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)!
I'm glad you've enjoyed it, & that's an interesting idea! Don't worry about the sub count - so long as everyone who's watching enjoys the material, I'm content. :)
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.
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
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.
"mathematical relationships between objects..." I'm not familiar with Max Tegmark. I'm curious about how, if the universe is math, there can be objects at all? It sounds like there are two things: objects and relationships between objects, substance and fields... ?
There's a very interesting way to get around this objection, with Structuralism and the philosophy Whitehead brings to the table. Whitehead posits that everything is "process"in his idea of process philosophy. Substance is transient, since all things decay and change form, so that nothing is static. All that remains is temporary, fleeting relationships between other objects. So although is seems like there is a "star" that interacts with planets through gravity, its atomic components are only in "star" from for a couple of billions of years before they decay and become something else. During its "star" phase, it is defined as a star by how it effects other, transient forms of substances, which are too undergoing constant change. Even the atoms that compose the star are composed of quarks which are only in their atomic configuration for an undisclosed (but finite) amount of time before they decay and become component to some other form of "substance". At this point its turtles all the way down, and nothing is untouched by this idea of process. Note that, combined with Tegmark's Mathematical Universe Hypothesis, I use the term "object" to reference "mathematical construct" just for convenience, since everything is a mathematical object in this view. As another, parallel way to get around the problem of substance, structuralism offers a very interesting way to define/differentiate things. Have you ever thought about what the definition of, say, "4" is? One way to do it is sort of an infinite recursion, and say that "4 is the number that is not the number 5, 6, 1, 0, pi..." and have an infinite list of things that it is not. The elements of the list pinpoints it as a particular, unique object. If you extend this idea to "real objects" (not just numbers), you both define and instantiate real objects by virtue of what they are not. This has the advantage of also addressing the fact that objects interact with each other in fields; interaction between things brings about uniqueness, and thus, existence (for what does it mean to exist except to be unique from other existing things?) ... LIke I said earlier, I could write a lot about this.
"Mathocolypse" is now the name of my Tool cover band. Max sounds like he'd fit in marvelously with the Pythagoreans. I actually find myself liking the opposite end of the spectrum (via Quine & Wittgenstein) that math itself (along with logic) is ultimately empirical, despite appearances to the contrary. But I wouldn't put my chips down any such notion - who could possibly know to any degree of certainty? :)
PriusOmega Why is it easier or more desirable when asked, "what's in the foreground of this picture?" to reply, "I won't tell you what is the foreground, but I'll list everything in the background and what's not in the background will be the foreground." It seems it would be much more straightforward to say, "It's a picture of my wife's car..." Change occurs over time. It can't occur without time. (That was one of the original objections to differential calculus: how can we speak of the 'instantaneous' rate of change, the amount of change over zero time? to which Jean Le Rond D'Alembert advised students "Continue. Eventually, faith will come.") As long as you're happy to have time and change in your universe the fact that substance is impermanent doesn't alone negate the idea that there is, or was, or will be substance. There are other reasons, of course, why things might not be substance. William Everdell in The First Moderns wrote of the ancient and very modern problem of the continuous and the discrete. There are logical problems with the idea that numbers or anything else in the world is infinitely continuous; but there are equally logical problems with the idea that anything can be reduced to its final indivisible essence... The number four may not have a definition. Perhaps we do not define it, we recognize it. Animals have been shown to count, yet being non-verbal, it's highly unlikely that your dog has a definition of four, for instance...
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.”
Go with manual focus, using a piece of masking tape to mark where you need to stand. Fix the colour correction in editing by getting a 50% grey card or a white card that you show at the start of any recording. Try and edit the 'levels' of the video so that white is pure white as well, you want parts of your coat to be *almost* blown out white. Edit: If you can, ramp up the lighting *a lot* and then use a big f number like 8 or 11, which closes down the aperture, and increases the depth of field so it's less picky.
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.
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 like this thought a lot; so because of their primal, pervasive nature, we would name the principles easily and just call it math without it actually being what we understand as math? Hm. I don't know how to get around this, but it seems like an admission of defeat without even really trying; why bother attempting to explain the workings of the universe? Anything we come up with would just be false names and labels. Any truth would forever be out of reach. I suppose that is a stance some people take, but it just feels defeatist. On the other hand, if you accept the descriptions as "accurate enough", then you've at least partially pinned down the fundamental natures of reality. Would you put such statements in the camp of mathematical realism?
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.
