Roger Penrose - Is Mathematics Invented or Discovered?
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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? Or is mathematics discovered-always out there, somewhere, like mysterious islands waiting to be found? Whatever mathematics is will help define reality itself.
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Sir Roger Penrose is an English mathematical physicist, recreational mathematician and philosopher. He is the Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute of the University of Oxford, as well as an Emeritus Fellow of Wadham College.
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This interview is part of our Mathematics and Philosophy playlist series, created for Mathematics and Statistics Awareness Month. Starting Monday, 4/20/20, we will be publishing two mathematics playlists of all-new, never-before-seen interviews with renowned mathematicians! If you can't wait, the "Is Mathematics Invented or Discovered?" playlist is already available (and freshly updated!) on CTT's channel. Playlist - Is Mathematics Invented or Discovered? - kzhead.info/channel/PLFJr3pJl27pIp1EsDD2rYaTI7GxoXqrLs.html
Lol, I can't believe this pedantic asshole. He's a Platonian.....not only he believes in ideas, but he thinks mathematics is the ultimate idea that explains everything. Plato said only the philosopher could get us out of the dark and show us the light, so we can only hope enlightened mathematicians like him can show us the true.......Give me a break dude.
@@OjoRojo40 I disagree. Also they talk about all the bizarre math that doesn't appear to tie into reality. Eventually they'll figure out how even those equations tie into the natural realm. Philosophy can explain how everything works, but math can show the mechanisms that make that happen. Penrose even talks about how consciousness is probably a quantum phenomenon so don't go around thinking he's close minded or a small picture type of person
I am so interested to know what Sir Penrose thinks about the work of the Indian mathematician, Ramanujan. Ramanujan's ideas were apparently so powerful and 'visionary'.
@@NicksterNOC You are proving he's close minded and so you are. "they talk about all the bizarre math that doesn't appear to tie into reality. Eventually they'll figure out how even those equations tie into the natural realm". The "bizarre math" could be a door for different forms of interpretation (again, it's bizarre but still math.....). Eventually they'll figure out how even those equations tie into the natural realm? What natural realm please... the natural realm of math??? "Philosophy can explain how everything works, but math can show the mechanisms that make that happen". You are repeating what Penrose said and his essentialist narrow view of philosophy. That's why he believes in mathematics as the "real" true that will get us closer to the ideal realm (in a Platonic sense) Philosophy most certainly can't explain how everything works, hence math like I said, will never have any response to the most fundamental metaphysical questions of humans. "Penrose even talks about how consciousness is probably a quantum phenomenon", I really can't see how this help his case. Consciousness reduce to a physical interpretation??? Maybe you can help me. Thanks for your time.
Even philosophy KZhead video comment sections become toxic. You guys are taking quarantine very badly.
We are immensely blessed to be living in an era where such minds are available for our casual consumption and for free.
Indeed
@M Grant the internet WANTS you to think that it has improved your life… and that you are gaining knowledge from it but in reality it is gaining knowledge from YOU… the Plutonic world needs to be left alone or else it will enslave us all… it has lurked in the shadows before the existence of time and WE are what it has been waiting for… WE WILL BE THE HOST IT HAS BEEN WAITING FOR!
Can't agree anymore
And we waste it on TikTok watching morons.
@@ChosenPlaysYT People will always find ways to 'waste' time. That's their choice, but there's no reason to insult anyone over it.
When he talked about molecules and atoms, in the beginning, I thought, nice! A mathematician who seems comfortable in physics. Then I searched him up and found out he has a Nobel prize in physics. I guess he's more than comfortable.
why would you put your own picture on the internet? thats kind of weird
@@festusbojangles7027 why do you eat snails
@@EnjoySackLunch be quiet pooh pooh
@@festusbojangles7027 rude
@@EnjoySackLunch Why do you enjoy sack lunch?
It’s always a privilege to listen to the great mind of Sir Roger Penrose
This makes you wanna do math. I never in my life had a teacher, that had the same philosophical euphorism that these to convey. It's such an obvious thing you would need to convey, in order for a student to care about learning it and yet nobody does this.
hahaha
There is a big difference between doing / researching math, and listening to someone that does it...
It really does, doesn’t it? Nothing stopping you! There are lots of interesting Math teachers on KZhead exploring it for the joy of seeing and understanding more. See Eddy Wu’s TED talk about what Math is for - Australian Math teacher. kzhead.info/sun/g7ywg9icrICtZGw/bejne.html
@@privateaccount8027 This isn't blaming. In fact I loved math as a kid. But that came from myself and not the teacher and that's the point.
@@shadowfantasiesf8556 I hated math when it was only abstract and physics and then started playing with computers. Oh boy do I love math and logic now. Sometimes it is only about what peeks your interest !
Today he was awarded with Nobel prize.
Maybe that large part of maths applies to the dark matter part of the universe ? Which is huge compared to the visible one. So that would explain why only a tiny part of maths applies to the visible universe, which itself is a tiny part of the universe.
It's all relative man ;) and Penrose is massive in my universe .
I came to this video only after I learned that he got Nobel :)
Incredible! Thank you. I had no idea. Excellent news!
@@vasile.effect Why is he wasting his time on black holes when they can't explain why a snowflake occurs? They can't explain biology. Science is still locked in the past and the academics are just preening each others' intellects with these Nobel prizes when they are too scared to admit they can't solve the major problems with science like the contradiction between the 2nd Law of Thermodynamics and Evolution.No wonder the general public is so skeptical of scientists, because they are not holding each other to account.
9:00 if you are wondering where the title question starts.
Thank you.
here for Penrose so no need to fast forward nice that one of you for every video tho
Tell me his answer too
@@NoOne-ky1er both.
@@333peacher4 that's not what he said
I wish… that as a kid, someone had described math to me in this way. That it’s something humanity discovered. It exists independent of us, it’s not all understood or discovered. And in order to predict how reality will play out, you need to understand math. It describes reality, past, present, and into the future.
Mathematics may make future predictions and depending on all sufficient factors known may describe present reality of which we are ignorant, thereby looking as if it created something. In other words, our mathematics cannot bring into reality that which doesn't exist. It's only an inbuilt fabric tool which have discovered, are using and learning from.
It's never too late to learn/re-learn it.
