Roger Penrose - Is Mathematics Invented or Discovered? (Short Version)
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- čas přidán 21. 02. 2016
- Mathematics describes the real world of atoms and acorns, stars and stairs, with remarkable precision. So is mathematics invented by humans just like chisels and hammers and pieces of music?
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I'm here in comment section to see what the geniuses have to say
I'm a self proclaimed genius and flat earther And I'm way smarter than this Penrose feller. Even though when calculus was up next I said fuck that.
@@tyhggb flat earthers can't be genius. They are dumbest people
Ameer Hamza they are the new breed of w0ke
I'd say math is a discovery.
Geniuses don't say anything when fools talk, only they listen, think and continue in silence.
Mathematics is only "invented" insofar as the set of axioms we use and the notation is "invented". All properties of the system that are a result of those axioms are discovered.
exactly, it´s like someone is speaking, and you invent the letters and language to write it down.. but the speaking exists independently.
mathematics is deductive; the properties of its axiomatic systems are deduced.
KEvron
2:30 that zoom in cracked me up
I thought it was going to turn into a Tim & Eric skit. Cheers.
Came here for this lmaoo
I love how closer to truth asks the same question to different people. This here makes the most sense to me.
"One reason why mathematics enjoys such special esteem above all the other sciences is that its laws are absolutely certain and indisputable, whereas the laws of all the other sciences are to some extent debatable and always lie in constant danger of being overthrown by newly discovered facts.
In spite of this, investigators in the other departments of science would not need to envy the mathematician were the laws of mathematics only applicable to our imaginations and not to objects of reality."
Albert Einstein
Your statement is only partially correct. Mathematics is defined by it's axioms and it's laws are a result of the axioms used to define it. The current axioms and the outcome of these axioms are still being developed.
Absolutely certain and indisputable does not apply to anything that the human mind creates. In order for your statement to be true mathematics would need to be complete, ie everything that can be known would be known. This is certainly not the case.
but math is a language, not a science.
KEvron
congrats Sir Roger Penrose. You are really a great mathematician.
but not a good philosopher of mathematics...
I’m beginning to suspect it’s a little of both
That this platonic reality of mathematical structures exists and our math systems are what we use TO discover and make sense of these thigns which I believe now to be the very “codes” of the reality we experience
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Thank you for these wonderful conversations, brilliant minds who are inspiring all of us.It's a pleasure to Listen and Learn.
Penrose is right here. The greatest philosopher of mathematics, Kurt Gödel, too said that mathematics has been discovered, not invented.
True! Mathematics has been discovered. Good that someone brought Godel into discussion. Any discussion about mathematics is INCOMPLETE without the mention of Godel.
Haha.. "Incomplete" in caps. It's amazing that a man who proved Mathematics is incomplete is perhaps the one who has rendered the greatest service to the field. Definitely the greatest service to mathematical logic if not to the mathematics as a whole.
Godel's incompleteness theorem is definitely among the top 5 discoveries of Mathematics
We can argue whether it was Gottfried Leibniz and Isaac Newton's discovery of calculus or Kurt Gödel's incompleteness theorem that should be regarded as the greatest achievement in the field of Mathematics.
I'm not convinced. To suggest mathematics must exist independent of human discovery otherwise how did the universe know what to do is like asking how did the plum know how to be purple. Penrose's suggestion of a Platonic world is fraught with issues, including the unanswered question of how abstract platonic forms interact with physical reality.
It just his method in explaining these difficult ideas is in itself exceptionally convincing and concise and is enough to make wonder 🤔 and allows you to really think.
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It’s interesting because in one sense mathematics is a language used to describe the physical world with accuracy but on the other there is the question of if another “language” is even possible.
It’s already founded on the most basic and important distinction that one of a thing is 1, two is 2, and so on. I don’t see how that’s negotiable to achieve the same end. Though perhaps that’s because it’s shaped to the understanding of our brains and a different alien civilization would be differently wired and understand the universe in possibly different terms but I can’t comprehend how.
Thanks, I love this stuff.
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Interesting to think of something abstract as "out there".
Before I even watch I'm going to say the answer has to be invented, I bet it sure feels like discovered though. My reasoning, Just as Mathematics feels like a more pure language to describe the universe when compared to the written word, it is still very human relative. Math is still just the best human created tool to help describe the universe around us.
