Mathematicians say the world is mathematical. Computer scientists say it's computational. For mystics it's mystical. In the 19th century they compared it to steam engines. In the 17th century it was clockwork. In the Middle Ages it was a kingdom. I'm no psychologist, but it seems like the universe is a Rorschach test.
@@hyperduality2838 - You might have the goal of presenting as really smart with deep ideas, but I'm calling bs on you. And so as we can see your little speech is directly associated with your username, and as we all know comments from people with agenda based usernames are usually agenda items, not worthwhile comments. Nice try.
@@hyperduality2838 - If you are invoking Noether's theorem or other conservation observations then cut the babbling prose style worthy of the head of a commune selling energy portals and the utility of standing on your head. PS For people who might fall prey to this carnival barker snake oil salesman I would point out that every RUclips poster who has a specific themed username that is also assiduously expressed in their posts (as with "hyperduality") is a crank. We see it all the time, some crank with a nmae like: "LibertyPatriotUSMC" and a US flag has his head stuck in jingoist military worship etc. The style is GLARING. Hyperdual you are muted, see ya.
Humans are rational. Math is not rational it is logical. Reason and logic are not the same thing. Logic deals with ideas and their relationships. Reason deals with actual things whose relationship to us is imperfect and unknowable. Logic deals with the known and knowable. Reason deals with the unknown and unknowable. Insofar as math is effective it is due to the pattern recognizing capability of the sensing mind capable of reason. Tigers recognize prey. Are they unreasonably effective at hunting said prey. Yes. Is their hunting skill due to math? No. Just so human pattern recognition is not due to math. Then what is math? Where does it come from? Just as philosophers discuss propositions and conclusions so mathematicians discuss equations and solutions. Insofar as both disciplines make arguments concerning their respective subjects their effectiveness lies in convincing others by their self consistent agreement with the consensual, experience of nature.
Of course tha same mathematical model is working everywhere, we built a simples model and refined it to fit in as many possibilities we could. Circles are everywhere just because they bring periodicity idea, so anything that is cyclic somehow (even if in a momentary period of time - even if it's too large compared to our lifetime) will be relatively well described by circle functions
Speaking as a mathematician, I don't think it's unreasonable at all. We designed maths around what we observed, to be able to deal with practical things on an abstract level like counting for example. So I don't understand why people regard it as "unreasonable effective". There are other examples where things are so complicated that we can't just cope with it, chaos and turbulence for example.
Isn't the astonishing thing that reality appears to have so much underlying similarity to mathematical structure? I think it probably is unreasonable, in that we only see what we have the means to see. Will we only ever be able to see with the eyes mathematics gives us? How radical might that mathematics become in time?
@@BB-sm8ey I feel like those mathematical structures still have a basis from the physical world. The idea of curvature (Riemann geometry)which has to come from nature first.
It is not Newton who discovered Calculus. It is Sangamagrama Madhavan who discovered it 300 years before Newton which later reached Europe. Madhavan's book Venuarohanam and that of his deciple Jyeshthadevan named YUKTIBHASHYAM explains this.
As I see it and I may well be wrong; math is a language like for instance French. Either can describe anything. And in either math or a spoken/written language, some of the arrangements of the terms are very beautiful-precise and/or recurring and therefore over time strike a chord in the heart & mind. Conversely most arrangements of words or numbers are closer to junk. We focus on what has meaning in any language, we set the rest to the side. Given this point of view I find nothing surprising in that math appears unreasonably effective at it's area of design (numeric relationships), like German appears unreasonably effective at coining words.
You wouldn’t expect a rocket launch to go according to plan by following the internal logic of French though. If a launch goes wrong, we expect human error to be the source, not the equations themselves. I think this says something truly incredible about the underlying nature of our universe. In short, I don’t believe in God, but I believe in math.
@@Tstorm731 - A successful French rocket launch will require endless use of precise French all along it's course. And it can fail if that language includes some errors. As we know the Hubble had a math error in the mirror curvature that screwed it up. You can restate (as far as I know off the top of my head) any math statement in words. Math does not of course cause anything, the universe is not "obeying" laws, that's a mistake of perception due to psychology, like the illusion of time or of straight lines. There is nothing to "believe in" in math, although young engineers are given to this heartfelt expression of affinity for their math tools. Math is (as a way of putting it) a numerical language that always leads to truth statements. Given enough data one can make math statements after the fact that are very descriptive just like Rudyard Kipling can describe perfectly why you don't bother to fight in Afghanistan in his poem, "Arithmetic on the Frontier." As I recall set theory did away with the notion that one needs numbers to create mathematics, one creates the number line out of continuous iterations of the empty set ie nothing. So mathematical ideas exist without math itself, but as a language for those ideas it is perfectly suited. There is nothing to believe in, it's not a call to faith.