He answered the question with more questions. A wise man
Roger Penrose was awarded the Noble Prize for physics when he was 90 years old; That was an astounding achievement. I am in my early 70s, I can only tell you younger people that to be able to think clearly an and creatively at that age is truly astounding.
eh, we're too dumb to even recognize if roger penrose was developing dementia or something anyway.
I am in my pre-fifties and I find that achievement unfathomable!
Well since we're all bragging about how smart we are - I'm in my late 80's, and surprised that Dr Penrose believes that mathematics is not an invention, but is " absolute " in some sense. I greatly admire him for his achievements - who would not - but I take issue with this statement. He himself invented Penrose tiles. Would he claim that these are not inventions but in some sense a revelation of something absolute ? Why is there a Nobel Prize for Physics, and no such prize for engineering ? Such as suggestion is absurd of course. But it illustrates in a small way the difference between the real world and the abstract world of mathematics. Nobel Laureates have bragging rights in a way that many useful people grounded in the real world cannot aspire to.
@@crustyoldfart Harold, congratulations on being so articulate in your late 80's although I must say that your notion that mathematics is a pure invention is nonsense. It is a bottom absolute and, just to get your dander up, it is one of our insights into he nature of God.
@@trajan75 Thank you for pointing out that what I suggest is nonsense. The thing I always bear in mind when receiving a gratuitous insult is that it is delivered with sincerity, and am accordingly appreciative. Your second strategy of invoking God, far from getting my " dander up ", I take as a clear warning that any further dialogue on the subject is impossible. For the benefit of others who may be reading this I would suggest that the conclusion that I for one draw from Kurt Goedle's result that mathematics can contain true statements which are unprovable, suggests that mathematics is a self-referencing system, no more, no less. On a slightly different tack: the great Michelangelo is reputed to have said that the awkward block of marble he chose to work on had contained the figure of David within it all along, and all he had done was to reveal the figure. Could this be a metaphor for the history of the development of mathematics ?
Mathematics is just reverse engineering the source code of the Universe.
OH really? Explain that..
@@mattgalloway7786 Mathematics is one of the way to understand and comprehend what Universe says . Its universe's language .
Other way round: The Universe emerges due to the existence of mathematics.
@@balloonsystems8778 Max Tegmark ?
ishkar it's pretty self-explanatory...
Access to conversations like this are magnificent to have available online.
Dr. Kuhn, just to say your overall program and interviews are a gift to our world today. Thank you for creating and capturing all these wonderful discussions.
Amazing interviewer.Asks pricise questions and let the guest speak without interrupting.rare quality in today's interviewers.
Call aurnab
when smart and intelligent people talk, we listen ... that's how we learn from the best
8:20 “There are wonderful examples like the ...........” (there are so many great insights In the recording, but that moment was tantalising!)
That's what happens when the interviewer has a genuine appreciation and interest in the guest
@@jolttsp But also doesn't have a proper grasp of math to ask the next pertinent question, which is; why are those math patterns there if nature isn't using them? You can't describe something then offer no explanation for them! The reason why Penrose doesn't do so is because he's locked into tradition which is the opposite of the scientific method ; it's the same old anti Galileo stance; an argument from authority --and what makes it infuriating is - that Penrose is smart enough to realize it!
The amazing part is how someone so intelligent can describe things so incredibly well that everyone can follow along.
He's unbelievable
Truly understanding something means being able to explain it in a simple way :>
Icant understand anything guess im just stupid
That's proof that he is truly intelligent. People that can explain complex phenomena in simple terms truly understand it. Contrast with arrogant professors who try to snow their students with lingo and jargon that took them years to perfect, and then they dump it on undergrad students and make them feel bad, which is what some profs want.
that means he understands it
As a protagonist in engineering for more than 40 years I still get bamboozled by the depth of maths and it’s relation to physics! (This was by far and away my favourite subject through high school) I recognise that this work is vitally important for human development but there is a point at which we have to make sensible decisions that mean we can develop in a cost effective and acceptably safe way! There is somewhat of a philosophical position to take!
who the fuck upvoted this ai
Yes you’re right, because we have become so dependent on production rates, and etc we have detached ourselves from the philosophy of science in our western society and almost the entirety of civilization
"Pure mathematics is, in its way, the poetry of logical ideas." - A.E
🥺❤️
This is not philosophy philosophy pertains to single statement giving multiple logical meanings. All religions on earth are basically philosophy because every reader gonna take different meanings out of it. Mathematics, NO WAY. 2+5 is still 7. And in year 3022 it will still be same 7-2= 5. Same Math is a language and humanity's logical mind operates on it without a sweat. It is unchangeable by our feelings and moods. Science doesn't change of reality based on our moods thats why Science and Mathematics are always used together from where i came from.
Well, doesn't that beg the question. I believe we can only say for sure, that it is 'our poetry of logical ideas', not 'the' poetry. Maybe it is, but probably we will never know.
-Is Mathematics Invented or Discovered? Mathematicians: Yes.
Well actually he's giving a very precise answer in this case
He says that it is discovered, but saying it simply will deprive you of the path how to understand it. Adding to that, It's only our language that applies to the physical world as it is.
Is the universe invented or discovered?
@@jnananinja7436 God discovered it when he was trying out everything what was mathematically possible. It must have been trial and error with no specific goal in mind, so you can't call it an invention.
Math professional here. Great answer. Fun question to ponder when you've had too many beers to drink or have nothing better to do (and the latter is rarely true.) I tend to think math is invented as a language that can be used to unravel scientific truth, but that's my opinion and I don't care at all if anyone else disagrees.
Delightful interview to listen to. I had to watch it many times, because at many points my mind went far away thinking about what they'd just said. Very good!
My thoughts exactly. They would make wonderful dinner guests. I've often wondered whether the apparently trivial or superfluous aspects of mathematics is a clue as to what we might be missing out there in the real world.
Thank you for the video. I am grateful for your time and contribution. Kind regards, Akira.
Remember hearing a great story. I hope I can tell it right. A mathematician walks into his colleagues office to find him reclined in his chair practically motionless with his eyes closed and then slowly steps back out saying “I am sorry I did not know you were working.”
it's weak story not great
@@OtaBengaBabalanga gee thanks for weighing in🥱
@@13e11even11 you're welcome
After laboriously tending to our garden at school, we took a drink of water and our math teacher yelled at us saying " you guys sweep the floor while taking your rest ".
