Why the “Unreasonable Effectiveness” of Mathematics? | Episode 2203 | Closer To Truth
Why do abstract mathematical equations produce exquisitely accurate descriptions of the world? The physicist Eugene Wigner called math’s usefulness “uncanny”-and he entitled his famous essay, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences".
Featuring interviews with Robbert Dijkgraaf, Edward Witten, @SabineHossenfelder, Leonard Mlodinow, and Max Tegmark.
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Closer To Truth, hosted by Robert Lawrence Kuhn and directed by Peter Getzels, presents the world’s greatest thinkers exploring humanity’s deepest questions. Discover fundamental issues of existence. Engage new and diverse ways of thinking. Appreciate intense debates. Share your own opinions. Seek your own answers.
What I thought was unreasonable was my ineffectiveness at math.
Math is just a language of relationship. That’s why there’s an equals sign. So any world, any universe that’s not completely random can be represented by mathematics because things will interact in consistent ways. They’ll have quantifiable relationships.
Einstein is said to have remarked, “The most incomprehensible thing about the universe is that it is comprehensible.” And I think this guy knew what he was talking about. To quote Wigner: “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.” Is this one of those cases where you introduce complexity when it isn’t really there, or is there something deep and meaningful here? Why should mathematics be able to describe physical events so well? As any Mathematician will tell you, the maths is already “out there” it has an existence of its own independent of us, all we do is occasionally turn over a new stone and find a new piece of maths that had always “been in existence” independent of us. Likewise with our physical measurements and experiments, the results of these experiments has always “been there” we just came along at this particular point in time to uncover some of them. If you were to apply Occam’s Razor to this problem, where Occam’s Razor states that the simplest most logical answer is usually the right one - you might be led to conclude - as some people firmly believe, that the reason mathematics so “unreasonably” describes the “real” world we live in is because we really are “living” inside a computer simulation - the Matrix had it right all along!
A relevant subsequent question is, in the words of Stephen Hawking, "What breathes fire into the equations?", quite apart from the equations themselves?
@@samuelarthur887That is a good definition of God.
God is the simplest answer in my opinion. Now the description of this God may vary but I don’t see how such order could come poof from nothing, that just seems un reasonable.
The success of mathematics in natural sciences shows some deep connection between human mind and the physical reality; one invents a language and the other understands it.
Can't some other animals see patterns or count?
Math is a language of logic. It seems very reasonable to me that we can understand the universe with logic.
The universe is not remotely logical to humans. Life itself makes no logical sense.
How I enjoyed watching this video and many previous ones. How humbling it is to listen to great minds talking about matters that underpin our humdrum lives. How I wish I could live forever to learn of the astounding things that such minds will continue to uncover.
I’ve been watching Closer To Truth since day one and can’t get tired of them.
The reason we don’t get tired of them is because of the genius of Robert Kuhn, a brilliant man, he is able to ask relevant and insightful penetrating questions based upon the response of the interviewee. He does this on a wide variety of subjects and with highly respected thought leaders. I’m always impressed.
Thank you Robert!
Math is divination magic that actually works.
Fascinating! I’ve always wanted to learn about the mathematics of knots but it seems so complicated! I suspect that the key to biology/life has something to do with knots - as well as the “stickiness” of atoms and molecules (molecular strands only remain tangled because of the friction that prevents them from unravelling).
Great as always. Keep on
Thank you for posting this video.
Wonderful!
great show!
Great video
FYI, this is the episodes premier on KZhead; it was already broadcast on PBS back in May.
FYI I already knew that.
They're not new interviews however. This is another 'new' episode that takes old interviews and adds new voiceovers and graphics inbetween segments. You can see these exact same interviews in older episodes. The Tegmark interview appears to have been filmed during the 5th FQXI Conference in 2016 for example. Of course even the graphics are a few years old now as well. It would be more accurately called a new edit of old material. You can see that Kuhn is clearly at different ages in different parts of the episode. He's not fully grey haired in the intro and then later in the episode he is etc.
Well, Im neither surprised nor have any problem with it. Not everyone lives in the USA.
@@jareknowak8712 What makes you think I have a problem with it? I'm just pointing out it's not actually a premiere, it's just its premiere on KZhead. It's not new material anyway as I pointed out in my subsequent post; it's repackaged old interviews. Doesn't mean it's not worth watching but it isn't actually new material even when it actually premiered on US television last May.
Universe has been around for 15 billion years - 6 months we can manage.
13:37 that's a very good question :) discovering order in the midst of a seemingly disordered surroundings from the subatomic units to gargantuan galactic formations is a great achievement👍 18:08 the logic that is build into mathematical equations is applicable to every interaction in the objective world therefore the objective world behaves/operates according to the mathematical framework 🤔
Sure, the _objective_ world can, it seems, be exhaustively described and understood with mathematics. But what about the _subjective_ world of conscious experiences, such as the experience of seeing a color? It seems self-evident, for example, that you can't mathematically describe the redness of red as it appears to us in our conscious experience, not even in principle. I wonder what that says about the nature of conscious experience... 🤔
@@BugRibcolors are subjectively represented after first being sampled and differentiated by photoreceptors and then the brain will identify each one acording to prior exposures of such stimuli... so, the objective photons and their frequencies have already been subjected to certain patterns that are afterward identified again by a processing system to finally give us the experience of the colors that we know of...
Thanks. Greetings from Ovalle Chile.
I think the answer is rather mundane, actually. Formulating physics theories in the language of mathematics works well because measuring apparatuses such as rulers, weights, clocks, all deliver their measurements in numbers. Therefore, you can compare measurements with theory. However, the "unreasonable effectiveness" is sometimes used to suggest that the world might be mathematical or geometrical in nature. I think that is wrong. I imagine the world is physical in nature. There is no reason to believe there are numbers, axes, dimensions, seconds, or masses, out there...
What does it mean to exist? Start there... The Greeks dealt with these questions and went very far with their answers (Aristotle). The final solution came through Christ (developed into scholastic realism).
