I like Davies' openness. I also like the way he admits unresolved issues of mind, math and reality-unlike others who commit to the dogma of reductive materialism. Davies admits that the reductionist paradigm is very insufficient to account for these amazing facts of reality. I saw the same intellectual honesty in Tom Nagel's MIND & COSMOS.
Mathematics is a language designed to model patterns. Reality is full of patterns. That methematics is effective at modeling reality is not so unreasonable.
@@les2997 The present is a consequence of the past. I suppose the purist could debate that -- that everything is just "now" -- but IF evolution happened the way Biologists claim, then our concept of mathematics may have evolved as well, and that would tell us a lot about the universe.
@@les2997 Mathematical reasoning, at its heart, is the pursuit of truth. Clearly defined terms combined with logic, symmetry, analogy, isomorphism, metaphor etc. A tribe is not going to survive long if it can't distinguish fact from fiction, or is unable to communicate truths about the world.
@@williamwolfe8708 This is where you are wrong because very many totally false beliefs aid survival. For example, lightly paranoid people will have a better chance of surviving if they falsely think that someone is after them, etc. Wouldn't you accumulate a small cache of weapons if you thought that your neighbors are after you? Anyway, if evolution were true, our cognitive faculties would be aimed at survival, not truth finding. In order to survive your beliefs don't need to be true.
I mean if you were to call it human mathematics, then perhaps the physical phenomenon/law that it can so effectively explain should also be termed "human observed physical phenomenon". After all, everything we see/feel/measure is processed and formed in our brain, human brain.
I'm not sure if I'm getting it or not. But it seems to me that mathematics is a way of describing regularities and patterns. And how can you create structures of any sort that do not involve regularities and patterns? If you have a universe where anything at all happens, then you must have structure. From the tiny drop of water that has an atomic structure, to the vast complexity of a human being. So why is it surprising that mathematics (a way of describing regularities and patterns) should be so effective at describing the things of this universe?
I’d actually like to interview YOU on how you’ve been able to get in front of and interview all of these “top dogs” through the years? Amazing .You must be a great charmer 😉
I like his emphasis on evolution, deep level of reality, etc. -- math is uncanny because it is in our bones. It was put there by evolution. Therefore, the essence must have been there at the big bang, or an explanation for the big bang.
I love the insights and perspectives of Paul Davies. Here I'd like to suggest also that animal and insect perception also provides remarkable and unique ways of knowing and experiencing aspects of the world which we are not always privy to and in many cases far exceeds the range and sensitivity of human awareness. Animal perception and sentience is as legitimate as any other modality of knowing whilst also broadening the range of knowledge about the natural world and of how it is experienced. Consciousness and knowledge is not the prerogative of humans, and this fact adds immensely to the 'sum total' of what is 'known' about the natural world by 'Mind at large'. The epistemic openness or revelations of the universe are certainly not confined to people. I'd also suggest that the possibility of plant, fungal and indeed bacterial perception and sentience is a credible one, as is evidenced by the rapid growth of research into these fields.
haven't we already hit a point where mathematics is breaking down? Non-linearity and chaotic systems are impossible to model precisely and yet these seem to be how the universe works in a macro sense. The inverse square law can describe 2 bodies in motion but breaks down at three or more. Also there are infinitely many types of mathematics that describe universes we don't live in so it seems like a massive tautology to me
Math is merely a language with a single rule: contradictions are forbidden. This rule comes from logic and forms the foundation for all logic. Math is simply a language of logic. The fact that math is so effective and and difficult for humans to identify as merely a language shows only that humans are terrible at logic. We simply do not take to logic naturally. It is difficult for humans to think logically. It is not a coincidence that modern civilization traces its roots directly back to Aristotle as the father of logic as all advanced thinking requires logic.
My dumb guess: Because there is some simple and reliable mechanism at work at the bottom level. From there, effects just scale up nicely because random noise will obey the law of averages. Perhaps there is a barrier between quantum and classical scales where some threshold enforces a new dynamic to emerge.
“Where do the laws of physics come from ...?” That is a fundamental question Dr Davies asks that has a “profound religious” inference. Great interview.
To my understanding (which granted is very limited when it comes to physics, let alone metaphysics) the laws of physics are descriptive, meaning they follow patterns we find in the universe. Being the pattern seeking animals we are I find it not at all surprising we would eventually figure out ways the universe behaves which are replicable.
@@TheYuvimon Yes, one answer to where did the laws of physics come from is they came from humans, we made them up to describe the regularities of the universe. Humans are pattern seeking animals. Seeking patterns is adaptive because of the regularities of the universe. But what really grabs our attention is a broken pattern, something are pattern matcher didn't expect.
@@myothersoul1953 stop believing in naive scientism. Do you think that adopting a Darwinist metaphysics comes with no self-defeating epistemological consequences? lol
I don't think we can tell them apart. For instance, the current conundrum between quantum theory and general relativity may be such a wall. We're been for 100 years to reconcile them. Maybe we can, maybe not.
Maybe adequate mathematics types works in different aspect of physics . As example to connect quantum mechanics to relativity is mathematics that is not compatible in the same time with both. So mathematics suits well describing some aspects of nature but is discretionary.
Gödel demonstrated that Hilbert's Program to try to deduce every true statement from a given set of axioms is impossible. The Halting Problem (which is almost the same problem but from another point of view) shows that there things that are uncomputable i.e. inaccesible to mathematics, logic or Reason.
Hm... sounds like the 'dictatorship of the question mark'. People sometimes seem to make this mistake: by adding a question mark to an observation or a statement, turning it into a question, the matter at hand suddenly seem to become more pressing. But that's not automatically true. You can turn everything into a question, but a lot of questions don't need an answer. What Paul Davis is providing as answers, feels like one of those cases to me.
