Edward Witten - Why the ‘Unreasonable Effectiveness’ of Mathematics
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- Опубліковано 18 кві 2020
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What is it about mathematics that it can describe so accurately the world around us? From quantum physics, the very smallest features and forces of the foundations of matter and energy, to cosmology, the very largest structures and forces of the beginning and evolution of the universe, mathematics is the language of description. Why does the physical world follow so faithfully equations of abstract symbols and variables?
Edward Witten is a theoretical physicist and professor of mathematical physics at the Institute for Advanced Study in Princeton, New Jersey. Witten is a researcher in string theory, quantum gravity, supersymmetric quantum field theories, and other areas of mathematical physics.
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Pure brilliance. Imagine winning Math's highest honor while being a physicist.
and becoming a prominent physicist while being an historian. this man is a fucking beast!
Imagine winning a Fields Medal without proving theorems... Ridiculous.
@@thepowerman8952 You should really take a look at Witten's work yourself. Why all the salt?
That was a side quest
@@iaexo No salt, I just think it's ridiculous. I have nothing against Witten, why would I? By all accounts he is a modest, self-effacing guy. Makes a change from most extremely intelligent people.
I emailed Witten with a question and was surprised that he answered me almost immediately, zero ego or arrogance.
What was the question and did his answer make any sense?
@@Za7a7aZ I asked him why did the chicken cross the road
@@xyzmediaandentertainment8313 it saw the truth
This interview is telling. The answer was probably mega-suggestive. Ed looks like one of the best answerers from this interview.
his a super human, probably from a higher civilized universe than ours.
Ed Witten is regarded as one of the most influential intellects of Theoretical Physics/Mathematics by his colleagues and peers in the scientific community. And he's probably one of the nicest, most humble individuals you'll ever meet.
He took my parking space once. sooooo.
Witten is speech affectation and verbosity: no lab results, no experimentation, no verification, no way to test hypotheses... Witten is not a physics theorist but a physics ideologue. For decades he has lived off the budget and NO NEW REAL THEORY.
He's the William Buckley of physics: verbosity without any real content or direction.
Don't forget Korzybski's statement: "The map is not the territory". Descriptions of reality are not necessarily properties of it.
Some mathematicians seem to believe otherwise. Even as far back as Pythagoras they have believed that "mathematical truths" are real, in the real world, and independent of mind.
Mental maps of reality (mathematical or otherwise) seem to me to be extremely simplified mappings or sketches. The mind-independent reality is far more (many trillions of times more) and very different.
But it is uncanny how reality bends toward the the math (Road to Reality?)
@@viveviveka2651Are you not, in fact, expressing the same thought, rephrased more elaborately?
@@AMindnamedAdam Forgive me, but you do not know that with certainty, and the hypothesis really deserves to be treated as such.
@@callmedeno reality does NOT bend toward math. It is the opposite.
I find in listening to Witten, I'm transported into another 'headspace' altogether, simply by the way he speaks; a hypnotic, almost celestial pitch and tenor. it's remarkable really. I can grasp very little of the concepts of which he speaks, but he does seem to effortlessly force you to start to think differently, when walking away from 10 minutes of conversation like this. I would liken it, in a way, as he does, to listening to a beautiful classic piece by Bach, or Chopin.
Just by listening to him you know how much knowledge he has. Truly incredible
Witten is widely regarded as THE scientist among other theoreticians and mathematicians. Listening to him is an education as well as entertaining.
I want to watch Him making a Fried Egg...🤔
The quality of Ed’s communication (signal to noise ratio) tends towards infinity, very few filling words or sounds. Raw genius.
almost robotic. looked like he was glitching.
Originally a history major and linguist minor: the guy knows effective language for communication.
Tends towards infinity as what? What's the dynamic variable here?
I didn't know Bill Shatner was raw genius; the more you learn...
JLongTom Time, he’s not at zero noise level yet, he’s getting better ;)
OMG Ed Witten on this show! Thanks a lot!
Notice how Witten avoids saying anything metaphysical, no matter how much the questioner tries to tempt him.
Ichiro Akuma very well observed
Everything he says implies a metaphysic posture, you can't get away without it. I'd love to hear him talk explicitly about it, though...