“Find an aspect of reality that cannot be described by math” Hmmm? If I understood Max’s challenge near the end of the video, it seems easy; for example, we know it is absolutely wrong to torture puppies for fun. That is a solid statement about reality, and yet not one that can be described mathematically. I might have misunderstood his challenge. Love the video series. So many bright people interviewed. Keep up the good work.
Sooooo, what if the puppy has information we need, it's not for fun, then, it's for info, is that O.K.?
Hi @@seanhewitt603, Well I’m not sure if my answer to your question would match your answer, but it’s somewhat unrelated to the point I was making. What we both know with 100% certainty is that it is wrong to torture puppies for fun; a firm description of one aspect of reality, yet not expressible by a math equation.
@stevekranz9826 Absolute? No. It is widely agreed, but still subjective. You say it is wrong to torture for fun. I (subjectively) agree. Humans have evolved to have a tendency for empathy, because empathy has helped our survival & replication in social groups. Others who have not inherited these genes, or have had brain injuries, or different conditioned experiences may (subjectively) disagree with us.
Hi @@canwelook, seems like a lot of speculation in your paragraph. I’m not seeing that it lines up very well with the point I was making. And actually, I don’t know what your last sentence has to do with anything. If we look at the simple absolute truth that 2+2=4, it doesn’t become the slightest bit more subjective just because a rare few delusional people feel that 2+2=5. As for your speculation that evolution favored empathy, couldn’t you just as easily (and more justifiably) speculate that evolution would favor those most aggressive at expressing selfishness as they forcefully took food, shelter, and mates for themselves in highly competitive manner? Wouldn’t that be an easier case to make? Those most successful at that goal would propagate more readily (and presumably pass the trait along), and how would that trend ever really reverse? And why would the notion that it’s wrong to torture puppies for fun ever emerge along the way? Yet, that Truth hangs out there all the same. An [absolute] Truth being no more an invention of evolution as the [absolute] truth that 2+2=4.
Hi@@steve_____K307 , it seems to me that you are confusing the imaginary with the real. I don't blame you for this error, I blame our education system. Maths and logic are powerful, human-invented tools that use deductive logic founded on assumptions. In contrast, science uses inductive logic to formulate theories which are testable through careful gathering of evidence.
Here is a list of the best content in the world today. These men knew the Intellect, inquiry, critical thinking, dialectic, Reason, Logic, retroduction, via negativa, arithmetic, science, evidence, the very nature of... I doubt any of you here are even serious. Both the commenters and those interviewed. Anyways: Periphyseon, by Eriugena, translation by O'Meara. Plotinus Enneads, select works translated by Thomas Taylor and complete translation by Lyyod. Plato complete works. Proclus books. Iamblichus books. Syrianus books. Bhagavad Gita Upanishads translated by Nikhilananda 4 vol. set, and the 18 principal Upanishads translated by Radhakrisnan. Upadesa sahashria by sankara, translated by jagadananda. Vivekacudamani by sankara, translated by Madhavananda. Philosophy as a rite of Rebirth by Algis U. Meister Eckhart complete works. The Unknown God, by D. Carabine. Mystical languages of unsaying, by M. Sells. Plotinus: Road to Reality, by JM Rist. Bible - KJV translation only. archaic is very important here with mysticism. Jacob Bohme books - a German mystics Emmanuel Swedenborg books - a scientist turned mystic and metaphysics. Coomaraswamy books. The presocratic Philosopher's - book. Sweet touches of harmony - book; Pythagorean influence. Lore and science in ancient pythagoreanism - book. The Universal One, by Walter Russel. The gods of field theory: Henri Poincare Tesla Steinmetz Maxwell Dollard
Nietzsche belongs on this list. And so does Wittgenstein (so philosophers will remember to speak clearly and carefully when they are doing philosophy). And for me, all the writings of Hume and Berkeley are a must, as well as the first _Critique_ of Kant. Although for this last work I would not blame anyone for eventually relying on the secondary literature. I have just begun exploring Plato. Mind blowingly good.
I think the uncertainty principle and the Planck theorem has shown us that there is a fundamental limit for what is possible.
One aspect of the world that can't be described by maths? Well Man, you physicists seem to be getting awfully puzzled when it comes to quantum mechanics. Not sure if you think there is really an absurd number universes branching off every time a radioactive nucleus decays. BTW if I were to present you with a single radio nucleotide how long would it last. I'll tell you the isotope, but all you'll be able to tell me is how long on average the nucleus would las if we were to repeat the exercise a few dozen times. I'm happy to see you understand so well the behaviour of matter at the centre of a black hole. Furthermore in practice a formula or computation can only model reality. Deterministic weather forecasts are usually totally useless a week out. When the atmosphere is chaotic they can fail in under a day. Whenever I hear this sort of talk I think they are confusing the model for the reality. You will not get your finger wet if you poke it into the guts a forecasting supercomputer. You will feel no wing. It's an abstract model that catches many relevant details and gives (mostly) useful forecasts. But it contains no wind or rain. Duh. Maths is crucial, and extremely useful but whatever you turn it to whenever physicists model some aspect of reality mathematically, they don't actually create the reality. You cannot model how humanity will be organised in two hundred years time. Just about anything is possible and outside of the original trio of foundation series psychohistory is science fantasy. Not even SF. Mathematicians are smart to be sure but sometimes they can display a trivial blindness to the obvious when required to think non mathematically. I think we may get a hint when AI matures further. It will undoubtedly be capable of exhibiting a lot of smart behaviour. But no matter how convincing it may be then so long as the neutrons are modelled digitally they will like all simulations be missing details. One of those details will be self consciousness. But it will be possible to fake it. I do think we could build a truly conscious machine but it will have to employ affects that are a result of its physical makeup. IOW if you can build a complex arrangement of artificial neutrons which interact in ways that cannot be captured computationally then you might succeed. IE this synapse fires in part due to electronic interference from a neighbour that is not logically connected. TLDR we will emulate intelligence with greater skill using arrays of number modelling synaptic weights but we will have build something that can evolve messily. The mess is part of the uniqueness. So long as you have a device that can be put into any state exactly you will not have an adequate model of the brain. No matter how good it is it will be a model and to be real you'll have to build something that captures the bevaiour of brains. And that involves more than nerve connections and synaptic weights. Bye!
