The way Neil didn’t even want to comment on the discovention, so he just kept on talking but was interrupted by singing instead so he tried to talk through that and couldn’t… he paused for one second and then just continued his sentence as if nothing had happened 😂😂😂
It’s an interpretation above all else. Our ability to use it, is biased on our ability. It’s like language, we invented it and use it to understand the world around us.
There is nothing natural in the world that is a parallel to speech. There are tons of naturally occurring mathematical phenomena going on whether or not humans have discovered them or not
I have no idea. I don’t remember this conversation. Merry Christmas👍 Cars are obviously created. So whatever that contradicts from what I was saying a year ago. Great. The ability and the knowledge to create cars are discovered though so you know…. I still don’t think it’s that simple. I honestly don’t even know what we are talking about and Im not watching a NGT video to try and remember
@@justinsane1119 if math is invented or discovered. It's invented, so are cars and tires. I like the way you ended your comment so much that I can't help it but to congratulate you for it. Merry Christmas buddy! ❤️
Neil is right, math is an infinite language that describes itself and only itself using patterns. It’s nether discovered nor invented. Its explanation can only be revealed by mathematics itself, no word in our conscious vocabulary can define it. It just describes itself in every equation.
The one thing that everyone misses in that debate is that we first have to agree on an ontology of math in order to tell if math is discovered or invented. We cannot tell if the structures preexist or come into existence as we start thinking about them as long as we didn’t agree on what we mean by „existing“. The major difficulty here is that physicists and many others have a hard time accepting any non-physical mode of existence. But for math, it is kind of a prerequisite. Mathematical statements are statements that acquire a truth value simply from definitions. The statement „all bachelors are unmarried“ is true by definition of the word „bachelor“ (an unmarried man). But notice how we do not require that any physical Bachelors exist for that sentence to be true. We could be in a universe where men aren’t a thing and consequently there are no bachelors, but the sentence would still have the same truth value as it does in our universe. When mathematicians say that their objects of study exist in an abstract sense, it is *this* what they mean. The truth values of their statements are independent of physical reality, they pre-exist. I have yet to hear any good arguments against this. Many mathematicians go a step further though and they claim that then there must in some sense be those things that the statements are about. I do see how that notion is not above criticism, but I can also see the appeal of that notion.
Everything has a potential to exist, in the sense of putting something together from creation. Thus, the ultimate creativity of the human mind maybe for all practical purposes, infinite. Honestly I see math as incorrect, but still useful to a point. Example computers calculate using basic AND, NOT, OR, NOR GATES just binary 1 and 0, On and Off. For more advanced calculations 1 and 0 Simultaneously or entanglement
It's an observation with an explanation that has been standardized and refined over time. Like literature or Music with structure and rules to create consistent communication and understanding.
Our understanding of math is incomplete. Actually, it always will be. Math is literally infinite. I disagree that we don't know if math is consistent. Consistency is part of the definition of math, therefore, it must be consistent. Otherwise, it's not math, and it doesn't exist.
@@markuspfeifer8473 zermelo-fraenkel set theory? These set theories are likely consistent. However, Godel's 2nd incompleteness theorum proves that it's consistency can only be proved if it is inconsistent. It is entirely possible for the proof of consistency of ZF set theory not to exist, while the theory itself is actually still consistent. What Godel is proving is that... The proof doesn't exist. We have to assume ZF set theory is consistent because so far, every piece of it has been consistent. When we come across a part of ZF set theory that's inconsistent, then we could say.. ok, we were wrong. In which case, we could say it turns into something like "fictional mathematics".
@@dmitryalexandersamoilov that sounds very different from your last post. Basically, we’re working on an unprovable (if true) assumption here. That’s far from „knowing“ that it is consistent. And even if it turns out to be inconsistent, we still did a lot of good math based on it, because the principle of explosion can only be applied after you actually derived a contradiction. Para-consistent logic shows that one can actually work with inconsistent sets of premises as long as you carefully avoid drawing certain types of conclusions.
"In order to get ahold of the wiggly world you've gotta put a net over it" - And so, the the art of calculus was born. Now we can number the holes of the net, so many so holes up, so many so holes across, and now we can measure, calculate, and talk about the wiggly world in regards to the net. The funniest part of all is that as human beings we tend to try and straighten out the wiggly world and build in straight lines with right angles, but each and every one of us is wiggly as all get out. The wiggliest wiggle of them all tries to straighten out a wiggly world. Lol This is Alan Watts by the way. One of his philosophical lectures on calculus and the universe. It is wonderful.
Think about how silly it would be to say Isaac Newton invented gravity... It was always there at a very specific reliable value making it a discovery. I believe math also is a discovery in the same way that 4 bananas plus 4 bananas always equaled 8 bananas. We just discovered a way to explain it. To invent math means you could assign any value to anything you want and call it true despite the entire universe laughing at you.
It’s impossible to separate the subject from object because there will always be the naming process which works at the same time creates something new and gives a name to that object the rest is just unconsciousness things we don’t see
what all went before the math book got published ( from whatever little a highschooler could gain) -nature reveals - humans capture (this is where the invention comes ) through symbols -understand ( " things around us will do what they are doing whether we understand them or not ") -understanding enables us to control - which helps us in utilizing. and why look so far behind and into something so big such as the the pyramids - maths is in our hands. *if we wouldn't have discovered the chaos around us we wouldn't have invented methods to place them in order* many a times when maths seems way to incomprehensible to me these lines calm my nerves 'these are a set of rules -discovered and what has been discovered though can be questioned but has no answer , so why not just leave it at that.' AND 'maths is not something you understand but something you get used to'
I have learned a lot of wisdom from old tales and religious quotes with a deep meaning my favourite was this, and I write it in hungarian because it sounds better: "Az ember tudatlannak születik, nem ostobának, ostobává az oktatás teszi". This sums up the operation we have here very well. The other thing I have learned when I went down alone to an illegal underground party was "sacred geometry". So, those people who exist behind the door says "do not enter" is actually people who possess wisdom that is sacred. You guys are doing media here. You not gonna know the world behind closed doors. You shouldn't.