Are there things in the Universe not describable by mathematics? The reason mathematics seems so effective is that it is only the universe's mathematical properties we can discover (paraphrasing Russell). Is there a 'vast ocean of truth' laying out there beyond the ken of mathematics?
The capacity of mathematics to capture or refer to aspects of reality is profoundly interesting, but so too of human language, philosophy, imagination, literature, art, humor, dreaming and so on ... there are many rooms in the mansion of the mind...
@@ferdinandkraft857 Thanks. Yes, that's more or less what I understood from Paul. But what is this "possible mathematics". How do we know that it is out there? Perhaps we just invent new mathematics and it doesn't exist until we invent it. I think the assumption of a greater realm of mathematics might be a little sleight of hand, a way of slipping a human role into the laws of physics. Intuitively, this does not feel right.
@@angelalahee5856 to me it seems the opposite. He is acknowledging that the possibilities for math may be greater than what has currently been discovered/invented and maybe even greater than what is feasible for the human mind.
Is Mathematics a product of the human species or of an individual human? Is it possible that every human can produce its own Mathematics? If there is intelligent life in other worlds would they have their own Mathematics? How can we possibly communicate with such alien species? What's more, would we ever be able of recognizing that we are in front of beings?
These are obviously rethorical questions. Mathematics is a sophistication of Reason, that's why Mathematics is effective, because reason is "reasonable". So what we have to answer is: where does reason come from? Can we imagine an intelligent alien being that uses something different than Reason?
IMHO, the fundamental principle of the universe is that there is Order and this Order exists even "before" the Big Bang. From Order comes hierarchy and from hierarchy Mathematics follows. To survive in this world we have to obey the rules of Reality which are the rules of Reason, so Reason=Reality. "In the beginning was the word"
So, the answer is, every intelligent being from the most obscure part of the universe, uses Reason, the same Reason every human possess and uses. Reason is reality. Mathematics is just a formalization of our Reason so it follows that Mathematics is effective because there is no other way it could possibly be.
@@donthesitatebegin9283 Thanks for the the reading recommendations and for taking the time to answer. I will think about and answer your points later, but now, just let me say this, if the Church-Turing Thesis is true (by the way, it is probably unprovable ), then there is no "beyond" Reason. No matter how advanced an AI or alien civilization could be. Of course, we could postulate that God possess "Super-Reason" which goes far beyond the Reason/Reality inside our Universe.
leading a target, even with a stone takes math, every Father who taught his son how to hunt taught him some math, they may not have used weight velocity and Gravity to explain that you do not throw at the target but to a spot further in the future where both the target and stone will meet. Then we naturally refine things and make them arts which would bring in questions about Weight Velocity figuring out what Drag is, and eventually Gravity when they noticed the stone always goes down. I'm sure even basket weaving requires some kind of ability to calculate which again would have been refined over generations.
We've already encountered something in nature that we can't describe with mathematics. It's the results observed from the collapse of wave functions in quantum mechanics. Edit: And I mean we can't describe because of our limitations, not because it's not describable in principle. Perhaps a more advanced alien species would be able to describe it, as he suggested.
Why do we and all living things possess this very strong and powerful innate instinct to preserve the atoms, molecules, and cells that we call ourselves it seems a little ridiculous but it is part of our being. Just maybe the u universe does have an obligation to make math and science work for us after all it has obligated us to protect the atoms, molecules, and cells that we call ourselves.
Why is the camera constantly moving? I'm feeling a bit motion sick from watching it. Talking heads will always be talking heads. Hopefully the material transcends that. But PLEASE nail down the camera!
It’s a poor question as it assumes we all agree that math is ”unreasonably effective”. A better form of the question: Why is mathematics so effective in modeling what we can observe?
Put simple mathematics creates reality from the virtual particles created by the photon... like this... E=MC2 The perception of movement C2 of Virtual particles gives them the PERCEPTION of Mass and Energy. Based on the frequency of those off on virtual particles, as they are being created on off on off on off ... just like a computer virtual reality program of 10101010..... those frequencies are then defined as angstroms and decibels that make up the SIGHTS AND SOUNDS we perceive that give life the MEANING ... referred to her by EINSTEIN .. ““It would be possible to describe everything scientifically, but it would make no sense; it would be without meaning, as if you described a Beethoven symphony as a variation of wave pressure.”
@Sam Bourgeois of course we have given life meaning ... but only to justify it. If we had no reason to believe we exist we would cease to exist because the PURPOSE of life is to enjoy it...Enjoyment comes only from fulfilling our purpose and giving our existence meaning... if our existence has no meaning then we must create a reason to live. The purpose of life is to find answers to the questions of why where how and since there is no reason or purpose we would cease trying to find one... the need for purpose and reason Is what keeps us searching and thus we create a meaning as the purpose of our existence...
@Sam Bourgeois you said it yourself “i In fact I can think of no more meaningful pursuit than science...why?.... because it empowers us to PURSUE ALLothee sources of meaning... it’s the search for meaning that is the PURPOSE of life..
Life is made up of complex, hierarchical, interdependent systems. Does anyone disagree with that? Yet errors (mutations) and selection don't accumulate to form complex, hierarchical, interdependent systems. Life was clearly designed and the "Errors did it" theory is false.
Well, the theory evolution has made the ase that yes, selection + mutation creates such systems, and it's better at explaining it so far than anx other approach. I mean the fundamental aspect of it isn't so hard to understand. If there is a thing that can replicate itself (which means it takes pieces that are not itself, and then arranges them so it are a copy of itself), there are going to be more of those things. Once you have just one thing randomly being arranged to have that property, a lot of those things will come into existence, as it replicates itself. But sometimes the process might go wrong (maybe a piece that it needs to replicate fully isn't around, or it seems to be the same but it's actually different and then a step in the replication process desn't work), and then you gte something that either doesn't replicate itself, or it still does. Both replicate side by side, but the change made could lead to one of the replicating things being able to handle some of the things that can go wrong better than the other, and so they start to grow in different direction. Or it's just plain better at the same circumstances, and then it starts to replace the "old" version because it can grow faster and takes away the pieces that the other needs to replicate.