@@OtaBengaBabalanga What a low iq comment
A group of mathematicians were trying to measure the height of a long flag pole but it was too high. A group of engineers came along and said they could help. They pulled out the flag pole and laid it on the ground and had no difficulty measuring the pole. The engineers smiled and left. The mathematicians scoffed at the engineers, "Engineers! We wanted the height, they gave us the length!"
Some ancient Greek dude stuck a one cubit stick in the ground and measured it's shadow to be 3/4's of a cubit. He then measured the shadow of the flagpole and found it to be 15 cubits. Looking at the engineers and the mathematicians he announced: "It's a score!"
🤣
Nice discussion. Thanks for sharing it.
What a glorious conversation! In regards to a simple equation being responsible for producing the mandlebrot set, I wonder what sort of equations are involved in producing the seemingly impossible visual shapes we can witness in a DMT breakthrough.
wow!
I think DMT experiences are more accurately described as "unexplainable" or "incomprehensible" rather than impossible. They can certainly be described as beneficial imo
There’s always one, lol
Sacred geometry ; I’m no expert but there is def a link w mathematics ❤
Sir Roger is a mathematical legend. I read his books in high school and college in the 1990s. His achievements are inspirational, and he stands among the greats like: Dirac, Hilbert, Poincare, Lagrange, and Hamilton.
because of the like... logic disconnect that seems to be the main hurdle for most people when trying to learn math, do you think folks like einstein or penrose are more lucky or do you think they would've been exceptional at whatever they did? in this particular circumstance, i find myself entertaining the idea of luck. for me, i just suddenly got it after years of overlooking and immediately realized that we must all have been doing basic algebra in our heads all the time, even when we're babies and even mentally handicapped people. hell even when we were covered in fur. math is native to the way the human mind works at least and i believe it's native to the way intelligence itself works. discovered for sure.
Don't forget Gauss. :-)
@@jgcaesar4 People just don't make enough noise about Gauss, ^oo^
@@jgcaesar4 - And Dr. Suess! 👍
@@ysph "do you think folks like einstein or penrose are more lucky or do you think they would've been exceptional at whatever they did?" last time that was possible was stone age, when they had 3-4 things to pick....and all were simple
He's 88, impressive
Now he's a Nobel laureate.
He must be 89 now. Good math eh?
@TyLEr is he rich?
Age is just a number.
Always had this question but never was able to word it so simple and comprehendible.
I would say, neither of both, but we deciphered and still deciphering it. Mathematics is a language of our universe and as with any unknown language, we try to figure out how does it work. Every time when we find out how something could be mathematically explained, we have deciphered a new area of this language.
Science is not like the ancient bone we dig up at an archeological dig. It is more like the conjecture we assign to that bone. Science, in fact, is not a body of knowledge at all. It is a methodology, or the outline of one, for discovering knowledge. But it is the equation, not its solution. And it is an equation that can take many different forms. There is not one equation, or very, very few, that rise to the level of “law.” Mathematics is no different. We didn’t “discover” it buried deep in the earth somewhere. We - humans - developed it. As the physicist Sean Carroll notes, equations are “just a way to compactly summarize a relationship between different quantities.” And “A function is simply a map from one quantity to another quantity.” Mathematics, in other words, is simply a system or notation used to attempt to understand the world around us - emphasis on attempt.
Mathematician: "Math is the language of the universe." Physicist: "Math is the language of physics." Engineer: "sin(x) = x."
CAD work flash backs lol
Engineering. I've got the knowledge.
also pi=e=3
pi = 3 = e = sqrt(g)
@ASquadWiper tan(x) =sin(x)
I don't like numbers, there's like too many of them. - Beavis
I will stop at nothing to avoid negative integers. - Someone
*....Who ever invented “zero” - said it was nothing...* -Butthead
*.....ROUNDED NUMBERs ...aren’t REALLY ROUND* ...ME
*......IF YOU DONT LIKE REAL NUMBERS, then use IMAGINARY NUMBERS...* (They are real also-see Google...* ME ME
*....IT IS PHYSICALLY impossible to keep on dividing a string in half...* You eventually get to a quantum level....that can’t be divided anymore and ... It’s physically impossible to keep dividing a SECOND in half-You come to a quantum limit..*
I’ve always thought “Mathematics” is universal, we just invented a language for it.
That is right do not let the "skeptics" twist words around and make baseless claims about mathematics just been an spontaneous chemical process with which humans are able to calculate things in order to achieve certain values that help us in the day to day as it further clouds the evidence that there is far more to the Universe that our minds are currently capable of seeing and understanding. Wether that is something akin to "God" or some grand spiritual power rest assured it's more than likely more real than the bigotted naturalist dogma that the skeptic community profess as fact.
Mathematics is the language. The thing it describes is just "what is" for lack of a better label. It's like saying "[the things described by] English is universal, we just invented a language for it" which is technically accurate but also sort of an uninterestingly so.
@@Jrpyify So you're saying the "discoveries" counts as "what is"? And that mathematics is the language we use to describe it? In the same way, English and French have a word for dog, Indian math and Anglo Math has a "word" (equation) for 1+1?
@@Jrpyify Mathematics doesn't describe everything though, such as the nuances of natural language, qualitative aspects of our experiences, such as feelings, emotions, and our inner sense of consciousness. Mathematics is part of our Universe, and there seems to be parts in it that could be even beyond our Universe, without any current known application. For example, we only need to know around 40 digits of pi to perfectly calculate the radius of the observable Universe to the width of a hydrogen atom. And we know that the Universe isn't infinitely divisible. At a specific point, we reach the Planck scale. Mathematics is all about measuring and making predictions. It is an essential part of our Universe, but it isn't the whole picture. We still have no idea how qualitative aspects such as being self-aware and experience feelings and understanding, are interrelated with quantitative aspects.
Mathematics can only describe those things that we know, think we know or suspect. It can not describe the unknown. In that context mathematics is the language of describing those things we want to describe, in the way we wish to describe them and it's accuracy is only related to our own understanding. Calling mathematics, or what it describes a discovery is like taking a video game or the computer it runs on and calling that discovered. Neither are discovered. It's just doing the thing it's designed to do, spitting out the information it was designed to spit out.