No, that's objectively wrong. Mathematics are a linguistic system (just as much as verbal communication/language and music theory) made by man and, thus, it's artifficial. What there certainly exists are the LAWS of nature, mathematics is just the system we made to better and more easily explain the LAWS of the nature that we can observe and identify with our minds. Every linguistic system we made is just to explain the laws of nature that we could observe with OUR MINDS first. So what we discover are the LAWS of nature, everything else (like math) are just the tools we created and use to ease our understanding of it.
@@FindingsOfAnArmouredMindtalked to gpt about this. It insists that there are 2 major views and they should be respected lol. Saying we discovered math is like saying we discovered painting, poetry or architecture. Intellectual masturbation and the display of ego, nothing more. You're spot on with your comment.
@@FindingsOfAnArmouredMind 2+2 will always be 4 even if no humans were alive. if we met another civilization they would know the area of a circle is pi r^2, as it is a fundamental truth. Assume it wasn't true, in such a case the reality we live in could not exist. Thus, it is true. Just because we formalised a language to represent the information does not mean we created the information itself, it is inherent. We didn't invent circles we just described them.
@@dariusus9870 Great argument buddy Talking about intellectual masturbation when you are just rambling spiteful conclusions with no logical coherency. Failed out of algebra or something?
@@Mendoza1414 yes, the pythagorean theorem would still exist if humans never existed, like the core principles of geometry would still exist. The object we describe as a "right triangle" would stil lexist and have the same properties. And thats just one example.
@@shyshka_ Absolutely. People confuse maths & syntaxes used to describe maths. E.G. An Atom was discovered. But, the word "Atom" was invented, to describe the discovery. E.G. The square of the hypotenuse being the sum of the square of the 2 other sides was discovered. The formula A2 + B2 = c2 was invented to describe the discovery. Math is a discovery. No in-between word is needed
Fundamental math concepts are most definetly discovered, more abstract models and number theory and so on just might be invented on top of that. Like the Pythagorean theorem would still exist even if humans never existed, concepts of geometry would still be the same, Pi would still be the same.. etc.
He tends to answer questions by just taking apart the question itself instead of actually answering it. It’s a way to try to present yourself as smarter than or above the question. It is annoying.
Related question for other commenters: are birds invented or discovered? Every single bird like every living thing on this planet can be said to be directly descended from its parents in many cases parent. Yet there exists an unbroken chain connecting every life on Earth to the same first ancestor. That bird had a mom who was a bird of a particular species however many generations is hard to give an exact answer and can only be given by an approximation. At some point most biologists would likely claim a bird of one species had an ancestor that belonged to a different species. This same reasoning can be applied beyond bird species to every species on Earth in the same manner. We may be comfortable saying a given individual is a bird of a given species but the species is less easily defined. It is real in that it is useful as a way to understand the world and to develop further ideas related to life, the animal kingdom, and birds, but it could be argued the bird was an invention despite agreeing with measurements and experiments. The bird is an abstraction that repeatedly produces results that correspond to reality yet I would argue is a human invention the same way math is. Math is a tool with great agreement and correspondence with nature. On the other hand there can be multiple systems of axioms on which a branch of mathematics may rest. Do all such systems of axioms including even those that may not correspond with reality have their own independent truth even if they are untestable or if they were to fail repeated experimentation? Does math have a standard of truth separate from that of science? Would you say she blinded me with math? 😉
Math that "we have right now" is an absolute invention, we can actually make our own math that matches the math that the early inventors made as long as you are smart enough you can make one.
No we can't. Because maths that we don't have right now. Is undiscovered. Wanna know why we can't just invent it? Because if you just "invent" a new piece of math. And it doesn't like up with everything else? It's wrong. Following this logic. Why can't 1x1 be 3?
The ancients built pyramids when they discovered geometry, lmao. they even speak of it in the hieroglyphs. 1:35. like he said math exists with out us. the english language is that because we except it to be, words take on new meaning but 3+3 will always be 6. Please NEVER EVER EVER DISRESPECT MATH. EVER. Thank you.
We invented the kickoff version of it to account for things like sheep but all of the laws existed beforehand, explorations of it's possibilities led to discoveries, not inventions of universal laws.
the rules of chess were discovered. the systems we use to do chess where invented. the rules of english were discovered. the systems we use to do english where invented. fact is, all values, all sets, all rules and all descriptions are products of the human mind. we must carry the one in order to describe the universe, but the universe does not need us to do so in order to be. KEvron
@verygoodusername name Since by your logic everything you know lives in your mind you can't tell me the capabilities of my mind . For all you know I created the universe and im the only other conciousness than you and everybody else is just an illusion that I created for you and Im the only one that can see it clearly.
Almost all of math is abstract and general, not particular. When we say a = b and b = c therefore a = c we're not just talking about a particular thing called "a" and a particular thing called "c". You can put in whatever variables you want, that's why we call them variables. However, if math is to be discovered, and we have to go out in the world and look, then it can't be as general as just described. You would have to observe each and every a, b and c to see if the relation holds up. Turns out that sometimes in quantum mechanics, like the the famous bell inequality, it doesn't. So mathematics cannot be discovered. It's a set of rules we've invented and chosen to follow. You can make the argument that the ones we choose to follow match reality, which of course requires some discovery / empiricism to verify, but the rules themselves are not derivable from raw reality input. Again, you would have to observe every a and b and c to conclude the rule is truly general and universal, which we can't do as humans with limited (and faulty) brains.