Thanks THUNK, but I had watched this video already and was hoping for something a little more concrete. Like any specific methods that helped you. Re-framing maths (in the right way) to be about puzzle solving is definately helpful but any personal tips, training regimes, or textbooks which are good.
The most helpful practices I've learned in math (and I definitely sucked at it before college) were to build my answers carefully & methodically (rather than racing to get an answer), to experiment with simpler pseudo-problems when I couldn't remember a particular rule, to treat all daunting terminology as technical names for important concepts, & to practice by inventing questions & solving them. The MIT lectures on RUclips were also invaluable!
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)
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.
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.
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.
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 .
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?
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.
We place so much interest on things like the 100th episode of a RUclips 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.
excuse me, I referred to the natural numbers. However this is a good point. perhaps we could look at the advancements in a formal calculus definition using the infinitesimals? I believe it has something to do with the multiplicative inverse of a number greater than any natural number, but I don't really know.
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?
Absolutely! There are also several philosophers from ancient Greece, Persia, & China who held similar viewpoints. I just felt that Galileo (& his privileged place at the beginning of the revolution of modern science) was the swing vote for the popularity of this view among scientists.
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?
I think that youtube's algorithms are chuncking away at the philosophical question "are these views real? or from a bot?" or something like that. My bet is that soon it will be much higher.
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.
ALSO SUBJECTIVE OPINION: I agree in that I've been a little cool on some of their more recent episodes, but I don't know if I'd say they've lost their way. Mike & crew are exceptionally nice people & some of my most persistent inspirations - I don't begrudge them venturing off & trying to do new stuff. (Coming up with a new topic every week since 2012 would make me want to break the formula a little, too - there's a reason I went to bi-weekly!) Regardless, I'm so glad you enjoyed this show. Sorry about the weird focus/lighting, I hope my new setup also continues to improve! ;)
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?
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.
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'.
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.
The surprising thing for me is that simple mathematical constructs *can* match *any* underlying structures in reality. I can imagine a universe where the "simple" mathematical tools we developed for (say) counting sheep don't map cleanly to the way that particle density falls off in 3D space. The fact that there is some deep underlying similarity between sheep and particle density distribution doesn't strike me as necessary or obvious.
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.
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.
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.
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!!!!! :/
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.
Yeah, "divide it into an infinite set of points" doesn't really make sense. The ball is an infinite set, which is divided into finite many pieces and then reassembled into two balls.
THUNK I believe it is more accurate to say that you are dividing the sphere into a finite number of disjoint subsets. These sets may each have an infinite number of points (carnality greater than or equal to that of the natural numbers).
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.
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.
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.
How deep is your math background? Basically everything I know about math and reality disagrees with you. I'm an engineering student so this may distort my math background somewhat. Everything up to 2nd year university differential equations applies directly to reality (I say from experience). Can you give an example of math that doesn't correlate to reality?
Skooteh Not very deep, I know some calculus, linear algebra, superficial stuff about differential equations. But because I'm very interested in the broader concepts I've also read popular science books on stuff like topology, dynamical systems etc. (but have no illusions about understanding them deeply and in a practical way) Maybe I just phrased my comment weirdly, but what I meant is that a lot of abstract math cannot be projected onto reality - the stuff you mention is taught to engineering students precisely because it can be and because it's useful, so it's not exactly the type of math I had in mind. A lot of other ideas cannot be "used", so far - number theory being the classical example. I mean it can be used for cryptography etc, but that's not a description of reality, it's more of a tool, designed to be useful for us humans. The deeper point I was trying to make, is that even if all math would be "useful" for physics and other fields - which to my knowledge it decidedly isn't - that doesn't imply that it is somehow "ingrained within the universe", whatever that would mean. It's like saying "the hammer wasn't discovered, it's fundamental to the universe". In my mind, differential equations are something like a pretty complicated and extremely useful hammer - to say it simply and briefly (because I've already written too much).
erraticbrain | video trash That's an interesting outlook. The way I see it is that logic, and by extension math, is discovered, not invented. For example, 1+1=2 is not an invention but a discovery. The exact value of pi and e were also discovered as maths continued to advance and are ingrained in the universe. IMO this also applies all "pure" math. I can understand that 5+ dimensional mathematics leaves the space of practicality and direct correlation to reality, but IMO, as logic it is still inherently true.
Mathematics isn't totally grounded in logic, and the mathematical foundations we currently use may be inconsistent. And which logical system are you talking about? There are many, introducing several different ideas of what it means for something to be true, and what that could depend upon.