Prof Davies does not believe in coincidences. Neither do I. Just come to the conclusion that the universe was designed and man was made in the image of the designer and you complete the mosaic. But "professing to be wise they became fool".
Inserting a comment here that I made in the Ed Witten video on the same topic. "I humbly disagree with Eugene Wigner's claim that mathematics is unreasonably effective. In fact, there are cases where mathematics lacks effectiveness, and in many cases, mathematical models are approximations. In addition, one would expect within reason, that mathematics would be effective in modeling the processes of the natural world. Thus far, mathematics is not doing too well to model, described, and explain "mind", "self," and "consciousness," all of which are part of the natural world. That said, I love mathematics and physics having taken a degree in both. Both are quite powerful and amazing at times, but not unreasonably so."
Neither of the above statements is true. Mathematics is extremely effective at modeling the naturel world and we know why: because mathematics is an extrapolation of physics. Physicists just strip the over-extrapolation (regarding infinite sets) away. What is really happening is this: even though mathematics is extremely effective, it does not provide a unique solution to physics, i.e. we continue to need the experiment to tell us which possible mathematical solution is the correct one.
@@lepidoptera9337 Sorry, but I am a matheimatician and physicist (applied). Math is the language of physics and nature. It is not "unreasonalbe effective", although it is reasonalble effective. Usually, it is physics, or chemistry, or biology, etc. that is, the science including social, then mathematics to model the phenomena. Occasionally, math comes first and then experiential science to validate or invalidate the math.
@@georgegrubbs2966 Physics is not "the modelling of phenomena". I hope they didn't teach that nonsense in your university. In science math never comes first. Empirical observations come first. That's high school knowledge. You either didn't go to a good high school or you were not paying attention.
@@lepidoptera9337 I said, "Mathematics is extremely effective at modeling the naturel world." I did not say physics modeled the natural world. You seem to be more interested in criticizing the messengers, me, rathery and paying attention to the message. That's called "ad hominem." Examine your motives.
@@georgegrubbs2966 Mathematics doesn't model the natural world, either. There are no infinite sets in nature. It's much more simple than that. People in the past observed nature. They found that if they put seven fruits in a basket, then later they would still find seven fruits in that same baskets. That's the birth of counting and set cardinality. Then they figured out how one can sort classical physical objects with different properties between baskets. An application of finite set theory was born. Eventually they found that one can abstract all of this and this leads to logic, which is isomorphic to set theory. None of this is serious mathematics, yet. It only becomes mathematics if we remove the requirement that physical objects are involved (abstraction) AND we introduce infinity by adding something like an induction axiom. There is no empirical equivalent to induction. Where all of this falls apart, and few if any mathematicians are aware of that, is that physicists have discovered a hundred odd years ago that "objects" don't exist. All of the rules (except for induction) that mathematicians have borrowed from physics are invalid. Instead nature implements a different set of rules for quanta of energy. To this date mathematicians have not (at least to my knowledge) built a new mathematics based on quantum inference. ;-)
I think that mathematics is very reasonably effective. In fact, I think it would be unreasonable for mathematics to NOT be effective. That would tell me that the universe is not governed by logical rules. As far as the notion that it's some kind of unreasonable coincidence that the mathematics we can do (or evolved as he says) can also explain things about the universe like black holes... I'm not sure I really believe that this is a problem. Sounds a bit like the puddle being surprised at how perfectly the hole it lives in fits it. Surely the puddle thinks there's a special significance to its existence.
There are games ruled by purely logical rules, for which our mathematics is absolutely hopelessly ineffective, such as the games of go and even the far more trivial game of chess.
If you throw a ball over a wall and miss, you can find out physical reasons why that happened. Play a game of go against, say, Leela Go, and then find, using no computers but pure logic, why did you lose, when did you make the losing move. Purely logical systems both of them. Our maths work for the one, but not for the other.
sir ,i read satanic verses which is written about an incidence when prophet was praying in kaaba and reciting chapter Al Najjam ..during recitation prophet uttered that intercession of goddess Lat ,Manat and Uza will be accepted and hearing that non muslims went into prostration believing that prophet compromised with them and accepted their goddess .waleed bin mugheera was head of chiefs of mecca .he was 92 years old and he took some soil and brought to his forehead because being old he could prostrate ,then holy spirit informed the prophet that those words were prompted by satan .this is written in the commentary of verses 52,53 of chapter 22.when i read about waleed bin mugheera in qurannic verses ,found that chapter 74 verses 11 to 17 states about waleed bin mugheera and He says leave this man to me whom He gave son and lot of wealth but still he wishes for more and in verse 17 He says that he will be raised to high mountains ( that is rise of islam with sword through execution of evil of Allah .waleed bin Mugheera had ten to twelve son and eldest was khalid bin waleed and second caliph was his son in law .then in chapter 68 the translation is done wrong because at the time of death prophet wanted to dictate so that they may not go astray but they refused to say that prophet,s state f mind was altered .the translation of chapter is done wrong because there are the present and future is merged into one . still they are doing wrong translation .the true translation is that they are not writing to say that prophet is in altered state of mind but Allah says that his state of mind is well and soon they will come to know who is mentally not well and who is on right path and who has gone astray .then H e says they want the prophet to compromise .and He says not to compromise and in verse 44 He says who deny this shall be brought down in such a way that they wil not understand . salman Rushdi simulated khomeni with jesus christ because christ was tempted by satan and Rushdie simulating khomenie made him ride the satan and made satan abuse dammed land him on bait al quds
Yes.Boring because It is absolutely obvious and known already to 4th cent BC Aristotle: math is a quantitive expression of order, that must have a cause/Programmer -Wisdom 11:20. All other laws of any science are more in detail (outside formal sciences) qualitative expression of this one divine order: "Subtle is the Lord, but he is not malicious one "(A.Einstein). A lot of mess and fighting each other camps in science because of not remembering this Aristotle on what is mathematics
yes.Already in Wisdom 11:20,2nd cent.BC. or the principle of least action,i.e. even a blind matter .."thinks". Science assumes an order in Universe and not proves like one assumes the principle of non-contradiction in order to create a systematic knowledge (axiomatic systems) and just communicate between humans! Try to deny this principle!