I think your confusing the fact that there is trial, and error in the discovery of math to mean that it isn't discovered at all. The fact that we don't have to make up new fundinental rules in order to make something new mathematically comprehensible is evidence of that
@@anthonypolonkay2681 If your standard is merely that it is "comprehensible", all kinds of fictional math, and other kinds of logic, are comprehensible, yet obviously invented. Also, I think you missed my point. My point wasn't that because we discover new math through trial and error, therefore it isn't discovered. That would be evidence of it being discovered, if anything. What I did was make a distinction between the general and the particular. Math deals with the former, experience and discovery deals with the latter. To bridge that gap requires work by the human mind that isn't just a mere logical deduction, therefore it is invented. Unless of course you think knowledge of math is somehow buried deep within our minds from birth, and if we just think hard enough, without any experience, then we can discover it. But that's a ridiculous claim in my view.
@@Google_Censored_Commenter Its not just that' it's comprehensible. It the fact that the same set of mathematical laws are followed throughout all examined areas of reality. You dont need fundamentally new sets of mathematics laws to describe the motions of planetary bodies vs the energy output of a chemical reaction. If math were invented the fundamental rules of it's use would change different phenomena, but they don't. Which means thos such mathematical laws are objective, and not products of invention or interpretation.
@@anthonypolonkay2681 Mathematical laws being invented is perfectly compatible with the qualities you describe, including objectivity. Quantum physics is largely all just math, new math at that, to describe a more complex reality of atoms. But you've still not really addressed the point I'm getting at. Take the speed of light being constant for example. Have we *discovered* that general law of nature? Not really. What we've discovered through experience, is the speed of light being constant in all types of atmospheric pressure. We've tested it a ton of different ways. We've tried falsifying it and couldn't do it. And yet still we have not really discovered it is a law of nature, as a general principle, because that would require examining all of the cosmos. Instead it is an *assumption* of the human mind that arises as a consequence of our discoveries. Just like it is an assumption it will continue to be constant in the future. There's no guarantee it will. That's what I mean when I say generalities have to be invented, they require the human touch of assumptions. No matter how many triangles in nature you observe, no matter how many you draw with pen and paper, you can never say you have "discovered" that all triangles have three sides through experience. If you want to say that, you have to use assumptions, axioms, language, and all the other inventions of the human mind. That's not problematic, human creations are still meaningful, if that's your concern.
@@Google_Censored_Commenter have you ever looked into the Mandelbrot set? That is a pretty easy example that disproves that all math is a construct. Humans cannot produce true infinites of any kind, but that is what the math leads to.
Math is a descriptive subjective system we've invented to describe the phenomenon in our observable universe. It's isn't some sort of divine objective prescriptive system that we discovered. It's our complex answers to complex questions arived at by our logic
Well, you can also say that the we have build a language/descriptive system, to examine something inherent to the universe (math). I think the main discussion here is the definition of math
@@beetlesstrengthandpower1890 The thing is that we have to interpret everything through our limited knowledge and understanding. To claim math is some inherent truth of the universe, rather than simply a man made system to explain universal phenomenon is absurd. This is a deeply philosophical question. I reject the concept of a "true world" beyond that of the apparent world. There are no systems of objective truths beyond our human perceptions.
No, that's objectively wrong. Mathematics are a linguistic system (just as much as verbal communication/language and music theory) made by man and, thus, it's artifficial. What there certainly exists are the LAWS of nature, mathematics is just the system we made to better and more easily explain the LAWS of the nature that we can observe and identify with our minds. Every linguistic system we made is just to explain the laws of nature that we could observe with OUR MINDS first.
So if we created math, was there ever math that was proven wrong? Or did we miraculously come with the correct equation systems every time some new mathematical field came up?
Think about how silly it would be to say Isaac Newton invented gravity... It was always there at a very specific reliable value making it a discovery. I believe math also is a discovery in the same way that 4 bananas plus 4 bananas always equaled 8 bananas. We just discovered a way to explain it. To invent math means you could assign any value to anything you want and call it true despite the entire universe laughing at you.
Math is like time and space !!! Without time and space there is no math !! Time and space the closer something is less time is needed if touching you no time needed at all or math coz nothing to work out !!! To me it's obvious time and space are the same thing !! Playing football you learn to run into the space so you have more time on the ball !!!!!!
A logic invention. Do We have one berry? 5 berrys? Im sure the package older form of humans had some sound or sign for how many of something there is. I do NOT however think they called math for a few hundred thousand years. I do also think its right that it’s already there in the world by it self
To the complex question what is not known.. still not know! Forgive me apply the 6Ws and we stop being Being complacent with a knowledge acquired go back to basics repeat that cycle with your AARs and the stagnant mine continues to seek enlightenment so as a beginner in applied astro physics I ask to you without your study’s and book how far did you as individuals excel on your own the beginning of year conundrums your thesis what was the spark. I ask cause my spark was why my answer to myself was why not simplicity being a self-proclaimed engineer with no mathematical scientific on the contrary combative war fighting skills yet my hunger for questions curiosity never failed and the question still baffles me how with all we have to humanities abilities the answers for such a small simple Conundrum to the vast emptiness of space so close yet so far why are these within our grasp yet light years away in his image is the biggest issue I have in text to date. Your thoughts
In linguistics rules are broken all the time... “i before e except after C” weird species we are. But math to me is closer to medicine and science, it’s discovered and the rules change because we can never be 100% sure of them. Math is very much a scientific experiment.
The mathematics of complex numbers are a natural extension of the concepts of adding and multipling real numbers. If you develop intuitions for what goes behind them, you are just one step before complex numbers. To understand what I mean, try to make sense of multipling √2 * π. It can't be repeated multiplication because what on earth would be √2 repeated π times?