Sabine nailed it. Nature has _some_ structures, and math is good at describing _some_ structures. Intersection of those set yields the "effectiveness". While at the same time, there are parts of math that seem "excessive" and have no implementation in nature; as well as parts of nature rather poorly described by the math. Nothing unreasonable here
I think another crucial part of the answer is that math is very good at *describing other math.* So as long as the structure of the Universe can be described by *some* math, the rest of math can then help. Obvious example: fluid equations that (approximately) describe systems of Newtonian particles. The Universe doesn't _literally_ have continuous fluids in it, but they're still a description.
I agree that the question hinges on what one considers "unreasonable." I think Dr. Hossenfelder pretty much has it right - it works in some areas and not in others, AND even in physics we get mathematically beautiful theories that turn out to be wrong. Personally I don't think there's anything magical, miraculous, or unreasonable about it. As Witten noted, there's a feedback loop going on. We invented mathematics originally from observation of nature...development of new mathematics often starts with observation of nature, and in turn we use observation and experiment to test and refine mathematics, especially when it comes to things like physics. Given that constant interaction, it seems to me perfectly natural that they fit together so well.
I enjoyed the episode but this wasn't a very good exploration of this question in my opinion. I don't think most viewers that aren't familiar with this question would come away from it with a good understanding of why so many scientists have wondered about this. They should have presented some simple examples of mathematical patterns in nature that most people could easily understand _why_ they're considered "uncanny". The best example is probably the number phi, also known as the Golden Ratio, which is the sum of 1 and the square root of 5 divided by 2, which is an irrational number approximately equal to 1.618. This ratio is found in an astonishing number of places in nature, from the structure of pine cones to flower petals to ram horns and nautilus shells and spiral galaxies etc. Really just that one example would suffice to clearly establish the concept and what exactly it is that many find to be mysterious. This can't be frivolously dismissed by saying it's just an example of selection bias where we pay attention to the math that effectively describes nature and not the math that doesn't or the parts of nature that seem ill suited to mathematical modeling. The more interesting speculation about this in my opinion, which was not brought up in this episode, is that the reason why math is so "unreasonably effective" at describing nature is not because there's some Platonic realm or that nature consists of instantiations of mathematical structures per Tegmark, but that mathematics is an artifact of neurology. In other words, the reason why mathematics seems so "unreasonably effective" at describing nature and that mathematical principles appear to be not created but discovered might be because our brains create mathematical models of the world we observe. Everything looks red through rose colored glasses; everything looks mathematical when you have a brain that models things mathematically. The equations and formulations of mathematics we 'discover' are essentially representations of the way our brain models reality, according to this view A being with an alien brain might have a very different but equally effective sort of mathematics. I think that's a much more interesting and plausible explanation than metaphysical musings about Platonic realms and talk of 'miracles' etc. There is perhaps a 'Platonic realm' where mathematical structures 'live", but it's not a spooky immaterial realm but rather is embedded in the grey stuff inside our skulls. A sort of 'materialist' or 'meaty' Platonism so to speak.
Great comment, although I think differently. "because our brains create mathematical models of the world we observe". I think: "because our brains perceive mathematical models of the world we observe" Maths is an abstraction of what we observe. Three oranges, three goats, three rivers. You abstract the three. It is rooted in reality. It is both made up and discovered. I mean our brains are where this happens. And our brains are products of evolution in the real universe. But mathematics is not formulated because of our mental processes. But yes, all ideas are material in some sense, including those of mathematics. I definitely agree with you there. Have you read "Anathem". I recommend it, I guarantee you will enjoy it.
Game of theory probably would explain unreasonable part of math, in the process i learn the equation, turns out its every line of arithmetic, which a journey to get an answer, is named after equivalent, which describes a many form of similar context, not a rigid form. A state of decision is what makes it effective.
Logic is the language of causation, merely non-contradictory sequence. As such it imposes time. It is not a presupposition of time that is generalizable to other models of mechanics, merely an overlay - dependent on the underlying sequence.
Veritasium has a video about the knot research. It's fascinating.
7:12 ...❤ the most undervalued symbol in mathis the equal sign now if you take a beautiful mathematical formula it looks like A equals B ( A = B ) and often A and B come from completely differet worlds and physics and science is a way to produce these kind of equations, e = mc^2, the most famous case. 7:28
Since there are people who are more equal than others, it doesn't quite work when applied to human beings who come from the exact same physical world, does it?
It's entirely reasonable, the effectiveness of mathematics.
This type of question isn't even a question for mathematicians.
The "language" of mathematics is derived from the universe around us, so it makes sense that it can be applied to anything we find in that universe. In other words, any physical process we can identify can be described with mathematics, it being a matter of simply finding whatever numbers/equations fit the process. Math is a language of numbers that represent physical entities and their interactions, just as verbal language represents the "things" we see and do. The universe is not "built" on mathematical equations, rather math is only one way of representing what we see.
What are *reasonable, rational* ? A statistical impossibility is defined as *_“a probability that is so low as to not be worthy of mentioning. Sometimes it is quoted as 1/10^50 although the cutoff is inherently arbitrary. Although not truly impossible the probability is low enough so as to not bear mention in a Rational, Reasonable argument."_* The probability of finding one particular atom out of all of the atoms in the universe has been estimated to be 1/10^80. Of all the physical laws and constants, just the Cosmological Constant alone is tuned to a level of 1/10^120; not to mention the fine-tuning of the Mass-Energy distribution of early universe which is 1/10^10^123. Therefore, in the fine-tuning argument, it would be more Rational and Reasonable to conclude that the multi-verse is not the correct answer. On the other hand, it has been scientifically proven numerous times that Consciousness does indeed collapse the wave function to cause information waves of probability/potentiality to become particle/matter with 1/1 probability. A rational and reasonable person could therefore conclude that the answer is consciousness.