Very interesting 'fact' - the Abstract is being explained in Mathematical precision... Listening to this, Mathematics is always there existing and We are just 'discovering'..
Sounds like Vilenkin's idea which I think is that the laws of physics in some platonic sense 'logically precede' the emergence of the universe.
Yes -- also Gödel
Yes - Vilenkin has revealed himself as a Platonist - but more recently, I think he has equivocated on this issue, by suggesting the possibility of a real "nothingness" giving rise to a universe. But again, he has not been clear on his position. In truth, I think he would prefer not to express an opinion on this, except that he is always pressured to answer the "why is there something rather than nothing" question. Robert Kuhn has had this discussion with Vilenkin, and never really got anywhere with it.
And the God of classical theism is not too far off from there. Which is why, I imagine, people get nervous around such ideas. If what Lourak613 reports is true, Vilenkin's current attempt to postulate a pre-existent nothingness that could give rise to a universe (a fairy tale for the children of post-modernism) smacks of a pretty desperate move to avoid or dodge the specter of what in symbolic terms is called the Creator.
"EXCELLENT"......"in reality ,it is already out there " ( means discovered.)..... beautifully , sweetly , eloquantly , in plain language & in seven words , explained by distinguished Sir.ROGER PENROSE , once for all & thus extinguishing the ambiguity on mathematics being as discovered or invented ....and that. is it ,no more discussions further........ thanks 🙏.
May I rent that library for ten years?
Mr. Owl, do you know how many joints it takes to get to the center of the universe?
I invented math in 1985.
My parents named me after you for that reason.
You are wrong. I invented math yesterday.
@@helsinki what!?! What's the big idea??? You taking the piss? I invented it 35 years ago, friend. X-wi-ze was present and witnessed it. (Even named himself after the coordinates.)
So if I was being generous I could say you discovered it (congrats) independently since I put it out there in the ether. But no, so yeah.
Expect to receive a cease and desist order from my lawyer. And id this continues, I will have my day in court.
@@enzoferrari8223 Hey man! You totally besmirched me and I demand satisfaction!
@@helsinki bro you know very well you started smirching. I may have besmirched u but I was presmirched. You even didn't even apologize.
I normally keep extra office hours for students. If u want to learn more please ready my paper entitled Foundation In Nigganometry and Algebro .
The key point behind objective reality is that it exists whether we describe it or not (or does it? That's another can of worms...), and Penrose touched on that in this video. Case in point; the universe didn't need a language invented by something borne of that universe to describe that universe, assuming that in order to exist, it isn't reliant on, say, a collective, subjective conscious to build an objective reality. For all intents and purposes, then, it was going to exist whether we were going to be in the picture or not. Contradictorily, the properties and behaviours that 'our invention' describes then exists with or without us, and _so in that_ sense, mathematics is a discovery. It really depends on what you're defining as 'mathematics'. If you readily define it as a type of objective language, then you're readily sitting on the invention fence. If you readily define it as the underlying properties of the universe, then you're sitting on the discovery fence. If you're doing both, then get a god-damned hobby, already.
Either way, it seems preferential, whether mathematics was invented or discovered. You say it was invented as an accurate way to describe reality, and you say it was discovered as a possible means of accurately describing reality, I say it was a good waste of several years of my school life in preparation for something Iw as never going to do. It doesn't matter - we can use it to describe things that our senses aren't going to. Mind over matter and all that shit.
The universe exists with or without us.
[Mathematics and Physics - Ideal and Actual Worlds]: Mathematics is often called a language that describes nature or its changes or movements, and is also used as a tool to model logic and judge their right and wrong.
Is mathematics simply an artificial thing created by human beings? Even its representing symbols are artificial, is a concept or a logic inherent? If it is inherent, does it exist only together with nature, or does it exist more priory and originally than nature?
The various symbols and expressions used in mathematics must have been defined by humans. But it can not be said that the concepts and theories in it are also artificial things created by humans.
For example, when describing a natural law with an expression, the law can not be said to have been created by a human being, and when any right logic is expressed by a formula, the logic itself can not be said to have been created by man.
The law of nature - if the law is right, regardless of whether it is good or bad to human beings - is a description of mathematical modeling of the causal relationship that the same phenomenon always occurs in the same condition in the physical world. It is a logical problem that human beings can not intervene.
The main task of physicists is to find these laws or principles that exist in nature. And engineers - even though they find such laws or principles themselves - make them available as machines or products mediated through matter, so that the found laws or principles can be used in real life.