But math has fallacies and paradoxes. It means what we want it to mean. It's just something else based on human perception. It works like language. Math is inductive and deductive because we make it fit and develop it. Many things don't have formulas. If you could use math for everything, everything would be calculated. Everything would have to be exactly like the other. Why is a circle 360° instead of 720° or 180°? Humans still barely understand how most things work and base everything on observation. It's almost becoming a religion.
@@KBdotHAQ So did 1+1 did not equal 2 until we said it was 2???? Why not 3? Or 31415.16??? I think it follows a logical sequence right??? Other wise we can just invent anything we want and make it work the way we want it. Why dont you invent a nunmber system that would give you something out of nothing? Like 0+0= everything! Show me that you can invent such a system and i will believe you!
@@victorvalencia6466 You can't add 0 because 0 is nothing. Even the fact that zero is considered a number is flawed. Like I said, these numbers are just based on human perception. I mean why can't 1+1 mean 1 if depending on your view, or whether or not the society in which you live uses numbers at all? If humans were gaseous beings we wouldn't view numbers as we do now.
@@KBdotHAQ you can view numbers as you wish... but the truth will not change. We get to invent the symbols and invent the names of numbers but the structure of the truth will still be the same no matter what. Its like the 5 plutonic solids, you can invent symbols to discribe them and even call them what you want, but what you cannot invent is the 6th plutonic solid because it does not exist.
Math was pre-existing. So math itself, the quantities are not really discovered or invented but Realized. The style in which we choose to code, or write down, the math concepts like a language of symbols are our human invention for the relationship of quantities that we realized. Similar to going outside in the sun and noticing your shadow. You didn't discover your shadow. You didn't invent the shadow. You realized a phenomenon that occurs when certain conditions are met, a phenomenon that was pre-existing.
We have a perfectly good model of how a mathematical framework can exist outside of the conscious experience. That's what we have created with computational devices. Just imagine yourselves as beings, made of pixel dust existing inside a matrix. Then you realize your thoughts come from underlying binary code also known as dark matter. You should know a physical architecture or server system can expand from the outside and that expansion is reflected on the inside. That's what dark energy represents, it's not only our container, but it's why the universe is expanding exponentially. The difference is you cannot physically interact with it internally. Through the mind and thoughts we can interact with the mathematical framework. E=MC² hence matter and energy are interchangeable. Light is used as a metaphor for intellect, wisdom and consciousness, without light (electromagnetic radiation), the mathematical framework we use everyday known as computational architectures, wouldn't be accessible to us in such a rich and interactive operating system experience. These architectures show us what mathematical frameworks look like from the outside in. This universe shows us what a mathematical framework looks like, from the inside out.
The way Neil didn’t even want to comment on the discovention, so he just kept on talking but was interrupted by singing instead so he tried to talk through that and couldn’t… he paused for one second and then just continued his sentence as if nothing had happened 😂😂😂
It’s an interpretation above all else. Our ability to use it, is biased on our ability. It’s like language, we invented it and use it to understand the world around us.
My ability to change a car tire is based on my ability and my bias. That doesn’t mean it’s an interpretation
There is nothing natural in the world that is a parallel to speech. There are tons of naturally occurring mathematical phenomena going on whether or not humans have discovered them or not
@@justinsane1119does that mean that tires and cars are discovered then?
I have no idea. I don’t remember this conversation. Merry Christmas👍
Cars are obviously created. So whatever that contradicts from what I was saying a year ago. Great.
The ability and the knowledge to create cars are discovered though so you know…. I still don’t think it’s that simple.
I honestly don’t even know what we are talking about and Im not watching a NGT video to try and remember
@@justinsane1119 if math is invented or discovered. It's invented, so are cars and tires. I like the way you ended your comment so much that I can't help it but to congratulate you for it. Merry Christmas buddy! ❤️
Neil is right, math is an infinite language that describes itself and only itself using patterns. It’s nether discovered nor invented. Its explanation can only be revealed by mathematics itself, no word in our conscious vocabulary can define it. It just describes itself in every equation.
Dude gave his son an ultimatum between math and astrophysics LOL
The one thing that everyone misses in that debate is that we first have to agree on an ontology of math in order to tell if math is discovered or invented. We cannot tell if the structures preexist or come into existence as we start thinking about them as long as we didn’t agree on what we mean by „existing“.
The major difficulty here is that physicists and many others have a hard time accepting any non-physical mode of existence. But for math, it is kind of a prerequisite.
Mathematical statements are statements that acquire a truth value simply from definitions. The statement „all bachelors are unmarried“ is true by definition of the word „bachelor“ (an unmarried man). But notice how we do not require that any physical Bachelors exist for that sentence to be true. We could be in a universe where men aren’t a thing and consequently there are no bachelors, but the sentence would still have the same truth value as it does in our universe.
When mathematicians say that their objects of study exist in an abstract sense, it is *this* what they mean. The truth values of their statements are independent of physical reality, they pre-exist. I have yet to hear any good arguments against this.
Many mathematicians go a step further though and they claim that then there must in some sense be those things that the statements are about. I do see how that notion is not above criticism, but I can also see the appeal of that notion.
Everything has a potential to exist, in the sense of putting something together from creation.
Thus, the ultimate creativity of the human mind maybe for all practical purposes, infinite.
Honestly I see math as incorrect, but still useful to a point.
Example computers calculate using basic AND, NOT, OR, NOR GATES just binary 1 and 0, On and Off.
For more advanced calculations 1 and 0 Simultaneously or entanglement
Intro chat ends at 0:57, it took 24% of total clip time :-(
It's an observation with an explanation that has been standardized and refined over time. Like literature or Music with structure and rules to create consistent communication and understanding.
Mathematics is fascinating. It's incomplete. We don't know whether it is consistent or not. Yet it helps people to understand reality.
Actually, we know about a lot of math that it is consistent. Finitary math for example.