It's the only way to be...
@insane hermit because he's not a pseud and he understood that mathematics is the only good metaphysics.
Lotta people under this comment need to open a book on philosophy 🤦♀️
And what?? He said “it’s as if the universe was made by a mathematician”. How is that not metaphysics?
Ed Witten is currently one of the giants of physics. Pure genius.
As much as I love theoretical physics and mathematics; before today, I honestly never heard of Prof. Edward Witten. I used to think that Sean Carroll would always remind me of how I little I know about theoretical physics, but after hearing this guy, I don't even think I know the meaning of "theory."
I don't mean it as an insult, but he sounds unhuman at times and more like a talking textbook or encyclopedia. His behavior, tone, and sharp focus is how I would imagine Isaac Newton explaining his laws of mechanics, optics, calculus, and analytic geometry.
he says pure maths which we think has no application to real world can infact be used for explaining phenomenon in our natural world also we could able to create new math by finding structures in our natural world like newton did when he found calculus
I think this is just a bi-product of trying to articulate concepts which layman people are unlikely to understand. It takes a lot of energy to form what occurs on your mind into words in a clear fashion, never mind then having to dumb it down for people.
Incredible to have Witten on. Hope to see more. Thank you for this.
I would imagine Ed Witten to have quite a captivating ethereal dance style at deep house or tance events.
Rich JMB same as Jeff Goldblum I imagine. How cool would it be if he talked like him?
@@kuruman1 Lol. Yes Ed is one of the select guests I expect Jeff invites to his private night club in the basement of his mansion. They can Trance out for hours to progressive house and slowly evolving chords, Jeff is very into his arm movements and uses them extensively as part of his repertoire
my favourite youtube comment ever congratulations
@@richjmb5522what the fuck have I just read😂
Great to see Edward Witten here, always interesting to hear him speak.
Ed Witten is brilliant and his insight never ceases to amaze me. A very worthwhile video.
I've watched a lot of these videos over the years. I appreciate that the host often asks profound questions. Prof. Witten is brilliant and I enjoy his simple and elegant answers.
What I love is he has pretty much the entire history of scientific discovery down pat in his head with the names of the discoverers and how they built understanding off of each other and cites the WAY they thought their way to each idea-including the blind alleys and how they arrived their ideas and then weaves all of it together into a coherent, seamless stream eleucidating sidebars as needed, without getting lost in any one tangent. You get a wonderful sense of the human dynamic, not just the dry facts rules and conclusions derived
Ed Whitten is a pure pleasure to listen to. What a great mind. 👍 His last comment was great 🙂
Ed Witten. Pure brain. No additives.
Even Robert Dijkgraaf, the former head of Princeton said od Edward Witten that when they would talk mathematics Robert would feel a dwarf and had difficulty in keeping up with the brilliance of Edwards mind!
Bro imagine sitting across from Ed mf Witten
Sounds like a WWE entry announcement
Amazing interview
Reading Graham Farmelo's _The Universe Speaks in Numbers_ tells how one stupendous math-physics intersection after another was happening from, around EW. Mind-boggling.
This video was underwhelming. Would love another video/series with this brilliant man.
This guy is so great! 👌👌👌
I like Sabine Hossenfelder's take: We think that the universe is governed by mathematically simple equations but that could be because we're only able to understand or are otherwise biased towards simplicity. We're also only able to perform experiments to a particular degree of specificity, so sometimes our equations can be a little off but on a human scale we don't notice and can't test for those discrepancies (like Newton's gravitational equations).
If I have a helium balloon and let go of the string I can be certain it will travel up, the path that the balloon will take as it rises is ridiculously complex. Even though on one level the math to describe "up" is extremely simple, once you get into the details that simplicity dissolves. I tend to think that nature isn't actually simple at all, but we've just found little pockets of simplicity based on our human frame of reference.
Yep, seems like we only just started in the grand scheme of what we call nature. I beleive that rightfully understand the relation between maths and what we call physical reality will take us to the next level.
Making the extremely complex into something simple and digestible...she may not be proving the point she thinks she's making.
She is not a big fan of untestable theories like Witten's though.
@@wyqtor She's thinks math is overrated. And I agree with her.
