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!
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.
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."
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
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.
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
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 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.
Universe is nothing but a system of mathematics. Mathematics are nothing but calculations. Strangely, calculations are all in our mind. That tells something!!
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.
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.
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.
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.
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.
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.
Based on our perception of what works and what works usually reflects those things we think matter in this world, (how to get things done). However, the picture maybe very different from the picture we have constructed.
I disagree....this is a question about eternal form....if we are destroyed by a comet tomorrow, will other civilisations elsewhere in the universe also discover numbers? I think so, so that tends to indicate that they are eternal, pre-existing forms. Very significant implication for founding a rational ontology. It is like the universe is receiving information to build itself from.
@@bradmodd7856 "will other civilisations elsewhere in the universe also discover numbers?' More accurately, will other civilizations elsewhere in the universe invent a system of symbols, numbers, to represent what they have discovered about the universe?
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!
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.)
“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 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.
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.
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.
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.
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).
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
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.
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.
Math is discovered since it is simply the manipulation of truth, but the way we represent it was invented. It could certainly be expressed in completely different ways.
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.
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.
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.
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.
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.
@Jesus Silva you percieve the universe only through your brain architecture. Are you sure your perception models the universe itself? Consider this basic is example: You percieve colors as reality. You can create models where colors are arranged in a circle "color wheel". Like the RGB or CMYK models. Works fine, math is fine there. We build monitors, we print and paint walls using the color models. The model fits reality (nearly) perfectly. But wait...the light you see is just a slice of the electromagnetic spectrum, nothing circular there! Red doesn't fade into violet as in a color wheel. So you just built a circular model of the "straight" slice of reality. How is that possible? It turns out that colors are just function of your eye, your nervous system, not the outside reality. So what this shows: you can create a perfectly working formal model of reality that is solely based on your nerve architecture. It works perfectly for everyone, it is complete and consistent. And "false". We only know how that part of the nervous system works because we could examine the eye better than the working brain. But we have little clue how understanding and human intelligence works in the brain. It may well turn out that upon understanding our brain we will see that more basic models of reality (like math, or qm, whatever) are representing not the outside reality but our brain. Then we can correct for it and understand the universe better.
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.
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?
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.
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.
Simple and clear answer in this video: Mathematics is discovered, Mathematical simbols are invented. Why this question brings so many disputes? One reason I am think about - usually atheists will do anything to argue this is otherwise.
Nothing to do with atheism. Wittgenstein rejected the Platonic view of mathematics and argued that maths were invented and not real propositions because they’re non-referential. Wittgenstein was religious, not an atheist.
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.
Wasn't clear Max. Every physical things can be described with some kind of Mathematics? Ok, then what? What has this to do with Platonic objects or pre-existing Mathematics?
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)".
The structures are limited by the axioms. All statements logically consistent with the axioms is the totality of what he is describing. They may be infinite, but limited in the richness of their structure. Logical structures which are consistent within themselves but not with the axioms are not inside this set.
@Ready Now&Forever, @Daniel Baker Are you two stupid or very stupid!?!? My guess is that you are very fucking stupid. Tegmark answers the question during the fucking first two minutes of this video.
MrJamesLongstreet If he had answered the “question”, it wouldn’t have been repeated several times. You are obviously a stultified oafish. You sound like Donald Trump trying to articulate thermo & electro dynamics. And check your grammar/syntax. I doubt that your abject ignorance allowed you to even identify the “question”, you fucking benighted nincompoop.
The Pirahã language has no words for exact integer numbers, so... perhaps Kant was right-it might be the case that all maths and our laws of logic are just generalizations of the way we perceive the world around us which is only a representation of Noumenon.
Do you mean to say they are not thinking in units? Do they have a concept of the self, one man? If yes, that means that at least have a concept of "one". If not, they must have a truly science-fiction society!... But I doubt that.
@@dAvrilthebear It's not that simple. The notion of the singularity of a self is hard-wired in us by our culture and language. But that's not the only way one could look upon the world. We just can't imagine these other ways, but were we born in some other cultures, maybe we would have trouble trying to equal our self (if there were such a notion) with the integer one.
Do they go fishing? Do they catch fish? One can't catch half a fish, because for a fish to exist as a wriggly slippery shiny wet entity, it must be a whole fish. If they catch fish, surely they must distinguish "a fish" from "two fish" ?
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.
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
Seems like a pretty limited language, then, since it fails to describe most things. Basically all of morality and aesthetics, all abstract concepts are not captured by the mathematical language. They must first be presupposed. So I can use mathematics to describe the movement of a car along a road, but I have to already know what “car” and “road” and “velocity” are before I can apply mathematical functions to them. Mathematics doesn’t do that.
@@lucasfabisiak9586 maybe all stuff around us is giving a sign on what , how is all of it established. Maybe there is an equation yet so simple. Or maybe we understand through indirect of our biological functioning , chemistry and physics. They are all perceiving data in one way or the other given that maths has proved infinity by our invention to create a language of it since we still lack the knowledge to discover the possibilities it holds.