Our understanding of math is incomplete. Actually, it always will be. Math is literally infinite.
I disagree that we don't know if math is consistent. Consistency is part of the definition of math, therefore, it must be consistent. Otherwise, it's not math, and it doesn't exist.
@@dmitryalexandersamoilov by your standard, Peano arithmetic and Hermelin fraenkel set theory aren’t math then?
@@markuspfeifer8473 zermelo-fraenkel set theory?
These set theories are likely consistent. However, Godel's 2nd incompleteness theorum proves that it's consistency can only be proved if it is inconsistent.
It is entirely possible for the proof of consistency of ZF set theory not to exist, while the theory itself is actually still consistent.
What Godel is proving is that... The proof doesn't exist.
We have to assume ZF set theory is consistent because so far, every piece of it has been consistent. When we come across a part of ZF set theory that's inconsistent, then we could say.. ok, we were wrong. In which case, we could say it turns into something like "fictional mathematics".
@@dmitryalexandersamoilov that sounds very different from your last post. Basically, we’re working on an unprovable (if true) assumption here. That’s far from „knowing“ that it is consistent. And even if it turns out to be inconsistent, we still did a lot of good math based on it, because the principle of explosion can only be applied after you actually derived a contradiction. Para-consistent logic shows that one can actually work with inconsistent sets of premises as long as you carefully avoid drawing certain types of conclusions.
"In order to get ahold of the wiggly world you've gotta put a net over it" - And so, the the art of calculus was born.
Now we can number the holes of the net, so many so holes up, so many so holes across, and now we can measure, calculate, and talk about the wiggly world in regards to the net. The funniest part of all is that as human beings we tend to try and straighten out the wiggly world and build in straight lines with right angles, but each and every one of us is wiggly as all get out. The wiggliest wiggle of them all tries to straighten out a wiggly world. Lol
This is Alan Watts by the way. One of his philosophical lectures on calculus and the universe. It is wonderful.
Its probably be the same as the light debate were two sides argued that light is a wave or light is a particle but end up being both correct.
Yeah except some people try to say math didn't exist before humans invented it and that makes no sense to me.
It's a sound like everything else
Think about how silly it would be to say Isaac Newton invented gravity... It was always there at a very specific reliable value making it a discovery. I believe math also is a discovery in the same way that 4 bananas plus 4 bananas always equaled 8 bananas. We just discovered a way to explain it. To invent math means you could assign any value to anything you want and call it true despite the entire universe laughing at you.
That's right, hallelujah.
This reminds me of the question who came first the chicken or the egg.
Yes it’s so Hegelian dialectic in the end that it works both ways( invention=discovery )
It’s impossible to separate the subject from object because there will always be the naming process which works at the same time creates something new and gives a name to that object the rest is just unconsciousness things we don’t see
what all went before the math book got published ( from whatever little a highschooler could gain)
-nature reveals
- humans capture (this is where the invention comes ) through symbols
-understand ( " things around us will do what they are doing whether we understand them or not ")
-understanding enables us to control
- which helps us in utilizing.
and why look so far behind and into something so big such as the the pyramids - maths is in our hands.
*if we wouldn't have discovered the chaos around us we wouldn't have invented methods to place them in order*
many a times when maths seems way to incomprehensible to me these lines calm my nerves
'these are a set of rules -discovered
and what has been discovered though can be questioned but has no answer , so why not just leave it at that.'
AND
'maths is not something you understand but something you get used to'
I have learned a lot of wisdom from old tales and religious quotes with a deep meaning my favourite was this, and I write it in hungarian because it sounds better: "Az ember tudatlannak születik, nem ostobának, ostobává az oktatás teszi". This sums up the operation we have here very well. The other thing I have learned when I went down alone to an illegal underground party was "sacred geometry". So, those people who exist behind the door says "do not enter" is actually people who possess wisdom that is sacred. You guys are doing media here. You not gonna know the world behind closed doors. You shouldn't.
The best word to describe math might be an interpretation of our world, not an invention or a simple existence
It had to be discovered. It just fits so perfectly
No, that's objectively wrong. Mathematics are a linguistic system (just as much as verbal communication/language and music theory) made by man and, thus, it's artifficial. What there certainly exists are the LAWS of nature, mathematics is just the system we made to better and more easily explain the LAWS of the nature that we can observe and identify with our minds. Every linguistic system we made is just to explain the laws of nature that we could observe with OUR MINDS first. So what we discover are the LAWS of nature, everything else (like math) are just the tools we created and use to ease our understanding of it.
@TheMahayanist who are you replying to?
@@FindingsOfAnArmouredMindtalked to gpt about this. It insists that there are 2 major views and they should be respected lol. Saying we discovered math is like saying we discovered painting, poetry or architecture. Intellectual masturbation and the display of ego, nothing more. You're spot on with your comment.
@@FindingsOfAnArmouredMind 2+2 will always be 4 even if no humans were alive. if we met another civilization they would know the area of a circle is pi r^2, as it is a fundamental truth. Assume it wasn't true, in such a case the reality we live in could not exist. Thus, it is true. Just because we formalised a language to represent the information does not mean we created the information itself, it is inherent. We didn't invent circles we just described them.
@@dariusus9870 Great argument buddy Talking about intellectual masturbation when you are just rambling spiteful conclusions with no logical coherency. Failed out of algebra or something?
I like that Asian guy lol. I know who Neil is already and have much respect for him but that discovention joke was freaking hilarious!
Discovery and invention are the same in this interactive MMORPG viz. "Discovention". Tyson is much smarter than I thought.
For that third word of description how about incovery 🤔
It's a discovery. The figures are concepts, but the base facts are incontrovertible.
Nah
So you think formulas you use for algebra were discovered? 😂😂
@@Mendoza1414 Yes, the principles are discovered, but the way we express it is an invention. Just like symbols, we use in math.