John Smith Point taken. I was being a bit poetic with “I believe in mathematics”. As soon as I sent my reply I started wondering about a universal spoken language that could actually succeed in launching a rocket. I suppose it’s the underlying logic that I think of when I say mathematics. It’s a very platonic notion. An ideal world distinguished by its clarity and precision. I see that as a left brain language dealing in a world of abstraction. French is ideal for a right hemisphere language. A world of living beings with all their complications, a human world etc. The reason math amazes me under these assumptions is that it seems incredible that an abstract language maps onto a human world. In retrospect, this is a bit silly. It’s something I always wrestle with. Maybe I just need a more well-endowed corprus callosum.
@@Tstorm731 - In my mind it is not math but our various native languages that "map on the human world" accurately for instance poetry or Shakespeare. Math maps onto an abstract world that does not actually exist as you say the Platonic. Calculations have accuracy limits, constants have odd bits after the decimal, there is no real circle or line, etc., and as for truth our best calculations are probabilities. It's all good of course, I appreciate the chat with you. It brings to mind an opposite impression I suffered in a talk I had with a young electrician at work, whereby I asked him one day if he knew what, at a fundamental level, is a number? (It's a ratio.) He was not sure. Then being curious as to how his mind works with respect to abstract concepts; I asked him; On a planet in a distant galaxy, 2+2 still = 4? He was sure about this one and said, "No not necessarily because like, you know, things could be different there." The irony is that he was more sure of that than either you or I about the subjects in this thread.
John Smith I love this subject. I enjoyed the exchange as well. I’ll have to think more about your position. It’s funny, I just had a similar conversation with a friend a few days ago, but you clarified some of his points. He even brought up Zermelo-Franken set theory. His argument didn’t really register but you explained it in more human terms. Philosophy has always had a problem with universals and particulars and I think our brains are built that way because of the hemispheric divide. I’m not sure if it’s a bug or a feature overall but it certainly makes some disagreements seem irreconcilable. That’s why it’s so refreshing to have a conversation where we are trying to iteratively approximate the truth as opposed to an outright brawl between true believers.
Insering 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."
I think the effectiveness of Mathematics in so many areas in reality is beyond simple Symbolic syntax reasons. The laws of nature are mathematical regardless of whether humans give them symbols or not.
Mathematics is an exercise in abstraction, whereas our investigation of the universe is ultimately grounded in particular phenomena. But we don't ever settle for the individual phenomena themselves. Inevitably we want to describe them categorically: not just an account of one photon or one collision, say, but a description common to all photons or all collisions of that category. In my view, this is why mathematics is such a good fit to natural phenomena, because (1) abstraction and categorization are compatible intellectual exercises, and (2) we happen to live in a substantially ordered universe which comports with a categorical account of phenomena. This may seem a bit of a circular argument. Do we say it's an ordered universe because we created the concept of ordinality to apply to it, or did the concept arise from observation? Well, I think we need to remember that we evolved into beings whose survival depends on cognition, which in essence controls our response to patterns in our environment. We were bound to develop this capacity to some degree, but once it became conscious we could begin to apply it abstractly. It evolved gradually, conditioned by our physical environment including our own physiology. So there's no chicken-and-egg problem, and I'd go a step further and say that this resolves the question of whether we invented or discovered mathematics. We were doing both simultaneously while our brains were evolving their capacity for pattern recognition. Evolution drove it all long before we became consciously aware of it.
It is a perfectly ordered universe or it wouldn't exist ,so math works, naturally. Or, it was made that way so that we could come to the conclusion that it was made ,that way.
WHY THE “UNREASONABLE EFFECTIVENESS” OF MATHEMATICS? This truly is a great question! It focuses directly on the problem addressed by the theory “The meaning of order”. Well, higher mathematics is an unbiased non-mechanistic description tool, while rationality always creates a mechanistic description which is shown to impose linearity upon its description. . Higher mathematics is non-mechanistic as time is unbounded within its field. On the other hand, rationality being able to create only a mechanistic description cannot at all deal with infinity. So, the beginning of time is always assumed in a rational description. This is not at all the same with higher mathematics. So, the description that higher mathematics provides always implies a circle, whether we are dealing with the wave-function or with Fourier transform or what have you. This is something that a rational description cannot ever provide, simply because the rational description is always headed by a plausible assumption that can never be confirmed. I am talking about principles, axioms and beginnings of any kind. The rational description being linear cannot ever curve back to confirm the original assumption that inaugurated it. . So, what higher mathematics provides is rightfully described as unreasonably effective, as rationality cannot emulate such description.
It is not unreasonable at all. In fact it should be expected that mathematics would describe the world effectively. What these brilliant and very learned people have overlooked b/c they are too immersed in it, is this. Mathematics and the world share an important common feature: regularity, order, predictability. In other words, math and the world both have order. All math equations are a description of order and relationship. The world has order and is composed of relationships. This must be so since the alternative is disorder or chaos. The first question in philosophy is, is the world chaotic or is it capable of being understood? If it is the former, everything stops right there, but the world is understandable and one way we understand things is to make observations about them and we use language to do that. math is a suitable language for understanding the world. Indeed it is the language we turn to when words prove to be inadequate. When we cannot describe in words how far something is from us, stars, water, 7/11, we use numbers. When we can't describe the size or scale of something we turn to numbers. Not unreasonable at all.