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.
The general theory of relativity was published by the physics genius more than a century ago, to refine Isaac Newton’s law of universal gravitation. Providing a unified description of gravity as a geometric property of space and time, or spacetime, this model is still currently used by scientists as an explanation of gravitation in modern physics. Einstein’s theory has important astrophysical implications as it alludes to the existence of black holes - cosmic phenomenons in which space and time are distorted in such a way that nothing, not even light, can escape. At the center of a black hole, as described by general relativity, may lie a gravitational singularity, a region where the spacetime curvature becomes infinite. But while mathematics says a singularity is possible, nature apparently proves these do not exist, Discovery Channel’s ‘How The Universe Works’ exposed. The series explained: “When a giant dying star collapses, the mass of the star falls in and keeps falling in crushing down into an infinitely small point. “This is called the singularity.” But physicist Max Tegmark believes the “singularity” is “just a fancy way of saying ‘we have no idea what is happening here’.” Astronomer Phil Plait explained why some experts have an issue with using this theory. He said: “The way our physics describes black holes when they form is you’re taking a finite amount of mass and you’re collapsing it down. “Its volume should shrink all the way down to zero, but that means it has infinite density and infinite gravity. “That doesn’t make sense.” Theoretical physics Lawrence Krauss then explained why some are questioning Einstein’s theory. He added: “If you make a prediction and the answer is infinite, then it tells you that there is something wrong with your prediction. “We have never seen infinity in the universe. “Maybe a black hole with an event horizon described by general relativity just isn’t the proper description of the physics.” Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. Leading astronomer and assistant director for Science Communication at NASA’s Goddard Space Flight Centre, Michelle Thaller, explained why it is key to the debate. She said in 2018: “Have you ever thought about the term quantum mechanics and what those terms actually mean? “Everything in the universe is broken up into tiny units and there is a basic unit of energy, time and space that cannot be divided any smaller. “There is a limit to how small those things can be.” The smallest unit in the universe is what is known as a Planck Length to physicists. But if there is a universal limit on the smallest size, then something infinitely small cannot exist, according to some scientists. Quantum mechanics expert Sean Carroll explained: “If infinity doesn’t exist, then singularities don’t exist. “And if singularities don’t exist, then Einstein’s theory of General Relativity is not correct. “The simplest thing we can do is change some equations, change his theory of gravity. “Let’s invent what we would call exotic speculative physics.” This has led scientists to invent the theory of the Planck Star. Passing one in space would look like a black hole, but without a point of singularity at its core. The star is just like a black hole, but it obeys the rules of quantum mechanics. Physicist Max Tegmark detailed the new theory that has been proposed. He said: “Maybe things can be collapsed down to less than the Planck Length, or maybe you get stuck with a Planck-sized nugget. “It stabilizes everything, keeps everything finite. “The reason why there are so many alternatives to black holes is because you can write down a gazillion different postulated mysterious new kinds of matter and say ‘this exists, so maybe that explains the data’. “The problem is there is no evidence that any of that kind of stuff exists.” After meteors enter Earth's atmosphere, blinding much of the planet's population in the process, plantlike creatures known as Triffids emerge from the craters and begin to take over. Military officer Bill Masen (Howard Keel), one of the few sighted people left alive, meets with other survivors in England and tries to find a safe haven from the vicious vegetation, as scientist Tom Goodwin (Kieron Moore) desperately seeks a way to defeat the leafy extraterrestrials...lol
Imagination - Process of Pure Creation The process of creation starts with thought - an idea, conception, visualization. Everything you see was once someone's idea. Nothing exists in your world that did not first exist as pure thought. This is true of the universe as well. Thought is the first level of creation. Next comes the word. Everything you say is a thought expressed. It is creative and sends forth creative energy into the universe. Words are more dynamic (thus, some might say more creative) than thought, because words are a different level of vibration from thought. They disrupt (change, alter, affect) the universe with greater impact. Words are the second level of creation. Next comes action. Actions are words moving. Words are thoughts expressed. Thoughts are ideas formed. Ideas are energies come together. Energies are forces released. Forces are elements existent. Elements are particles of God, portions of ALL, the stuff of everything. The beginning is God. The end is action. Action is God creating - or God experienced. Hang on. There's one thing more I have to tell you. You are always seeing what by your terms you would define as the "past," even when you are looking at what is right in front of you. I am? It is impossible to see The Present. The Present "happens," then turns into a burst of light, formed by energy dispersing, and that light reaches your receptors, your eyes, and it takes time for it to do that. All the while the light is reaching you, life is going on, moving forward. The next event is happening while the light from the last event is reaching you. The energy burst reaches your eyes, your receptors send that signal to your brain, which interprets the data and tells you what you are seeing. Yet that is not what is now in front of you at all. It is what you think you are seeing. That is, you are thinking about what you have seen, telling yourself what it is, and deciding what you are going to call it, while what is happening "now" is preceding your process, and awaiting it. To put this simply, I am always one step ahead of you. My God, this is unbelievable. Now listen. The more distance you