Why are you cut and pasting this debunked nonsense again?
we do live in a mesmerizing world today. thanks to our overblown ideologies about anything and everything we can think of. good luck world. the funnies are going to go on for even more decades
It's getting to the point where the b-roll noticeably features RLK 15+ years ago lol
It doesnt diminish the value of the program.
The thing is a "new" Closer To Truth episode doesn't necessarily mean new interviews. This particular episode is actually only 'new' to KZhead; it debuted on television last May. But these aren't new interviews anyway; they're new edits of old interviews. The KZhead channel is obviously just a repository for clips of episodes from over the years but even the television show rarely films new interviews. They did do it a year or so ago but in recent years, even before the pandemic, I noticed they tend to just recycle old material with new graphics and voiceovers between segments. As long as the topics are interesting and well edited I have no problem with it but they're basically all essentially clip shows at this point.
Because nature is totally consistent (hence the quantum in QM), or at least that this consistency emerges in aggregate.
Is it really that surprising? Assuming there is an underlying theory of connectedness or TOE that we can’t yet see, one might expect to see a seemingly unconnected set of objects that conform to the underlying logical structure
The question we need to ask is: Where does mathematics come from? If we understand that, we may gain some insight regarding it's 'unreasonable effectiveness' in describing physical reality
Holy cow there have been over 2,000 episodes of this?!?
The Effectiveness of Mathematics in describing the Universe is an extremely well established FACT and Very Reasonable for a Mind, Consciousness, Intelligence. The ones who do not understand this well established fact are the believers in a strictly Materialistic Ideology / worldview. The narrow, subjective Materialistic belief / ideology / worldview is incongruent with observed reality.
For one, mathematics do not describe Humankind effectively at all.
Math works in relatively well behaved ("simple") regimes, such as physics. It works where it works. A measurement in one location, allows one to extrapolate into another location. But there are regimes where this is not the case, such as biology, evolution. Even before that, eliminating all stochasticity, if one have a relatively simple rule, that happens to be generative, one cannot predict what will happen, without going through all the steps of the computation itself. Wolfram talks about this in "computational irreducibility". Is "computation" "math"? Depends on one's definition of "math".
Max Tegmark sounds like he’s describing the matrix
Mathematics is always an approximation of the real dynamic of the Universe. It works because, exactly like a real causal chain, it tries to bridge logically ( =causally) the real causes and their effects, but the mathematical ( = theoretical ) apparatus is always "finite" ( = gives you a local logical answer ) in results ( = concrete "logical" solutions ), while the real-natural causal chain is continuously neverending. For example, draw a line on a piece of paper and think about it: is it continuous or is it made of discreet aggregates? Let's say the answer is 'aggregates'. Then take one "aggregate" and magnify it until it is seen as being of the size of the initial drawn line. Then take two arbitrary points on this magnified aggregate and see an imaginary line made of that aggregate between these two points. Is this new aggregated line continuous or is it further made of discreet 'aggregates'? Etc. Mathematics, in order to have a concrete solution, ( in this cases that refer to physical-universal realm ) chooses a logical outcome which evidently is an approximation. If it doesn't have a concrete answer then it can't say something concrete about the modeled ( ="observed" ) "object". Then it can still approximate a logical outcome down the logical chain, either being logically correct or logically erroneous. ( 'Logic' = mathematics is not absolutely and automatically equal with TRUE REAL and universal dynamic. ) I know that many indoctrinated mathematicians don't understand what I mean here, including Edward Witten, because if they understood everything correctly, they would know exactly how the correct dynamic of the Universe works. Etc.
I think “the unreasonable effectiveness of mathematics” is really nice poetic language, but isn’t it a classic example of begging the question? Is it unreasonably effective? Or just reasonably effective?
Yes, what's unreasonably effective are rhetorical flourishes.
I think it just means that it exceeds one's expectations (link between math and nature).
How to use Mathematics to measure feelings and emotions?
This is where statistical analysis comes into play. If we have a large enough subject pool we can then give percentages about what emotions may come into play at what level of intensity in many or most cases. But mathematics and statistical analysis cannot not ever pinpoint exactly how any one particular individual is likely to exactly react emotionally to any particular situation. You’ll get better results in that by simply asking friends and family who know the person well. But then they aren’t using math.
A measure of hormones divided by the receptor and a ton of other factors/variables included, not just in the brain's neurons, but in the body as well.
All we can’t see in our space , we can see in our planet maybe not by see it rather to look at it.
Who would have thought a universe based on natural laws would be predictable and predicted by mathematical formulation of those rules???? Crazy right???
No reasonable person would expect that. So unreasonable.
Always searching
Try to imagine a universe where 1+1 does not equal 2... Or a universe where no math works at all... I personally can not. It seems to me that if physics were completely different - no gravity, no particles, everything different - then 1+1 would still equal 2. The inverse square function would still exist and work perfectly even if it didn't describe anything real. And in this universe, there is lots of math that does work perfectly but does not describe anything real. So some math is effective and some not.
Scholastic realism is the answer. We are able to (partially) understand an intelligently-ordered universe through our (limited) rationality.
24:20 Sir ... Consciousness may be described mathematically,..but its definitely not mathematical in nature. Consciousness may be the 1 from the 0 World. Consciousness is definitely not limited to our understanding. Consciousness may definitely be the doorway to unclock the secrets of existence. Only we need to find the keys to unlock it. I have been reading books of western scientists and eastern mystics. I stronly feel that the highly evolved western scientific community should step into their study and research of eastern mysticism. They will all be shocked at the quantity of scientific information available from eastern mysticism. Because there are so many aspects of research in every subject . And it brings so much excitement when we see two different subjects understood by one single scientific information.