The universe is fundamentally based on information, mathematics, and probability. Nothing unreasonable about it. Don't like it? Find yourself a different universe.
@@georgecostopoulos2862 ok. So you drawa simple picture, like a tree, dog, etc. You give it a code, like fgtr or 12de. Give me the code I try see yr pic ok?
I find Paul Davies' position to be nothing more than mysticism. Didn't most physicists move on from the idea that "human beings" are special in the 17th century when the geocentric model had to give way for something better?
Why the “Unreasonable Effectiveness” of Mathematics? Good question. Answer: after the 0 axiom that nothing is certain: that rules itself out subsequently taking the first axiom that the universe exists as a dualistic absolute something (atomos) and absolute nothing thus binary Bayesian mathematically all-encompassing paradoxical niche affair. Only applicable for education and (ironic) humor. Bayes can be logically consistently divided in number mathematics (i.e. counting), picture mathematics (I.e. geometry without the numbers and a set theory weighing machine) and other logic such as the English language used as unambiguous i.e. logic. These three “languages” are all part of the soul of our synapsis in our brain being consistent with the soul (defined as the physical order function of the cosmos (taken identical to “god”)). Then we see humans as mammals with more yet still too little memory space. Apes changing their biotope faster than that their neural networks can cope with. Making two axiomatic whopping axiomatic mistakes: 1. Egoistically placing humans outside the cosmos: god doesn’t play dice mistake: On the first axiom a given that it is deterministic. Yet the Socratic Bayesian yin and yang formula demands what risk you want to take on your whatever egoistic goal of even bare survival? Well given risk is chance x consequence you must logically go for the inverse: we have a free will and there is an meaning in life. How small that chance may be. Then we get that the cosmos must be described in an Euclidian way with the five axioms including that the cosmos is fundamentally not curved as Louis Carrol already explained. You’ll get in Alice and Wonderland and it will become unreasonable. The second mistake was forgetting the instrument between the ears during all lab sessions in school and afterwards. Had all scientists actually done that then one would of asked: “Is this correct that it doesn’t matter what I measure, because it is nurture and not nature the working of the human brain?” It does matter, for all thinking is DNA classical mechanical quantum (sub atomic) robotics. All observations are illusions that in drawn conclusions differ depending on the exactly identifiable sort of brain that you have. The greatest mistake you can have is have triumphs as Einstein knowing he was wrong had with a mistake. Humanity (and all mammals) can as a quick triage be divided in 20% mentally healthy ADHD types (such as Einstein, and Michelle Obama) having talent for spotting fresh irony / paradoxes, 40% healthy autistic people who have the most talent for number mathematics and are average in picture mathematics and thus can’t grasp fresh irony or paradoxes and the here not so relevant 40% healthy hysterics who don’t have any talent for picture mathematics and thus set theory and thus have incurable gender neutral female logic. The HRM / sales department of humanity. Due to the success of a mistake under a majority it has as a consequence become a religion even for artistic and spiritual R&D leaders (the ones with resounding voices) to become religious in the autistic “shut up and calculate” church. Most to blame for this are psychologists. Assessment is their social contracted job, and they knew this all along. Yet being mostly hysterics they didn’t spot the logic, for they couldn’t yet being dominant in the social sciences.
Hey all you scientists and physicists are pretty smart man, although human made mathematics are the laws of nature... We are not Gods shaping our universe, instead we are God's children growing up and learning about daddy's home - God's universe. If you don't believe in God, than for you it's the aliens universe cuz it sure as hell ain't yours. 😇
I like Davies' openness. I also like the way he admits unresolved issues of mind, math and reality-unlike others who commit to the dogma of reductive materialism. Davies admits that the reductionist paradigm is very insufficient to account for these amazing facts of reality. I saw the same intellectual honesty in Tom Nagel's MIND & COSMOS.
Yes, I do, too. He's been quite courageous in the face of materialistic orthodoxy for some time now. Nagel's been cool that way too, as you point out.
Mathematics is a language designed to model patterns. Reality is full of patterns. That methematics is effective at modeling reality is not so unreasonable.
Great interview. Succinct, clear and profound.
Fantastic. I've had some of these thoughts before but couldn't have articulated them so beautifully.
Paul Davis ideas are so phenomenal and insightful. Perhaps philosophically he is the Niels Bohr of our time.
Excellent... thanks 🙏.
This was better than I expected. The formation, processes and behavior of the universe on all levels seems to fit with how the mind operates.
He describes the connection between evolution, the mind, and mathematics -- very profound -- in such a short interview.
Quite stupid if you ask me since no empirical evidence supports evolution.
@@les2997 The present is a consequence of the past. I suppose the purist could debate that -- that everything is just "now" -- but IF evolution happened the way Biologists claim, then our concept of mathematics may have evolved as well, and that would tell us a lot about the universe.
@@williamwolfe8708 The ability to do abstract math/reasoning is totally irrelevant to survival and reproduction.
@@les2997 Mathematical reasoning, at its heart, is the pursuit of truth. Clearly defined terms combined with logic, symmetry, analogy, isomorphism, metaphor etc. A tribe is not going to survive long if it can't distinguish fact from fiction, or is unable to communicate truths about the world.