@@peterdamen2161 I don't think that is true. However, she has stated that seeking for mathematical beauty is non-sense.
This Witten video made my day.
He is witty
An updated interview with Nima Hamed Arkani would be interesting. I know you have already interviewed some years back but Nima has some interesting views on the relationship between Math and Physics I am sure you could extract from him.
Awesome new Closer To Truth !
I love the unencumbered clarity of thought and commitment to curiosity and truth that isn't embodied by most scientists today. Far too many are engaged with the religious truth of their science as their god-head rather than remaining curious and open to whatever science presents to them as truth via objective observation.
I do think you'r not actually describing scientists, but "geeks" or non-educateds who are "into science". That said, I think learning about the nature of the scientific method has its subtle nuances that are not easily understood, so its somewhat understandable, though not deemed desirable. What is a scientific fact, versus what people hear "is fact", and what are personal beliefs (alternative facts/truths), are nuances not often discussed with enough care and attention in, say, comment sections or twitter. The problem itself takes more than 160 characters...
Thank sir E.Witten.
He is on another planet. Brilliant
It is great that he is giving direct answer then just speaking stories
He's so practical. He says "interesting" so many times. I wonder how he might see interest as being metaphysical or if he sees it as practical application or if there is something more.
What a treat! Thank you!
Sad...check in with Sabine Hossenfelder on that one. She disagrees and has written a book.
@@deevnn I know, I watched her interview as well
Witten,the greatest living,most celebrated and cited Mathematical Physicist in the world!
Sceptical Scientist
Now Freeman has gone😷
Gary Shepherd
I know but even Dyson,Hawking and Penrose,called Ed special
@@rationalsceptic7634 Feynman and Dirac are also great.
Fanboy 375
Of course..but they are dead... Witten has won more Awards...only Physicist ever to win a Fields Medal...which is astonishing!
Hawking and Penrose call him unique in the World!
Fanboy 375
Living?
I could listen, with rapt attention, to this man forever.
It's great to see an intellectual and intelligent human being, wearing a suit, elegantly describing the hard truth and mathematical reality of a theory. This is how scientists used to talk if you Google some interview in the 1990s.
Thanks a lot for this interview.
Big thumbs up from me,
And Subscribed ....
One of the smartest walking the face of the planet.
I hear this type of comment about Witten often (Terence Tao is often included alongside him), but I think it's just a meme. What exactly distinguishes him from a thousand other utterly brilliant people?
@@JLongTom well, he said 'one of the' smartest.
@@JLongTom his work. what else would it be.
@@JLongTom … his papers
@@JLongTom Read about his contributions before asking such a nonsensical question. You have Google at your fingertips
I didn't understood a single argument or idea that they are discusding but still I watched this completely.
I undestood everything what Mr Written said. about the fundations of particle and energy stuff. Legend.
Great interview! I love that there is a whole branch of mathematics devoted to the theory of knots. I guess really, really smart people (like Edward Witten) see things very differently. I could play with string or paper clips for weeks, and not invent a new branch of maths.
Knot theory has nothing to do with "the world around us."
Claude Massé Quite! That’s the point.. that such a highly esoteric branch of maths can start from something as mundane as varieties of possible knots in a loop of string! There’s something beautiful about that.
Everyone has different talent and everyone has a right to be wrong. For example, in Hawkings’ last book he declares philosophy dead. Sorry…wrong…he is a scientist making a claim that is not based in science but is a philosophical statement. Hmmm
@@clmasse If that was true, there’d be no way to apply it in the real world. Same with other fields of mathematics, yet so much pure math suddenly winds up as “Just the right tool” for whoever needs it…some kind of connection is there, otherwise that wouldn’t happen.
@@clmasse How do you know that?
Ed's voice doesn't fit with his face. Something got mixed up during assembly.
Very nice comment. Thanks for the contribution
Witten is so interesting to listen to how the way he formulates what he says. He nails it down saying "it's as if the universe was created by a mathematician". Certainly after studying Quantum Mechanics I got that feeling of the maths taking you along for the ride rather than the physical motivating the maths.
Witten is spot on with the remark: "universe created by a Mathematician". The sovereign creator is the greatest Mathematician! There would be no universe without mathematics, because it is the foundation of physics.