There can only be a 1 from the 0 world if -1 has gone off to play on his own as well. Let’s hope they never meet again.
@@longcastle4863 they always remain connected.
@@sujok-acupuncture9246 Hopefully only through email. Otherwise they would cease to exist.
Exactly its just math's
No doubt that man are searching for theology in his podcast. Sabine saw right through his him. She’s amazing 😊🎸
Who's dishonest, the person open to all possibilities, or the person with a predetermined worldview?
This isn't a podcast.
@@aisthpaoitht Someone refusing the very mention of a possible creator is not open to all possibilities.
The reason why mathematics is not so effective in non-natural sciences is that these sciences have not yet mastered measuring their subject of study precisely, and therefore, they cannot formulate their quantitative laws or patterns.
Or, alternatively, mathematics cannot completely contain or bind living matter to its deterministic foundations. Because living matter tends to sometimes have a mind of its own that doesn’t care what the determinism of physics is telling it it must do.
@longcastle4863 I am sorry the indeterministic character of living matter is irrelevant because indeterminism can also be described by precise mathematical formalism (I mean Quantum Mechanics). The reason in question is that non-natural science, psychology, for instance, cannot precisely measure non-natural quantities, the quantity of emotion, for example, in order to ascertain quantitative laws or patterns. Thank you for the like.
I was taught "Why the Inverse Square Law" by Edward Witten. Who taught it to you?
Sir Isaac Newton
sabine always cuts through the "woo"
Tegmark knows why
I think you need to outline more clearly what a world that does not comply with math laws would be like. Just random? No doubt we would instead ask why the universe does not follow laws if we were able to exist in such a universe. And aren’t quantum physics random anyway?
I suppose the big question is. Is Mathematics invented or discovered
That question is tangled up in a long history of our quest for reducibility and pinning down the truth to its simplest form, and I think it's led to a fundamentally bad understanding of what mathematics is - and indeed whether it's invented or discovered. I still struggle to put into words that can untangle the mess fully, but I can clearly see another connection to reality - and any artificial system with any kind of regularity of entities and interactions e.g. cellular automata, Turing machines, for that matter - that makes the question of invention or discovery moot. I think two important things are quite clear: - The universe is made up of parts and interactions between parts that seem to be governed by some kind of regularity, i.e. there are rules for things and how they interact. The opposite would be a complete mess of randomness or some substance with no parts. - The language of mathematics is obviously an invention made (continually) by humans that we use to describe parts and interactions between parts. Why can this totally abstract invention describe reality? It all comes down to the regularity, i.e. rule-boundedness of the entities and interactions of reality. If there is regularity then there can be a set of symbols and rules for manipulating those symbols that correspond to that regularity. If we ask the wrong question, then reality can easily be mistaken for being "mathy". However, if we ask differently, and to my mind this is in some sense more simple, we get the answer that regularity is discovered and our language to describe that regularity is invented. Given that computational universality exists and any universal system can take the place of any other universal system, it's clear that "our" mathematics could look vastly different, but would still correspond to what we've discovered. If mathematics is "merely" an invention then can it tell us something about reality that is not readily apparent? Sure! Take the phenomenon of computational irreducibility - a thorn in the side of old school reductionism. The presence of computational irreducibility in systems that are computationally universal, like Turing machines, tells us that if we encounter systems in nature that are as complex as universal systems, we can't expect to make great leaps of reducibility. Newton was likely to first human to encounter this problem - the three-body problem. The paradox of the set of all sets that are not members of themselves tells a somewhat similar story about something that I think we can readily assume can't be found in nature.
God is the most satisfying answer for all the mysteries!
I'm not convinced mathematics is all that effective in certain cases. There's parts of physics that are experimentally completely dominated by noise, and our physical theories are describing a very small amount of the system. Perhaps it's better to think of the universe as representing a spectrum from pure noise to pure order, and systems for everything in between can be found. This is the problem with the purely mathematical view of the universe. In practice, the concepts you'll be using to describe it will include probabilism and indeterminacy, which is an admission that the system does appear to be non-mathematical in a critical, inescapable sense. Mathematics is a way to move phenomena from indeterminate to determinate. There's fundamental limits on this process.
Is that just another way to describe the second law of thermodynamics
@@theklaus7436 The second law of thermodynamics is highly suggestive about the fate of attempts to make the universe appear determinate. Heisenberg's uncertainty relationships seem to imply that the starting point isn't on especially firm ground, either. This is the thing about physics, it's really not entirely mathematical, and there's some very important theories that we hold to be universally true that make exactly this case. Mathematics is entirely mathematical, and the story is written in mathematics. This is a different issue. The story is miniscule in comparison to the context in which it's written!
The 'unreasonable' effectiveness of modern maths => natural reasoning replaces supernatural reasoning
Life is supernatural.
Because physics is statistics of matter.
Newton did not use the calculus in Principia. There is no indication that he understood what he "discovered" Níor úsáid Newton an calcalas i Principia. Níl aon leid gur thuig sé cad a "chruthaigh sé"
Mathematics is a case of perfect world which is not bended or grainy... You can divide into infinity while in real world there are limits... That means to create physical world you need something which destroys that perfection of mathematics that lack of symmetry. Otherwise physical world would not exist.
Almost like there is a divine realm of infinite perfection and we live in the non-divine, non-perfect realm...
Yeah... If there is divine realm... I wonder what they would say about Godel Incompleteness Theorem. Like... "Jesus my friend! Tell me about Godel Incompleteness Theorem. Is it valid in divine realm? XD"@@aisthpaoitht
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I like that due to Wittens explanation it is now clear you shouldn't tell kids the explanation of the inverse square law is the radiation surface fact, because that assumes a field (like electromagnetic fields with radiation) and we don't know that yet if we only had Newton and not Einstein in school. So stop using that explanation in high school, because you cannot connect Newton to the field concept! Instead say Hooke's law would result in a poor elliptical orbit (Lissajoux ellipse) but Kepler's law requires a real ellips, which you can get from a Joukowski transform of Hooke's law, which results in the inverse square law! This is the only truth in the Newtonian reality!