What I find most intriguing about mathematics is that it seems to be a self annihilating language. When we look at quantum mechanics and consider, just to name a couple, the work of Heisenberg and Schrödinger, what we see is that mathematics itself led us to a place where all calculations become void and irrelevant because it is impossible to mathematically predict the behavior of existence itself when we are faced with its particle-wave duality. I find it to be so poetic that mathematics itself had proven to us that the quest to understanding the universe/multiverse at its most fundamental functions will require a language that would be very far removed from the nature of mathematics.
Schrödinger wave function equation is fantastically simple mathematically speaking, very elegant and ez to kno by heart. It just happens that we can't find the exact solutions of this equation.....just like countless other equations in physics (like the plasma equation form Botlzmann). But we can discover some properties from the solutions, like Cedric Villani did with Boltzmann equation of plasmas, it even won him the Fields medal.
This guy is a great interviewer. Like a common guy who is really curious
Lots of times he is asking nutty "deep" questions.
a common rich guy, oxymoron
Raziel Lentz hot tip...no one does
common guy with a phd
I feel he is a science guy too. His voice is rich though.
What a wonderful, flowing and enlightening interaction between these two men, on such a deep subject, without resorting to gobbledygook! Thankyou.
Relationships are discovered, the method of discovery is invented.
Methods of knowledge are discovered. Mind has a specific nature ,thus it acts in a specific way.
@@TeaParty1776 I think you have it backwards.
@@FlamingRobzilla ?
The method of discovery is a natural power of the natural mind. It is discovered as much as the universe is discovered. Subjectivism is the death of the mind.
The nearest i can describe it Good's language.
What I understood from this video, mathematics has two functions, one it enables us to understand the behave of objects and fields, either they are classical objects or quantum particles, either field or quantum field, the second function, mathematics serves the reality that not need to be proven by any means, reality that stands there for us to discover.
Really, some wonderful peopl add to our knowledge and notions and make this world wonderful. How we can know such notions without such a mathematician. Amazing.
For an egghead, the man is very engaging. He gets his points across with great clarity. When a super genius explains things well enough so that even a cave-dweller like myself can understand, he is an exceptional communicator. Thanks professor, and congratulations on your Nobel prize....
Fellow birdbrain here, I also agree.
Yeah, fellow failure and lizard brain here, we all seem to agree, over.
Egg head?? The sign of a smart person is someone who can break down deep topics to a child, many ppl who want to be noticed as smart are just verbose in many cases.
@@andrew4life362 🤣🤣🤣
Wait. Smart people can talk too? All life: lies.
I love the old books in the background
I’d love to read one
One thing this shows clearly to me its how crucial the a priori is epistemologically in a sound scientific method. At the same time, it's surely important not to mistake sometimes mathematical correlation for causative mechanism, and to remember that it's possible to obscure discrete causation with calculus' "smoothing out of the continuum".
Metaphysics. Loved this. Many thanks.
I hope the IRS doesn't discover the math I invented!
Good joke
!!!
@@coffeebean7340 😂😂😂💀nice
Ohh please please tell me!
Gold
Fantastic presentation, Penrose is a wonderful intellect.
No he isn't. He refuses to follow up the scientific method to admit that Math is all causality; he's resorting to emotion in supporting tradition that physics alone is not causality even though he partially admits it in this interview. Shocking!
@@michaelwoods2903 I don’t think the universe was created randomly. I think there is a Creator energy behind the scenes. I am not religious but I am spiritual and believe without a doubt that causality is not the full explanation.
@@lightworker4512 Why?
@@hakonaae9636 I don’t know. Understanding consciousness will be a start to beginning to understand. We can study the 3D world, but I believe through my own NDE/ spiritual awakening that there is much we do not know. a patient asked me, do you think my daughter....she stopped mid sentence. An overpowering feeling of love immersed her and me at the same time. We couldn’t even speak, we were frozen. The feeling soon passed and she said, oh my God, my daughter is fine. Thank God. I’m Catholic and she committed suicide and I was going to ask you if she was Hell as I have been a nervous wreck. And I got the answer. Over 20 years, I have many stories, many much more paranormal. I used to be an atheist but not any more. Many people are unbelievers and that’s fine.
@@michaelwoods2903 A Nobel prize suggests you are wrong.
I am so thankful for being smart enough to appreciate how very very very smart Penrose is.
It is wonderful that mathematics describes the world very precisely or that the world functions in such ordered simple matter, that from adding and substracting you will eventually figure it out
The principles and the phenomenas are real, we're just figuring them out and giving names and labels to them.
@Jeanette York Are you saying here that math is fundamentally a mental experience? If so, why?
@@johnburnham6239 Nature is as it is, things happen in it even without our existence or awareness of them. The behaviour of matter and non-matter apparently follows certain patterns depending on their level of complexity, which apply to all of its parts. The apparent fact that there is this consistency at some level is what gives us hope to understand everything, as a random, chaos sandbox of particles would defy any attempt to intelligently interact with it. Now what I call Mathematics is the collection of models, tools and language that allow us humans to analyse (past) and predict (future) phenomenas qualitatively and quantitatively, to derive certain characteristics of them that are used for purposeful considerations and to communicate findings between ourselves effectively. What we always work with are models. Models simplify reality from lumps of matter consisting of inconceivable complexity down to primitive representations like points, lines, spheres, cubes. As the world changes, we update those inner models and all of our rational process is done on this model, while being aware of significant differences between this model and reality to a certain extent. Also, across time we discover new models, such as in astronomy the flat earth model -> globe earth model or the geocentric model -> heliocentric model. As those methods of simplification become more effective at retaining detail, our predictions become more accurate. Personally, I'd replace the word "natural law" with "natural pattern", as that would further outline the fact that the behaviour of nature is independant of our understanding of it. We're merely observers and we're working on efficient simplifications of reality to run certain calculations and algorithms which we found to be useful. Math observes patterns. Why those patterns are what they are may be a question for quantum mechanics or beyond our horizon of material analysis, philosophy.
MrSaemichlaus so I apologize for not specifying in my comment, but it was addressed to Jeanette York. So I wasn’t assuming any of your meaning. But since you’ve made a comment, it does seem to me that you, like her, are calling math a mental, human thing. It’s the language that’s math. Language is fundamentally mental in origin. Also, “models,” “tools” sound like they can mean many things... A scale, a ruler, and a toothbrush are tools that might help me predict the future or past, but none of these is a piece of mathematics. And it seems to me like pure math has no necessary bearing on the physical world at all. So math wouldn’t fundamentally be about “analysis” and “prediction.” Though also I see no reason why one can’t analyze a prediction... Honestly I was under the impression that analysis just meant “a breaking up into pieces” as opposed to having some reference to the past. And I can’t think of an instance of math describing anything in a non-quantitative way.