Needing a Creator is such a Human Thing to think...🙄
@@superfuss1984 Can you explain the origin of the universe without a first causal agent? I cannot. And why not put a name on that agent, if it is a person with a greater purpose for humans?
@@The_Revealer_7 If you need a Explanation, good for you. I am happy with Things just happening. Seeing the Size of the Current Universe, i guess i am closer to the Truth. Never forget: Man created God, not the other Way around. 🤷
Hat off for this sir
Ed Witten explained M theory (which unifies all consistent versions of superstring theory) to a room full of the world's best physicists. Apparently the lecture was too difficult for most of them.
No, that lecture was relatively easy compared to others of his, it was just shocking.
@@annaclarafenyo8185 How so?
@@sclogse1 of course it was shocking, the theory is not complete
That’s not something to be proud of …
Or maybe they didn't want to waste their time with a theory making no useful predictions whatsoever.
"It is uncanny how powerful mathematics is in understanding physics." Could have stopped right there.
He could but we would have missed the biggest point of it all , part of it may be proven to be wrong by a better discovery ,our grasp of reality is not very solid and it can change in a dime as recent history shows
@@rovidius2006 Could we be on the verge of a major breakthrough in the understanding of the universe?-- the use of math in everything, simulations, computer games, artificial intelligence, realistic simulations -- all seems to be pointing at what the universe is made of -- relativity, quantum theory was 100 years ago -- we are due for a major breakthrough -- "It's uncanny how powerful mathematics is in understanding" our world.
@@williamwolfe8708 While math is a powerful tool for understanding and projecting processes in the observable universe it is limited in its scope ,it explains how it works but not how it came into being .While it is a big deal to most people many top scientists reveal of how little we know of the universe around us and how powerless we are if forces of nature would not be so friendly to us .
@@rovidius2006 Yes, we are all on a rock flying through space at, what, 490,000 miles/hr give or take, with nobody at the helm. We are truly lost in space -- total mystery. In the midst of our ignorance is the weird thing that every time we seek to clarify the truth about the little we do seem to know, it comes out in mathematical terms -- uncanny.
@@williamwolfe8708 Someone may be at the helm as we cant even see it nor the helmsman ,this is a well organized apparatus .Trajectory is well protected and its been so for life to get where it is now ,for reasons higher than our understandings .
There is no one better than David Deutsch to answer this question. In fact, after listening to some of the answers others have given, he may be the only one who can answer it.
This guy la perfect for a science fiction production!!!,
And his opinions are very intresting.
The end statement is very true.
Thanks
I greatly love Witten's work in Knot Theory and its application to String, but let's keep this in perspective, that nothing besides "beautiful theories" have come out of them. I wish he has spent the talent on Quantum Gravity and Cosmology and such. Unfortunately his works contributed, and still does, to dragging a big crowd of young and very talented theoretical physicists in the direction of "lala land" of Strings and SUSE and such.
String theory is a quantum gravity theory, you don't know what you're talking about. There is not a good quantum gravity theory apart from string theory.
@@holliswilliams8426 quantum gravity is likely a dead end. It’s going to take a major paradigm leap in understanding to find a different idea that works.
It's probably best rephrased like this: it's astounding that reality seems to follow precise patterns even when it seems asymmetric and complicated. As we probe deeper and deeper into how the world works, we see patterns show up where everyday intuition would tell you they wouldn't. At least intuition would suggest that the patterns should be different - but at some high level we probably don't understand fully yet, those are the only possible patterns for things to make sense. That's all. And if the universe didn't obey these patterns there wouldn't be much to say about it, and we wouldn't be here to ask why. I think it's the human perspective and not the nature of reality that makes it astounding.
Maybe a deeper question is: why does it have to be the case that things even should make sense? Why anything at all, let alone something so structured? Why is there such a notion as structure in the first place? That's what keeps me up too late, probably for no good reason.
Could be that universes which are more explainable, tend to be more stable and therefore more likely to have suitable conditions for producing an intelligent observer?
Perhaps true reality does _not_ make sense, at least not to us (perhaps not yet) and not completely. Perhaps we, with our evolved faculties (so far) have made _some_ sense of what we perceive, a subset of reality that concerns perpetuation of our genetic information.