@@williamwolfe8708 This is where you are wrong because very many totally false beliefs aid survival.
For example, lightly paranoid people will have a better chance of surviving if they falsely think that someone is after them, etc. Wouldn't you accumulate a small cache of weapons if you thought that your neighbors are after you? Anyway, if evolution were true, our cognitive faculties would be aimed at survival, not truth finding. In order to survive your beliefs don't need to be true.
Diversity of thought is so important.
great, interesting as hell
I mean if you were to call it human mathematics, then perhaps the physical phenomenon/law that it can so effectively explain should also be termed "human observed physical phenomenon". After all, everything we see/feel/measure is processed and formed in our brain, human brain.
mathematics is literally just a system of abstract symbols with which we try to describe the way the universe already is...
Thank you. Everyone here seems to think numbers and maths are Real in the Platonic sense. That numbers exist whether humans are around or not.
I'm not sure if I'm getting it or not. But it seems to me that mathematics is a way of describing regularities and patterns. And how can you create structures of any sort that do not involve regularities and patterns? If you have a universe where anything at all happens, then you must have structure. From the tiny drop of water that has an atomic structure, to the vast complexity of a human being. So why is it surprising that mathematics (a way of describing regularities and patterns) should be so effective at describing the things of this universe?
I’d actually like to interview YOU on how you’ve been able to get in front of and interview all of these “top dogs” through the years? Amazing .You must be a great charmer 😉
I like his emphasis on evolution, deep level of reality, etc. -- math is uncanny because it is in our bones. It was put there by evolution. Therefore, the essence must have been there at the big bang, or an explanation for the big bang.
I love the insights and perspectives of Paul Davies. Here I'd like to suggest also that animal and insect perception also provides remarkable and unique ways of knowing and experiencing aspects of the world which we are not always privy to and in many cases far exceeds the range and sensitivity of human awareness. Animal perception and sentience is as legitimate as any other modality of knowing whilst also broadening the range of knowledge about the natural world and of how it is experienced. Consciousness and knowledge is not the prerogative of humans, and this fact adds immensely to the 'sum total' of what is 'known' about the natural world by 'Mind at large'. The epistemic openness or revelations of the universe are certainly not confined to people. I'd also suggest that the possibility of plant, fungal and indeed bacterial perception and sentience is a credible one, as is evidenced by the rapid growth of research into these fields.
It's misnamed, it should be the completely reasonable effectiveness of mathematics in physics. What else would one expect?
he is the best
Good
haven't we already hit a point where mathematics is breaking down? Non-linearity and chaotic systems are impossible to model precisely and yet these seem to be how the universe works in a macro sense. The inverse square law can describe 2 bodies in motion but breaks down at three or more. Also there are infinitely many types of mathematics that describe universes we don't live in so it seems like a massive tautology to me
Math is merely a language with a single rule: contradictions are forbidden. This rule comes from logic and forms the foundation for all logic. Math is simply a language of logic. The fact that math is so effective and and difficult for humans to identify as merely a language shows only that humans are terrible at logic. We simply do not take to logic naturally. It is difficult for humans to think logically. It is not a coincidence that modern civilization traces its roots directly back to Aristotle as the father of logic as all advanced thinking requires logic.
My dumb guess: Because there is some simple and reliable mechanism at work at the bottom level. From there, effects just scale up nicely because random noise will obey the law of averages. Perhaps there is a barrier between quantum and classical scales where some threshold enforces a new dynamic to emerge.
I've actually read scientists with those exact hypotheses.
Great series, great interview, sadly hindered by Film school level camera work.
“Where do the laws of physics come from ...?” That is a fundamental question Dr Davies asks that has a “profound religious” inference. Great interview.
The assumption that they came from something is unjustified.
To my understanding (which granted is very limited when it comes to physics, let alone metaphysics) the laws of physics are descriptive, meaning they follow patterns we find in the universe.
Being the pattern seeking animals we are I find it not at all surprising we would eventually figure out ways the universe behaves which are replicable.
@@TheYuvimon Yes, one answer to where did the laws of physics come from is they came from humans, we made them up to describe the regularities of the universe.
Humans are pattern seeking animals. Seeking patterns is adaptive because of the regularities of the universe. But what really grabs our attention is a broken pattern, something are pattern matcher didn't expect.
@@myothersoul1953 stop believing in naive scientism. Do you think that adopting a Darwinist metaphysics comes with no self-defeating epistemological consequences? lol
@@JustinHerchel I will stop believing in science when science stop producing the most accurate explanations for the world as we experience it.
How will we know if we hit a wall where maths isn't adequate? How will we distinguish this state from just needing to try harder?
I don't think we can tell them apart. For instance, the current conundrum between quantum theory and general relativity may be such a wall. We're been for 100 years to reconcile them. Maybe we can, maybe not.
Maybe adequate mathematics types works in different aspect of physics . As example to connect quantum mechanics to relativity is mathematics that is not compatible in the same time with both. So mathematics suits well describing some aspects of nature but is discretionary.
Gödel demonstrated that Hilbert's Program to try to deduce every true statement from a given set of axioms is impossible. The Halting Problem (which is almost the same problem but from another point of view) shows that there things that are uncomputable i.e. inaccesible to mathematics, logic or Reason.
Hm... sounds like the 'dictatorship of the question mark'. People sometimes seem to make this mistake: by adding a question mark to an observation or a statement, turning it into a question, the matter at hand suddenly seem to become more pressing. But that's not automatically true. You can turn everything into a question, but a lot of questions don't need an answer. What Paul Davis is providing as answers, feels like one of those cases to me.
Mathematics is inside of us, bred into us by evolution, because the physical world is made of mathematics.
@Language and Programming Channel Yes, what is real?