No, 1/r² also works assuming a spray of particles.
@@brothermine2292 that is basically what radiation is. Anyway, at what speed does that spray of particles move? And at what speed does Newtonian gravity move?
@@Robinson8491 : The speed doesn't affect the 1/r² law. Newton didn't define the speed of gravity. Why are you asking me about speed?
@@brothermine2292 because your explanation with the spray paint works with the speed of light, which is relativity by Einstein, which didn't exist in Newtons time. In Newtons time, gravity was instantaneous. Therefore you can't use a non-instantaneous explanation in the Newtonian framework. It's comparing oranges and apples and will confuse people when they really have to think about how they relate and how it works. Only mathematical transformations can be instantaneous
@@Robinson8491 : No, the 1/r² law does NOT require speed to be the speed of light, nor does it require relativity. It works for any spray at any finite nonzero speed, because the surface area of a 3-dimensional region of space is proportional to the square of distance and is independent of the speed of its expansion. Whether it also works at infinite speed is unclear. But Newton's math calculations often used limits, and when g(r,speed) = g(r) for all finite speed, then the limit of g(r,speed) as speed goes to infinity is also g(r). So the 1/r² law is independent of speed even for Newton's model of instantaneous gravity.
Nothing is as neat as he suggests, i.e. Pi is an irrational number. Humans see patterns everywhere and there are levels of resolution. Math is the language of man seeing relationships in common phenomena.
Math is a tool, philosophy is a tool. They both have their applications, but neither explains “everything” in and of themselves.
In a word, geometry
All these talks point to a unique and special phenomena, "Faith in UNSEEN ". We can't see, hear, sense, smell, feel everything around us. 10^-15m & 10^15 billions of light years are mere faiths.
Math is a tool of the mind, used by the mind to analyse and understand whatever it encounters. This tool is not a perfect one. In the majority of cases, it gives only approximations. In other cases, it falls flat with no clues, whatsoever. Here is a simple and daily example of maths giving us only approximations: divide two of anything into three equal parts. In mathematics, this is impossible. Maths will only give you an approximation of 0.66666666.... to infinity. This is wrong because for all practical purposes, at the very dead end, we will ultimately be left with two equal parts that are indivisible. Any attempt to divide further will consequently obliterate the specimen out of existence. As for mathematics, it does not end there. It simply goes on and on and on into infinity. I think this very simple example should demonstrate that mathematics is a tool of the mind for making practical approximations for a few stuffs but not all.
We know so little and speak as if we knew everything about everything. We don't.
Nobody interviewed in this episode spoke as if they knew everything about everything. In fact they all acknowledged that there's a lot we don't know.
@@b.g.5869 Maybe not here, but elsewhere there are people claiming wrong things. Thus opens a debate.
That's like asking, Why is the English language so effective at describing the Universe? I can say the word "dog," and there are dogs in the universe! How does that happen? Because we made it to describe the Universe!
Why, oh whyyyy, why is it so unreasonable??? 😭
Read Wigner’s paper. (It’s open access.)
Once again, we see that Lawrence Kuhn does not understand English grammar (even though Wigner, from Hungary, understands it perfectly). The title of Wigner's famous paper is "The Unreasonable Effectiveness of Mathematics in the Natural Sciences." The word 'unreasonable' modifies 'effectiveness'; it does not modify 'mathematics'. But Kuhn insists on reading Wigner's title as an assertion that mathematics is "both effective and unreasonable." That's nonsense. If Kuhn had actually read Wigner's paper, or if he possessed Third Grade English proficiency, he would not keep making that mistake. (There are at least two earlier Kuhn videos on this same topic: [1] With Max Tegmark, about two years ago. There, Kuhn just listens to his guest and does not reveal his misunderstanding of Wigner's title. The 9-minute video is worthwhile (though largely tangential the Wigner article itself). [2] With Sabine Hossenfelder, also about two years ago (?). There, Kuhn starts off with the same misunderstanding of Wigner's title that occurs in the present video, where he thinks Wigner said mathematics is "both effective and unreasonable." Hossenfelder ignores his absurdity and tries to forge ahead with something more to the point.
14 min, look at when disease repeats in family DNA, for history overlaps as well of self simlar events.
If the universe is deterministic would that mean that it’s obvious that math is so effective?
It's not deterministic. Godel's incompleteness theorem also shows that the universe cannot contain its own truth.
@@aisthpaoithtGodel's Incompleteness theorem does not show that the universe cannot contain its own truth. It says that there are true statements in any consistent formal system that cannot be proven in terms of that system. This does not entail that "the universe cannot contain its own truth".
The resealable defectiveness of Mathematics.
1st AI interview
Very well built program with diverse , complementary and enlightening views. The universe as a computer game powered by an algorithm-based program is the solution for our mathematical universe without the need to resort to miracles.
Seeing all reality as being similar to whatever our latest technology is, has no staying power. Go ask those who saw all reality as a watch that had been wound up and was now running its course.
