93. Math: Discovered or Invented? | THUNK 

I believe that in the same way planting seeds implies the (future) existence of a tree, creating a set of axioms implies the existence of all mathematical statements following from those axioms. Therefore even if the axioms are a solely human construct, the statements are there wether or not we discover, prove or disprove them.

I just came across your videos. Love them. As an artist I have been amazed at how much math is involved in producing any visualization of the natural world - i.e. The golden mean (the most important 3)

To quote Alain Badiou, "mathematics is thus ultimately a rigorous aesthetics. It tells us nothing of real-being, but forges a fiction of intelligible consistency from the stand point of [the norm managing the fiction of separation in the transparent beauty of the simple relations in it constructs], whose rules are explicit.”

Dude your chanel is the best. You da real MVP. Keep it up!

Always excited to see a new video. Always disappointed that more people haven't discovered your channel. On topic: I do think these are unanswerable questions. Certainly, many 'truths' have been discovered by approaching problems with either perspective, so neither can be said to be invalid. I'd like to think that, on some level, math is both discovered and invented. Like wave-particle duality. Anyway, it's fun to think about. Thanks for making the video (and all your videos, for that matter)!

Really enjoyed the show, it seems to be a great synopsis of a variety of subjects, which someone could research themselves.

Josh, you'll want to check out the short story "Luminous" by Greg Egan. It's an exploration of a way math could be embedded into the fabric of the universe. -Josh

ITS SO BEAUTIFULL

Math is the language of the universe. How we comprehend math is through human conventions. Everyone is born with some natural talent for math expressed either purely in numbers or as art or music.

it was confusing my brain the whole time that you appeared more blurry than the background

Great video. Great shirt.

Just discovering this channel, great stuff

Great Great video

This is one topic where I simply retreat to Pyrrhonian skepticism, and say I don't know. I'm not even sure where to lean towards, and I suspend judgment whether a sufficient answer can ever be found.

The background color looks great , but you don't look as well lit next to the darker color. Great video and thanks for the links

that picture of the chalkboard killed me the sound just echoed in my brain. you should make a video why the brain can simulate sounds , smells , and all sorts of stuff .

My hunch is that the word 'mathematics' references many phenomena that are grouped together by habit rather than any "real" connections. If 'oneness' or 'twoness' are among the most obvious quantities we shouldn't be surprised that our pragmatic mammalian brains came up with a grunt for them early or quickly, likewise that commonness is their prevalence in our universe. The crucial foundational principles of our universe are likely to be common, therefore likely to be named. I guess I'll provisionally stand with the nominalists on this one.

I love this topic.

I find it interesting how words and even human thought can fundamentally be broken down into mathematical functions. Abstractly one can think of how everything is built up from the mathematics of atoms growing into more and more complex structural abstractions until human thought exists.I also read an article about how google translate works translating language into a vector that when applied to the vector space of a different language means roughly the same thing.

Maths are basically the language of logic and I think two questions are mistaken there : "Does logic exist independently of matter ? " and "Does matter follow the rules of logic ?" Because maths are self-referent, given the definitions of an addition and an equality, the proposition x+y = y+x would be true even if no universe existed, just like the rules of chess would leave the game unchanged even if the words bishop, queen or knight referred to no reality. You can demonstrate Pythagoras theorem to a alien living in a 1 dimensional universe if you manage to teach them the rules of 2D geometry, just like we can make calculations in n dimensions even though we can neither perceive nor conceive n dimensions objects when n>3. Logic exists independently of matter. If A implies B and B implies C, then A implies C no matter what. You can't escape it. It is inevitable. That is precisely why we write it with letters A,B and C ; because it works for everything. The implacable logic is self-contained in the definition of "implies" . Now, if you happen to live in a deterministic universe, where causes "imply" effects, then every deterministic particle will have to follow that logical principle. Matter can't escape logic. We know that maths are true even before they are discovered and formalised by human brains if we think about the next mathematical discovery. When we will understand it, the very fact that we will be able to demonstrate it proves that it is already true according to what we already know. Nothing can escape formal logic but that is not exactly a one-way street. Maths usually infer knowledge by deduction but, in some specific occasions, maths relies on empirical induction. Those are the axioms. But it is worth mentioning that our axioms relying on practical concepts like numbers and practical necessities like counting are what "our" human mathematics come from, but that that is arguably a very small part of all the maths there is to know. Our maths describe our reality when our axioms are chosen to fit our empirical observations. That is where the confusion between the two questions come from. Maths and logic are inescapable universal truths but science has to discover the axioms of nature by observing it. For example, is the universe deterministic. That is a question for empirical induction. But if so, then A implies C, because maths.