I think you misunderstood the meaning of what they are talking about. A difference of the meaning of "unreasonableness". I can send a video which goes in depth to the controversial topic if you'd like.
Our universe is 'mathematical' because the axioms we choose are based on experience (eg we know from experience we can apply the concept of the number 1 to the real world). If our axioms apply to the world then that which follows from the axioms should apply to the world, otherwise there is a logical inconsistency and we should choose better axioms. But really it would be much more surprising if mathematics wasn't useful for describing the universe.
I can agree. But in my opinion I would phrase it in terms of the activity of abstracting away from particular instances. So it's kind of like taking that individual cases where quantity shows up (using your example) abstracting away from those cases, for example a particular instance would be the number of books on the table then seeing that this is true for other instances like the number of trees in a forest we then abstract away from them (like generalizing) about quantity in any given set (of items let's say) . With this new field we can then use our intuition to think of different quantitative values that any given set can take (this being analogues to forming conjectures and proving them, i. e. expanding what we know about quantity by pure intuition). And so it's this universal idea (abstracted field of knowledge) that can have a variety of applications.
I don't understand the "unreasonable" expectation. If any universal property exists, then it would be very reasonable to find it in the microcosm, as well as, the macrocosm. No big surprise there.
A=B and A and B from two different worlds is inaccurate. They might come from two different disciplines or two fields of study or subjects. Everything we know cant be learned all at once so it has to be divided to make learning it can be managed. But it isnt amazing that different parts of what we know about the world would line up.
It's so much fun to hear someone trying to explain the effectiveness of mathematics to a non-mathematical audience. First step in a long journey. Learning mathematics is just so much more difficult than philosophy.
Left hand side and right hand side of E = mc^2 at least typechecks. Things get really confusing when physicists equate stuff that don’t even have the same type or unit
Just so. A lot of the success of mathematics in physics consists of addressing the right problem to solve - which will yield to techniques we already know. Our methods may be woefully limited in understanding many things but we prefer to dwell on the successes
"The surprising redness of rubies." Does that mean "Rubies are surprising"? No, it means their redness is surprising. In the three segments of this series that I've viewed so far, the host invariably starts by giving a bizarrely twisted interpretation to Wigner's title, phrased slightly differently each time, but always indicating that he believes this to be its meaning: "Mathematics is effective [in the natural sciences] AND mathematics is unreasonable," and this prompts the host to add: "I understand that mathematics is effective, but why is mathematics unreasonable?" (This is like interpreting my sample sentence as follows: "Rubies are red AND rubies are surprising. I understand that rubies are red, but why are they surprising?") In short, the host simply does not understand English grammar, much less the (moderately) nuanced thrust of Wigner's title. So how can we trust that he understands anything inside the article itself?
He doesn't mean that mathematics is unreasonable, he means the effectiveness of mathematics is unreasonable. Instead of saying "I know mathematics is effective, but why is *that* unreasonable?" he ends up saying "I know mathematics is effective, but why is *it* unreasonable?" which is the kind of mistake that happens from time to time in casual language use, especially when speaking rather than wtiting
I feel like this video is priming for 'there's God' in the next video. Please no 'miracles'. It's quite reasonable to suppose that there are only a very few fundamental 'laws' that went into building this universe, so it shouldn't come as a surprise that the same regularities show up anywhere you dig. When you engage in *hierarchical* architecture (like evolution), you don't reinvent things in every domain you touch. You do more of the same thing, which is also why you will find a lot of similarities between humans and algae when you start digging into cells.
It's easy to see what mathematics can do, take a look trough modern telescopes and microscopes. This makes me wonder if light has something to do with that unreasonable effectiveness, maybe it doesn't just frame how can physics unfold or so called time but light is mathematics. We have this thing when mathematics became complete description of some system, light speed somehow limits what can happen with all involved potentials. It also prevent us to see further in the past or smallest parts of reality, like we can go only so far as we can literally see or measure with our electromagnetic wave devices. Nobody can say what exist outside of this cave of light.
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.
xante8 Man that's some fancy word salad - could not get beyond the first 3 lines. Is it "AI" generated ? Well xante8 to answer your question, alas no, I’m a Dutch human using his own name. This contrary to you using a R2D2 type name and trying furthermore to hide behind your self-marked thus no longer visible response. Begging the question if you are a defect R2D2 robot yourself for R2D2 even would make more of the “word salad” as being “unreasonable” mathematics? Being defect if trying to find the question for the answer to fashionable number 42. Being healthy knowing from its data bank that the Dutch mathematician Buys Ballot, knowing him from the law of Buys Ballot, that you if you are indeed human and have more than grammar school would know. He wrote a complete “word salad” work on geometry, not a picture in the entire book. He knew that it doesn’t matter whether you write, draw or calculate the logic, as long as it remains logically consistent. Furthermore he contrary to you knew that the tree of mathematics is enormous, say now some two hundred different languages. Much like English and Double Dutch languages have some three hundred different languages. You should normalize / translate these for else it becomes reasonably incomprehensible word salad for the uneducated. Being that the problem on topic.