@@Mendoza1414 yes, the pythagorean theorem would still exist if humans never existed, like the core principles of geometry would still exist. The object we describe as a "right triangle" would stil lexist and have the same properties. And thats just one example.
@@shyshka_ Absolutely. People confuse maths & syntaxes used to describe maths.
E.G. An Atom was discovered. But, the word "Atom" was invented, to describe the discovery.
E.G. The square of the hypotenuse being the sum of the square of the 2 other sides was discovered. The formula A2 + B2 = c2 was invented to describe the discovery.
Math is a discovery. No in-between word is needed
Is this a podcast? Where can I find it??? Neil Degrase Tyson please start your own podcast and talk about space !!!!
Math is a pidgin between the language of the universe and the language of our minds.
This the best thing ive read all day
2:35 weird crazy Japanese dude 😅
Fundamental math concepts are most definetly discovered, more abstract models and number theory and so on just might be invented on top of that. Like the Pythagorean theorem would still exist even if humans never existed, concepts of geometry would still be the same, Pi would still be the same.. etc.
I don't like Neil's response here, all he did was move the question back a step... we can now ask: 'Is language invented or discovered?'
bruh😐
sometimes its more fun to ask deeper question, instead of to look for a definite answer i guess
Math is the interpretation of the natural world. Just like language is the interpretation for communication.
Language is definitely an invention considering it isn’t universal lol . If it was discovered then we would all speak one language
He tends to answer questions by just taking apart the question itself instead of actually answering it. It’s a way to try to present yourself as smarter than or above the question. It is annoying.
Related question for other commenters: are birds invented or discovered? Every single bird like every living thing on this planet can be said to be directly descended from its parents in many cases parent. Yet there exists an unbroken chain connecting every life on Earth to the same first ancestor. That bird had a mom who was a bird of a particular species however many generations is hard to give an exact answer and can only be given by an approximation. At some point most biologists would likely claim a bird of one species had an ancestor that belonged to a different species. This same reasoning can be applied beyond bird species to every species on Earth in the same manner. We may be comfortable saying a given individual is a bird of a given species but the species is less easily defined. It is real in that it is useful as a way to understand the world and to develop further ideas related to life, the animal kingdom, and birds, but it could be argued the bird was an invention despite agreeing with measurements and experiments. The bird is an abstraction that repeatedly produces results that correspond to reality yet I would argue is a human invention the same way math is. Math is a tool with great agreement and correspondence with nature. On the other hand there can be multiple systems of axioms on which a branch of mathematics may rest. Do all such systems of axioms including even those that may not correspond with reality have their own independent truth even if they are untestable or if they were to fail repeated experimentation? Does math have a standard of truth separate from that of science? Would you say she blinded me with math? 😉
We understand the circle, but one has never been discovered.
well when we say it was discovered we said the concept, not some actual mathematical number or shape that is floating around somewhere in space
Math that "we have right now" is an absolute invention, we can actually make our own math that matches the math that the early inventors made as long as you are smart enough you can make one.
No we can't. Because maths that we don't have right now. Is undiscovered. Wanna know why we can't just invent it? Because if you just "invent" a new piece of math. And it doesn't like up with everything else? It's wrong.
Following this logic. Why can't 1x1 be 3?
So we discovered it, and then invented using it 😁, kinda like the wheel. (Snowballs roll downhill)
Twinsiees 😂😂😂😂
Its an Anomaly, Constantly tested in constantly used on different scales.
The ancients built pyramids when they discovered geometry, lmao. they even speak of it in the hieroglyphs. 1:35. like he said math exists with out us. the english language is that because we except it to be, words take on new meaning but 3+3 will always be 6.
Please NEVER EVER EVER DISRESPECT MATH. EVER. Thank you.
Field - Science without Numbers
Get rekt.
Math was invented with people living Thor best life and in the desperate need to create something to not go crazy 😝
We invented the kickoff version of it to account for things like sheep but all of the laws existed beforehand, explorations of it's possibilities led to discoveries, not inventions of universal laws.
The rules of mathematics where discovered.
The system we use to do mathematics where invented.
@verygoodusername name Every word is made by humans this the dumbest shit anybody ever said and doesnt add on at all to what i said
the rules of chess were discovered.
the systems we use to do chess where invented.
the rules of english were discovered.
the systems we use to do english where invented.
fact is, all values, all sets, all rules and all descriptions are products of the human mind. we must carry the one in order to describe the universe, but the universe does not need us to do so in order to be.
KEvron
@verygoodusername name Since by your logic everything you know lives in your mind you can't tell me the capabilities of my mind . For all you know I created the universe and im the only other conciousness than you and everybody else is just an illusion that I created for you and Im the only one that can see it clearly.
@verygoodusername name the mind is all life is perception
what about programming language isn't it completely arbitrary?
Almost all of math is abstract and general, not particular. When we say a = b and b = c therefore a = c we're not just talking about a particular thing called "a" and a particular thing called "c". You can put in whatever variables you want, that's why we call them variables. However, if math is to be discovered, and we have to go out in the world and look, then it can't be as general as just described. You would have to observe each and every a, b and c to see if the relation holds up. Turns out that sometimes in quantum mechanics, like the the famous bell inequality, it doesn't.
So mathematics cannot be discovered. It's a set of rules we've invented and chosen to follow. You can make the argument that the ones we choose to follow match reality, which of course requires some discovery / empiricism to verify, but the rules themselves are not derivable from raw reality input. Again, you would have to observe every a and b and c to conclude the rule is truly general and universal, which we can't do as humans with limited (and faulty) brains.
I think your confusing the fact that there is trial, and error in the discovery of math to mean that it isn't discovered at all.
