world, and the success of the model depends on how closely its properties imitate the properties of the real world.
Mathematics is necessary to be able to do physics at all, how will you do physics if you don't first assume the existence of numbers (quantity and difference), mathematical truths such as 2+2=4 and the like, so it can't just be things that they do not exist; Tegmark is very smart and realizes how ridiculous the materialist paradigm is that mathematical entities are just a fiction even though I may not agree that all reality is just mathematical.
You must have a very good dad, Max.
I didn't know that Michael J. Fox was a physicist, he should've built the time machine himself.
People discover things that the universe has always understood if we resist that that we devised to enslave and stick with that that the universe gave use and can’t be destroyed -love
Beautiful 👌
Not only he's smart
But he communicates his smartness thro a second language just like that
Maybe in higher dimention we could invent it, but best answer to this question ,
The Language of Mathematics is invented whereas the structures of mathematics are discovered.
No difference-both are created by us. Who else ascribed the "meaning" to those structures but us?
The Next question would be" Are natural laws invented or discovered?
surfinmuso no....the ratio of the circumference of a circle to its diameter will always be π. 2+2 will always equal 4. Those structures will always be true no matter what, and we discovered them. However the symbols and languages we use to describe them is invented.
simple guy discovered. The laws of physics are constant.
Which would mean that we created ourselves. To resolve this, neoplatonists postulated the necessity of a universal "intellect".
To me the answer to the question is tritely obvious: mathematics is a reality awaiting discovery. What interests me more, though, is how it comes to pass that there is often more than one way to describe what is essentially the same mathematical reality. The most obvious example that springs to my mind is Newton's fluxions. Those fluxions, which provide a way of expressing the same notion as calculus, were cumbersome to work with. Coming from a different angle, though, Leibniz conceived of a language of mathematics that looks much more like modern calculus. Both geniuses saw the same essential problem (how to address change over time), but from two distinctly separate viewpoints. Reality, then, can be conceived in different, though yet compatible ways. Is this distinction merely semantic - a matter of nomenclature - or does it of itself reveal some further mystery about the nature of mathematics? That is to say, do mathematic truths cast out from them the shadow of perspectives of meaning, expressed in different, though arguably identical, ways? And are those shadows of meaning mathematical in nature? If not, what are they?
Language but not the structure? I don't know I think the jury still out but I like this guy
That which is, exists, whether we know of it and can describe it or not. Since Pythagoras, we have developing our knowledge of what is, and the language that we use to describe it is mathematics. Today we are a point whereby we discover things by observing the physical reality, but will not accept as reality unless we can describe it mathematically. It begs the question, which came first the chicken or the egg; the math or the universe?
Amazing
"...nature prefers simplicity." very important concept.
a dumb agreement of a dumb statement. literally fuck all about the observed universe is simple. the fact that after some 200+ years of life even the brightest minds still remain utterly ignorant of fundamental principles of the universe stands testament to that.
This guy is my idol
Are you back to making new interview videos or is this a repeat of an older post?
Thank you Spot on, Doug:).
But why does the physical world behave in a way such that it remains in lock step with our creation of symbols and expressions of quantity? What dictates this obvious symmetry that allows us the use of mathematics?
I don't have an answer for why or how it is, but reality seems very fractal to me. And so a description of something on one scale tends to have an analogy on another.
Because our universe appears to obey laws (recurring behavior). It would be hard to imagine a physical reality which contains stuff but has no repeated behavior, and even more difficult to imagine intelligence developing there.
jakejakeboom yes and thus this “recurring behavior” can be thought of as a fundamental fingerprint of the universe which can be mathematically quantified. But the question remains if there exists a substrate for what we may regard as fundamental or could our consciousness perception of the symmetry of the universe be a mirage? Where we have placed order and meaning onto that which is inherently devoid of such a truth.
We don't know how the physical world behaves. We only extract information that is pertinent to us, by projecting mathematical structures upon it. We have no mathematical formalism that describe the world in full details and in a consistent way. We must use patches that work for particular domains, according to the type of information we are interested in. The set of all these patches is not the description of a behaviour.
Nature prefers simplicity like a builder prefers simplicity. These things build themselves first and in an infinite universe are going to be most common.
If the magnetoc field is objectively real, what about the Newtonian gravitational force? Is Newton's force of gravity part of external reality?
Certainly if the magnetic field is real (and all quantum fields for that matter) then the gravitational field would be objectively real as well. The current trouble in physics is that we cannot characterize or describe the gravitational field using the same mathematical language that we describe quantum fields. Therein lies the challenge of quantizing gravity, which most physicists believe is a difficult but ultimately solvable problem. This would mean the gravitational field is as "real" as any other.
Math was created, built into the very creation. We are composed of it,part of it. When you discover this, you discover a part of yourself, who you are. So yes, in a sense math, which is part of YOU is a discovery.
Kind of fun when he talks on a metalevel that the other guy cant grasp.
Because the argument aginst it would be like:
- we set the rules and without them there would be nothing to discover.
Tegmark is moore like:
- there are infinit rule sets that could give you some kind of math, and sometimes we discover one simple form that we like.
Mathematics are human invention, just like a PC or an abacus (which in itself uses properties that we didn't invent, just learned to control), it's a tool we use to simplify things and predict, etc. The properties that Math and Physicists try to predict/understand are what we didn't invent.
I love philosophy of math, and this guy is on point.
I think the is finite and isnt infinity...i thin all the math structure is what is called the string landscape ..its 1 and 500 zers next to it...its huge but finite....
I think discovery forces itself upon the observer to freeze into rules, what we confined our selves into it...to feel safe..
Max is, like, a really cool guy. My cat can count. She is a counting cat and sometimes I hold her accountable for how many mice she brings into the house.
It's both. First invented and soon after used to discover phenomenons in reality.
Mathematics is its own world, totally disparate from our physical one.
The fact that aspects of the physical world might be described in terms of Mathematics does not feed back to the Mathematical one.
If we found our universe to be contradictory to Mathematics, Mathematics would still be the same.
You cannot "bend" Mathematics to adapt to our world, you cannot influence the appearance of the Mathematical world - there is no way for creativity in Mathematics - everything is already fixed, all you can do is stumble upon.
@@w1darr Math isn't in it's own world. No floating triangles in extra-dimensional space. We didn't discover circles, but the fact we can invent circles and they seem to contain consistent properties, suggests they reflect something metaphysical beyond our physical world. But unlike delusional Neo-Platonist, we don't have direct access to truths.
Man creates the language of Mathmatics. The pronciples of Mathmatics exist inatue. Man discovers those principles and
Mathimatics discribes them.
"pronciples" ? In a field full of cows, do you experience Moothematics?