Math has been bred into us via evolution -- something at the big bang set the seed of mathematics and it has grown throughout our minds -- and continues to grow -- it tells us something about the origins of the universe -- where we came from -- and where we are going.
my " Efficacy of Applied Mathematics in Non Traditional Application" pretty much speaks of this as most would not reasonably apply math in the human example my paper speaks of but guess what? ....it worked...as in Einstein's equation my example solves for an equality...the equal sign as mentioned in this video is an important symbol in math in my example the math worked flawlessly 😁💕
Unlike language symbols, the mathematical symbols are not merely shadows and images of reality but they are operators of reality. The relation is in the fact that the universe EVOLVED according to the states that existed at the time and any additional input to what existed in a given zone just to keep it to an evolution that we may comprehend. With mathematics, we have emulated the operators of evolution in that we have mathematical functions that can operate with each other in that they depict the past and present states and they combine them together to predict the future state. Basically, if we had to find the motion of a car all one needs to do is to notice its law of motion which normally depend on its mass state, its velocity and drag and acceleration forces and what forces are available to make it all happen, There could be another function close by which would give some contribution to the motion of the car as the load or the wind be it blowing continuously or in gusts................... all these states can be defined with the mathematical operator and what is more one acceleration can become a velocity through a relation as The new velocity equals the old velocity plus the accelerated contribution. while a location can be deduced by the logic The new location equals the old location plus the addition of what was gained by any new motion. So while the language symbols are merely dead and static images and shadows of reality, mathematical operators depict the law of nature itself and it is simply an evolving state once we can define the relation between the states. If one had to write John is running after Jill up the hill then that statement does not have any operators which will tell you how John can catch up with Jill but if we had to write. The distance John covers is S= u.t + (1/2) a. t^2 then while the symbolic letters and numbers we use are the same as that we use in language form they are now OPERATING on a calculation even in our absence and if we had to use a computer to do it for us then what is being emulated is, in fact, John running along accelerating to catch Jill. No language symbol can be as accurate and as quantitative to guarantee exact results in its calculations as a mathematical operator. In that last statement, there exists the reason why many people take up a profession which never guarantees their products as Politicians, Priests, Psychologists, Prostitutes, Pilots, Doctors, Lawyers, Accountants, Bankers, Teachers, Entertainers, and many other social workers in fashion and all the emotional profession which NEVER GUARANTEE THEIR SERVICES. All the mentioned professions do not deal with science, physics, and mathematics and they never carry any tools nor hew and form materials that must have perfect relations so that the product must work and must be guaranteed. When any nation becomes overloaded with such qualitative professions which use a language as a vociferous tool with no tangible guaranteed operators or products at the end then the whole nation would collapse............... we have seen this in the last six months where a little virus as the COVID -19 brought all the social professions to a stop but the basic professions as farmers and fishermen and those who deal with guaranteed operations still proceeded with their own basic life. In is interesting how many speakers on RUclips as now seeking an income through being vociferous on videos as Richard Dawkins, Christopher Hitchens, Jordan Peterson, and thousands of others who prefer a vociferous language rather than the silent operators of mathematics that operate accurately on a universal accurate sequence of states. It is so unfortunate that emotional people outnumber all those who seek logic, reason, and rational thinking through guaranteed operations rather than colorful emotional descriptions, as Picasso depicted a woman which does not exist in reality but he gave people what they thought they could understand and not the real complexity of life! Ah, emotions rule the world. ruclips.net/video/jawVsSnzFz0/видео.html ruclips.net/video/0Y_rb-sFxR4/видео.html
Mathematicians say the world is mathematical. Computer scientists say it's computational. For mystics it's mystical. In the 19th century they compared it to steam engines. In the 17th century it was clockwork. In the Middle Ages it was a kingdom.
I'm no psychologist, but it seems like the universe is a Rorschach test.
You are cherry picking, and making it up as you go along. Mathematicians do NOT say what you say they do, nor do CS guys, or the rest.
@@johnsmith1474 I was speaking broadly, not cherry picking. If you didn't understand, so be it.
Your observation is correct, accurate and scientifically sound.
This conclusion doesn't make sense at all. You just picked another standpoint and made another oversimplification.
@@SinoSene So be it.
I’m still confused, but at a much higher level.
That's reasonable. 🙂
Your expression hasn't suffered.
@@hyperduality2838 - You might have the goal of presenting as really smart with deep ideas, but I'm calling bs on you. And so as we can see your little speech is directly associated with your username, and as we all know comments from people with agenda based usernames are usually agenda items, not worthwhile comments. Nice try.
@@hyperduality2838 - If you are invoking Noether's theorem or other conservation observations then cut the babbling prose style worthy of the head of a commune selling energy portals and the utility of standing on your head.
PS For people who might fall prey to this carnival barker snake oil salesman I would point out that every RUclips poster who has a specific themed username that is also assiduously expressed in their posts (as with "hyperduality") is a crank. We see it all the time, some crank with a nmae like: "LibertyPatriotUSMC" and a US flag has his head stuck in jingoist military worship etc. The style is GLARING.