The fact that we don't have to make up new fundinental rules in order to make something new mathematically comprehensible is evidence of that
@@anthonypolonkay2681 If your standard is merely that it is "comprehensible", all kinds of fictional math, and other kinds of logic, are comprehensible, yet obviously invented.
Also, I think you missed my point. My point wasn't that because we discover new math through trial and error, therefore it isn't discovered. That would be evidence of it being discovered, if anything.
What I did was make a distinction between the general and the particular. Math deals with the former, experience and discovery deals with the latter. To bridge that gap requires work by the human mind that isn't just a mere logical deduction, therefore it is invented. Unless of course you think knowledge of math is somehow buried deep within our minds from birth, and if we just think hard enough, without any experience, then we can discover it. But that's a ridiculous claim in my view.
@@Google_Censored_Commenter
Its not just that' it's comprehensible. It the fact that the same set of mathematical laws are followed throughout all examined areas of reality. You dont need fundamentally new sets of mathematics laws to describe the motions of planetary bodies vs the energy output of a chemical reaction.
If math were invented the fundamental rules of it's use would change different phenomena, but they don't. Which means thos such mathematical laws are objective, and not products of invention or interpretation.
@@anthonypolonkay2681 Mathematical laws being invented is perfectly compatible with the qualities you describe, including objectivity. Quantum physics is largely all just math, new math at that, to describe a more complex reality of atoms. But you've still not really addressed the point I'm getting at. Take the speed of light being constant for example. Have we *discovered* that general law of nature? Not really. What we've discovered through experience, is the speed of light being constant in all types of atmospheric pressure. We've tested it a ton of different ways. We've tried falsifying it and couldn't do it.
And yet still we have not really discovered it is a law of nature, as a general principle, because that would require examining all of the cosmos. Instead it is an *assumption* of the human mind that arises as a consequence of our discoveries. Just like it is an assumption it will continue to be constant in the future. There's no guarantee it will. That's what I mean when I say generalities have to be invented, they require the human touch of assumptions. No matter how many triangles in nature you observe, no matter how many you draw with pen and paper, you can never say you have "discovered" that all triangles have three sides through experience. If you want to say that, you have to use assumptions, axioms, language, and all the other inventions of the human mind. That's not problematic, human creations are still meaningful, if that's your concern.
@@Google_Censored_Commenter have you ever looked into the Mandelbrot set? That is a pretty easy example that disproves that all math is a construct. Humans cannot produce true infinites of any kind, but that is what the math leads to.
Yeah, never ask physicists that question…
Math : Discovered
Numbers : invented
Math is a descriptive subjective system we've invented to describe the phenomenon in our observable universe. It's isn't some sort of divine objective prescriptive system that we discovered. It's our complex answers to complex questions arived at by our logic
Well, you can also say that the we have build a language/descriptive system, to examine something inherent to the universe (math). I think the main discussion here is the definition of math
@@beetlesstrengthandpower1890 The thing is that we have to interpret everything through our limited knowledge and understanding. To claim math is some inherent truth of the universe, rather than simply a man made system to explain universal phenomenon is absurd. This is a deeply philosophical question. I reject the concept of a "true world" beyond that of the apparent world. There are no systems of objective truths beyond our human perceptions.
Math is definitely a discovery. It exists, whether we knew about it or not.
Ure as dumb as the people who raised you... Or maybe a bit more I guess
What math describes, yes.
No, that's objectively wrong. Mathematics are a linguistic system (just as much as verbal communication/language and music theory) made by man and, thus, it's artifficial. What there certainly exists are the LAWS of nature, mathematics is just the system we made to better and more easily explain the LAWS of the nature that we can observe and identify with our minds. Every linguistic system we made is just to explain the laws of nature that we could observe with OUR MINDS first.
@yoshi_drinks_tea YOU GET IT
So if we created math, was there ever math that was proven wrong? Or did we miraculously come with the correct equation systems every time some new mathematical field came up?
Well,, thats exactly why we didn't create it. We only created our description and use of it.
if we created english, was there ever a language that was proven wrong?
math is descriptive.
KEvron
Mathematical theories can be wrong by producing inconsistencies or paradoxes. See Frege's set theory, proven contradictory by Zermelo and Russell.
He is asking if the fundamentals of math were ever proven wrong, not any particular theory. And the answer is no. It hasn't.
Think about how silly it would be to say Isaac Newton invented gravity... It was always there at a very specific reliable value making it a discovery. I believe math also is a discovery in the same way that 4 bananas plus 4 bananas always equaled 8 bananas. We just discovered a way to explain it. To invent math means you could assign any value to anything you want and call it true despite the entire universe laughing at you.
maths is discovered to understand maths numbers are invented
couldn't have a better explanation
You nailed it
The basics were discovered, over time things were invented in it.
This is what I've been thinking since I was seven.
We have invented a way of applying something that we did not create
isn't "expressing" a better word than "applying" here?
Well explained
What's the name of the first man who spoke? For research purposes only.
Instead of joking around, I think they should have provided more explanatory examples.
Discovention yayyyy👍👍
It's groovy
Math is the substrate from which the universe springs forth.
Omg that Asian guy is hella nerdy. No hate. it’s all good.
For some reasons most Asian’s are.
@@theconsciousmovement9669 🤔
He fun! He was trolling Neil deGrasse which is a challenge to do so in itself...lol
They all pretty nerdy(they are discussing mathematics what do you expect)
Everything is discovered nothing is invented
Neil meets his match among fellow superficialists at last😅
Oh my Jesus.
OMJ!!!
Math is like time and space !!! Without time and space there is no math !! Time and space the closer something is less time is needed if touching you no time needed at all or math coz nothing to work out !!! To me it's obvious time and space are the same thing !! Playing football you learn to run into the space so you have more time on the ball !!!!!!