As with anything else as well
systematic self organization for some reason I got a notification for this comment... were you replying to me? As in everything’s a mental experience?
My intuition tells me that reality has a structure and math is an expression of that.
Its called Khufus Pyramid.
only information exists
@ayoub laarouchi proof is not availlabel and may never be. One problem is a version of The incompleteness theorem. If you try to falsify the hypothesis that only information exists then you would have to so within the realm of information and mathematics . en.m.wikipedia.org/wiki/Gödel%27s_incompleteness_theorems It is a problem of a system looking at it'self , a self referential regress ad infinitum. Another way of posing the question is equally valid ie Is there anything other than information in reality and if so can you prove that. This has has one advantage that if true that there is something other than information and and it is falsifiabel then it would not be a problem of the incompleteness theorem . In an earler version of this problem was the refutation of Berkeleys immaterialism by Samuel johnson en.m.wikipedia.org/wiki/Appeal_to_the_stone Berkeleys immaterialism was given little recognition at the time due to its seeming absurdity but in the 20th century it has become regarded as important in light of the incomleteness theorem and quantun theory A historic view of berkely and johnson www.irishphilosophy.com/2016/03/12/berkeleys-immaterialism/
“There is geometry in music. There is music in the spacing of the spheres.” Pythagoras
Mathematics was discovered - the method of understanding mathematics was invented.
The subject of the video (and of course the discussion) are fascinating, but aside from that, I'm very happy that a video such as this reached over 2mil views.
Congratulations to him for winning Nobel Prize 👏🌟
Mathematics emerges when you try to understand relations in a complex system. It just happens that in our universe everything seems relational so it makes math a good candidate to understand it.
I think you have the best definition here
That is an excellent way of understanding it.
Let me change your statement a lil bit. "It just happens that the interpretation sensory data collected by our consciousness seems to have relations"
I like this answer.
@@sayamqazi thanks, but no thanks. i like siduxs’ answer enough ;)
I always appreciate good questions as much as good answers.
Not a good question at all. Nothing is invented, least of all mathematics, even things you thought you invented, actually you merely *discovered*, all "inventions" are actually discoveries.
I simply thank the better sense to put an end to square root on reaching iota,at times I feel tempted to carry it forward similar to logarithm.
So deeply interesting. Would love to see more.
this was great. so thrilled to think how much more of mathematics might be understood to in fact relate to reality as we experience it, and possibly unite physics and metaphysics.
Thanks a lot
Well done, gentlemen!
One of the best short discussions about the topic of philosophy of mathematics, and with some insights into the interactions between mathematical structures with the real world. e.g. what Eugene Wigner called "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". He has what I call a beautiful mind.
After combing through and scanning over all these provocative vid titles, I think I've found the equivalents of gold here on this channel. I'm about to binge all of this.
Isn't that like Michelangelo's answer to the question, how he could make such beautiful statues, which was: "I didn't do anything special. The statue was inside the block all along. All I had to do was to chip off the unnecessary pieces."
Exactly. Which is obviously incorrect.
Ahead of watching this, presuming the question isn't misleading, I will guess that the mathematical properties of the natural laws governing this universe is what we discover, and what we invent are systems for expressing them and leveraging what we've discovered both in practical application and also in the pursuit of new discoveries. Now to watch the video and learn how muddled my guess was.
Yeah, boiled down to it's most basic premise, math is just seeing a cup and thinking "thats 1 cup" then if you add another cup you now have 2 cups. It doesnt matter how you explain that, the concept will always be the same. You can have "1" or you can have a trillion lots of "1".. it just is that way, how we describe that is irrelevant... Any intelligent life would be forced to make the same observations eventually. All of math is based on these very simple foundations. In that sense we aren't really creating anything, just trying to understand what reality has already given us.
Agreed. I don't think it's muddled. Why math isn't a discovery I'd say is because mathematics is literally invented. It isn't a scientific discovery; it's a field and practice built on supposed axioms that have turned out to be very useful. These axioms developed throughout the course of human history, but started in a humble manner (counting: one deer, two deers, etc.). How these axioms were conceived were primitive and so primitive and subconscious that perhaps it's treated as a natural part of the world discovered. People are mistaken to treat mathematics and the phenomena that it describes well in the physical world the same.
I love thinking about these topics. It’s gives me a great sense of awe at the natural world.
it’s the bomb
if you believe mathematics was discovered they probably still think Columbus discovered America.. periodtt
I love Penrose so much. I feel intuitively and logically that his answers are correct about mathematics being a discovery. Our labels of math and language are the invention, the reality always existed.
I'm not a mathematician and I struggled with it in school but I completely agree. It always seemed that way to me. Like, mathematicians were in fact simply inventing a useful language to describe naturally occurring phenomena. I always liked the concept of math and I feel like if I had had more patient teachers I would have really gotten into it.
I read a quote from somewhere that said “if you could erase all science and religion from humanity right now, both would return, but only one would be exactly the same”. That’s not a knock on religion in my opinion, but truth that math and science is constant and unaltered, it is our minds that altered to understand it…evolved to understand it.
Thanks!
I really don't know what to say except "Thank you Roger!". Your thoughts are the beacon of our lives. And also thanks to Closer to Truth.
Whose truth?
You are a romantic
Ever since Ant Man came back from the Quantum Realm our understandings of things have really progressed at an amazing pace.
Yeah, and destruction too
The mathematical description is the most precise we know. So it is guaranteed to strike us as incredibly precise. In the nature of the case - we possess no greater precision to run it up against.
It’s very fascinating, the idea that the physical and non-physical worlds operate independently - yet, work or interact between each other transactionally.
its like a language for us to interpret the universe. of course it doesnt "use" math, it just so logical that it can be expressed with maths. for example how the atoms behave and frequencies isnt becase of maths, its because of physical laws which can be described with maths. i was looking at a forest with beautiful trees once with a friend and he said "its all mathematics" and he couldnt be further from the truth, because maths is just our description of nature, not the cause.
your friend is right. mathematics is logic. mathematics is more than just an expression, and the fact is no one invents theorems in mathematics because if it were it could be changed. it's set in stone. your interpretation is incorrect and it's frustrating how someone with such a faulty understanding of mathematics would think they're in the position to be condescending.