Ed Witten himself "it seems like God is a mathematician" thats when my mind opened up a bit.
Are there things in the Universe not describable by mathematics? The reason mathematics seems so effective is that it is only the universe's mathematical properties we can discover (paraphrasing Russell). Is there a 'vast ocean of truth' laying out there beyond the ken of mathematics?
Many hold that maths is a created human language we use to try and describe how things function and attempt to see what else might be probable.
Is physical reality made through mathematics?
Mathematics is a language we create in order to describe the world around us.
I thought Bertrand Russell explained the Laws of Nature: evolving statistical averages?
The capacity of mathematics to capture or refer to aspects of reality is profoundly interesting, but so too of human language, philosophy, imagination, literature, art, humor, dreaming and so on ... there are many rooms in the mansion of the mind...
Can someone explain to me the difference between "human mathematics" and "mathematics"?
Human mathematics = the subset of all possible mathematics that are simple enough for us to understand
@@ferdinandkraft857 Thanks. Yes, that's more or less what I understood from Paul. But what is this "possible mathematics". How do we know that it is out there? Perhaps we just invent new mathematics and it doesn't exist until we invent it. I think the assumption of a greater realm of mathematics might be a little sleight of hand, a way of slipping a human role into the laws of physics. Intuitively, this does not feel right.
@@angelalahee5856 to me it seems the opposite. He is acknowledging that the possibilities for math may be greater than what has currently been discovered/invented and maybe even greater than what is feasible for the human mind.
Is Mathematics a product of the human species or of an individual human? Is it possible that every human can produce its own Mathematics?
If there is intelligent life in other worlds would they have their own Mathematics?
How can we possibly communicate with such alien species? What's more, would we ever be able of recognizing that we are in front of beings?
These are obviously rethorical questions. Mathematics is a sophistication of Reason, that's why Mathematics is effective, because reason is "reasonable". So what we have to answer is: where does reason come from? Can we imagine an intelligent alien being that uses something different than Reason?
IMHO, the fundamental principle of the universe is that there is Order and this Order exists even "before" the Big Bang. From Order comes hierarchy and from hierarchy Mathematics follows. To survive in this world we have to obey the rules of Reality which are the rules of Reason, so Reason=Reality.
"In the beginning was the word"
So, the answer is, every intelligent being from the most obscure part of the universe, uses Reason, the same Reason every human possess and uses. Reason is reality. Mathematics is just a formalization of our Reason so it follows that Mathematics is effective because there is no other way it could possibly be.
@@donthesitatebegin9283 Thanks for the the reading recommendations and for taking the time to answer. I will think about and answer your points later, but now, just let me say this, if the Church-Turing Thesis is true (by the way, it is probably unprovable ), then there is no "beyond" Reason. No matter how advanced an AI or alien civilization could be.
Of course, we could postulate that God possess "Super-Reason" which goes far beyond the Reason/Reality inside our Universe.
leading a target, even with a stone takes math, every Father who taught his son how to hunt taught him some math, they may not have used weight velocity and Gravity to explain that you do not throw at the target but to a spot further in the future where both the target and stone will meet. Then we naturally refine things and make them arts which would bring in questions about Weight Velocity figuring out what Drag is, and eventually Gravity when they noticed the stone always goes down.
I'm sure even basket weaving requires some kind of ability to calculate which again would have been refined over generations.
The mind of a Genius
Geniuses are required to understand the basics of both math and physics and he doesn't understand either. ;-)
We've already encountered something in nature that we can't describe with mathematics. It's the results observed from the collapse of wave functions in quantum mechanics.
Edit: And I mean we can't describe because of our limitations, not because it's not describable in principle. Perhaps a more advanced alien species would be able to describe it, as he suggested.
Why do we and all living things possess this very strong and powerful innate instinct to preserve the atoms, molecules, and cells that we call ourselves it seems a little ridiculous but it is part of our being. Just maybe the u universe does have an obligation to make math and science work for us after all it has obligated us to protect the atoms, molecules, and cells that we call ourselves.
Why is the camera constantly moving? I'm feeling a bit motion sick from watching it. Talking heads will always be talking heads. Hopefully the material transcends that. But PLEASE nail down the camera!
It’s a poor question as it assumes we all agree that math is ”unreasonably effective”. A better form of the question: Why is mathematics so effective in modeling what we can observe?
Put simple mathematics creates reality from the virtual particles created by the photon... like this...
E=MC2
The perception of movement C2 of
Virtual particles gives them the PERCEPTION of Mass and Energy.
Based on the frequency of those off on virtual particles, as they are being created on off on off on off ... just like a computer virtual reality program of 10101010..... those frequencies are
then defined as angstroms and decibels that make up the SIGHTS AND SOUNDS we perceive that give life the MEANING ... referred to her by EINSTEIN .. ““It would be possible to describe everything scientifically, but it would make no sense; it would be without meaning, as if you described a Beethoven symphony as a variation of wave pressure.”
@Sam Bourgeois of course we have given life meaning ... but only to justify it.
If we had no reason to believe we exist we would cease to exist because the PURPOSE of life is to enjoy it...Enjoyment comes only from fulfilling our purpose and giving our existence meaning... if our existence has no meaning then we must create a reason to live. The purpose of life is to find answers to the questions of why where how and since there is no reason or purpose we would cease trying to find one... the need for purpose and reason Is what keeps us searching and thus we create a meaning as the purpose of our existence...
@Sam Bourgeois you said it yourself “i
In fact I can think of no more
meaningful pursuit than science...why?.... because it empowers us to PURSUE ALLothee sources of meaning... it’s the search for meaning that is the PURPOSE of life..
The Nature is a dual existence, math. is one of these existence.
First! Wow!!!