Hyperdual you are muted, see ya.
😆
Humans are rational. Math is not rational it is logical. Reason and logic are not the same thing. Logic deals with ideas and their relationships. Reason deals with actual things whose relationship to us is imperfect and unknowable. Logic deals with the known and knowable. Reason deals with the unknown and unknowable.
Insofar as math is effective it is due to the pattern recognizing capability of the sensing mind capable of reason. Tigers recognize prey. Are they unreasonably effective at hunting said prey. Yes. Is their hunting skill due to math? No. Just so human pattern recognition is not due to math. Then what is math? Where does it come from?
Just as philosophers discuss propositions and conclusions so mathematicians discuss equations and solutions. Insofar as both disciplines make arguments concerning their respective subjects their effectiveness lies in convincing others by their self consistent agreement with the consensual, experience of nature.
Dijkgraaf is a good speaker.
Very much loving this new unreasonable math mini-series!!!
Of course tha same mathematical model is working everywhere, we built a simples model and refined it to fit in as many possibilities we could. Circles are everywhere just because they bring periodicity idea, so anything that is cyclic somehow (even if in a momentary period of time - even if it's too large compared to our lifetime) will be relatively well described by circle functions
Speaking as a mathematician, I don't think it's unreasonable at all. We designed maths around what we observed, to be able to deal with practical things on an abstract level like counting for example. So I don't understand why people regard it as "unreasonable effective". There are other examples where things are so complicated that we can't just cope with it, chaos and turbulence for example.
Isn't the astonishing thing that reality appears to have so much underlying similarity to mathematical structure? I think it probably is unreasonable, in that we only see what we have the means to see. Will we only ever be able to see with the eyes mathematics gives us? How radical might that mathematics become in time?
@@BB-sm8ey I feel like those mathematical structures still have a basis from the physical world. The idea of curvature (Riemann geometry)which has to come from nature first.
Is a shovel unreasonably good at digging?
Is a car on a highway unreasonably fast?
Wittgenstein could ask this.
Very Wittgensteinian ;)
It is not Newton who discovered Calculus. It is Sangamagrama Madhavan who discovered it 300 years before Newton which later reached Europe. Madhavan's book Venuarohanam and that of his deciple Jyeshthadevan named YUKTIBHASHYAM explains this.
Saying something is unreasonable is arrogant. Nature works the way it works. There is nothing reasonable or unreasonable about it. It simply is.
As I see it and I may well be wrong; math is a language like for instance French. Either can describe anything. And in either math or a spoken/written language, some of the arrangements of the terms are very beautiful-precise and/or recurring and therefore over time strike a chord in the heart & mind. Conversely most arrangements of words or numbers are closer to junk. We focus on what has meaning in any language, we set the rest to the side.
Given this point of view I find nothing surprising in that math appears unreasonably effective at it's area of design (numeric relationships), like German appears unreasonably effective at coining words.
You wouldn’t expect a rocket launch to go according to plan by following the internal logic of French though. If a launch goes wrong, we expect human error to be the source, not the equations themselves. I think this says something truly incredible about the underlying nature of our universe. In short, I don’t believe in God, but I believe in math.
@@Tstorm731 - A successful French rocket launch will require endless use of precise French all along it's course. And it can fail if that language includes some errors. As we know the Hubble had a math error in the mirror curvature that screwed it up. You can restate (as far as I know off the top of my head) any math statement in words.
Math does not of course cause anything, the universe is not "obeying" laws, that's a mistake of perception due to psychology, like the illusion of time or of straight lines. There is nothing to "believe in" in math, although young engineers are given to this heartfelt expression of affinity for their math tools.
Math is (as a way of putting it) a numerical language that always leads to truth statements. Given enough data one can make math statements after the fact that are very descriptive just like Rudyard Kipling can describe perfectly why you don't bother to fight in Afghanistan in his poem, "Arithmetic on the Frontier."
As I recall set theory did away with the notion that one needs numbers to create mathematics, one creates the number line out of continuous iterations of the empty set ie nothing. So mathematical ideas exist without math itself, but as a language for those ideas it is perfectly suited. There is nothing to believe in, it's not a call to faith.
John Smith Point taken. I was being a bit poetic with “I believe in mathematics”. As soon as I sent my reply I started wondering about a universal spoken language that could actually succeed in launching a rocket.
I suppose it’s the underlying logic that I think of when I say mathematics. It’s a very platonic notion. An ideal world distinguished by its clarity and precision. I see that as a left brain language dealing in a world of abstraction. French is ideal for a right hemisphere language. A world of living beings with all their complications, a human world etc.
The reason math amazes me under these assumptions is that it seems incredible that an abstract language maps onto a human world. In retrospect, this is a bit silly. It’s something I always wrestle with. Maybe I just need a more well-endowed corprus callosum.
@@Tstorm731 - In my mind it is not math but our various native languages that "map on the human world" accurately for instance poetry or Shakespeare. Math maps onto an abstract world that does not actually exist as you say the Platonic. Calculations have accuracy limits, constants have odd bits after the decimal, there is no real circle or line, etc., and as for truth our best calculations are probabilities.