@@Surtweig I suppose anything is possible, but if we can't even hope to view it through some kind of structured framework then we really have no hope of making sense of it. A maybe somewhat controversial viewpoint is that anything that's mathematically possible is what makes up reality. Solutions to various systems and axioms that exist somewhere "out there" in some weird way.
@@manaeiou I'd comment on this the same way I did to Dmitry Ivanov. Please see that response above.
Mathematics is merely an extension of logic, and logic delimits the possible. And since anything that is must begin by being possible, any world that is must be susceptible to be understood mathematically.
There is a question of course about why much of the basic mathematics that drives our understanding of the world should be relatively simple. One can imagine coherent alternate realities in which the mathematics required to model even the simplest phenomena would be much harder. In such a case, whether there would have been the cultural impetus to develop the advanced mathematics needed to model the universe, which was clearly motivated in our actual history by the stunning successes of something like the Newtonian model, which was simple enough to appear early in the piece, and yet was very encouraging in the degree of success it had, may be questioned.
Another valid point, as you say, is about structure itself. We could easily have a fatalistic world which did not follow any local patterns. Or the structure may depend on more data than we could gather - for example even simple models of mechanics may require not merely the current state vector of the universe, but the history of the state vector over the last 100 years, which would be impossible in practice to supply, so that it is doubtful we could ever evolve any theory or test such a theory empirically.
There are two ways to answer such a question. One is of course a many worlds theory which says that all these possibilities have been realized in one universe or another, and in those universes where these awful possibilities are realized, civilization(at least in the scientific sense) never progressed beyond a certain point.
But another way is to say that in any universe with some local structure, some questions will be easier to answer than others. For example, even in our world, we can ask questions, even in mechanics(let alone psychology or history and such) such as what would be the probability of getting heads or tails for a coin with a given nonuniform weight distribution, which involve vastly more difficult mathematics. A lot of the progress of science has always depended on asking the right questions at the right time - questions for which relatively easy answers are both empirically testable and relatively easy to model. So we keep making progress, little by little, and keep adding to our store of useful applicable knowledge. So in an alternate universe, the march of knowledge would depend on asking different sets of questions at different times. Maybe the mechanics of individual objects would be too difficult to model early on. But the mechanics of large aggregates or complexes of such objects may turn out to follow much simpler statistical patterns. And having modeled it, and used it to build useful technology and an industrial civilization, the intelligent beings in this universe may sustain the motivation in their society to develop more advanced abstract models as well as more sophisticated empirical tools to probe deeper into the fundamental laws of their world.
that was nice interaction between Einstein and Witten
gotta love a physicist who intimidates other great physicists - and mathematicians - with his intellect.
I’d love to see Ed on JRE or Lex’s Podcast
Follow his Twitter mobile.twitter.com/witten271
as long as Joe stay's away from 'the simulation' - those shows were just too painful to watch
Oh wow, Ed on JRE would be next level
Mathematics: "im the most unreasonable thing on the universe"
My Wife: "Hold my beer..."
😂
Hope you have out on the running shoes. Good luck!
Great humour, never heard that joke before, except on every fucking sitcom ever.
Fucking loser.
Glob Two Says the one listening to abstract philosophical discourse. Does your comment have a purpose? Mine does. (Hint: It’s pedagogical)
@@BlackIndigenousPosse name me one sitcom where you heard that joke please.. Mister. We will be waiting for you.
Witten, Maldacena and Nima have appeared on this show. You are only missing Nati Seiberg for the whole IAS super quartet.
Orbifold Yeah. Nima with his formulation of the Amplitudhedron is astounding work.
Ed Witten should deserve a Nobel price in physics.. as a lot of these theories may perhaps only be proven right after he’s gone. Indeed, what a brilliant mind.😮❤
Clearly you are ill informed and don't know what you are talking about. He can NEVER win the Nobel because he makes completely untestable predictions that are for all practical intents and purposes pure fiction. He has NEVER offered ANY hypotheses that can make contacts with physical reality.