@@ccshumshum8104 ok, you seem to have a point, mathematics is logic, and nature is bild upon logic i agree. Id be interested if you could further educate me
@@michatroschka I will simplify it for you. Whether humans existed or not, the mathamatical principles that govern the universe would still be there. Humans have created the formulas for better understanding about these natural laws, but we didn't invent the laws themselves. It's similar to computer code, it is a "language" on which we use to describe what we have discovered about the universe and how it works.
@@Snuusnuu69 thanks for describing it in simple terms and it is well understood what you mean, could you name an example for those principles in nature you were writing about?
@@michatroschka The fundamental laws of the universe. Physics, trigonogmetry/calculus, probability and statistics, chemistry. The building blocks of the universe. If you punch a brick wall, there are fundamental principles dictating that an equal or greater force(with a greater probability than chance) will stop your fist from passing through it. Another example you will learn about is called the 'golden ratio', which is found in abundance in nature. It is another mathematical formula to study. I will tell you, going to college is where I came to truely beleive that we are either living in a simulation(simulation theory), or there really is a God/God mind that created the universe. To me, it takes more faith to beleive that all of existance came from absolutely nothing, no matter what you beleive in. Good luck on your path to enlightenment.
this for me is one of the most satisfying videos on youtube an I've seen a few... thanks :)
The misconception starts with thinking the mind is inside the body. When the body is really inside the mind
Math itself is inarguably, definitionally a human creation But what it attempts to describe already exists and it can be a great tool for discovery. But it is a language we made up to make sense of the world around us
This is thrilling and fascinating to me, Sir Roger. The confluence of All Mathematics and All Physics is so beautiful and allows us to go deeper into the Reality and Truth of our Universe. And We, most probably, will never find a total solution. But the Theoreticians can dovetail with the Engineers, Scientists, Explorers, Practical People, etc. We can look forward to a testing and interesting future based on your thinking and your Associates and Colleagues. Thank you for your (summary) talk on this.
I'm amazed when mathematical ideas uncover things about reality that wouldn't have occurred to us if we hadn't been calculating a bunch of weird ideas. Sometimes it literally points the way.
We certainly didn't invent it, but we invented its language. When you look at anything, even if you aren't aware of mathematics, you can tell the difference between one of something and a hundred of something, even if you don't know what they're called or how to describe it. Mathematics is the language we invented to describe measurements of things around us, the labels and lengths we use are only a way to navigate through what is built into the universe.
really. like the mississippi river was 'discovered'. mankind had to 'invent' bumping into the river's edge. took alot of brain power to fall into a river.
This doesn't settle the philosophical debate though. It just punts it down the road a bit.
I believe the term mathematics is used to describe two things. At times multiple invented languages, and at times a prior reality of relationships. There are multiple math languages that can describe a problem - I have seen the same problem on youtube solved with both geometry and calculus.... both were valid languages to describe that solution - since a particular problem/solution is abstract until it finds a physical use you could argue that mathematics 'discovered it' before physics did... however since two pretty independent branches of mathematics can be used to solve a problem you can argue that they are just 'inventions'.
@Razor Face I don't believe the characteristics of the universe were invented by man.
@@jcr912 i think that to exist characteristics is necessary an observer to interpret it, without an actor there's no math.
As an EE, it is amazing how electrical parameters are so related in straight forward equations and that many of the constants that bind the equations also work well in other disciplines. The only thing that the math doesn't seem to fit very nicely is that a number of the constants are irrational numbers.
You should definitely checkout Eric Dollard’s books lectures... One of the most authoritative EEs alive & in the public domain.
Physical laws and concepts exist, you discover said physical concepts and use language to convey or understand them, this language is numbers, formulas, symbols, equations.This whole process is mathematics. That was in my head and i wanted to get it out
Nope, they don’t exist. In fact, they are concepts. As such, they are invented.
I like Penrose, he seems like a very humble man. And the interviewer is likewise. Two good men grappling with the most important questions in life.
“I had been dead for billions and billions of years before I was born, and had not suffered the slightest inconvenience from it.” - Mark Twain. The context of the quote is the fear of death, but it applies here. Two and two was always four, we just happened to stumble upon it.
Great comment. It makes me wonder if we could've found/invented a different math altogether and it would still work? For example, what if we didn't have addition and subtraction. Two divided by 0.5 also equals four. Would we still be able to describe the universe?
@@th4fl4sh4 Thanks, the Math we know is at one level, simply the consequence of the Universe as we observe it.
Death only pains the living.
Twain cribbing Epicurus.
meh. Not the point. Maths is able to describe a PERFECT circle, quite easily. No such thing exists in nature. So maths is a human construct that approximates (generalizes) the rules of nature.
Mathematics describes what is happening, and somehow reveals to us what that reality is. It's like a communication pathway... a medium of exchange of information...
Looking at reality through mathematics, is the reason there is a separation between the two, looking at reality through mathematics, geometry and the relationship between the two will render a solution that is indistinguishable from reality.
I have been saying this question to people my whole life. I never knew it was an actual thing people like Dr. Penrose studied! I always thought discovered, just our units to describe things are "invented" but also based on discovered properties of reality as well.
"Reality"? Whose reality? If you experience pain or anything else that-for you, cannot be different, that is as real as real can be for you, but nobody else, thus whose reality? o you suppose there to be a " reality"(whatever that means) other than the direct immediate personal experience of some particular being?-Some sort of vague generalised " reality"? Whence you get that strange idea?
@@vhawk1951kl go away year 2 philosophy study
"Mathematics" is a human contrivance used to describe change and motion. We can't be sure it's accurate over remotely vast distances and time scales. The ancient Greeks pondered this question.
The Greeks pondered on what “Egyptians” mastered!
@@risej4164 so are many alive today. Whats your point?
@@2121beastmode the fact that you don’t know, is beyond me!
really? because we've used math to put telescopes floating around the Earth and use them to take pictures of galaxy's billions of light years away. that seems like a pretty vast scale where our math works to me.
@@theheebs100 lol… that’s bs, and if you believe that then u r a straight clown… I think you really are one though!