I subscribe to Max Tegmark's "Mathematical Universe Hypothesis" which is essentially one step stronger of a statement than platonism/realism and asserts that the universe _is_ math. Mathematical relationships between objects and the mathematical nature and qualities of objects is exhaustive; there is nothing else. I realize this seems radical, but the more I thought about it, the more it really jives with me. As a pre-requisite, he states that you need to accept that there is an real external universe we are observing (basically that solipsism is false, and a handful of other really hard to disprove positions), but if you do accept that, you can assert total mathocolypse and claim all of reality is Math, with a capitol M. I could write a whole lot more about this, but this is already long for a youtube comment. Thanks for doing this episode - this is a topic that is very important to me and my world view, and it was very well done as an introduction to these lines of thinking.

I have one question as a new philosophy major who just took a course in Critical Thinking and Informal Logic with a renewed fascination in symbolic reasoning, and was just amazed by this Banach-Tarski Paradox, How do I not suck at math!!?? Also keep up the good work.

It would seem Galileo was echoing what the Pythagoreans asserted centuries earlier.

Wouldn’t “invented” OR “discovered” potentially be a false dichotomy? Could there be a third option like “descriptive” ? What if we arbitrarily used a base-27 system. Would the elegant equations seem less elegant and physicists would be assuming that a complex and muddled equation was likely more correct?

We place so much interest on things like the 100th episode of a RU-vid channel when base 10 is completely arbitrary. It is, however, very interesting that math still works whatever base, or writing system we choose to use when doing it.

Question: What did you study in college? What are your favorite books/what books had the greatest impact on you?

Mathematics is the language humans have invented to describe the observed properties of the universe. Just as the underlying piece of fruit is not invented when we came up with the word "apple" for it, it is merely our language for describing what we observe to one another. Other species in the universe will have a different language for it, but it will be based on the same fundament.

Do you know how Gödel's theorem affected the philosophical debates in this area? It seems to me a multi-faceted question. We can make a formal system which happens to describe some aspect of the universe. In that manner of thinking, how many possible distinct theoretical formal systems can there be which describe a given phenomenon? If it is a countable amount, would this not have massive implications into the idea of "discovering" math? edit: related hypothetical (or not) question: Were the principles of, say, clockmaking discovered or invented?

You seem to be very knowledgeable about a great many things, especially those to do with philosophy. How did you get so smart? What did you learn in school and what did you learn on your own? How did you learn those things on your own?

I think it's a coincidence that math describes so much (infinite understatement), because I also think that there is a science that we have yet to discover in why math exists in the first place. Pure math only describes applications impractical to current life, but what describes....math? I'm not sure I'm getting my thought across the way I think it. If math exists, what explains singularities if they, too, exist?

Front page of Reddit and only 995 views? Not what my mathematical mental model would have predicted.

Axioms are the statements which we don't need to prove to be true. And using those axioms we prove theorems , later corollary and so on. So we could say that the basis of mathematics is dependent upon the first fundamental prior assumptions we make. We can understand this trough an example. What if, on a certain planet were aliens have developed on the same scale that humans are developed. So in that case, they too would require some sought of tool to progress and would they have started with the same axioms that humans have started with? Or something different. Is the basis to start the progress in writing the language to interpret the word is universal or it's just a product of human intellectual dimension. I think mathematics is discovered. This is because we can make an equation of any system and predict its further consequences. Recently, I made the equation of a mango leaf. Which explains mathematically why a mango leaf as particular shape, color, and characteristics. No matter if we are not been able to construct an equation of some complex system just because we have very interrelated small systems inside complex systems. Hence we never reach to an absolute answer. We need to SEPARATE the line which differentiates pure mathematics and abstract mathematics.

Enumeration is a consequence of categorization. Once you name things you can count them, if more exist. Our existence as observers is intrinsically connected to the existence of numbers. No math can exist without someone to describe it.

If people are really interested in "getting closer to the truth about this matter", I strongly suggest reading up on linguistics rather than math. Once you know more about how our brain evolved into conceptualizing and objectifying reality via abstract "words" and "patterns", it becomes a lot more intuitive to dissect this question.

Use a stand in, even just an object, while grabbing focus for the camera before shooting. This will prevent the soft focus on yourself throughout. :D

SUBJECTIVE OPINION: Ahem, As Idea Channel looses its way you seem to continue to get better. I know channel comparing is a bit fopaux, but i couldn't put it any other way. Thanks for the great content.

Question: Could you run us through all the stuff behind you on the THUNK letters?

I have found truth... I have seen the light...and it is.....the THUNK channel.....👍👍👍

To me is a problem of how we define mathematics... But if you say that mathematics is a kind of 'order' of the Universe (and our writings is just a poor way to look and express it) then i believe that mathematics is 'universal' in some sense... The problem is... For me this 'order' is infinitely complex... So we could never describe totally the 'multiverse'.