However, the individual cases that occur in nature or are applied in real life correspond to special cases of actual cases that - can be expressed as numerical values - are infinitely possible in these mathematically modeled natural laws and principles. Thus, realization in nature and everyday humans life can be said to be the realization of some cases of mathematics based on matter.
In this case, if the mathematical logic is wrong, the behavior of the manufactured product will not work consistently with the corresponding principle as it is predictable, and - especially for satellite or missile - remote observing, monitoring, control, adjusting, management and maintenance will not be possible.
The question is that if there is a perpetual logic that human beings have found or thought out through thinking, even not in nature, that is always judged to be right for anyone who thinks right, transcending the physical space and time, anywhere, anytime, then who made the logic and how can it always remain right?
Examples of such logic include the consequences of reasoning proven through various pure mathematical axioms or rational thought processes. As an example, the logic of the most basic arithmetic rules (addition, subtraction, multiplication and division) has been found and used separately in different parts of the world in the past when traffic and communication never developed, and the logic that the physical world is finite and always changes has never been denied and confirmed right in natural daily life.
Thus, mathematics, logic, and philosophy are more primitive than physics, and they are independent of the physical world - or have no relevance to physics - and have been able to study independently. Concept or right reason has been felt to exist before the physical world.
Plato felt mathematics as the domain of the Idea world and the God’s world. Mathematics deals with infinity, but physics rejects infinity. This is because the world of matter is fundamentally a finite world, and mathematics can handle any logical world away from the physical world.
For the fact that while the physical world is an imperfect, always changing, temporary, and relative world that includes tangibleness, finite, quantized discontinuity, and error rates, the world of reasons is intangible, infinite, continuous, complete, immutable, permanent and absolute, it is dealt with in ‘3. Physical World - incomplete, ever-changing and temporary Material World’ and ‘4. Truth's World - never-changing and ever-right God's World’.
For example, the theorem that the sum of two sides is greater than the other side in a triangle - corresponding to the pure concept of logic that the straight line distance is shorter than a certain curve distance - is right in the ideal world, but it is impossible to realize it perfectly in the actual world where refraction occurs even in light.
Repeating the process of bisecting each line of the oblique sides and attaching them to the base side on an equilateral triangle in an infinite number of turns, results in the final that the sum of the two oblique sides becomes equal to the base, and the above theorem becomes wrong. This means that it is not possible in the actual world to repeat the bisecting without any loss and infinitely.
The Pythagorean theorem that the square of the base of a right triangle plus the square of the height equals the square of the hypotenuse, and the mathematical formulas that determine the circumference or width of a circle are also ideal cases. In he actual world, we can not make perfectly right triangles or circles without error.
This is why some industrial products (eg, construction, machinery, electronics, etc.) used in the actual world can not be completely perfect, and - this is because the physical world is ceaselessly and interchangingly changing as a whole - have limited performances and life spans. And we may understand that the fact that the natural exponents and cosmological constants (eg, the ratio of the circumference of a circle to its diameter π, natural exponent e, light speed c, Planck constant h,
[Difference between mathematics and physics in 0 and infinite handling]
Physics deals with the physical world. And mathematics deals with the logic world. Physics deals with a world in which material existence exists, and mathematics deals with a logical world that may not require any material existence.
Therefore, in physics, zero (0) and infinity are not handled. The physical world treats the change mainly on the assumption that there exist somewhat physically in finite space-time, and it does not handle the case that existence is infinity. In other words, physics deals mainly with the existence of certain physical beings in a finite world.
However, mathematics can treat zero (0) without physical existence, and also treat infinity. The world without a physical being is a primordial world, and the world of infinity means to contain all possible cases.
Thus, physics corresponds to special cases of mathematics and can be explained based on mathematics. In other words, the laws of physics appear as mathematical expressions in special cases in various cases in mathematics. This shows that the physical world is a realization of a part of the logical world.
(Extracted from OnCharm's book "Humans & Truth")
Max Miner, thank you for your comments. I want you to understand that the zero I'm talking about here focuses on the fact that there is no physical presence at all, but not zero in relative expression.
Are we talking about the centers of London and LA, or different points on the cities' borders? Which point, and which center?