place between your Self and the physical location of any event, the further into the "past" that event recedes. Place yourself a few light-years back, and what you are looking at happened very, very long ago, indeed. Yet it did not happen "long ago." It is merely physical distance which has created the illusion of "time," and allowed you to experience your Self as being both "here, now" all the while you are being "there, then"! One day you will see that what you call time and space are the same thing. Then you will see that everything is happening right here, right now. This is....this is....wild. I mean, I don't know what to make of all this. When you understand what I have told you, you will understand that nothing you see is real. You are seeing the image of what was once an event, yet even that image, that energy burst, is something you are interpreting. Your personal interpretation of that image is called your image-ination. And you can use your imagination to create anything. Because - and here is the greatest secret of all - your image-ination works both ways. Please? You not only interpret energy, you create it. Imagination is a function of your mind, which is one-third of your three-part being. In your mind you image something, and it begins to take physical form. The longer you image it (and the more OF you who image it), the more physical that form becomes, until the increasing energy you have given it literally bursts into light, flashing an image of itself into what you call your reality. You then "see" the image, and once again decide what it is. Thus, the cycle continues. This is what I have called The Process. This is what YOU ARE. You ARE this Process. This is what I have meant when I have said, you are both the Creator and the Created. I have now brought it all together for you. We are concluding this dialogue, and I have explained to you the mechanics of the universe, the secret of all life. Okay. Now as energy coalesced, it becomes, as I said, very concentrated. But the further one moves from the point of this concentration, the more dissipated the energy becomes. The "air becomes thinner." The aura fades. The energy never completely disappears, because it cannot. It is the stuff of which everything is made. It's All There Is. Yet it can become very, very thin, very subtle - almost "not there." Then, in another place (read that, another part of Itself) it can again coalesce, once more "clumping together" to form what you call matter, and what "looks like" a discreet unit. Now the two units appear separate from each other, and in truth there is no separation at all. This is, in very, very simple and elementary terms, the explanation behind the whole physical universe. Wow. But can it be true? How do I know I haven't just made this all up? Your scientists are already discovering that the building blocks of all of life are the same. They brought back rocks from the moon and found the same stuff they find in trees. They take apart a tree and find the same stuff they find in you. I tell you this: We are all the same stuff. (I and the Father are One Energy) We are the same energy, coalesced, compressed in different ways to create different forms and different matter. Nothing "matters" in and of itself. That is, nothing can become matter all by itself. Jesus said, "Without the Father, I am nothing." The Father of all is pure thought. This is the energy of life. This is what you have chosen to call Absolute Love. This is the God and the Goddess, the Alpha and the Omega, the Beginning and the End. It is the All-in-All, the Unmoved Mover, the Prime Source. It is that which you have sought to understand from the beginning of time. The Great Mystery, the Endless Enigma, the Eternal Truth. There is only One of Us, and so, it is THAT WHICH YOU ARE.
X-Files. Like turkeys and chickens become colorless over time...this is what happened with the alien beings who spliced DNA (shared ribs) with US. Metaphysical Hierarchy Mystic... beautiful dreaming Magical... harmony Musical... language of music Artistic... pictures/metaphors Poetic.. language of words Numerical...we are here Mystics create the most joy (smart). Accountants create the least joy (ignorant). Yet accountants rule the world (ignorant). Ever notice that beings who speak in the language of music can create joy that energizes thousands of beings to celebrate and dance? Ever notice that corpses who speak with brain numbing, soul sucking numbers do the exact opposite? Sanction, starve, torture, murder and bomb (wheeeee)! Ignorance (hate) is bliss for vampires (greed). But not much fun for the humans (love) who they are sucking the joy out of. Light and truth (love) cause vampires (greed) great pain and suffering. That's why the words society (socialism), "care for all" and "green new deal" cause the counting corpses that rule US such misery. Like bats that fly around in the darkness of caves... Vampires (greed) are "blind" and cannot "see" the ignorance of transforming heaven (peace) into hell (war). The capitalist counting corpses are also blind and cannot see the ignorance of transforming this paradise planet lifeboat into a polluted pig pen. The counting corpses can create stark, sterile, space stations floating in emptiness and futuristic bombers. But the vampires (greed) can't create harmony (real intelligence) because the counting corpses are ignorant (dead). The evangelical monsters are "desperate" to control a darkship called the Whitehouse. Because working in the dark to suck the joy out of life and devour earth is the only way that the loveless, lifeless parasites can survive and thrive. Unlike earthling poets, artists, musicians, mystics, human beings and creators of joy...the evangelical counting corpses that rule US can't create harmony (real intelligence) because vampires (greed) are ignorant (dead).
SQUIRRELS discovered that they can jump from post to post using observed distance quantities using brain computation. That is how they use math structures and not human-like math language. The information about distance goes in and the forces, and directions to direct their muscle-skeleton system are computed. Many disagree for a limited number of reasons, e.g. there are no squirrel schools. An implication is that organisms discovered math. A second example of an organism using math is the hook-beak raptor diving for a moving field mouse, calculations involving speed, distance and geometry allow it to intercept the mouse with its talons.