Math is an abstract generalization of the empirical (real) world. Nobody has ever seen a perfect circle. The sun and moon were real world inspirations for the concept of a circle. The "invention" of PI as a constant, is only possible because our generalization (circles) of what is physically real (sun and moon) carries certain consistencies. In other words, because we consistently define circles as being perfectly round, the constant of Pi can emerged. Circles and Pi are not part of some platonic truth that we don't have physical access to, but only part of an invented model of the universe around us. Mathematical abstractions are ultimately rooted in the empirical world, and the empirical activity of mixing elements together, and then imagining what happens in and between. Essentially what an artist does on canvas, mathematicians do in their mind, and instead of with paint, with numbers, lines, circles, and other abstract figures.

Often the physical laws end up being mathematically simple because they are based on underlying interactions that are simple. Gravity and electromagnetism fall off as 1/r^2 because they are mediated by emitted particles, and the density of such particles falls off at this rate in 3D space. Conic sections show up for the same reason. They are simple mathematical constructs that match simple underlying structures in reality. This isn't surprising.

Mathematics is merely the human ability by which we express our mental ability to discover, understand and correlate numbers in expressions of meaning (numbers being the building block of math) . . . just like we use sound to speak and letters to write language, or notes to express music. With us or without us, all these things exist by definition of the existence. I think!!!!! :/

If you want to read a science-fiction philosophical thriller inspired by this very topic, I recommend Neal Stephenson's Anathem.

I've always preferred the maths is hardwired into our brain as a way of seeing the world. Most animals don't seem to be able to count, even though their brains have a common evolutionary ancestor with ours. I doubt an alien would use maths, or a maths remotely similar to ours.

I think it is discovered. Something that follows certain patterns and rules is mathmatical by nature. And our universe can only exist and doesn't collapse because it does exactly that. Maybe there are dimensions where rules didn't exist, but they collapsed instantly. About that math problem... i still have my problems accepting that infinity is an actual logical operator to work with. To me it's an abstract concept that you cannot find anywhere in nature. But then again I'm not a scientist and also not a genius.

I see math as being where our mental capabilities overlap with some true aspect of reality. Our understanding of the universe is almost certainly limited by our cognitive capabilities; not unlike how our senses miss most of the information around us. Math is the best we can do, and I wonder to what degree it does overlap with reality; potentially very little, though enough to be evolutionarily advantageous. After all, Newton's laws were only decent approximations, supplanted by Einstein's better approximations. My guess is that our understanding of the universe is, by nature, unfathomably, and disappointingly limited. We can't experience the universe as anything other than human; math is no exception.

2:03 doesn't a theorem say finite amount?

Simulation theory confirmed!

To me it seems obviously invented. There's a lot of math that cannot be reasonably projected onto reality, so it's just a set of rules derived from other rules that humans are following when "doing math" (game analogies are pretty helpful here). I'd go further and say that the physical laws are also "invented" by humans, or at least an artificial distortion of "reality". That doesn't imply any sort of defect- but physical law is by it's very nature an incomplete slice of something big and entwined that we do not understand.

What IS the sound of one hand clapping?

math is an abstract invention which models/generalizes the physical world.

Mathematics is orderly and internally consistent and the universe is orderly and internally consistent. That is why math is a great tool for describing the universe. Mathematics is a human invention. If didn't work we would have stop using long ago, but it does work so we continue to use it and develop it.

still waiting for aliens to see what stuff they use

Now hold on one of those avocados was a bit bigger.. I think you were actually holding π avocados.

math is like the blanket of the universe and gravity and shit warps the blanket "space-time". or just a measure to show difference in more than one entity

The Tao that can be told is not the eternal Tao; The name that can be named is not the eternal name. The nameless is the beginning of heaven and earth.

It would be interesting if aliens use something else completely different that math to understand the universe

I think that the ceos of google learned this same thing when they found math to be useful.

This would be easier to watch if the host was in focus instead of the background behind him.

it's discovered in human's way. different kind has their own kind of discover way. a car looks like human invented, but human had to learn form nature to collect knowledge, without nature prove to human that human is right, human can not invent anything, so human discover and use what human discover, similar to eat, digest, absorb and produce, but by brain not stomach. maths is a by-product from nature, like thought/mind is the by-product of human.

Invention is just the discovery of an entity in idea-space. Discovered vs. invented is one amongst many seemingly deep questions that become trivial when you ask: "What do these words really mean".

I think humans invented mathematics right along with God. However, physical reality is discreet and countable. This is related to mathematics.

I am, and always have been, a humanities guy. BUT, I believe that the essence of the universe is mathmatical, not invented by men. God is, was, and will eternally be a Stud mathmetician.

meh good non pretentious commentary... although you should have tried a bit more to make it not look like you are just reading a text from a wiki