I've been following various research and likely the brainiacs are way ahead of me, but if you mix pilot waves as hydrodynamic carrier waves involving spheres at spacetime intersection, and fluid phase change (black holes as ice, maybe white holes) into M Theory, does anything interesting (possibly local) pop out? Hydrogen-1 may even be a good description of that sphere. Banach-Tarski math may be useful.
This guy is a genius.
I hope you asked Ed Witten on "time"
It’s hard to explain but when he speaks, you can almost hear that his words are being plucked from a space of unfathomable depth.
Particularized numbers are a cheat code. For instance, why isn't the number three, 'pi'?
The interviewer is excellent.
At 15:13 Witten mentions the equations. Usually if I type into a search engine what I think someone said, simply guessing at the spelling, I find what I'm looking for. Not this time. Can anyone tell me what that word is? It sounds to me like "insolon" but nothing comes up when I type it into my preferred search engine, which is DDG.
At 4:45, Ed Witten says: “instanton equations”; necessary to understand “4-model”(?) field theories.
@@andrefletcher7970 Thanks for the info
where is the complete interview ?
Most likely the smartest man on the earth right now, and I will be going to learn under him soon... I cannot wait :)
Did you ever end up studying under Witten?
How's that going? I met him in ~ 1983 when I was choosing a grad school and visited Princeton. I certainly had no idea what a giant he was, and was to become.
Usually such geniuses tend to be very bad teachers. They cannot explain concepts at a low enough level for their audience to understand.
@@wyqtor considering the absolute perfection of that interview, I tend to believe he gives the best teaching experience available
How come I so rarely see Ed on any of these shows, podcasts, etc?
It’s like that Douglas Adams quote about how amazing it is that the hole in the ground is perfectly shaped for the puddle to fit into it.
Mathematics is simply making up a set of rules and axioms, and then seeing if you can do anything useful with it. By definition we’re going to keep the stuff that’s useful and discard the other stuff.
Lots of things in mathematics are not useful at all, such as the 3x+1 problem.
And if the Universe is just a Simulation, some Cat will change the Channel and everything turns out to be for naught...🤷
In the case of inverse square distance for gravity . It is not yet concluded that this empirically assumption is a continuous mathematical function rather than a linear statistical one distributed on a sphere. Why field would work like that? It seems to not be efficient for nature.
Fun fact...the physics/math super genius Dr Witten actually started out in college as a history major!
Super into history and math. Guess me and him have something in common.
Finally something I share with him!
This guy is probably the smartest human who ever lived. I never attended a single one of his seminars that didn't lose half the audience halfwah through. For over thirty years now.
He's extremely smart, but I think you're going a bit far with the smartest ever. Rare geniuses like Ramanujan, Gauss, Euler etc exceed Witten imho.
@@blueboy189 terence tao is one of them as well
@@mrhatman675 Terence is probably the smartest man alive to be fair
Tell me if this guy is so smart, what has he really accomplished in physics other than leading half of all theoretical physicists down the unfalsifiable+ black hole that is string theory
@@natevanderw because he spent his life achieving greatness rather than trying to tear it down ...
For those interested in the development of theoretical physics in recent decades, this is a timeline video ranking the most cited theoretical papers in high energy physics: ua-cam.com/video/yDrudWnAlyc/v-deo.html. One of the most cited papers is Witten's important paper on holography.
Interesting. My very first thought was that small numbers appear just from the amount of dimensions we have
I would love to know what Edward thinks about S. Ramanujan.
I want to hear more about what this guy thinks.
Many of his lectures at the Institute for Advanced Study at Princeton are on you tube. Just search UA-cam with his name and you can spend months watching his lectures
@@Cooldrums777 well, that´s too hard for me, I was rather refering to his philosophical believes.
You'd probably be disappointed, he strongly avoids thinking in such directions..
@@whataboutthis10 he has given many interviews and talks that are on u tube .
He is a nice guy a family man
He doesn't answer philosophical questions.
Anyone catch what Witten said at 7:04? Something sounding like "temporal Lie algebra of statistical mechanics"?
Akhil Jalan - “Temperley-Lieb Algebra: From Knot Theory to Logic and Computation via Quantum Mechanics”
But the warping of space by massive objects how can we experimentally see it and measure it what is spacetime made of there must be some kind of matter that formulates the fabric of it
Serious question and I would love to hear people’s thoughts on this. Is there anything that math cannot describe? My current thinking is that math can be formulated to describe anything, so it’s not surprising that math can describe our universe.