In. Vent. Ed Or dis the cover So much they do not know This is why they called them the describers Shortened to scribe Which comes from The word Scribble
If mathematics and physics (the sciences) were discovered and they were in some Platonic place, space, room, or balcony, where this balcony is located or spread over? Every mathematician and physicist MUST learn a bit philosophy in order to graduate in their major. Otherwise the answer BS to the questions of this character. Mathematics is our reflection on space and physics is the same on matter - nothing more. Humans struggled all the time to find right way to describe and predict the world that surrounds them. Look at the geometry of Euclid. If it existed objectively somewhere in a Platonic space, while Euclid, Pythagoras, Archeriids, and others discovered it, then what they discovered was taken some wrong closet/storage/space - the Euclidian geometry came to be not precisely true. Even it was not useful in our space endeavors.
Math neither invented nor discovered. It is given to us just before the end of Golden Period. 0-9 given liberation to human being from Abacus. Before the book Liber abbasi introduced means in the Roman numerals it's hard to calculate fastly.
Is all maths about quantification? From knowing one counting stick plus another = two counting sticks. From there onwards. He's not answering the question whether maths exists or is invented. He's floundering
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?
To us, it wouldn't matter if the universe were divine or magical. Indeed, we were happy believing so for millennia. But it so happens nature behaves mathematically, and can be described and predicted mathematically. Why that is so is the mystery. Either way I'm grateful it all makes us possible.
My take: it is both and it is neither. I say this because math object may have nothing to do with creation apart from creation itself. Is that good enough? Somethings were already created for us and math created somethings that have no known equivalent in reality. And this is somewhat dependent upon the state of knowing and understanding at that time. But who created math? Was it there awaiting discovery? Was creation calling out loud for calculus and rates of changes in variables to be learned, discovered and created but only Newton and Leibniz heard the call? Is it too bold for me to say I found this on google? Or should I say: look what google found for me? Or further still: look at this thing that universe made and brought the thing, google and myself into a state of awareness? Because before that moment of meeting we were not fully aware neither me, google nor the thing and what set of circumstances brought such events to manifest themselves into an existence?
Man, you should polish a little your questions. Ask them, for example, if there is such a thing as a continuous line, or if it is just a juxtaposition of infenitesimal points in space, very close together, but never quite. Ask them if there is real continuity in space or if everything is discreet.
Malé autíčko som videl dvakrát malé menšie opačne dva krát veľké to samé auto zhora dole cez deň dole v bane auto vyzeralo asi len 10 cm v škôlke autíčko vyzeralo vetšie než ja pri priblíženie sa z výšky dole v kruhu auto vyzeralo veľmi veľké do stavu kým sa ne vyrovnal obraz uhol pohľadu o ktorom som nevedel ale stále zostal autíčko ktoré som videl v škôlke vetšie než ja
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".
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.
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've always enjoyed when Max says: "We physicists..." he loves saying that in all his interviews haha
More than Michio Kaku?
@@RunnerBrain lol
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 always looks intoxicated to me.
🤣🤣
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.
I love Max...but everytime I see him, I hear in my head, "Say hey-low tu mah lit-tel freh!"
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 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.
Oh no. You've employed that moving cameraman again. I'm dizzy.
Pussy
It is a little distracting and unnecessary
Lol
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!
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 host looks like a bootleg Jeff Goldblum lmao
I think he looks like Sidney Freedman from MASH
If Goldblum and Einstein had a baby, this guy would be it
@@simongross3122 great pull 💯💯💯
If a mathematician says: "The symmetry of mathematics is beautiful", I immediately have to think of observers bias - Still, I agree :-)
We discover mathematical truths and invent our ways of understanding them.
the hosts confused smile and nod at the end says it all
Don't over complicate mathematics> It is a system for human beings that helps them under their existence. It is nothing more.
What a perfect idea, Jeff Goldblumb cosplaying Steve Jobs just WORKS FOR ME
Incredibly Interesting. Thank you.
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.
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.
Universe is nothing but a system of mathematics. Mathematics are nothing but calculations. Strangely, calculations are all in our mind. That tells something!!
There seemingly are strictures put on reality, which enable stuff to exist and we discover their limits.
Amazing..new sub👌
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".
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.
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.
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.
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.
Can the camera man stand still?
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.
A system of symbols and concepts invented to describe the structure and workings of the universe.
Based on our perception of what works and what works usually reflects those things we think matter in this world, (how to get things done). However, the picture maybe very different from the picture we have constructed.
I disagree....this is a question about eternal form....if we are destroyed by a comet tomorrow, will other civilisations elsewhere in the universe also discover numbers? I think so, so that tends to indicate that they are eternal, pre-existing forms. Very significant implication for founding a rational ontology. It is like the universe is receiving information to build itself from.