It's all good of course, I appreciate the chat with you. It brings to mind an opposite impression I suffered in a talk I had with a young electrician at work, whereby I asked him one day if he knew what, at a fundamental level, is a number? (It's a ratio.) He was not sure. Then being curious as to how his mind works with respect to abstract concepts; I asked him; On a planet in a distant galaxy, 2+2 still = 4? He was sure about this one and said, "No not necessarily because like, you know, things could be different there." The irony is that he was more sure of that than either you or I about the subjects in this thread.
John Smith I love this subject. I enjoyed the exchange as well. I’ll have to think more about your position. It’s funny, I just had a similar conversation with a friend a few days ago, but you clarified some of his points. He even brought up Zermelo-Franken set theory. His argument didn’t really register but you explained it in more human terms.
Philosophy has always had a problem with universals and particulars and I think our brains are built that way because of the hemispheric divide. I’m not sure if it’s a bug or a feature overall but it certainly makes some disagreements seem irreconcilable. That’s why it’s so refreshing to have a conversation where we are trying to iteratively approximate the truth as opposed to an outright brawl between true believers.
Insering 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."
I think the effectiveness of Mathematics in so many areas in reality is beyond simple Symbolic syntax reasons. The laws of nature are mathematical regardless of whether humans give them symbols or not.
Mathematics is an exercise in abstraction, whereas our investigation of the universe is ultimately grounded in particular phenomena.
But we don't ever settle for the individual phenomena themselves. Inevitably we want to describe them categorically: not just an account of one photon or one collision, say, but a description common to all photons or all collisions of that category.
In my view, this is why mathematics is such a good fit to natural phenomena, because (1) abstraction and categorization are compatible intellectual exercises, and (2) we happen to live in a substantially ordered universe which comports with a categorical account of phenomena.
This may seem a bit of a circular argument. Do we say it's an ordered universe because we created the concept of ordinality to apply to it, or did the concept arise from observation? Well, I think we need to remember that we evolved into beings whose survival depends on cognition, which in essence controls our response to patterns in our environment. We were bound to develop this capacity to some degree, but once it became conscious we could begin to apply it abstractly. It evolved gradually, conditioned by our physical environment including our own physiology.
So there's no chicken-and-egg problem, and I'd go a step further and say that this resolves the question of whether we invented or discovered mathematics. We were doing both simultaneously while our brains were evolving their capacity for pattern recognition. Evolution drove it all long before we became consciously aware of it.
It is a perfectly ordered universe or it wouldn't exist ,so math works, naturally. Or, it was made that way so that we could come to the conclusion that it was made ,that way.
WHY THE “UNREASONABLE EFFECTIVENESS” OF MATHEMATICS?
This truly is a great question! It focuses directly on the problem addressed by the theory “The meaning of order”.
Well, higher mathematics is an unbiased non-mechanistic description tool, while rationality always creates a mechanistic description which is shown to impose linearity upon its description.
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Higher mathematics is non-mechanistic as time is unbounded within its field. On the other hand, rationality being able to create only a mechanistic description cannot at all deal with infinity. So, the beginning of time is always assumed in a rational description. This is not at all the same with higher mathematics.
So, the description that higher mathematics provides always implies a circle, whether we are dealing with the wave-function or with Fourier transform or what have you. This is something that a rational description cannot ever provide, simply because the rational description is always headed by a plausible assumption that can never be confirmed. I am talking about principles, axioms and beginnings of any kind. The rational description being linear cannot ever curve back to confirm the original assumption that inaugurated it.
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So, what higher mathematics provides is rightfully described as unreasonably effective, as rationality cannot emulate such description.
I knew I recognized this guy from numberphile.
Jakob Bogale
He is a String Theorist at Princeton with Ed Witten
Robbert Dijkgraaf is the director and Leon Levy professor at the prestigious Institute for Advanced Study in Princeton.
You can’t explain math. Math is what explains!
It is not unreasonable at all. In fact it should be expected that mathematics would describe the world effectively. What these brilliant and very learned people have overlooked b/c they are too immersed in it, is this. Mathematics and the world share an important common feature: regularity, order, predictability. In other words, math and the world both have order. All math equations are a description of order and relationship. The world has order and is composed of relationships. This must be so since the alternative is disorder or chaos. The first question in philosophy is, is the world chaotic or is it capable of being understood? If it is the former, everything stops right there, but the world is understandable and one way we understand things is to make observations about them and we use language to do that. math is a suitable language for understanding the world. Indeed it is the language we turn to when words prove to be inadequate. When we cannot describe in words how far something is from us, stars, water, 7/11, we use numbers. When we can't describe the size or scale of something we turn to numbers. Not unreasonable at all.
I think you misunderstood the meaning of what they are talking about. A difference of the meaning of "unreasonableness". I can send a video which goes in depth to the controversial topic if you'd like.