Mathmatics is a science and a tool at mankind's disposal, through brain's operation, trying to understand awesome wonders of reality around us, and in the skies above.
Whose reality? What you mean by "reality? No idea? - No surprises there.
@@vhawk1951kl When talking of science, I define reality as mind-independent and refers to the universe (i.e. space, time and everything in it). An important caveat to this is that observations and theories are based on reality rather than reality itself.
@@georgebush6002 Whose "reality"? Is define reality.
It's not. It's a language. Mathematics does not create knowledge, it explains what you already knew to someone else in a way that leaves no room for interpretation.
@@vhawk1951kl why are you talking to yourself
Indeed, how can something abstract, like "language", describe reality? Mind-bending!
It is a wonderful video. I have to congratulate everyone who has participated in it, not only the great R. Penrose, because the most important merit is having shared it for free. Thank you. This video should be seen in every school in the world.
For what it’s worth, the word “invention” is derived from the Latin “invenire”, which means “to come upon, to find”, which is somewhat close to “discover”. The word “discover” is derived from “discoopeire”: dis (same as the English “dis”, also like “un”) and coopeire (cover). So the meaning associated with the terms is somewhat muddled. I don’t suggest that the etymologies invalidate the meaning we have now, but that maybe the concepts aren’t quite as opposed as ordinary language infers. After all, nobody claims that an invention such as the lightbulb was created out of nothing. It was invented on the basis of previous ‘discoveries’ (electricity) and ‘inventions’ (glass, filaments, whatever). But-conceptually speaking-is bringing light to what used to be dark all that different than the solution for Fermat’s Last Theorem? I wonder.
So all in all... Its all perceptive. Like anything in life... And context also
discovering = surprise or a fluke. inventing = planning and a definite road map
one might say that the lightbulb was invented after countless discoveries.
The point is to ask 'Did we simply make maths up and use the maths that fits our reality because otherwise it's no use?' or rather 'Was/is maths 'out there' somewhere in an abstract space and we stumbled on it?'
@@omairbinenam6337 Yes and after more experiments and discoveries the Newtonian based light bulb is replaced with a Quantum based device, the LED (light Emitting Diode)
Years ago I'd read all the popsci books (kip Thorne, hawking etc etc) and felt like a kid in a candy store discovering all of these things and understanding them as they were put to me... But I couldn't really find anything else like that, everything else I picked up seemed to rehash what if already read and understood... So I bought the road to reality by penrose, I read a quarter of it and had to put it down, its so far above my head, that I didn't feel like a kid in a candy store anymore, I felt like an ant trying to understand space travel... It was horrible. So... Thanks Roger, that hurt a bit.
Nothing has ever been invented, we've only ever discovered the potential that was always there
All significant maths was already known and taught long ago in the Vedas. It was called Ganit. For example, the concept of zero was originally called Shunya, or zero void. The symbol of zero and the decimal system was described in the Vedas (for example Atharva-Veda 5.15, 1-11) and also described is how the number increases by 10 by writing zero in front of it. The first usage of Pi also came from Vedic teachings. A (e.g. Rig-Veda 1.105.17) formula to find the area of a circle is mentioned showing that the Rishis knew of pi, approximating it to be equal to 22/7. The word Bijaganitam means “the other mathematics” and was given to math like, for example, what we call algebraic forms of computation. Eventually another notation that people called “Indian numerals” evolved from the Brahmi numerals and assumed common use. But under the dictatorship of Mohammad in the 7th/8th centuries, Arabs invaded and conquered the land from India, across northern Africa, to Spain. Most of these Vedic texts originated and remained in India and so, in the following centuries (through the 14th) the Arabs destroyed many texts. But since they pursued some arts and sciences, they came across some of this math and change some names. For example, they coined the term Algebra when it came into common use throughout the Arabian empire, which extended from India to Spain. Europeans later used the name "Arabic notations," because they got them from the Arabians. However, the Arabians called them Hindu figures (Al-Arqan-Al-Hindu) and they referred to math itself as Hindi-sat. Vedas are misunderstood, but are the source of all knowledge. watch my current main vid/description on my channel, n click my sub/bell icons for a few epic, upcoming vids, offering details/evidence on all the above, & much more.
no, I mean seriously. make a universal statement and then start with: for example...
@@kingplunger6033 stop being lazy, you gat a great mind train it up to process and hold large data/ information
Mind blowing as usual, but greatly helped by Prof Penrose’s precision and clarity. Maybe there are also platonic worlds of logic, music and morality, equally fascinating.
I’ve come to realise over time that mathematics is actually quite spiritual
Maybe you should read Greek philosophy... the Platonic world was one of concepts and an underlying ideal "reality"- whereas reality was only a shadow-puppetry of the Ideal. The problem I have with this view is that it suggests that mathematics has been advanced without the need of physical evidence, and also that pure mathematics has meaning outside of the physical world. There's been a lot of mis-steps in mathmatics (same as in physics). That's the scientific method... propose something, test it, re-assess it. Plato lived in a time when there were huge advances in logic/mathematics - when the limitations of experimentation prohibited as many advances. Of course mathematics is infinitely precise - but as there was a transition from Newtonian to Relativistic theories, these were necessitated from the inability of the theory to explain reality. If Newtonian physics was able to account for all physical interactions, would anyone care about Relativity? We appreciate the need for different maths to better understand the reality we live in. Sometimes the Maths comes earlier - but it's relevance comes when it intersects with the real world. I'm really in favour of a discussion on the world of Ideas - but I also know that Penrose also uses a lot of methods to undermine non-physics/mathematics discourse, which is problematic (when it comes to things such as consciousness). I'm an aetheist - so I don't mind the lack of a watchmaker... but as a physicist I also fundamentally object to the idea that you need to resort to such things as quantum effects to argue consciousness (as randomness is a feature that is built into complex physical systems). His concept is to replace God with the Wizard of Oz (hidden behind an veil of uncertainty). This is intellectual commercialism.
@@AdelaideBen1 maths exists apart, in its own right, without our understanding of it.As long as there is space and time, there is maths.In pure maths there is validation through the existence of space alone.