@@bradmodd7856 "will other civilisations elsewhere in the universe also discover numbers?' More accurately, will other civilizations elsewhere in the universe invent a system of symbols, numbers, to represent what they have discovered about the universe?
Right
@Language and Programming Channel Concepts aren't, but I'll grant symbols.
Math is god. God created man in his image. If we didn't know the world around us to a mathematical degree, then we would be animals living in a cave.
@Memento Mori it's like time and reference frames, it's all relative, and perspectives.
'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.
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 🙏🏻
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
“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
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.
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.
I didn't know that Michael J. Fox was a physicist, he should've built the time machine himself.
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.
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.
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.
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
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
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.
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.
I didn't know Bruce Dickenson knew that much about mathematics.
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.
Great analogies.
Math is discovered since it is simply the manipulation of truth, but the way we represent it was invented. It could certainly be expressed in completely different ways.
There are 27 words in your post, which is 19 more words than the one above yours at the moment. Did I manipulate truth by subtracting the two numbers?
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 😉
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.
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.
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.
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.
Discovered. The relations already exist.
Jobo so Excellent point. Mathematics is used to define and explain the relationships that already exist.
@@17ultralimited69 but maybe those relations exist only in the human brain.
@Jesus Silva you percieve the universe only through your brain architecture. Are you sure your perception models the universe itself?
Consider this basic is example:
You percieve colors as reality. You can create models where colors are arranged in a circle "color wheel". Like the RGB or CMYK models. Works fine, math is fine there. We build monitors, we print and paint walls using the color models. The model fits reality (nearly) perfectly.
But wait...the light you see is just a slice of the electromagnetic spectrum, nothing circular there! Red doesn't fade into violet as in a color wheel.
So you just built a circular model of the "straight" slice of reality. How is that possible? It turns out that colors are just function of your eye, your nervous system, not the outside reality.
So what this shows: you can create a perfectly working formal model of reality that is solely based on your nerve architecture. It works perfectly for everyone, it is complete and consistent. And "false".
We only know how that part of the nervous system works because we could examine the eye better than the working brain. But we have little clue how understanding and human intelligence works in the brain. It may well turn out that upon understanding our brain we will see that more basic models of reality (like math, or qm, whatever) are representing not the outside reality but our brain. Then we can correct for it and understand the universe better.
@Jesus Silva Yes, I think understanding our brain is the paramount question.
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.
Mathematics is discovered. Datums and reference points are invented.
Datums?
We can't discover math, we can only invent abstract representations of abstract objects.
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?
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.
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.
Simple and clear answer in this video: Mathematics is discovered, Mathematical simbols are invented.
Why this question brings so many disputes? One reason I am think about - usually atheists will do anything to argue this is otherwise.
Nothing to do with atheism. Wittgenstein rejected the Platonic view of mathematics and argued that maths were invented and not real propositions because they’re non-referential. Wittgenstein was religious, not an atheist.
Now THIS is the kinda shit I'm interested in
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.
👌👌👌👌👌
Wasn't clear Max. Every physical things can be described with some kind of Mathematics? Ok, then what? What has this to do with Platonic objects or pre-existing Mathematics?
map is not the territory
He keeps dancing around the elephant in the room: Why is there organization in a supposedly materialistic naturalistic reality at all?
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)".
The structures are limited by the axioms. All statements logically consistent with the axioms is the totality of what he is describing. They may be infinite, but limited in the richness of their structure. Logical structures which are consistent within themselves but not with the axioms are not inside this set.
He seemed to have never answered the question.
the whole video he never answered the question it was a waste
@Ready Now&Forever, @Daniel Baker
Are you two stupid or very stupid!?!? My guess is that you are very fucking stupid. Tegmark answers the question during the fucking first two minutes of this video.
MrJamesLongstreet If he had answered the “question”, it wouldn’t have been repeated several times. You are obviously a stultified oafish.
You sound like Donald Trump trying to articulate thermo & electro dynamics.
And check your grammar/syntax.
I doubt that your abject ignorance allowed you to even identify the “question”, you fucking benighted nincompoop.
The Pirahã language has no words for exact integer numbers, so... perhaps Kant was right-it might be the case that all maths and our laws of logic are just generalizations of the way we perceive the world around us which is only a representation of Noumenon.
Do you mean to say they are not thinking in units?
Do they have a concept of the self, one man?
If yes, that means that at least have a concept of "one".
If not, they must have a truly science-fiction society!... But I doubt that.
@Language and Programming Channel The bulk of what we know are claims we take for granted. Look for Numberless cultures.
@@dAvrilthebear It's not that simple. The notion of the singularity of a self is hard-wired in us by our culture and language. But that's not the only way one could look upon the world. We just can't imagine these other ways, but were we born in some other cultures, maybe we would have trouble trying to equal our self (if there were such a notion) with the integer one.
Do they go fishing? Do they catch fish? One can't catch half a fish, because for a fish to exist as a wriggly slippery shiny wet entity, it must be a whole fish. If they catch fish, surely they must distinguish "a fish" from "two fish" ?