Our universe is 'mathematical' because the axioms we choose are based on experience (eg we know from experience we can apply the concept of the number 1 to the real world). If our axioms apply to the world then that which follows from the axioms should apply to the world, otherwise there is a logical inconsistency and we should choose better axioms. But really it would be much more surprising if mathematics wasn't useful for describing the universe.
So like axioms is inherit and universal
I got stuck on the idea of choosing axioms.
We don't choose
I can agree. But in my opinion I would phrase it in terms of the activity of abstracting away from particular instances. So it's kind of like taking that individual cases where quantity shows up (using your example) abstracting away from those cases, for example a particular instance would be the number of books on the table then seeing that this is true for other instances like the number of trees in a forest we then abstract away from them (like generalizing) about quantity in any given set (of items let's say) . With this new field we can then use our intuition to think of different quantitative values that any given set can take (this being analogues to forming conjectures and proving them, i. e. expanding what we know about quantity by pure intuition).
And so it's this universal idea (abstracted field of knowledge) that can have a variety of applications.
This year, theoretical physicist ?
Kuhn searched for the unreasonableness of mathematics, but couldn't arrive at Ramanujan's q-series, providing complexity and entropy.
I don't understand the "unreasonable" expectation. If any universal property exists, then it would be very reasonable to find it in the microcosm, as well as, the macrocosm. No big surprise there.
Holland 🇳🇱
A=B and A and B from two different worlds is inaccurate. They might come from two different disciplines or two fields of study or subjects.
Everything we know cant be learned all at once so it has to be divided to make learning it can be managed.
But it isnt amazing that different parts of what we know about the world would line up.
It's so much fun to hear someone trying to explain the effectiveness of mathematics to a non-mathematical audience. First step in a long journey. Learning mathematics is just so much more difficult than philosophy.
I'd like to talk about the unreasonable effectiveness of hammers: You can hit anything and anyone on their heads!
Left hand side and right hand side of E = mc^2 at least typechecks. Things get really confusing when physicists equate stuff that don’t even have the same type or unit
God exists.
In nature there are no such things as perfect cubes circles or straight lines. Like numbers they are inventions of the mind.
The concept that has to emerge is the understanding of magnetism. See Ken Wheeler. Gravity, space and time are emergent properties of magnetism.
There we go again. The answer to all these questions is already cleared long time ago by Sir Douglas Adams and the answer is 42 !
I was interested to read Dirac himself was not very pleased with his own formula (and what people did and derived from that)
Hmm, unsolvable non-linear diff-eqs, perturbation theories, renormalizaion, singularities...all not so unreasonably effective....
Just so. A lot of the success of mathematics in physics consists of addressing the right problem to solve - which will yield to techniques we already know.
Our methods may be woefully limited in understanding many things but we prefer to dwell on the successes
not every function can be Fourier。math develop all the way。
Major lost opportunity. When the guest said mathematics “is a gift” the obvious follow up would be “does that imply a Giver?” Bummer.
Existence = 1; non existence = 0. There you go - that's why !
"The surprising redness of rubies."
Does that mean "Rubies are surprising"? No, it means their redness is surprising.
In the three segments of this series that I've viewed so far, the host invariably starts by giving a bizarrely twisted interpretation to Wigner's title, phrased slightly differently each time, but always indicating that he believes this to be its meaning:
"Mathematics is effective [in the natural sciences] AND mathematics is unreasonable," and this prompts the host to add: "I understand that mathematics is effective, but why is mathematics unreasonable?"
(This is like interpreting my sample sentence as follows: "Rubies are red AND rubies are surprising. I understand that rubies are red, but why are they surprising?")
In short, the host simply does not understand English grammar, much less the (moderately) nuanced thrust of Wigner's title. So how can we trust that he understands anything inside the article itself?
He doesn't mean that mathematics is unreasonable, he means the effectiveness of mathematics is unreasonable. Instead of saying "I know mathematics is effective, but why is *that* unreasonable?" he ends up saying "I know mathematics is effective, but why is *it* unreasonable?" which is the kind of mistake that happens from time to time in casual language use, especially when speaking rather than wtiting
I feel like this video is priming for 'there's God' in the next video. Please no 'miracles'. It's quite reasonable to suppose that there are only a very few fundamental 'laws' that went into building this universe, so it shouldn't come as a surprise that the same regularities show up anywhere you dig. When you engage in *hierarchical* architecture (like evolution), you don't reinvent things in every domain you touch. You do more of the same thing, which is also why you will find a lot of similarities between humans and algae when you start digging into cells.
Everything in the Universe is changing and Will always do so.
And when does that change? When is flux fluxed? If it is the only constant, then it too must bow to it's own will eventually.
Thank you Heraclitus.
Good
Thanks
It's easy to see what mathematics can do, take a look trough modern telescopes and microscopes. This makes me wonder if light has something to do with that unreasonable effectiveness, maybe it doesn't just frame how can physics unfold or so called time but light is mathematics. We have this thing when mathematics became complete description of some system, light speed somehow limits what can happen with all involved potentials. It also prevent us to see further in the past or smallest parts of reality, like we can go only so far as we can literally see or measure with our electromagnetic wave devices. Nobody can say what exist outside of this cave of light.