Let me begin by saying that I'm not religious nor have any mystical inclination. You will agree that the watch analogy has very little explanatory power. By contrast, the program hypothesis fully explains our universe. For instance, longstanding issues in physics such as the fine tuning, become instantly explained - the laws of physics and constants of nature are parameters of the program and so are the mathematical equations, theme of the video. On the other hand, I invite you to think for a moment what can possibly be the source, meaning and role of mathematical equations (and for that matter, of information, laws and constants) in the necessarily random and purposeless Darwinian universe (D. Futuyma)? Of course, because of the extrapolation from random mutation to the universe, to defend a programmed universe one needs to demonstrate that mutation is programmed rather than random, hence the primacy of biology in my book "Beyond Darwin the program hypothesis". Very briefly, adaptive mutation was described by J. Cairns 35 years ago, yet it's still taboo for mainstream biology for, as you may understand random and adaptive mutation are mutually exclusive. According to molecular biology (e.g. James Shapiro) mutation is the result of cellular engineering systems, and mostly occurs via transposition, an obviously non-random phenomenon (please remember that due to its description in the early 50s, B. McClintock was marginalised for decades, only to receive the Nobel price in the 80s). One news release from an N.I.H. project declared, “Much of what has been called ‘junk DNA’ in the human genome is actually a massive control panel with millions of switches regulating the activity of our genes”. And despite playing the executive role of the program of the cell by orchestrating gene activity, junk DNA doesn't follow Darwinian evolution, for it functions and evolves independently of natural selection (it yields no protein product). Further upholding the program thesis is the algorithmic view of life. And another misconception is the analogy between genetic algorithms and the random tenet, when in fact what they mimic are the processes of adaptive evolution - indeed, it's worth noting that algorithms are wilfully designed, goal-oriented mathematical constructions acting on a specific target and taking advantage of a stringent selection mechanism. But the fact they use random optimisation iterations (like in adaptive mutation) is good enough for the ideological biased to jump into wrong conclusions. Finally, natural selection, a passive mechanism, has no creative power - rather, in the program view, it represents the biology arm of the second law of thermodynamics - the elimination that permits reconstruction and evolution in a finite universe. I apologise for the lengthy reply. @@longcastle4863
@@miguelribeiro5902 I think mathematics came out of the minds of homo sapiens and probably stem from our original cause and effect reasoning, which we found helpful for survival. I find the rest of what you write interesting, but do not think I was able to follow it well. It sounds like you think something else was / is going on in Evolution besides the usually noted mechanisms, including Natural Selection. That instead of selecting for random mutations helpful to the species, mutations might be driven by needs to meet environmental demands. I probably got that wrong, but I do find it interesting.
The idea that mathematics, rather than a human invention, is mostly (though not entirely) a discovery of the principles running the universe, is becoming increasingly accepted. The point I was trying to make is that a universe run by mathematical equations is incompatible with the randomness and purposelessness of the Darwinian universe. Max Tegmark, who views the universe as a mathematical structure, wrote in relation to AI: "computation is a pattern in the spacetime arrangement of particles, and it’s not the particles but the pattern that really matters! Matter doesn’t matter. In other words, the hardware is the matter and the software is the pattern". The fact that the universe's substrate consists of evolving patterns of atoms and radiation and that these translate into the coherent world we perceive, suggests computation by the universe, i.e. a program-powered - not a random - universe. The biology considerations I made are in line with this programmed view of the universe. @@longcastle4863
Max Tegmark is of origin Scandinavian (Swedish) and his blind belief in Mathematics is a part of the Scandinavian culture. In the Scandinavian countries there is a proverb saying "Alt er tall" (Norwegian version), meaning "Everything is numbers". I am myself a Scandinavian (Norwegian) , but have never believed that proverb. This culture is pushed upon the public by the elite of society, because it serves as a tool to control and herd the common population. The belief, along with certain other thoughtrules, makes people think in a preconditioned way without understanding anything in depth, and without discovering things the elite does not want common people to discover. Tegmark as a person seems to either having fallen pray to that culture. Or - he considers himself as a part of the elite that uses this cultural element to control hov people thinks without really believing it himself.
Just 🤔... Math is patterns. The universe, as we currently understand, was chaos after the big bang. It was when gravity appeared that structures started to form. Structures are patterns. So, Math being patterns is a descriptor of the inherent patterns that emerge. It's a language that is able to describe and predict patterns. Without gravity and the subsequent formation of structures, and ... sentient beings, Math wouldn't exist.
Calculus was invented by Madhav of Kerala School of Mathemetics (13- 14th century). He discovered Infinite Series. Newton and Leibniz rediscovered calculus in 17th century.
Everything is invented by Indians. The biggest invention of course is gomutra.
@@PomegranateChocolateYes that's correct....it cures so many diseases 😊
@@rupesh_sahebrao_dhote Absolutely!😁
@@PomegranateChocolate 😁
Wait, I thought it was Islam who discovered everything first!
Reality is an illusion
Why does math even exist? Why isn’t there just pure chaos, or nothing at all?
You said I-Style at NASA. Inventing Krem as the inventor of nuclear weapons, J. Robert Oppenheimer thought of it as an extension of biological weapons captured from the Nazi army. After Hitler was ordered by God to surrender the war, otherwise W3 would not have happened in this era. (with Newton) Good physics, calculations are absolutely ridiculous. Pioneer of the W1 era Received knowledge from God in the early era of globalization is Srinivasan ramanujan and the origin of Shivastar, an underground particle accelerator in the U.S. Air Force in New Mexico. It is thought that Calculate the stars and the origins of Greek, Roman, Hebrew, and Islamic mythology and the pagan religion Mitraiusm Supreme God Roman is Kill Cow of Zoroastrianism . Who is it from? He is Varahamihira. But these people did not betray God like Bharmin Guru Baba in the materialistic age now. More importantly, you guys will never know because when the Matrix was ordered to open 6-7 years ago. It has been determined that the language that no one in that era knew Even myself now or AI. Until he becomes the Great Emperor of Utopia according to his rightful right, it is the law of the universe.
Wigner's unreasonable effectiveness of mathematics is Penrose's ;mathematics is based on faith', is the same statement.
I think we enter these conversations from the wrong perspective. There are an uncountably infinite number of mathematical functions and statements that could exist, but the laws of physics have instantiated a countable set of functions that are actually computable in our universe. There is a sort of anthropic question there as to why this particular countable set of mathematics, out of an uncountable sea, became instantiated and computable in our universe. My assumption is that at fundamental levels math, computability theory, and physics aren't separate things.