I am a Senior in college coming close to finishing my undergrad as an Economics major, although sometimes I wish I had studied Physics or possibly been an Econ/Physics double major. I have a profound love for mathematics and the way it explains our natural universe. I often contemplated ideas like this when going through high school. Although I have enjoyed my studies thus far, I wish that I was pushed towards math more by my parents and instructors.
Mate, no one gives a fuck.
I hope you've at least learned enough economics to be a socialist poltically.
A lot of people seem not to know enough about numbers to say that mathematics is "only" a language. Numbers have autonomous properties which are not only arithmetical and algebraic but geometrical also. Numbers are shapes and shape generators. Square numbers, for instance, are actual squares (a basic example which an astounding number of people are unaware of). Or all natural numbers are the side of an equilateral triangle. According to the pythagoreans "all things are number" - this is to be taken literally, but the mistake most people make is to project their own understanding of "number" onto this thesis and then consider it absurd. So, before you do this you have to ask what in reality is number.
Even though there are invariant structural elements of language, language does not possess the same autonomy as mathematics does. There's also a difference between mathematical reality itself and mathematical description, which may depend on human constructs. Most people don't even know the difference between digits, numerals and numbers. But the interesting fact is that the ancients didn't seem to make a rigid distinction between digit, numeral and number. To say that mathematics is just a language is an unjustified opinion.
I won't say that numbers are eternal ideas and archetypes, as it seems the pythagoreans and platonists have claimed, but the fact is that reality is mathematical. The dualism between "logic" and "being" is an artificial one (I am aware that to equate mathematics and logic is problematic, but we may suppose that mathematics has a logic of its own). The best would be to say that in our human constructs (mathematical description) we try to approach mathematical reality, NOT that mathematics is a tentative description of (illogical, unmathematical) reality.
Back to basics: www.mathsisfun.com/numbers/numbers-numerals-digits.html
templesein i like your last sentence
"In the begining wase the word" The word wase before, light. What we describe to de "sound" is the vibraţion highter, or lower. Indead, some people knows alittle what matematics is , wich matters! But you dont know what "sound" an language is, so dont act out as if you created matematics. Matematics is the information of the language that is emit from the esence of the infinit, wich is God.
You may know a little about numbers, wich is a definition of language (number) but you don't seem to know what language is! Language and numbers are just definitions of a language, we have our own, and the Uni-Verse haves its own language. Only differ in wich one you go by. You may be a smart guy, but wisedom is about reading between the lines!
You seem to be lost in your language of describing numbers. Matematics is not something wich we create. But is the information wich the mecanics of the uni-verse wase build with. But humans act out, as if they created everything without realising it! Matematics has to deal with the spiritual mecanics of the uni-verse(one song, one truth) wich knowloadge of man, by their own language and knowloadge canno't comprehend in the laboratory! You get to understand matematics and numbers with your language (English) the Uni-verse don't speack English! Or Dothraky!😀 You can be logic in something complex, and wrong in everithing complex.
"Precision beats power, timing beats speed"
-Conor McGregor
One of the brightest people around
Hay una conferencia de carlos madrid, de la escuela filosofica materialismo historico, fundada por el prof Gustavo Bueno. La recomiendo!!!!
Mathematics describes relationships. The question thats really being asked is wether the relationships that we observe exist with or without an observer. The answer is yes because how else would they give rise to an observer.
IT'S VERY NEAR CORRECT, IT GIVES US SOME GOOD ORDERLY DIRECTION
What happened of number 9 wasn't added/invented/discovered? e.g. 12345678-10?
Its out there and its in there, as well, simultaneously!!
Mathematics can be used to describe the physical world, but sometimes only to a certain level of accuracy.
Mathematics can also be entirely self consistent, but not describe the world, or any other world.
For example it was assumed for millenia that Euclid's geometry was the only geometry and described physical space. Then at the end of the 19th century, non Euclidean geometries were discovered which had different axioms and gave different theories. For example the interior angles of a triangle could be greater or less than 180 degrees.
So the question became, does Euclid's geometry describe the space in our universe? It seems that Euclid's "flat" space with internal angles of a triangle adding to 180 degrees is only an approximation on a 'small scale' but on cosmic dimensions space is curved, according to relativity. whther the curvature is 'positive' or negative is another matter, not determined.
So the question of whether the maths is 'there' waiting to be discovered or is an invention of the human mind is really one of choice according to philosopical inclination. Not being much of a mystic, I find the idea of a disembodied mathematics existing somewhere waiting to be discovered problematic.