James Wood "Mathematics isn't totally grounded in logic, and the mathematical foundations we currently use may be inconsistent." I've yet to encounter this. I'm not saying you're wrong but you've given no examples, citations or credentials to back up this statement. I'm also unsure about what you mean by "logic systems". Either it's outside the scope of my education thus far or I don't remember it (which is unlikely because this kind of thing I find really interesting).
well it must be so, we can use i or matrices in calculations. both are very valid. I think it is very possible that an alien civilization can use mind bogglingly different mathematics, but at the end everything comes down to analyses of change. whatever math method we or they use it doesn't really matter, I think we can communicate after a short period
+FairyRat horrible and terrifying because we have no methods of understanding them. And when we are in the dark about things we tend to assume the worst. Its primal survival instinct. I'm sure that if any alien that we met didnt have as much empathy as humans do, they wouldve nuked themselves to oblivion upon discovering nuclear weapons like we almost did. Or might in the future.
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.
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
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".
It is all a game of words. What does the word 'exist' mean? Does the concept of a thing exist before it is instantiated? That is not a question about how the world works, but rather a question about how words work. Some will say that 'the first number we haven't used yet' exists and some will say it doesn't. Now suppose we banned the use of the word 'exists' and instead used the expressions physically-exists and abstractly-exists. Both sides agree that if something physically-exists, that is exists in the real world, then it exists. Their disagreement is about whether something that abstractly-exists exists. If we define 'exist' such that abstract concepts exist then invention is a subcategory of discovery which is the choice I make. Alternatively you can choose to only accept physically-existing entities in the definition and mathematics is only invented. Either way it doesn't change the nature of the world. It is a semantic argument and it doesn't really matter
Esben Bregnballe How many cell phones did Alexander the Great's army use? Or maybe they didn't exist at the time?... The word 'exist' means what it means. If you don't allow words to mean what they mean then they won't mean what they mean - which is not a surprising conclusion, but neither is it very helpful.
Yes, but words are not unambiguous, and this is a case of ambiguousness. Both definitions of the word 'exist' is used by groups of people and both groups believe that their definition is right. Furthermore, they accept the other groups arguments as valid, given their definition of 'exist'. This is not a fight about the world we live in, it is a fight about what the word 'exist' means.
Esben Bregnballe Isn't this just moving the goal posts? If we ban the use of 'exists' because it can't be defined unambiguously and substitute 'actually exists' and 'conceptually exists' don't we need to define 'actually' and 'conceptually' in an unambiguous way? Does Superman live in Metropolis and Batman live in Gotham City? We might say that they do 'conceptually' but of course they don't 'actually' live at all - problem solved! But the number 3 exists conceptually and maps to the real world, while Superman and Batman don't map to the real world in any way...
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.
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.
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)!
I'm glad you've enjoyed it, & that's an interesting idea!
Don't worry about the sub count - so long as everyone who's watching enjoys the material, I'm content. :)
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.
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
Thanks Josh, I'll definitely check it out!
-Josh
-Josh
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.
"mathematical relationships between objects..."
I'm not familiar with Max Tegmark. I'm curious about how, if the universe is math, there can be objects at all? It sounds like there are two things: objects and relationships between objects, substance and fields... ?
There's a very interesting way to get around this objection, with
Structuralism and the philosophy Whitehead brings to the table.
Whitehead posits that everything is "process"in his idea of process
philosophy. Substance is transient, since all things decay and change
form, so that nothing is static. All that remains is temporary, fleeting
relationships between other objects. So although is seems like there is
a "star" that interacts with planets through gravity, its atomic
components are only in "star" from for a couple of billions of years
before they decay and become something else. During its "star" phase, it
is defined as a star by how it effects other, transient forms of
substances, which are too undergoing constant change. Even the atoms
that compose the star are composed of quarks which are only in their
atomic configuration for an undisclosed (but finite) amount of time
before they decay and become component to some other form of
"substance". At this point its turtles all the way down, and nothing is
untouched by this idea of process. Note that, combined with Tegmark's
Mathematical Universe Hypothesis, I use the term "object" to reference
"mathematical construct" just for convenience, since everything is a
mathematical object in this view.
As another, parallel way to get around the problem of substance,
structuralism offers a very interesting way to define/differentiate
things. Have you ever thought about what the definition of, say, "4" is?