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.
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 👌
I think mathematics is an invented sientific interpretation/language of what is.
Seems like a pretty limited language, then, since it fails to describe most things. Basically all of morality and aesthetics, all abstract concepts are not captured by the mathematical language. They must first be presupposed. So I can use mathematics to describe the movement of a car along a road, but I have to already know what “car” and “road” and “velocity” are before I can apply mathematical functions to them. Mathematics doesn’t do that.
@@lucasfabisiak9586 maybe all stuff around us is giving a sign on what , how is all of it established. Maybe there is an equation yet so simple. Or maybe we understand through indirect of our biological functioning , chemistry and physics. They are all perceiving data in one way or the other given that maths has proved infinity by our invention to create a language of it since we still lack the knowledge to discover the possibilities it holds.
Since humans are a manifestation of the universe the answer to the question would be: YES!
👁
How illogical is this question? Was the universe created or did humans impose consciousness upon it?
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.
Is a song an artistic creation or a discovery. The possibility of the melody has always existed.
The general theory of relativity was published by the physics genius more than a century ago, to refine Isaac Newton’s law of universal gravitation. Providing a unified description of gravity as a geometric property of space and time, or spacetime, this model is still currently used by scientists as an explanation of gravitation in modern physics.
Einstein’s theory has important astrophysical implications as it alludes to the existence of black holes - cosmic phenomenons in which space and time are distorted in such a way that nothing, not even light, can escape.
At the center of a black hole, as described by general relativity, may lie a gravitational singularity, a region where the spacetime curvature becomes infinite.
But while mathematics says a singularity is possible, nature apparently proves these do not exist, Discovery Channel’s ‘How The Universe Works’ exposed.
The series explained: “When a giant dying star collapses, the mass of the star falls in and keeps falling in crushing down into an infinitely small point.
“This is called the singularity.”
But physicist Max Tegmark believes the “singularity” is “just a fancy way of saying ‘we have no idea what is happening here’.”
Astronomer Phil Plait explained why some experts have an issue with using this theory.
He said: “The way our physics describes black holes when they form is you’re taking a finite amount of mass and you’re collapsing it down.
“Its volume should shrink all the way down to zero, but that means it has infinite density and infinite gravity.
“That doesn’t make sense.”
Theoretical physics Lawrence Krauss then explained why some are questioning Einstein’s theory.
He added: “If you make a prediction and the answer is infinite, then it tells you that there is something wrong with your prediction.
“We have never seen infinity in the universe.
“Maybe a black hole with an event horizon described by general relativity just isn’t the proper description of the physics.”
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles.
Leading astronomer and assistant director for Science Communication at NASA’s Goddard Space Flight Centre, Michelle Thaller, explained why it is key to the debate.
She said in 2018: “Have you ever thought about the term quantum mechanics and what those terms actually mean?
“Everything in the universe is broken up into tiny units and there is a basic unit of energy, time and space that cannot be divided any smaller.
“There is a limit to how small those things can be.”
The smallest unit in the universe is what is known as a Planck Length to physicists.
But if there is a universal limit on the smallest size, then something infinitely small cannot exist, according to some scientists.
Quantum mechanics expert Sean Carroll explained: “If infinity doesn’t exist, then singularities don’t exist.
“And if singularities don’t exist, then Einstein’s theory of General Relativity is not correct.
“The simplest thing we can do is change some equations, change his theory of gravity.
“Let’s invent what we would call exotic speculative physics.”
This has led scientists to invent the theory of the Planck Star.
Passing one in space would look like a black hole, but without a point of singularity at its core.
The star is just like a black hole, but it obeys the rules of quantum mechanics.
Physicist Max Tegmark detailed the new theory that has been proposed.
He said: “Maybe things can be collapsed down to less than the Planck Length, or maybe you get stuck with a Planck-sized nugget.
“It stabilizes everything, keeps everything finite.
“The reason why there are so many alternatives to black holes is because you can write down a gazillion different postulated mysterious new kinds of matter and say ‘this exists, so maybe that explains the data’.
“The problem is there is no evidence that any of that kind of stuff exists.”
After meteors enter Earth's atmosphere, blinding much of the planet's population in the process, plantlike creatures known as Triffids emerge from the craters and begin to take over. Military officer Bill Masen (Howard Keel), one of the few sighted people left alive, meets with other survivors in England and tries to find a safe haven from the vicious vegetation, as scientist Tom Goodwin (Kieron Moore) desperately seeks a way to defeat the leafy extraterrestrials...lol
Imagination - Process of Pure Creation
The process of creation starts with thought
- an idea, conception, visualization. Everything you see was once someone's idea. Nothing exists in your world that did not first exist as pure thought.
This is true of the universe as well.
Thought is the first level of creation.
Next comes the word. Everything you say is a thought expressed. It is creative and sends forth creative energy into the universe. Words are more dynamic (thus, some might say more creative) than thought, because words are a different level of vibration from thought. They disrupt (change, alter, affect) the universe with greater impact.