Math isn't something that exists by itself - the Intellect and the sense perception organs that interact with things are required for math. The very models are made up in our minds so to mimic, what we think really is. The problem that Platonics acknowledges is that this realm we think to be reality is actually the reflection of the real one - the intelligible realities. Matter is seen as a mirror and the reflection therein is the form of the thing in existence from the intelligibles. Math goes to a point, but a threshold is this ^ Pythagoras, Platonics, Neoplatonics, they were all about arithmetics - 0 is a place holder, 1 is principle. Mathematics lack this accountablility and comprehension. Thinking about it, arithmetics is more about the Intellect, whereas mathemetics is circumscribed to man's sense perception organs, their activities, and mind which is a condition - implying greater limitation. We mimic things to understand them, make models and theories, but what is the very essence & substances of what we are trying to mimic has been forgotten. Metaphysics is imperative. The lack of respect and consideration today for Metaphysics is great mistake. What do people think metaphysics has been dealing with for thousands of years?
Totally agree with you until around where you write 0 is a placeholder. And then it isn’t that I disagree with you; it’s that I had trouble following, which I’m beginning to think is more me than you. But understand, most people here are not so well read to discuss this stuff using technological language.
That was really fun. Interesting that math still doesn't explain many things----consciousness, intuition, instinct, mythology, synchronicity, language, neural networks. Gia might be information.
Math doesn't _explain_ anything per se; it's a descriptive and modeling framework. Neural networks can absolutely be described in terms of mathematics by the way.
People studying the brain, psychology, consciousness, etc use math all the time in their research.
Neural networks are calculus.
Qualia are non-mathematical
If I want to create blue green I mix 2/3rds blue with 1/3rd green.
@@longcastle4863 kzhead.info/sun/dtOFgaprmpiuqWg/bejne.html
I think Sabine misses the point, and the point addresses her question about why math isn't as effective in other areas...the point of the unreasonable effect of mathematics is that the fundamental laws of nature are so simple that humans can actually understand them mathematically. You might imagine that they were much too complicated to be described mathematically by humans, as biology and some other sciences are. Physics is the only science with this unusual property. Edit: I'm glad to see Robert understands this. The thing Max Tegmark says about falsification isn't actually falsification, there is no way you could prove that something can't be described mathematically 😂
Mathematical effectiveness is not unreasonable, it's reasonable, based on reason and *reasoning, as well as logic and logicality.
Maths is the symbolic language of humans to represent... reality along with our actions. Maths can only answer HOW. It will never be able to answer WHY. That's the job of philosopher. 😊
😂
The Jewish people clearly have the Universe covered.
Kant answered this question. We understand the world with the logic of math. That in no way suggests that math is depicting true reality
exactly. Math is just a system of tautologies that lets us translate one formulation to another.
You could have stopped at the word logic. No need to add mathematics there. More precisely the law of non-contradiction. Wait...didn't Kant say that? And actually quantum mechanics is 'contradictory' due to superpositions? Mmm...maybe Kant wasn't right after all...
I disagree... Consider the following... 1. Mathematics and Empirical Validation: One of the most compelling arguments for the realism of mathematics in describing true reality comes from its empirical success. The predictions and descriptions made using mathematics in fields like physics, chemistry, and engineering have been verified to astonishing degrees of accuracy. For instance, the mathematical equations of general relativity predict the bending of light by gravity, which has been observed and measured. 2. Mathematics in Natural Sciences: Mathematics is not just a tool for understanding the world; it often forms the foundation of our most fundamental physical theories. The fact that the universe behaves according to mathematical principles (like the laws of physics) suggests a deep-seated relationship between mathematics and the structure of reality. 3. Universality of Mathematical Truths: Mathematical truths are not contingent upon human beliefs or experiences; they are universal. This universality implies a connection between the abstract world of mathematics and the fundamental nature of reality. 4. Inherent Mathematical Structures in Nature: Patterns and structures that are describable by mathematical concepts are inherently present in nature, such as fractal patterns in snowflakes or the Fibonacci sequence in the arrangement of leaves. This occurrence of mathematical patterns in nature suggests that mathematics is more than just a human-constructed logic but is, in some sense, embedded in the fabric of reality. 5. Predictive Power Beyond Intuition: Mathematics often leads to discoveries that go far beyond intuitive understanding. For example, the mathematics of quantum mechanics predicts phenomena that are completely counterintuitive, yet these predictions have been confirmed experimentally. 6. Instrumentalism vs. Realism in Mathematics: The statement leans towards an instrumentalist view of mathematics (mathematics as a useful tool, but not necessarily reflective of an underlying reality). However, mathematical realism (the view that mathematical statements have a truth value independent of our knowledge or understanding and are deeply connected to the fabric of the universe) is supported by the uncanny effectiveness of mathematics in describing the physical world. 7. Mathematics in Theoretical Predictions: There have been instances where mathematical theories have predicted the existence of physical entities before their empirical discovery, such as the prediction of black holes and the Higgs boson. This suggests that mathematics is not just describing our current understanding of reality but is also uncovering aspects of reality that are not yet observed. So, while it's true that mathematics is a tool for understanding the world, the profound effectiveness of mathematics in both describing and predicting natural phenomena suggests a deeper connection between mathematical structures and what we consider to be "true reality."...
@@BradHoytMusic math can be adjusted to accomodate for anything. its a no brainer that we can find mathematical forms that follows physics.
@@Robinson8491we live in a logical world, but that’s only from our point of view
The fact that the forces of nature seem to work according to the rules of mathematics, does not constitute an argument for You, that everything had a common source, and at the very bottom of it there is some kind of algorithm, a self-replicating program, something like a cellular automata??
Don't get me wrong, I love this series and have followed it for years. I have the utmost respect for Robert Kuhn and feel his work distills greater wonder in our reality which is so important in propagating compassion and empathy. But I've seen an unsettling tendency for the, alas, few women who are featured to be mansplained and paraphrased. Jus' sayin'.
Physicists prefer to avoid the philosophical implications of a mathematical reality because they realize all roads inevitably lead to an intelligent designer