Is thought faster than light and if so, how could we measure distance traveled in mental dimension?
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.
xante8
Man that's some fancy word salad - could not get beyond the first 3 lines. Is it "AI" generated ?
Well xante8 to answer your question, alas no, I’m a Dutch human using his own name. This contrary to you using a R2D2 type name and trying furthermore to hide behind your self-marked thus no longer visible response. Begging the question if you are a defect R2D2 robot yourself for R2D2 even would make more of the “word salad” as being “unreasonable” mathematics? Being defect if trying to find the question for the answer to fashionable number 42. Being healthy knowing from its data bank that the Dutch mathematician Buys Ballot, knowing him from the law of Buys Ballot, that you if you are indeed human and have more than grammar school would know. He wrote a complete “word salad” work on geometry, not a picture in the entire book. He knew that it doesn’t matter whether you write, draw or calculate the logic, as long as it remains logically consistent. Furthermore he contrary to you knew that the tree of mathematics is enormous, say now some two hundred different languages. Much like English and Double Dutch languages have some three hundred different languages. You should normalize / translate these for else it becomes reasonably incomprehensible word salad for the uneducated. Being that the problem on topic.
First
Sly.
Congratulations
PixelPhobiac thanks. Now where is my cookie.
@@knavesaria6715 free cookies tomorrow
Math has been bred into us via evolution -- something at the big bang set the seed of mathematics and it has grown throughout our minds -- and continues to grow -- it tells us something about the origins of the universe -- where we came from -- and where we are going.
my " Efficacy of Applied Mathematics in Non Traditional Application" pretty much speaks of this as most would not reasonably apply math in the human example my paper speaks of but guess what? ....it worked...as in Einstein's equation my example solves for an equality...the equal sign as mentioned in this video is an important symbol in math
in my example the math worked
flawlessly 😁💕
Unlike language symbols, the mathematical symbols are not merely shadows and images of reality but they are operators of reality. The relation is in the fact that the universe EVOLVED according to the states that existed at the time and any additional input to what existed in a given zone just to keep it to an evolution that we may comprehend.
With mathematics, we have emulated the operators of evolution in that we have mathematical functions that can operate with each other in that they depict the past and present states and they combine them together to predict the future state.
Basically, if we had to find the motion of a car all one needs to do is to notice its law of motion which normally depend on its mass state, its velocity and drag and acceleration forces and what forces are available to make it all happen, There could be another function close by which would give some contribution to the motion of the car as the load or the wind be it blowing continuously or in gusts................... all these states can be defined with the mathematical operator and what is more one acceleration can become a velocity through a relation as
The new velocity equals the old velocity plus the accelerated contribution. while a location can be deduced by the logic
The new location equals the old location plus the addition of what was gained by any new motion.
So while the language symbols are merely dead and static images and shadows of reality, mathematical operators depict the law of nature itself and it is simply an evolving state once we can define the relation between the states.
If one had to write John is running after Jill up the hill then that statement does not have any operators which will tell you how John can catch up with Jill but if we had to write.
The distance John covers is S= u.t + (1/2) a. t^2 then while the symbolic letters and numbers we use are the same as that we use in language form they are now OPERATING on a calculation even in our absence and if we had to use a computer to do it for us then what is being emulated is, in fact, John running along accelerating to catch Jill.
No language symbol can be as accurate and as quantitative to guarantee exact results in its calculations as a mathematical operator.
In that last statement, there exists the reason why many people take up a profession which never guarantees their products as Politicians, Priests, Psychologists, Prostitutes, Pilots, Doctors, Lawyers, Accountants, Bankers, Teachers, Entertainers, and many other social workers in fashion and all the emotional profession which NEVER GUARANTEE THEIR SERVICES. All the mentioned professions do not deal with science, physics, and mathematics and they never carry any tools nor hew and form materials that must have perfect relations so that the product must work and must be guaranteed.
When any nation becomes overloaded with such qualitative professions which use a language as a vociferous tool with no tangible guaranteed operators or products at the end then the whole nation would collapse............... we have seen this in the last six months where a little virus as the COVID -19 brought all the social professions to a stop but the basic professions as farmers and fishermen and those who deal with guaranteed operations still proceeded with their own basic life.
In is interesting how many speakers on RUclips as now seeking an income through being vociferous on videos as Richard Dawkins, Christopher Hitchens, Jordan Peterson, and thousands of others who prefer a vociferous language rather than the silent operators of mathematics that operate accurately on a universal accurate sequence of states.
It is so unfortunate that emotional people outnumber all those who seek logic, reason, and rational thinking through guaranteed operations rather than colorful emotional descriptions, as Picasso depicted a woman which does not exist in reality but he gave people what they thought they could understand and not the real complexity of life! Ah, emotions rule the world.
ruclips.net/video/jawVsSnzFz0/видео.html
ruclips.net/video/0Y_rb-sFxR4/видео.html
The most incomprehensible thing is that the universe in comprehensible - Einstein
God?