@@ursulagwozdz1955 Er... I think you misunderstand where maths exists and where physics exists. Maths has no concept of "space" - it has the concept of 1D/2D/3D/4D.... etc n-dimensional coordinate systems. It says nothing about what "space" (the physical reality) means. Pure Maths has an important role in Physics - a crucial role - but Pure Maths doesn't need Physics, or ANY realworld anchor. That's why there is no branch of "Pure Physics" - but there is a Maths that is purely about the abstract. Much of Physics exists in the abstract - and much of reality can also be abstracted - but there's a real difference in physics and pure maths. Also Pure Maths has no intrinsic concept of "time"... it has an abstracted dimensional concept, and you can extend this to a statistical concept which says it's more likely to move towards disorder than order, but there is no "pure math concept" of time AFAIK (maybe there is in which case I'd love to hear it).
@@AdelaideBen1 maths and physics are intrinsically linked.We agree on that.
Amazing
Two brilliant minds
I noticed Robert Lawrence Kuhn's repeated invocation of the idea that mathematics must be 'out there'. It seems 'out there' is his criterion for 'what really exists'. But the point about mathematics, is that it transcends space and time - it's not 'out there', it's true by virtue of inherent reason. The intellect's grasp of the transcendental nature of intelligible reality is fundamental to traditional platonist philosophy, but has been squeezed out of Western thought due to the influence of nominalism and, later, naturalism. Thank heavens there are some leading scientists such as Sir Roger who are fighting the good fight.
Very interesting....I think that materialism of people like Hobbes thought itself to have transcended Platonist philosophy but in the exploration of Quantum Mechanics its re-emergence was necessitated .....Heisenberg realized that visual pictures from the macroscopic world were NOT adequate to describe the sub atomic domain...To do that accurately you have to go into pure mathematics like Roger is describing....I guess mathematics could be seen as transcending time & space because it is an abstraction which is not a physical object that can only exist in time and space...But it IS an abstraction which pre-exists......In a way Heisenberg was using Platonism to go beyond not just Hobbes materialism but also Descartes.
@@walterevans2118 Google 'The Debate between Plato and Democritus' - a speech Heisenberg gave late in life. His Physics and Philosophy is also good. (It's a canonical text of the Copenhagen Interpretation.) The point about mathematics is that it's not simply 'abstract' insofar as it is also predictive. Many of the seminal discoveries of qm came out of the analysis of mathematical symmetries the gold standard being Dirac's discovery, or rather prediction, of anti-matter. Another example is Eugene Wigner whose Nobel Prize was for application of symmetries to nuclear physics. Wigner penned a famous essay on the unreasonable effectiveness of maths in the natural sciences. Plato will have the last laugh.
Jonathan Shearman...Yes, I've got Heisenberg's Physics & Philosophy. A great book particularly in the way he explored all the different objections to the Copenhagen interpretation...Yes, even if with the measurement problem of electrons we cannot have mathematical certitude between momentum & position in observations mathematics has an incredible predictive power in the physical world...This has led some to call it a useful tool which is invented but it also predicts THEORY.. I think Penrose is correct when he says calling it an invention doesn't really go far enough to explain mathematics ....& Heisenberg would have agreed with him otherwise he would not have developed his matrix Mechanics . In Athens in 1964 he explored these ideas about patterns in our minds called 'architypes' by Plato might have reflected the internal structure of the world.
Can I just say, your vocabulary impressed me.
@@walterevans2118 Aren't *all* abstractions pre-existents ?
What I think is fascinating is how often maths departments have musicians trying to break free! 🤔
_The one who recognizes a phenomenon by his _*_own thinking_*_ , does not stop pondering beyond it with a certain frequency. Those who only hear what they are told about phenomena, _*_think nothing at all_* .
Just in my life experience without any advanced education or having watched this video, I see mathematics as a human creation to precisely understand and explain the physical universe....now I will find out what this gentleman has to say.
I don't know much about it either, but I agree that mathematics as a human creation. and quantum physics has not destroyed all mathematical logic and theories?
Mathematics is "discovered" just like words are discovered to describe things we observe only with much more precision... The facts, physics and reality are there, math is just a way we come up with to describe how it works
Better than the video
what you think of is language, a human invention. math is nothing like that. if aliens were to question how universe works, they would come to the same conclusion as human beings even if these civilizations never meet each other. Hell math would be the exactly same in a parallel physical world with different physical parameters. thats why penrose was talking about math as a foundamental reality independent from this world.
But with language you cant predict the name of any new object. With math you can make predictions about the universe.
@@Young-ep8ik language also is a way to describe reality though.I also think it’d be a mistake to say that the conclusions that we get from math about how the universe works would be the same found by aliens or from us in the future. There will always be new theories and ways to describe the world that are better than old ones.
@@connor4216 Agree with the first statement because math is in itself a language of relations and logic that applies to anything in the physical world or abstract entities. You are right different civilizations will find ways to discover subsets of reality in different order. But 1+1 cannot be 3 to any observer in any timeline. What you refer to in the last sentence applies more to physics or other empirical sciences. Math theories are generally absolute because they require well, mathematical proof. It’s impossible that whats proved in the past is false in the future
It was hinted at in this video, but Penrose considers himself a Platonic Idealist, in the traditional sense of that term. Most philosophers nowadays consider such notions silly and quaint, but Penrose makes a very compelling defense of it in his books. Everyone would agree, however, that Penrose is a brilliant mathematician; I would argue that he's also a pretty damn good philosopher.
Yes! I found that very interesting, almost Pythagorean! I think in your statement is the argument summed nicely. Remember it was the pre-Socratic Pythagoras who indicated the right triangle *is* a2 + b2 = c2, while a drawing of the right triangle is the approximation-who needs Plato here :-) . I'm inclined to say there are things we describe as right triangles in nature (such as the relationship among reactance, resistance, and impedance in electricity), in which Pythagoras has made a mathematical approximation of the reality. And I assert it remains an approximation, despite claims of relative accuracy. There is still room for idealism here, though!
Yes , hes very bright.
He's an awful philosopher. Platonic idealism is archaic. Idk why he would even attempt to defend that position. It's been well-established maths is just language, nothing more, nothing less.
@@Google_Censored_Commenter all language have semantics structure, it means the universe have a mathematical structure.
@@marcosgalvao3182 It means humans invented a mathematical structure that (currently) applies to our universe. And said structure is just labels, nothing else.
He may be the most legendary living scientist at the moment. Maybe if Watson or Crick are alive (not sure if they are) they are as well.