I view it as an invention of the human mind.
A true intuitionist! I’m somewhere in the middle. Mathematics is 100% created by the human mind, but at the same time the fact it can be self contained yet still describe our world is pretty astonishing to me. And that begs the question of whether our mathematical systems have some intrinsic root in existence, for which we were guided to “create”. Non-Euclidean geometries is a good example actually. Before their discovery/creation, our system was confined to those axiomatic rules. A simple thought experiment by Einstein prompted us to probe and question more things, ultimately deciding to maybe reformat some or all the rules. At the end of the day, we humans create the math, but I think that existence of and certain aspects of physical reality guide what kind of math is created. So in a way, the math is there but “uncovered” or “hidden” because we haven’t been prompted to look there yet. I’m not looking for an argument or anything, or trying to change what beliefs you may hold, just wanted to share what I think, because these types of conversation are so mind blowing to think about, it make me appreciate the works of the field that much more.
@@tjayoub The human mind is a product of the laws of nature which are described by mathematics so in a sense you can say mathematics created the human mind which created mathematics.
@@pshehan1 never even thought about that. Bckwhaaa. (That was my "mind blown" sound effect)
This is the deduction vs. induction debate that dates back 400 years or more.
It’s cool he was on JRE
This guy must know huge times tables. Awesome.
Fascinating fascinating fascinating
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What year was this recorded?
2009
Wish everyone had this kind of understanding of maths, and not that it is boring and hard,
Maths has its own beauty, which is independent of the reality.
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Good people. So spiritual in many ways
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Are poems invented or discovered?
What is your favorite number?
Yes!
I’ll try this again when I’m not high.
What does platonic reality mean?
The reality of Form & Geometry; think of the "platonic solids". (Tetra, cube, icosa, dedeca, etc.)
Mathematics is a formal symbolic language not an inherent set of truths about reality. It has high consistency with experience in the same way that any language provides some level of description (explanation, prediction and control) as any language does. We tend to emphasize the aspects of mathematics that are consistent with our actual experience - and we tend to ignore those parts of math that do not. Reality is not mathematical - it is not a set of ones and zeros.
I hope to be able to download his knowledge to mine some day
If you do it , call me
Mathematics is discovered, mathematical machinery is invented imo.
Edit:
Like any other thing in mathematics , you must firstly understand the definitions before expanding your theory. Despite this discussion being technically out of mathematical range ( Russel's paradox ) , we should and must apply the same rule. So , before jumping into any conclusions , what is mathematics ?
Ok I understood the discovery aspect of maths:) however at 2:26 a resality outside of reality of chairs and tables doesn’t seem doable. I think maths is still epistemological :p thanks sir penrose
I love Penrose , undogmatic as usual here . Some truths are true even though no one sees them ! Is beauty in the eye of the beholder ?????
In my dreams, mathematics is very simple and easy to understand. Everything could be whatever, total absence of mathematical axioms doesn't affect dreams at all.
"As we/humans understand it... mathematical description".
obviamente descubierta
Mathematics does not exist "out there". But physical reality can be described in a mathematical language because matter is constant, uniform, simple and quantifiable. Differently than a human organism, that could never be described by an equation, only by an description or concept.
2:35 that looks is me
I could not agree more on that. Thank you Mr Penrose!
Mathematics is just a symbolic language for describing interactions in the natural world. You can also ask, "Are natural languages invented?" Well, no. They developed naturally as a way to better describe/suit the realities of any particular geographic region.
Diiagonal of a unit square : sqr(2) , discovered . Square root of -1 = i , invented .
it doesnt exist any square in the World.
I truly believe that it's geometry and topology all the way down
Our universe is ordered with such awesome precision and must needs be organised with laws... which are describable as math.
If there are intelligent creatures on other planets, I think we could only use mathematics to communicate with them in the first contact
Theorems are discovered. Proofs are invented.
Penrose said that it's a mathematical truth, independant of humans that there is no largest prime number. But what about the concept of prime numbers? Did humans invent that? Or the concept of division that defines prime numbers?
Unfortunate that Penrose wasn't asked to address the question of who created Platonic reality. And could it have been different than it is?
One day we may communicate with an extraterrestrial intelligence. When we find that their math is the same as ours, the question will be settled. Euler's identity is too beautiful to have been invented.
how do we know? and what of the electron? surely it's either there or it's not. but it isn't. or so we're led to believe. maybe there was mathematics until we discovered them.