One way to do it is sort of an infinite recursion, and say that "4 is
the number that is not the number 5, 6, 1, 0, pi..." and have an
infinite list of things that it is not. The elements of the list
pinpoints it as a particular, unique object. If you extend this idea to
"real objects" (not just numbers), you both define and instantiate real
objects by virtue of what they are not. This has the advantage of
also addressing the fact that objects interact with each other in
fields; interaction between things brings about uniqueness, and thus,
existence (for what does it mean to exist except to be unique from other
existing things?)
... LIke I said earlier, I could write a lot about this.
"Mathocolypse" is now the name of my Tool cover band.
Max sounds like he'd fit in marvelously with the Pythagoreans. I actually find myself liking the opposite end of the spectrum (via Quine & Wittgenstein) that math itself (along with logic) is ultimately empirical, despite appearances to the contrary. But I wouldn't put my chips down any such notion - who could possibly know to any degree of certainty? :)
PriusOmega
Why is it easier or more desirable when asked, "what's in the foreground of this picture?" to reply, "I won't tell you what is the foreground, but I'll list everything in the background and what's not in the background will be the foreground." It seems it would be much more straightforward to say, "It's a picture of my wife's car..."
Change occurs over time. It can't occur without time. (That was one of the original objections to differential calculus: how can we speak of the 'instantaneous' rate of change, the amount of change over zero time? to which Jean Le Rond D'Alembert advised students "Continue. Eventually, faith will come.") As long as you're happy to have time and change in your universe the fact that substance is impermanent doesn't alone negate the idea that there is, or was, or will be substance.
There are other reasons, of course, why things might not be substance. William Everdell in The First Moderns wrote of the ancient and very modern problem of the continuous and the discrete. There are logical problems with the idea that numbers or anything else in the world is infinitely continuous; but there are equally logical problems with the idea that anything can be reduced to its final indivisible essence...
The number four may not have a definition. Perhaps we do not define it, we recognize it. Animals have been shown to count, yet being non-verbal, it's highly unlikely that your dog has a definition of four, for instance...
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.”
Sir Hilbert brilliantly stated
it was confusing my brain the whole time that you appeared more blurry than the background
Go with manual focus, using a piece of masking tape to mark where you need to stand. Fix the colour correction in editing by getting a 50% grey card or a white card that you show at the start of any recording. Try and edit the 'levels' of the video so that white is pure white as well, you want parts of your coat to be *almost* blown out white.
Edit: If you can, ramp up the lighting *a lot* and then use a big f number like 8 or 11, which closes down the aperture, and increases the depth of field so it's less picky.
Thanks a ton for this. I'll try it this week!
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.
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
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 like this thought a lot; so because of their primal, pervasive nature, we would name the principles easily and just call it math without it actually being what we understand as math? Hm. I don't know how to get around this, but it seems like an admission of defeat without even really trying; why bother attempting to explain the workings of the universe? Anything we come up with would just be false names and labels. Any truth would forever be out of reach. I suppose that is a stance some people take, but it just feels defeatist.
On the other hand, if you accept the descriptions as "accurate enough", then you've at least partially pinned down the fundamental natures of reality. Would you put such statements in the camp of mathematical realism?
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.
Simple! ruclips.net/video/BNqVvH2jqzI/видео.html (And thanks!)
Thanks THUNK, but I had watched this video already and was hoping for something a little more concrete. Like any specific methods that helped you. Re-framing maths (in the right way) to be about puzzle solving is definately helpful but any personal tips, training regimes, or textbooks which are good.
The most helpful practices I've learned in math (and I definitely sucked at it before college) were to build my answers carefully & methodically (rather than racing to get an answer), to experiment with simpler pseudo-problems when I couldn't remember a particular rule, to treat all daunting terminology as technical names for important concepts, & to practice by inventing questions & solving them.
The MIT lectures on RUclips were also invaluable!
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)
Really enjoyed the show, it seems to be a great synopsis of a variety of subjects, which someone could research themselves.
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.
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.
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.
maybe. I don't think we have the computational abilities to test this, however.
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 .
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?
Dude your chanel is the best. You da real MVP. Keep it up!
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.
We place so much interest on things like the 100th episode of a RUclips 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.
if only we could count without a base... maybe numbers would make more sense.
+Stefan Chase it becomes very difficult to keep track of numbers less than 1. I guess fractions work, but those have complications
excuse me, I referred to the natural numbers. However this is a good point. perhaps we could look at the advancements in a formal calculus definition using the infinitesimals? I believe it has something to do with the multiplicative inverse of a number greater than any natural number, but I don't really know.