NTF: ok/60/use
The hubris is a little thick...we have created symbols to describe reality. Reality is what is amazing 😉
More than describe. People created symbols that also predicted reality. See black holes
Life is made up of complex, hierarchical, interdependent systems. Does anyone disagree with that? Yet errors (mutations) and selection don't accumulate to form complex, hierarchical, interdependent systems. Life was clearly designed and the "Errors did it" theory is false.
Well, the theory evolution has made the ase that yes, selection + mutation creates such systems, and it's better at explaining it so far than anx other approach. I mean the fundamental aspect of it isn't so hard to understand. If there is a thing that can replicate itself (which means it takes pieces that are not itself, and then arranges them so it are a copy of itself), there are going to be more of those things. Once you have just one thing randomly being arranged to have that property, a lot of those things will come into existence, as it replicates itself. But sometimes the process might go wrong (maybe a piece that it needs to replicate fully isn't around, or it seems to be the same but it's actually different and then a step in the replication process desn't work), and then you gte something that either doesn't replicate itself, or it still does. Both replicate side by side, but the change made could lead to one of the replicating things being able to handle some of the things that can go wrong better than the other, and so they start to grow in different direction. Or it's just plain better at the same circumstances, and then it starts to replace the "old" version because it can grow faster and takes away the pieces that the other needs to replicate.
Prof Davies does not believe in coincidences. Neither do I. Just come to the conclusion that the universe was designed and man was made in the image of the designer and you complete the mosaic. But "professing to be wise they became fool".
Inserting a comment here that I made in the Ed Witten video on the same topic.
"I humbly disagree with Eugene Wigner's claim that mathematics is unreasonably effective. In fact, there are cases where mathematics lacks effectiveness, and in many cases, mathematical models are approximations. In addition, one would expect within reason, that mathematics would be effective in modeling the processes of the natural world.
Thus far, mathematics is not doing too well to model, described, and explain "mind", "self," and "consciousness," all of which are part of the natural world.
That said, I love mathematics and physics having taken a degree in both. Both are quite powerful and amazing at times, but not unreasonably so."
Neither of the above statements is true. Mathematics is extremely effective at modeling the naturel world and we know why: because mathematics is an extrapolation of physics. Physicists just strip the over-extrapolation (regarding infinite sets) away. What is really happening is this: even though mathematics is extremely effective, it does not provide a unique solution to physics, i.e. we continue to need the experiment to tell us which possible mathematical solution is the correct one.
@@lepidoptera9337 Sorry, but I am a matheimatician and physicist (applied). Math is the language of physics and nature. It is not "unreasonalbe effective", although it is reasonalble effective. Usually, it is physics, or chemistry, or biology, etc. that is, the science including social, then mathematics to model the phenomena. Occasionally, math comes first and then experiential science to validate or invalidate the math.
@@georgegrubbs2966 Physics is not "the modelling of phenomena". I hope they didn't teach that nonsense in your university. In science math never comes first. Empirical observations come first. That's high school knowledge. You either didn't go to a good high school or you were not paying attention.
@@lepidoptera9337 I said, "Mathematics is extremely effective at modeling the naturel world." I did not say physics modeled the natural world. You seem to be more interested in criticizing the messengers, me, rathery and paying attention to the message. That's called "ad hominem." Examine your motives.
@@georgegrubbs2966 Mathematics doesn't model the natural world, either. There are no infinite sets in nature.
It's much more simple than that. People in the past observed nature. They found that if they put seven fruits in a basket, then later they would still find seven fruits in that same baskets. That's the birth of counting and set cardinality. Then they figured out how one can sort classical physical objects with different properties between baskets. An application of finite set theory was born. Eventually they found that one can abstract all of this and this leads to logic, which is isomorphic to set theory.
None of this is serious mathematics, yet. It only becomes mathematics if we remove the requirement that physical objects are involved (abstraction) AND we introduce infinity by adding something like an induction axiom. There is no empirical equivalent to induction.
Where all of this falls apart, and few if any mathematicians are aware of that, is that physicists have discovered a hundred odd years ago that "objects" don't exist. All of the rules (except for induction) that mathematicians have borrowed from physics are invalid. Instead nature implements a different set of rules for quanta of energy. To this date mathematicians have not (at least to my knowledge) built a new mathematics based on quantum inference. ;-)
I think that mathematics is very reasonably effective. In fact, I think it would be unreasonable for mathematics to NOT be effective. That would tell me that the universe is not governed by logical rules. As far as the notion that it's some kind of unreasonable coincidence that the mathematics we can do (or evolved as he says) can also explain things about the universe like black holes... I'm not sure I really believe that this is a problem. Sounds a bit like the puddle being surprised at how perfectly the hole it lives in fits it. Surely the puddle thinks there's a special significance to its existence.
There are games ruled by purely logical rules, for which our mathematics is absolutely hopelessly ineffective, such as the games of go and even the far more trivial game of chess.
If you throw a ball over a wall and miss, you can find out physical reasons why that happened. Play a game of go against, say, Leela Go, and then find, using no computers but pure logic, why did you lose, when did you make the losing move. Purely logical systems both of them. Our maths work for the one, but not for the other.
@@u.v.s.5583 You don’t understand how games work.
What is the meaning of life?
42!