I think there is an order to the universe that can be represented in mathematics though mathematics may be in no way essential to its mechanics
It's a concept only exists in math like particles for example my odds go very much against them being real.
Mathematics is the realization.
It depends on our definition of what we define as conscience and reality, mathemathics is the direct transcription of how our brain chemistry and senses and pre frontal cortex works to perceive and analise data we gather from our environment, from a survival and decision making support view
If we think of the universe as a whole conscience, then the way we view the world MAY coincide with the actual reality of the world, therefore mathematics is a discovery and not an invention
But if we think of the universe as something that is fundamentally beyond human comprehension, and we just have our human way of perceiving things, that doesn´t mean our way of perceiving is the actual real way the universe works, and math is just a human construct mimicking our neural network way of critical thinking and abstraction, and the universe may be so complex that it´s data is just too complex for our brain to process
The fact that even the equations that (try to) describe physical phenomena are not 100% accurate just proves one of two things: either we need work the math to perfect the formula itself (because math is fundamentally the real way of describing the universe), or it proves that the universe is too complex for us to try to understand it and we just work with the best aproximations that our brain is capable of handling the complex reality
"Something"
language inspired or invented
Math is a tool in the human toolbox for understanding. It resides in minds and nowhere outside of them, just like vision and touch and other such tools. We map the universe with these tools to varying degrees of accuracy, but reality exists independently from your or my understanding of it. There is no mathematics to be found anywhere in the universe outside the mind.
The workings of reality neither rely nor are in any way affected by how we choose to describe them. Before there was mathematics, before there were thinking minds, there still existed a universe. There was light long before there were eyes to see it. A ringing bell propagates sound waves even in the absence of a means to hear them.
If you're seeking a mathematical universe, look to virtual worlds. These were created by human tools of understanding and not merely described by them.
The funny thing is that "mathematics" is really a network of various related fields...the word does not describe just one thing. Geometry studies the relations between forms and constructs in space (in various dimensions), then there is number theory, calculus, topology, set theory, etc. What mathematics are you talking about, when asking if "it" is invented or discovered? I'd say some fields within Math are more or less "discovered", while others are more "constructed". Of course, ultimately, our symbols and definitions are constructed, but there are indeed amazing quantitative, numerical, geometrical...patterns out there in the "real world" that are discovered. Its a bit of both. I mean, does it even make sense to generalize about mathematics as if it were one monolithic thing? Let's get a bit more specific with our questioning and philosophizing, people!
Yes.
Isn't it kinda obvious that the physical world can only exist if the physical stuff reacts with other physical stuff? Matchematics is our way of describing what the physical stuff does to itself. Probably conciousness is thee same, just physical stuff in the brain that we dont understand yet.
I find this discussion to be highly relevant to the phrase "If a tree falls in the woods an nobody is not around to hear it does it make a sound?". Of course it does. Humans think themselves special. Its irrelevant whether humans have discovered something or not, its exists. Math is not an invention. Its a discovery of something that already exists. Mathematicians job is to describe it.
How can it be invented if it always has been existing?
To me it is obvious that math has been discovered.
@Richard Doherty Is this a real question or a joke?
No I don't have any proof. It's like me asking you to prove that a glass of water is half full instead of half empty.
@Richard Doherty maybe for this case is the same, both answers are correct, And maybe it's goes against any logic in our brains, like the uncaused cause or something like that, the unmoved mover, so to speak..
@Richard Doherty yeah, your comment make sense, I also thinks that math are a tool, but it seems to be a mathematical truth anyway, I like the way max tegmark thinks about this, there are platonic mathematical objects even prior to any physical law or even prior to the existence of something, obviously I don't know this is true, but it makes o lot of sense to me, perhaps this is the ground of existence, the most fundamental fact, something like the default state of a state, my God, my brain is now melting down
Stefan Löfven - The notation is certainly invented, so you are sayingthat is not a part of mathematics.
@@GH-oi2jf You obviously have no clue about philosophy.
The platonic world is a heaven for our imagination
your imagination is more than malleable enough to grasp complexity in nature. The hard part isn't learning, its discovering.
tic tac toe - invented or discovered?
Discovered through innovation
Agree, we innovate tools such as numbers and methodes then use them to discover and to understand the structures or how universe works.