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?
It would seem Galileo was echoing what the Pythagoreans asserted centuries earlier.
Absolutely! There are also several philosophers from ancient Greece, Persia, & China who held similar viewpoints. I just felt that Galileo (& his privileged place at the beginning of the revolution of modern science) was the swing vote for the popularity of this view among scientists.
sciencmath I thought the same thing
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
Thanks! I really have no clue what I'm doing in here. :(
Could have fooled me, this video is fantastic.
Keep up the good work.
ITS SO BEAUTIFULL
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.
I think that youtube's algorithms are chuncking away at the philosophical question "are these views real? or from a bot?" or something like that. My bet is that soon it will be much higher.
Just discovering this channel, great stuff
Glad you're enjoying it! :D
I love this topic.
RIGHT?!
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.
ALSO SUBJECTIVE OPINION: I agree in that I've been a little cool on some of their more recent episodes, but I don't know if I'd say they've lost their way. Mike & crew are exceptionally nice people & some of my most persistent inspirations - I don't begrudge them venturing off & trying to do new stuff. (Coming up with a new topic every week since 2012 would make me want to break the formula a little, too - there's a reason I went to bi-weekly!)
Regardless, I'm so glad you enjoyed this show. Sorry about the weird focus/lighting, I hope my new setup also continues to improve! ;)
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?
Added into the queue for Episode 100!
I have found truth... I have seen the light...and it is.....the THUNK channel.....👍👍👍
AAAAAAUUUUUGGGHHHH! A TALKING HORSE!!!
...thank you. :)
Question: Could you run us through all the stuff behind you on the THUNK letters?
You got it!
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.
Great video. Great shirt.
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.
Question: What did you study in college? What are your favorite books/what books had the greatest impact on you?
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'.
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.
The surprising thing for me is that simple mathematical constructs *can* match *any* underlying structures in reality.
I can imagine a universe where the "simple" mathematical tools we developed for (say) counting sheep don't map cleanly to the way that particle density falls off in 3D space. The fact that there is some deep underlying similarity between sheep and particle density distribution doesn't strike me as necessary or obvious.
Great Great video
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.
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.
What IS the sound of one hand clapping?
It's a malformed question; "clapping" is an action which definitionally requires two hands, so there can be no such thing as one hand clapping.
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.
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!!!!! :/
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.
2:03 doesn't a theorem say finite amount?
Yeah, "divide it into an infinite set of points" doesn't really make sense. The ball is an infinite set, which is divided into finite many pieces and then reassembled into two balls.
there are multiple types of infinities. If you remove all the points represented by fractions there are still an infinite number of points left over.
Absolutely right; I've added an annotation. Thanks for catching this!
THUNK
I believe it is more accurate to say that you are dividing the sphere into a finite number of disjoint subsets. These sets may each have an infinite number of points (carnality greater than or equal to that of the natural numbers).
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.
If you want to read a science-fiction philosophical thriller inspired by this very topic, I recommend Neal Stephenson's Anathem.
Anathem was actually one of my inspirations for writing this one. I've been more or less writing & editing it for months now! O_O
We thunk alike :)
Simulation theory confirmed!
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.
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.
How deep is your math background? Basically everything I know about math and reality disagrees with you. I'm an engineering student so this may distort my math background somewhat. Everything up to 2nd year university differential equations applies directly to reality (I say from experience). Can you give an example of math that doesn't correlate to reality?
Skooteh Not very deep, I know some calculus, linear algebra, superficial stuff about differential equations. But because I'm very interested in the broader concepts I've also read popular science books on stuff like topology, dynamical systems etc. (but have no illusions about understanding them deeply and in a practical way)
Maybe I just phrased my comment weirdly, but what I meant is that a lot of abstract math cannot be projected onto reality - the stuff you mention is taught to engineering students precisely because it can be and because it's useful, so it's not exactly the type of math I had in mind.
A lot of other ideas cannot be "used", so far - number theory being the classical example. I mean it can be used for cryptography etc, but that's not a description of reality, it's more of a tool, designed to be useful for us humans.