Words are the second level of creation.
Next comes action.
Actions are words moving. Words are thoughts expressed. Thoughts are ideas formed. Ideas are energies come together. Energies are forces released. Forces are elements existent. Elements are particles of God, portions of ALL, the stuff of everything.
The beginning is God. The end is action. Action is God creating - or God experienced.
Hang on. There's one thing more I have to tell you. You are always seeing what by your terms you would define as the "past," even when you are looking at what is right in front of you.
I am?
It is impossible to see The Present. The Present "happens," then turns into a burst of light, formed by energy dispersing, and that light reaches your receptors, your eyes, and it takes time for it to do that.
All the while the light is reaching you, life is going on, moving forward. The next event is happening while the light from the last event is reaching you.
The energy burst reaches your eyes, your receptors send that signal to your brain, which interprets the data and tells you what you are seeing. Yet that is not what is now in front of you at all. It is what you think you are seeing. That is, you are thinking about what you have seen, telling yourself what it is, and deciding what you are going to call it, while what is happening "now" is preceding your process, and awaiting it.
To put this simply, I am always one step ahead of you.
My God, this is unbelievable.
Now listen. The more distance you place between your Self and the physical location of any event, the further into the "past" that event recedes. Place yourself a few light-years back, and what you are looking at happened very, very long ago, indeed.
Yet it did not happen "long ago." It is merely physical distance which has created the illusion of "time," and allowed you to experience your Self as being both "here, now" all the while you are being "there, then"!
One day you will see that what you call time and space are the same thing.
Then you will see that everything is happening right here, right now.
This is....this is....wild. I mean, I don't know what to make of all this.
When you understand what I have told you, you will understand that nothing you see is real. You are seeing the image of what was once an event, yet even that image, that energy burst, is something you are interpreting. Your personal interpretation of that image is called your image-ination.
And you can use your imagination to create anything. Because - and here is the greatest secret of all - your image-ination works both ways.
Please?
You not only interpret energy, you create it. Imagination is a function of your mind, which is one-third of your three-part being. In your mind you image something, and it begins to take physical form. The longer you image it (and the more OF you who image it), the more physical that form becomes, until the increasing energy you have given it literally bursts into light, flashing an image of itself into what you call your reality.
You then "see" the image, and once again decide what it is. Thus, the cycle continues. This is what I have called The Process.
This is what YOU ARE. You ARE this Process.
This is what I have meant when I have said, you are both the Creator and the Created.
I have now brought it all together for you. We are concluding this dialogue, and I have explained to you the mechanics of the universe, the secret of all life.
Okay.
Now as energy coalesced, it becomes, as I said, very concentrated. But the further one moves from the point of this concentration, the more dissipated the energy becomes. The "air becomes thinner." The aura fades. The energy never completely disappears, because it cannot. It is the stuff of which everything is made. It's All There Is. Yet it can become very, very thin, very subtle - almost "not there."
Then, in another place (read that, another part of Itself) it can again coalesce, once more "clumping together" to form what you call matter, and what "looks like" a discreet unit. Now the two units appear separate from each other, and in truth there is no separation at all.
This is, in very, very simple and elementary terms, the explanation behind the whole physical universe.
Wow. But can it be true? How do I know I haven't just made this all up?
Your scientists are already discovering that the building blocks of all of life are the same.
They brought back rocks from the moon and found the same stuff they find in trees. They take apart a tree and find the same stuff they find in you.
I tell you this: We are all the same stuff. (I and the Father are One Energy)
We are the same energy, coalesced, compressed in different ways to create different forms and different matter.
Nothing "matters" in and of itself. That is, nothing can become matter all by itself. Jesus said, "Without the Father, I am nothing." The Father of all is pure thought. This is the energy of life. This is what you have chosen to call Absolute Love.
This is the God and the Goddess, the Alpha and the Omega, the Beginning and the End. It is the All-in-All, the Unmoved Mover, the Prime Source. It is that which you have sought to understand from the beginning of time. The Great Mystery, the Endless Enigma, the Eternal Truth.
There is only One of Us, and so, it is THAT WHICH YOU ARE.
02:24 to 02:30 : My reaction while listening to this with no clue what Tegmark is talking about
Go back to sleep
X-Files. Like turkeys and chickens become colorless over time...this is what happened with the alien beings who spliced DNA (shared ribs) with US.
Metaphysical Hierarchy
Mystic... beautiful dreaming
Magical... harmony
Musical... language of music
Artistic... pictures/metaphors
Poetic.. language of words
Numerical...we are here
Mystics create the most joy (smart). Accountants create the least joy (ignorant). Yet accountants rule the world (ignorant).
Ever notice that beings who speak in the language of music can create joy that energizes thousands of beings to celebrate and dance?
Ever notice that corpses who speak with brain numbing, soul sucking numbers do the exact opposite?