Penrose is a brilliant physicist. I especially like his work with microtubules. Math is in fact a creation of our imagination which can then be used to create Math Models to help us understand the 'real world'. A great mathematician once said a mathematician is someone who knows a lot about nothing. All Axiomatic Systems start with Undefined terms which scientists give meaning to via ostensive definitions.
Math consists of Axiomatic Systems we invent. Then within a specific Axiomatic System we discover meaningful statements which we call Theorems if we can prove them. The Pythagorean Theorem is only true in the Axiomatic System of Euclidean Geometry. It is not true in a non-Euclidean Geometry like the surface of a sphere like we live on. Wolfram is correct that there are many possible Axiomatic Systems we could invent and the one's we have invented are essentially an artifact of Sapiens. Indeed, Einstein could not have developed his Relativity Theories with Euclidean Geometry. I discuss this for high school students in a video at my website @t
Like words
Mathematics are a component of human language. A description of real things. To say that reality is hinged on a system that humans made to understand their surroundings is quite egotistical. It's the equivalent of saying, "It is, because I said so." That is grossly unreasonable. Now, is reality inherently based on some kind of mathematical system? How would you know, unless you made one that describes it, exactly, that is, without error? There are many mathematical ways to make excuses for that...
Maths is out there.
No Maths is projected out there.
Because human brains are pattern recognition systems and mathematics is a pattern so therefore it is there but only by the grace of desire and curiosity.
I wish mathematicians would formulate how completely unaware of thier existence and how thier senses minds bodies work.
MATHEMATICAL REALITY IS A THIN LINE BETWEEN REAL AND ARTIFICIAL INTELLIGENCE
Mathematics should have a special word. It wasn't invented, it wasn't discovered. It was invovered.
It's like arguing if a blue apple is red or yellow. Just invent a new word and call it "blue" instead of arguing that it's red or yellow.
The problem is that most inventions that have been created can be thought of in the same way. In a sense, the electrical transistor was invented by one specific person looking to solve a specific problem with specific materials. But in another sense, the transistor was discovered, and anyone who wanted to achieve something similar with electricity would inevitably find the same approach. It doesn't make sense to say that math is not invented just because the solutions and questions of math existed before anyone thought of them. The same is true for the solutions to all kinds of practical problems. Ultimately, the distinction isn't really meaningful. Mathematics can't be talked about in a mind-independent way, but obviously must be mind-independent. In the same way, inventions need a creator, but we should expect aliens to know about wheels and pulleys even without any prior communication between them and us. All of invention is in some sense discovery, not just math.
Is it possible to create something that doesn't follow math laws?
burt591 the music of soundcloud rappers. Lol
@Oswald Mosley alchemy is real but that other thing is wack
@Oswald Mosley
Haha, I know what you mean, and I also know that alchemy as it was described in ancient texts was not meant as a process for transmutation of physical objects, but was rather an allegory for psychological experience, the act of turning lead into gold being analogous to the act of becoming the image of christ, or the perfectly balanced and realized human psyche, in comparison to the dull lead creatures most of us are. And it works in practice, and it's what the entire field of psychology is predicated on.
Penrose would not know that Pythagoras visited ancient India and got the theory from the Brahmins there, would he?
Well, the first mention of Pythagorean theorem (C2 = A2 + B2; C being the hypotenuse of a right triangle) comes from Shuba Sutra of Baudhayan around 800 BC.There is also mention of similar theorem in ancient Egypt.
This is from the winner of Field Medal in Mathematics (the equivalent of Nobel), an American of Indian origin:
www.rediff.com/news/special/did-india-discover-pythogoras-theorem-a-top-mathematician-answers/20150109.htm
Mathematics is all around you. The leaves of a tree are so arranged in a Fibonacci sequence so as to get maximum sunlight!
Of course Mathematics is discovered!
Penrose is right. All things are about discovery. Quantum entanglement has been around forever, we just now discover it. In essence, our notion of "invention" is silly, we are just discover what is already there.