Define describe. Mathematics is very powerful at laying basic postulates of physical theory, however if one is encrouch into the domain of application, mathematics, due to our own limitations more so than others, has not provided us with an easy to grasp analytical solution. Furthermore, invistigations from a purely mathematical lens, do not give rise to all possible interesting phenomina, thus within the scope of more complex systems mathematics, again due to our own inability does not provide answers. Now, a major revolution of the past hundred years or so, is the militarisation of mathematics in attempting to solve complex real world systems, be it for applications or for exploration's sake by the use of computational methods. Mathematics is the study of order in a sense, thus anything disorderly, can not be described. Mathematics can not genreate true randomness as an example.
the Human Being, the Soul, Love, Art, Peace, Freedom, Equality, Family, Relationship, Society, Morality, Literature, Consciousness.... Anguish, Danger, Perseverance, Purity of Spirit, Intentions of the Heart.... that should get you started. Basically..... everything that matters in this life...
except for, "How do things that either contain that list inside them, or are in the same universe as the things that have all that inside them, move around and interact physically with each other."
There's something called Godel's Incompleteness Theorem that describes some limitation of mathematics. I can't remember how it works, but it may well answer your question.
There is really nothing unreasonable or surprising about the effectiveness of mathematics. Mathematics can be thought of as the abstract study of of structure - it encompasses *all possible* structures, so any possible concrete physical structure has a correlate in mathematics. This is why mathematics can be used to model the world. If the universe *has* a structure, mathematics can model it, and if it can model it then it will be effective. What is not a given is a) the *metaphysical* matter that the universe *has* a (relatively comprehensible) structure, and b) that the areas that pure mathematicians explore, investigate, and develop theorems for should often turn out to be so very useful for physics. Most of the advances in theoretical physics only became possible once mathematicians had developed the tools capable of expressing the deeper structures the universe happened to have. But mathematicians have brains that evolved in the same physical world that physicists explore, so that too should not be *so* terribly surprising. I think all mathematics can be thought of as the rigorous development and extension of the structures present or implicit in the world in which we evolved. Mathematics and physics start in the same place, and both explore more deeply those structures: the one bounded by logical rigour, the other bounded by empirical rigour.
Well said
Absolutely! Not knowing (and being too lazy to google for) the context of Wigner's "unreasonable effectiveness" quote, I am struggling to believe that someone with his skills could have meant it quite so literally.
I'd be tempted to extend your constraint a) (that the universe has a structure) to speculate that, if it did not, a universe such as ours with structured things in it would be impossible. This is, of course, an "argument from personal incredulity" logical fallacy, or possibly "personal ignorance", so large pinches of salt are required.
Agreed. I don't fully appreciate this fascination with the simple idea that mathematics corresponds well with physical description. As you seem to suggest, it seems more like an unsurprising certainty since much of math has been developed to describe those physical objects. As he says, calculus was developed to describe the physical world. Well, had calculus not been useful, Newton (and Leibnitz) wouldn't have adopted it. And had they anyway, we'd instead be talking today of how much math doesn't describe the physical world! So, the choice of invention of the mathematical object matters a great deal, and such objects are usually chosen to match up with the physical world. And we're then surprised at the "unreasonable" correspondence? Calculus was hand-picked to describe the physical world. Of course it's going to then correspond. It was invented to do just that.
If I understand you correctly you seem to say that structure is geometry and therefore fits into both mathematics and physics. But what you miss in this statement is that many physical equations using math describe other thing such as charge, behavior of quantum particles etc and has no direct connection with geometric structures. I agree with Wittens and Tegmark and many other brilliant people that there is indeed an incredible fundamental and mysterious connection between math and our world. Its as if our universe is built up by pure mathematics.
@@dpie4859 The notion of structure I was employing is completely general and not specifically geometrical. The natural numbers form a structure, for instance, and there are algebraic structures, and so on.