Sanction, starve, torture, murder and bomb (wheeeee)! Ignorance (hate) is bliss for vampires (greed). But not much fun for the humans (love) who they are sucking the joy out of.
Light and truth (love) cause vampires (greed) great pain and suffering. That's why the words society (socialism), "care for all" and "green new deal" cause the counting corpses that rule US such misery.
Like bats that fly around in the darkness of caves...
Vampires (greed) are "blind" and cannot "see" the ignorance of transforming heaven (peace) into hell (war).
The capitalist counting corpses are also blind and cannot see the ignorance of transforming this paradise planet lifeboat into a polluted pig pen.
The counting corpses can create stark, sterile, space stations floating in emptiness and futuristic bombers. But the vampires (greed) can't create harmony (real intelligence) because the counting corpses are ignorant (dead).
The evangelical monsters are "desperate" to control a darkship called the Whitehouse. Because working in the dark to suck the joy out of life and devour earth is the only way that the loveless, lifeless parasites can survive and thrive.
Unlike earthling poets, artists, musicians, mystics, human beings and creators of joy...the evangelical counting corpses that rule US can't create harmony (real intelligence) because vampires (greed) are ignorant (dead).
SQUIRRELS discovered that they can jump from post to post using observed distance quantities using brain computation. That is how they use math structures and not human-like math language. The information about distance goes in and the forces, and directions to direct their muscle-skeleton system are computed. Many disagree for a limited number of reasons, e.g. there are no squirrel schools. An implication is that organisms discovered math. A second example of an organism using math is the hook-beak raptor diving for a moving field mouse, calculations involving speed, distance and geometry allow it to intercept the mouse with its talons.
In. Vent. Ed Or dis the cover
So much they do not know
This is why they called them the describers
Shortened to scribe
Which comes from
The word
Scribble
If mathematics and physics (the sciences) were discovered and they were in some Platonic place, space, room, or balcony, where this balcony is located or spread over?
Every mathematician and physicist MUST learn a bit philosophy in order to graduate in their major. Otherwise the answer BS to the questions of this character.
Mathematics is our reflection on space and physics is the same on matter - nothing more. Humans struggled all the time to find right way to describe and predict the world that surrounds them.
Look at the geometry of Euclid. If it existed objectively somewhere in a Platonic space, while Euclid, Pythagoras, Archeriids, and others discovered it, then what they discovered was taken some wrong closet/storage/space - the Euclidian geometry came to be not precisely true. Even it was not useful in our space endeavors.
Were Beethoven's Sonatas invented or discovered ?
I discovered them. He invented them.
So the answer is "both".
Math neither invented nor discovered. It is given to us just before the end of Golden Period. 0-9 given liberation to human being from Abacus. Before the book Liber abbasi introduced means in the Roman numerals it's hard to calculate fastly.
Is all maths about quantification?
From knowing one counting stick plus another = two counting sticks. From there onwards.
He's not answering the question whether maths exists or is invented. He's floundering
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?
To us, it wouldn't matter if the universe were divine or magical.
Indeed, we were happy believing so for millennia.
But it so happens nature behaves mathematically, and can be described and predicted mathematically.
Why that is so is the mystery.
Either way I'm grateful it all makes us possible.
My take: it is both and it is neither.
I say this because math object may have nothing to do with creation apart from creation itself. Is that good enough?
Somethings were already created for us and math created somethings that have no known equivalent in reality. And this is somewhat dependent upon the state of knowing and understanding at that time.
But who created math? Was it there awaiting discovery? Was creation calling out loud for calculus and rates of changes in variables to be learned, discovered and created but only Newton and Leibniz heard the call?
Is it too bold for me to say I found this on google?
Or should I say: look what google found for me?
Or further still: look at this thing that universe made and brought the thing, google and myself into a state of awareness?
Because before that moment of meeting we were not fully aware neither me, google nor the thing and what set of circumstances brought such events to manifest themselves into an existence?
If you want to drive any one of these super intellectuals crazy... just keep responding with "but why?".
Fibonacci suite always existing, but it’s discovered by Fibonacci...🤔🤔🤔
How about you wait to hear the full answer to your last question before you ask the next?
He didn't answer the question asked twicely: is every number in the platonic space or "just algortithm".
Had humans evolved with paws or hooves, neither science, nor religion, nor mathematics would exist. Fingers made the difference.
Man, you should polish a little your questions. Ask them, for example, if there is such a thing as a continuous line, or if it is just a juxtaposition of infenitesimal points in space, very close together, but never quite. Ask them if there is real continuity in space or if everything is discreet.
Malé autíčko som videl dvakrát malé menšie opačne dva krát veľké to samé auto zhora dole cez deň dole v bane auto vyzeralo asi len 10 cm v škôlke autíčko vyzeralo vetšie než ja pri priblíženie sa z výšky dole v kruhu auto vyzeralo veľmi veľké do stavu kým sa ne vyrovnal obraz uhol pohľadu o ktorom som nevedel ale stále zostal autíčko ktoré som videl v škôlke vetšie než ja