As philosophical as Neil is, he sure outed himself as not a philosopher when he couldn’t pick an option in a difficult situation
The truth is everyone pretends to know but deep down they know they don’t know
A logic invention. Do We have one berry? 5 berrys? Im sure the package older form of humans had some sound or sign for how many of something there is.
I do NOT however think they called math for a few hundred thousand years.
I do also think its right that it’s already there in the world by it self
GREEKS INVENTED MATH 💪🏼🇬🇷🇨🇾
Nope lmao but they invented gay sex
I thought Calculus was an emperor of Rome it works only in English lol
The Name of the Asian guy?
Yeah the people who figured out a lot of shit would look at nature
The Chinese singing guy is cringe
true
@@fredward2428 yes bro
Nah he cool
I had to quickly turn it off when the singing started.
Yes, but he's smart enough to get a pass
So you are saying you invented 2+2=4
Blue lotus wings 🪽
🧠 💥
It’s obviously a discovention
No, that's disco and convention.
To the complex question what is not known.. still not know! Forgive me apply the 6Ws and we stop being Being complacent with a knowledge acquired go back to basics repeat that cycle with your AARs and the stagnant mine continues to seek enlightenment so as a beginner in applied astro physics I ask to you without your study’s and book how far did you as individuals excel on your own the beginning of year conundrums your thesis what was the spark. I ask cause my spark was why my answer to myself was why not simplicity being a self-proclaimed engineer with no mathematical scientific on the contrary combative war fighting skills yet my hunger for questions curiosity never failed and the question still baffles me how with all we have to humanities abilities the answers for such a small simple Conundrum to the vast emptiness of space so close yet so far why are these within our grasp yet light years away in his image is the biggest issue I have in text to date. Your thoughts
kkkkkkkkkkk 2:30
The problem is, even rules are invented in mathematics. One good example is the mathematics of complex numbers.
In linguistics rules are broken all the time... “i before e except after C” weird species we are. But math to me is closer to medicine and science, it’s discovered and the rules change because we can never be 100% sure of them. Math is very much a scientific experiment.
The mathematics of complex numbers are a natural extension of the concepts of adding and multipling real numbers. If you develop intuitions for what goes behind them, you are just one step before complex numbers.
To understand what I mean, try to make sense of multipling √2 * π. It can't be repeated multiplication because what on earth would be √2 repeated π times?
@@hdrabba Math is a priori. Science is a posteriori. Math is deductive. Science is inductive.
@@gustavoalexandresouzamello715 science is not just inductive it uses both deductive and inductive..with out science maths just some concepts..
@@gustavoalexandresouzamello715 4.4428
Maths is a discovered puzzles? Existed already?
Nothing is new under the sun Nothing was invented
unfruitful discussions that's it
Neil Degrasse is wrong here. The universe does not "follow" rules. This is actually hard for som people to grasp. Grasp it - don´t Degrasse it.
🤣🤣
Tyson loves to interrupt
But math has fallacies and paradoxes. It means what we want it to mean. It's just something else based on human perception. It works like language. Math is inductive and deductive because we make it fit and develop it. Many things don't have formulas. If you could use math for everything, everything would be calculated. Everything would have to be exactly like the other. Why is a circle 360° instead of 720° or 180°? Humans still barely understand how most things work and base everything on observation. It's almost becoming a religion.
Could you please give an example of the fallacies or paradoxes you refer to in your comment?
@@Estadistica-Matematica-Labs Cantor's paradox and dividing by zero are a couple.
@@KBdotHAQ So did 1+1 did not equal 2 until we said it was 2???? Why not 3? Or 31415.16??? I think it follows a logical sequence right??? Other wise we can just invent anything we want and make it work the way we want it. Why dont you invent a nunmber system that would give you something out of nothing? Like 0+0= everything! Show me that you can invent such a system and i will believe you!
@@victorvalencia6466 You can't add 0 because 0 is nothing. Even the fact that zero is considered a number is flawed. Like I said, these numbers are just based on human perception. I mean why can't 1+1 mean 1 if depending on your view, or whether or not the society in which you live uses numbers at all? If humans were gaseous beings we wouldn't view numbers as we do now.
@@KBdotHAQ you can view numbers as you wish... but the truth will not change. We get to invent the symbols and invent the names of numbers but the structure of the truth will still be the same no matter what. Its like the 5 plutonic solids, you can invent symbols to discribe them and even call them what you want, but what you cannot invent is the 6th plutonic solid because it does not exist.
Math was pre-existing. So math itself, the quantities are not really discovered or invented but Realized. The style in which we choose to code, or write down, the math concepts like a language of symbols are our human invention for the relationship of quantities that we realized. Similar to going outside in the sun and noticing your shadow. You didn't discover your shadow. You didn't invent the shadow. You realized a phenomenon that occurs when certain conditions are met, a phenomenon that was pre-existing.
We have a perfectly good model of how a mathematical framework can exist outside of the conscious experience. That's what we have created with computational devices. Just imagine yourselves as beings, made of pixel dust existing inside a matrix. Then you realize your thoughts come from underlying binary code also known as dark matter. You should know a physical architecture or server system can expand from the outside and that expansion is reflected on the inside. That's what dark energy represents, it's not only our container, but it's why the universe is expanding exponentially. The difference is you cannot physically interact with it internally. Through the mind and thoughts we can interact with the mathematical framework.
E=MC² hence matter and energy are interchangeable.
Light is used as a metaphor for intellect, wisdom and consciousness, without light (electromagnetic radiation), the mathematical framework we use everyday known as computational architectures, wouldn't be accessible to us in such a rich and interactive operating system experience. These architectures show us what mathematical frameworks look like from the outside in. This universe shows us what a mathematical framework looks like, from the inside out.
Invention. This is really not a hard question.
Why do people act like neil is a genius ? Hes a scientist in 1 field not every field.