At first glance, this question of whether math is invented or discovered seemed outrightly absurd to me. I mean, it is of course invented, right? How can those equations and assumptions and numbers etc be discovered? We made them up to understand our world better and to apply this knowledge. Fair enough. But, we are assuming here that that's all what mathematics is. But actually when I began to dig deeper, I realised that the point made by this video or elsewhere in the argument is that it is extraordinary and not just coincidental that mathematics can describe all physical phenomena with such precision. And not only describe, it even predicts what will happen in the physical world if we do have sufficient data. It seems instead of being just a language invented to understand what's happening around us, it is something more primary which is the underlying soul of the entire universe. A language is secondary and derives its existence from the primary meanings and doesn't have an existence beyond them. However, math, as it seems, is the underlying fabric of the physical universe, may be a divine structure which governs and even creates physical reality, which then becomes secondary. It then, can only be discovered. This argument makes much more sense when we consider "the simulation theory" of the universe, whose basis is a world built of codes.
Mathematics - "that which was, is, and always will be".
Maths is a way of thinking.
The precision of measurement has nothing to do with whether mathematics "exists", it isn't even clear what "exists" means in that context. Mathematical statements are "true" because they are tautologically implied by whatever definitions and axioms you choose to start off from. See the discussion with Wolfram for a much more clear headed and modern understanding of what maths is.
Discovered.
Mathematics never be invented . It's the science on which all natural phenomenon are based. And it's never wrong to say that Mathematics is the base language in which Supreme God written his Mysterical universe🙂
*"It's the science"*
no, it's a language.
*"on which all natural phenomenon are based."*
phenomena don't need math in order to occur. math is a language which may describe those phenomena.
KEvron
"Discovering" mathematics is looking in. Wolfram has a lot to say on this subject. We are using parts of our brain that evolved to do something else. In a way mathematics is a glimpse in how our own brains function. The limits of our minds inpose the limits on our mathematics. Our math isn't the ultimate language to explain what the universe is and does. Many, many things are "incalculable" or produce "infinities" and need to be "renormalized" because our mathematics are not sufficient. Ultimately the human mind limits human math. AI will greatly exceed us and we probably won't understand the methods they use. 😁
To say that Mathematics is a language wouldn't be precise. Every language takes time to learn, and most of us speak English. If we grow up with a specific language then it would eventually be part of our intuition and could speak it fluently. This is different with Mathematics, however, as you build on your knowledge, for example, explaining Pythagoras theorem to a 5 year old child would be like explaining higher order concepts to a non Mathematician. It takes much longer to learn Mathematics to the level of Einstein, for example, than it does to learn a language. Although the symbols used is Mathematics were invented by us, the insights they provide still apply in our reality. Pi, the ratio of a circle's circumference to its diameter, applies to all circles. Likewise, e equals the summation of one over n factorial from n equals 0 to infinity. Surely, these laws would still apply without the intervention of human discoveries to prove it. Mathematics was discovered.
Wouldnt you say that spoken truths would also be discovered, not invented then? I think you could make an argument that objective truths were out there before we humans had the ability to discern it.
Communication is what you mean and know most people suck at language. Can you say hello to a women and get her to sleep with you that day? No probably not. You don’t understand or know what to say or how to say it why to say it or when to say it.
pi is an interesting example because you might say a perfect cirlce doesnt exist ....probably
You took the language analogy way too literal.
To say that mathematics isn’t a language wouldn’t be precise. Mathematics takes time to learn, and many of us can do mathematics. If we grow up with mathematics, it eventually becomes part of our intuition. This is the same as with spoken languages because you build upon your prior knowledge. For example, explaining metaphor to a 5 year old child would be like explaining ‘logos’ comprehensively to a non-philosopher. It takes much longer to learn a language to the level of Shakespeare, for example, than to become proficient in mathematics.
Although the words in our languages are invented by us, the insights they provide still apply in our reality. Circles are round. Likewise, trees are made of wood. Surely, circles would still be round and trees made of wood without the intervention of human languages to state this fact. Mathematics is a language.
If the claim is to be made that mathematics was discovered, it must be made for spoken languages as well.
2 clues that mathematics isn't actually "real" but is not merely a human construct.
1. our mathematical models merely have "precision". They are never exact. We refine our models, and they always lack perfection (never perfectly model actual reality).
2. the stuff the universe is made of, must exist before any representations of it. If there is nothing to represent then there is absolutely nothing.
These two simple fact work together: something exists, and so it necessarily means that this is not-nothing. This state of affairs can then be represented and the simplest relationships can then be stated, such "one is not nothing". This is not mearly logical but is mathematical, and is not simply fabricated, but is tested against what exists. If nothing existed there would be nothing to compare any mathematical statements against.
Just because you idea of the universe is powerful in your mind, does not mean it can create the universe.