It is not Newton who invented Calculus. It is Sangamagrama Madhavan who lived 300 years before Newton. This later reached Europe. Newton simply used this principle of infinitesimal calculus to develop his equations. Fundamentals of Infinitesimal calculus is elaborated in Madhavan's book Venuarohanam and of his deciple Jyeshthadeva named Yuktibhashyam.
It is not just that math works so well. The truth of physics is often very simple. Starting with a million possible mathematical theories, the ones that end up matching the physical truth often are simple. Often the simplicity of physics is because there is some simple geometry underlying it, just like the inverse square law they discuss. Geometric algebra is a good example of the use of simple geometry to explain seemingly complicated physics. The six equations of Maxwell, all interrelated, turn into one very simple equation using Geometric algebra.
I don’t know that I agree with the inverse square law only being explained by Einstein. Newton’s theory of gravity can also be expressed as a field theory where mass is the source of the field.
Gauss’s law then tells us that integrating over a volume containing a point mass gives a field strength that drops as 1/r^2. The same way we get Coloumb’s law by integrating around a point charge.
He's got it maybe backwards: perhaps a mathematician is the universe!? What if the basis of the universe is divisive and additive ie, simple processes that undergo emergent phenomena that evolves self-organisingly to more and more interesting maths. That would put consciousness as a higher order self-organising system able to observe lower order universe mathematical structures and think: a mathematician designed this. Yet, if the whole thing has a simple mathematical underpinning, every evolution would fabricate more and more higher order structures until the structures themselves became to rigid for self-organising systems to continue.
What’s his mmr in league?
"It's as if the universe has been created by a mathematician". Right Edward. Right.
Is that sarcasm?
@@swavekbu4959 definately
We formulate math from set laws instilled into nature at the very beginning, the thought we can formulate new laws at will from math is totally ridiculous because the laws of nature are set. Math is a great tool used wisely of course.
The universality of computation explains the effectiveness of mathematics in physics
Your answer is the smartest and more succint thing I've heard on the subject
help this man live longer.
What did he mean by Newton couldve changed the inverse sqare law?
I would love to see the math on Consciousness
Perhaps mathematics is a real / actual field which space, time and forces act in or on, because of which math can communicate what goes on in physical reality.
Incredible to listen to this man.
I don't find it odd that the inverse square law is exactly 2. What I think is really really really inexplicable is that PI is irrational. A constant used in almost every equation explicitly or implicitly through sin, cos, etc. and yet cannot be exactly known.... We can appreciate the elegance of the inverse square being exactly 2, but let's not pretend that math (or physics) is always simple and elegant (or should be). And don't get me started on the square root of -1...
He was the first to actually answer why the force of gravity is inversely proportional to the square of the distance. Robert has been asking everyone that.
@Willy Bilky It's because the wave propagates in sphere form in 3 dimensions, and the energy is concentrated on the surface of the sphere. The surface of the sphere is 4piR^2. 4pi is constant and R^2 varies. So the energy has to be distributed on an area proportional to the square of the radius. If it was in 2 dimensions it would be 2piR, in 4 dimensions it would be (2pi^2)R^3, in 5 dimensions ((8/3)pi^2)R^4 and so on...
I dream of being half as brilliant, which won’t happen but at the very least I can admire it
Actually inverse square law has been understood by Poisson and other postnewtonian physicists very well. Einstein wasn’t the first person to explain the reason for the existence of inverse square law it was Poisson who formulated the Poisson’s equation for gravity which achieved to explain the field interpretation of gravity which restricted inverse square law as other fields such as electric field. Also elliptic orbitals cannot exist in a form other than inverse square law.
A quadratic potential can also generate elliptic orbits
According to "The Grand Design" by Stephen Hawking, Ch7, p160 para2 your last statement is true. It also applies to circular orbits. Another requirement is that there must be only three spatial dimensions. And your point on Poisson's equation for the Newtonian potential is well taken as it is used in GR courses to establish the Newtonian limit since GR must subsume Newtonian theory in flat spacetime. Thanks for the rabbit hole, that was fun.
No better conversions than those with Ed Witten. I know Tagmark has provided math that blew up the Hammerhof / Penrose, platform of microtubules that facilitate quantum states, however, if any person may be used as antidotal evidence for a quantum mind, perhaps Ed should be the focus of that research.