😖Lol
sir ,i read satanic verses which is written about an incidence when prophet was praying in kaaba and reciting chapter Al Najjam ..during recitation prophet uttered that intercession of goddess Lat ,Manat and Uza will be accepted and hearing that non muslims went into prostration believing that prophet compromised with them and accepted their goddess .waleed bin mugheera was head of chiefs of mecca .he was 92 years old and he took some soil and brought to his forehead because being old he could prostrate ,then holy spirit informed the prophet that those words were prompted by satan .this is written in the commentary of verses 52,53 of chapter 22.when i read about waleed bin mugheera in qurannic verses ,found that chapter 74 verses 11 to 17 states about waleed bin mugheera and He says leave this man to me whom He gave son and lot of wealth but still he wishes for more and in verse 17 He says that he will be raised to high mountains ( that is rise of islam with sword through execution of evil of Allah .waleed bin Mugheera had ten to twelve son and eldest was khalid bin waleed and second caliph was his son in law .then in chapter 68 the translation is done wrong because at the time of death prophet wanted to dictate so that they may not go astray but they refused to say that prophet,s state f mind was altered .the translation of chapter is done wrong because there are the present and future is merged into one .
still they are doing wrong translation .the true translation is that they are not writing to say that prophet is in altered state of mind but Allah says that his state of mind is well and soon they will come to know who is mentally not well and who is on right path and who has gone astray .then H e says they want the prophet to compromise .and He says not to compromise and in verse 44 He says who deny this shall be brought down in such a way that they wil not understand .
salman Rushdi simulated
khomeni with jesus christ because christ was tempted by satan and Rushdie simulating khomenie made him ride the satan and made satan abuse dammed land him on bait al quds
Yes.Boring because It is absolutely obvious and known already to 4th cent BC Aristotle: math is a quantitive expression of order, that must have a cause/Programmer -Wisdom 11:20. All other laws of any science are more in detail (outside formal sciences) qualitative expression of this one divine order: "Subtle is the Lord, but he is not malicious one "(A.Einstein). A lot of mess and fighting each other camps in science because of not remembering this Aristotle on what is mathematics
Intelligent design?
No. Just internal consistent and not needing any help from outside.
yes.Already in Wisdom 11:20,2nd cent.BC. or the principle of least action,i.e. even a blind matter .."thinks". Science assumes an order in Universe and not proves like one assumes the principle of non-contradiction in order to create a systematic knowledge (axiomatic systems) and just communicate between humans! Try to deny this principle!
The universe is fundamentally based on information, mathematics, and probability. Nothing unreasonable about it. Don't like it? Find yourself a different universe.
Who wants to try remote viewing with me? C'mon I'm bored. Let me know I tell you how. Its that or mop my floor. I d rather play remote viewing....
@@kensho123456 no it's fun! Wanna try with me?
ok
@@georgecostopoulos2862 ok. So you drawa simple picture, like a tree, dog, etc. You give it a code, like fgtr or 12de. Give me the code I try see yr pic ok?
@@kensho123456 oh ..yr not playing are you?
@@kensho123456 you are a welk
I find Paul Davies' position to be nothing more than mysticism. Didn't most physicists move on from the idea that "human beings" are special in the 17th century when the geocentric model had to give way for something better?
Why the “Unreasonable Effectiveness” of Mathematics? Good
question. Answer: after the 0 axiom that nothing is certain: that rules itself
out subsequently taking the first axiom that the universe exists as a dualistic
absolute something (atomos) and absolute nothing thus binary Bayesian mathematically
all-encompassing paradoxical niche affair.
Only applicable for education and (ironic) humor. Bayes can be logically consistently
divided in number mathematics (i.e. counting), picture mathematics (I.e.
geometry without the numbers and a set theory weighing machine) and other logic
such as the English language used as unambiguous i.e. logic. These three “languages” are all part of the
soul of our synapsis in our brain being consistent with the soul (defined as
the physical order function of the cosmos (taken identical to “god”)). Then we
see humans as mammals with more yet still too little memory space. Apes
changing their biotope faster than that their neural networks can cope with. Making
two axiomatic whopping axiomatic mistakes: 1. Egoistically placing humans
outside the cosmos: god doesn’t play dice mistake: On the first axiom a given
that it is deterministic. Yet the Socratic Bayesian yin and yang formula
demands what risk you want to take on your whatever egoistic goal of even bare
survival? Well given risk is chance x consequence you must logically go for the
inverse: we have a free will and there is an meaning in life. How small that
chance may be. Then we get that the cosmos must be described in an Euclidian
way with the five axioms including that the cosmos is fundamentally not curved
as Louis Carrol already explained. You’ll get in Alice and Wonderland and it
will become unreasonable. The second mistake was forgetting the instrument
between the ears during all lab sessions in school and afterwards. Had all scientists
actually done that then one would of asked: “Is this correct that it doesn’t matter
what I measure, because it is nurture and not nature the working of the human
brain?” It does matter, for all thinking is DNA classical mechanical quantum
(sub atomic) robotics. All observations are illusions that in drawn conclusions
differ depending on the exactly identifiable sort of brain that you have. The greatest
mistake you can have is have triumphs as Einstein knowing he was wrong had with
a mistake. Humanity (and all mammals) can as a quick triage be divided in 20% mentally
healthy ADHD types (such as Einstein, and Michelle Obama) having talent for
spotting fresh irony / paradoxes, 40% healthy autistic people who have the most
talent for number mathematics and are average in picture mathematics and thus
can’t grasp fresh irony or paradoxes and the here not so relevant 40% healthy
hysterics who don’t have any talent for picture mathematics and thus set theory
and thus have incurable gender neutral female logic. The HRM / sales department of humanity. Due to
the success of a mistake under a majority it has as a consequence become a
religion even for artistic and spiritual R&D leaders (the ones with
resounding voices) to become religious in the autistic “shut up and calculate”
church. Most to blame for this are psychologists. Assessment is their social
contracted job, and they knew this all along. Yet being mostly hysterics they
didn’t spot the logic, for they couldn’t yet being dominant in the social
sciences.
What a stupid damn title!
Hey all you scientists and physicists are pretty smart man, although human made mathematics are the laws of nature... We are not Gods shaping our universe, instead we are God's children growing up and learning about daddy's home - God's universe. If you don't believe in God, than for you it's the aliens universe cuz it sure as hell ain't yours. 😇
He doesn't understand either math or physics. So sad. ;-)