The deeper point I was trying to make, is that even if all math would be "useful" for physics and other fields - which to my knowledge it decidedly isn't - that doesn't imply that it is somehow "ingrained within the universe", whatever that would mean. It's like saying "the hammer wasn't discovered, it's fundamental to the universe". In my mind, differential equations are something like a pretty complicated and extremely useful hammer - to say it simply and briefly (because I've already written too much).
erraticbrain | video trash That's an interesting outlook. The way I see it is that logic, and by extension math, is discovered, not invented. For example, 1+1=2 is not an invention but a discovery. The exact value of pi and e were also discovered as maths continued to advance and are ingrained in the universe. IMO this also applies all "pure" math.
I can understand that 5+ dimensional mathematics leaves the space of practicality and direct correlation to reality, but IMO, as logic it is still inherently true.
Mathematics isn't totally grounded in logic, and the mathematical foundations we currently use may be inconsistent. And which logical system are you talking about? There are many, introducing several different ideas of what it means for something to be true, and what that could depend upon.
James Wood "Mathematics isn't totally grounded in logic, and the mathematical foundations we currently use may be inconsistent." I've yet to encounter this. I'm not saying you're wrong but you've given no examples, citations or credentials to back up this statement.
I'm also unsure about what you mean by "logic systems". Either it's outside the scope of my education thus far or I don't remember it (which is unlikely because this kind of thing I find really interesting).
Now hold on one of those avocados was a bit bigger.. I think you were actually holding π avocados.
DAMMIT NICK AVOCADOS ARE QUANTIZED WE TALKED ABOUT THIS
still waiting for aliens to see what stuff they use
math is an abstract invention which models/generalizes the physical world.
no, mathematicians don't care about the real world.
It would be interesting if aliens use something else completely different that math to understand the universe
well it must be so, we can use i or matrices in calculations. both are very valid. I think it is very possible that an alien civilization can use mind bogglingly different mathematics, but at the end everything comes down to analyses of change. whatever math method we or they use it doesn't really matter, I think we can communicate after a short period
It would be interesting if aliens existed at all...
It would be more interesting if they don't exist, to be honest. The implications of this are horrible and terrifying.
Absolutely. Check out the SETI talk I linked in the description, Keith Devlin lays out some very compelling points about precisely this.
+FairyRat horrible and terrifying because we have no methods of understanding them. And when we are in the dark about things we tend to assume the worst. Its primal survival instinct. I'm sure that if any alien that we met didnt have as much empathy as humans do, they wouldve nuked themselves to oblivion upon discovering nuclear weapons like we almost did. Or might in the future.
This would be easier to watch if the host was in focus instead of the background behind him.
I think that the ceos of google learned this same thing when they found math to be useful.
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.
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
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".
Discovered means it was always there and you found it; invented means it was never there and you made it.
It is all a game of words. What does the word 'exist' mean?
Does the concept of a thing exist before it is instantiated?
That is not a question about how the world works, but rather a question about how words work.
Some will say that 'the first number we haven't used yet' exists and some will say it doesn't.
Now suppose we banned the use of the word 'exists' and instead used the expressions physically-exists and abstractly-exists.
Both sides agree that if something physically-exists, that is exists in the real world, then it exists.
Their disagreement is about whether something that abstractly-exists exists.
If we define 'exist' such that abstract concepts exist then invention is a subcategory of discovery which is the choice I make.
Alternatively you can choose to only accept physically-existing entities in the definition and mathematics is only invented.
Either way it doesn't change the nature of the world. It is a semantic argument and it doesn't really matter
Esben Bregnballe
How many cell phones did Alexander the Great's army use? Or maybe they didn't exist at the time?...
The word 'exist' means what it means. If you don't allow words to mean what they mean then they won't mean what they mean - which is not a surprising conclusion, but neither is it very helpful.
Yes, but words are not unambiguous, and this is a case of ambiguousness.
Both definitions of the word 'exist' is used by groups of people and both groups believe that their definition is right.
Furthermore, they accept the other groups arguments as valid, given their definition of 'exist'.
This is not a fight about the world we live in, it is a fight about what the word 'exist' means.
Esben Bregnballe
Isn't this just moving the goal posts? If we ban the use of 'exists' because it can't be defined unambiguously and substitute 'actually exists' and 'conceptually exists' don't we need to define 'actually' and 'conceptually' in an unambiguous way?
Does Superman live in Metropolis and Batman live in Gotham City? We might say that they do 'conceptually' but of course they don't 'actually' live at all - problem solved! But the number 3 exists conceptually and maps to the real world, while Superman and Batman don't map to the real world in any way...
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.
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.
I think humans invented mathematics right along with God. However, physical reality is discreet and countable. This is related to mathematics.
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