Whether you believe in god or not, Nihilist or an optimist, just being is awesome. Imagine not having to walk thousands of miles to listen to these intelligent men and women!
Thanks for another great video, Robert. The impressive description you make of the topic shows how effective the English language can be at describing nature. Like mathematics, English is a language that works quite well... Perhaps a video on the "unreasonable effectiveness of English" would also be interesting!
Another totally fascinating video. Wow! This work (Closer to Truth as a whole) is a testament to Robert's impressive hard work and is also a real contribution to our common need to understand nature and our place and destiny in it. Thank you Robert. 👏💯
Great topic. I think the example of Newton's gravitation being replacd by Einstein's General Relativity shows that mathematics is only giving us an approximate model of what is real and true. Physicists hope to replace GR and Quantum Mechanics with another model that embraces both. Even if they are successful, it is not unreasonable to predict that the "theory of everything" will have gaps that will need to be filled by an even more all-encompassing theory in centuries to come. So the effectiveness of mathematics is its ability to be used in a wide variety of contexts to approximate what we observe and make predictions. One doesn't have to look very far to encounter problems where our mathematics fails us. Consider trying to predict the positions of the planets in a million years, or what the weather will be in a month, or where and when the next 6.0 magnitude earthquake will happen. So Nature is not really built around simple mathematics, either. The series title "Closer to Truth" is perfect, because it expresses the persistance of the gap between Truth and our models of reality.
What you state in a fashion is that math can not make a model more complete then the potential of the model contains intrinic. In other words, math can not rise above the perspective it is used for. It is a tool.
Robert here’s a notion you might be interested to explore: where mathematics cannot predict (based on unknowable-in-advance variables and parameters in complex evolving systems and the “unknowable different uses of a screwdriver” argument), but can retrospectively explain things, THAT IS “the arrow of time” (along with entropy - and likely the two concepts are fundamentally related, as well). Then, the substrate for the mathematics is pure, infinitely-intelligent consciousness that by its very nature posits and calculates absolutely everything that is possibly logically self-consistent (because what else would it do with itself - everyone needs a hobby!) and it sees what unpredictable stuff pops out of it as time passes in the direction of its “arrow”. Some particularly complex mathematical objects (e.g. brains) trap within themselves bit of the consciousness (the radio receiver metaphor) unable to perceive the rest of the total consciousness that gave them their own consciousness, but being conscious, can experience their own interactions with the rest of the calculations that are going on as their own internal qualia, and have (a degree of) free will. This scenario reduces the number of existing entities to (arguably) one - one great consciousness that contains all the platonic ideals, and if you assume its existence, then you remove the mystery of where our consciousness comes from, and you solve the unreasonable effectiveness of mathematics but also those areas where mathematics might not be in principle able to make predictions. Many worlds and multiple universes are just the one consciousness exploring other mathematical calculations. Finally, it gives a hope for an afterlife - death releases the trapped limited individual consciousness, and at the price of losing our individuality, we all after death rejoin the one consciousness and as part of it know all the answers to the mysteries of the universe. Simple summary of key idea: the arrow of time IS where mathematics cannot predict complex systems that evolve. Can you get any of your interviewees to give their take on this?
Oh, and it would account for how information itself seems to be of primal importance, and you could imagine discrete quantisation as pixelation or resolution to simplify the calculations so they need not be calculated to infinite resolutions, and the speed of light as the top speed of information processing. So perhaps the intelligence isn’t infinitely infinite, but is more like one of those infinite sets that nevertheless contain gaps (a simple example is that the set of even numbers is infinite, even though it doesn’t include odd numbers, so in a way, while infinite, its less wealthy infinite than the set of all integers, which is less infinite than the set of all rational and irrational and real and complex numbers, etc). It doesn’t fully resolve the problem of suffering, but opens up all sorts of new ways to think about it.
But are you saying that the individual qualia can be effectively described or defined mathematically? Surely, the ability to make predictions is yet another step along the path of effectiveness and not even a necessary one.
2:56 holy crap I was not expecting such a shrill sounding voice to come out of this guy. He sounds like more like a Disney character than a real person.
Lol, yeah, hes awkward. I imagine he's a brilliant dude though. he kept finding himself agreeing with the idea of mathematics being unreasonably effective. For some reason, he decided to play mental gymnastics to reject the idea outright. I don't think he put too much thought into this before the interview.
It's frustrating how many of these academics misunderstand the titular quote and what "in principle means"...you essentially write down the initial positions and momenta of all of the relevant particles. In practice this is impossible, but in principal it is possible.
@19:14: What is said is 100% correct. But to avoid misunderstandings that could arise given the context: Hartry Field did NOT claim that science can be done without math. He claimed SCIENCE can be done WITHOUT NUMBERS (e.g., by using geometry instead). His book "Science without Numbers" is worth checking out. He succeeds in making his case for one of Newton's laws.
I suspect it's mainly selection bias. If geometry wasn't useful for construction, then it wouldn't be used. We would use some other model instead. As an analogy, if screwdrivers weren't useful, then we would use hammers instead.
I find it embarrassingly easy to answer: It means one holds a lacking or wrong view of the relation of mathematics to reality and vice versa. The effectiveness of mathematics is both reasonable and limited. Talk to Stephen Wolfram about it. Other embarrassing ideas: - It seems that many of those that appear in programs like these have some ideas about mathematics - but non whatsoever about computation. Like mathematics is a thing that just happens, viola, results! - That an astonishing number of thinkers are willing to consider ideas like mathematical platonism. - The concept (and reality) of computational irreducibility is largely ignored. Likewise, it seems that many have a poor grasp on how readily complexity can come about from the very simplest of rules.
Maths is excellent at creating abstract representation of reality, like a scluptures work of art. But knowing/recognising the difference between finding the actual fundamentals/foundations of creation and a near approximation of creation, is where people become fundamentally unstuck. Thats where tolerance and precision comes in to sort out the wheat from the chaff. Its the practical engineers argument of a representation thats 'good enough' vs a philosophical search for 'the truth'. Then comes the subjective prejudicial argument, at what level of tolerance is something considered genuine understanding of creation, rather than a mere approximation of creation, adopted through the process of self delusion ? Which itself is also utterly dependant upon the genuine reliability of the observational data that its all based upon. Much of which is now inferred rather than directly observed....if not highly/wilfully selective. Basically, a simulation of creation, is not an emulation of creation...unless that simulation has zero tolerance for error.
Paul Davies explains so well what the others are blind to or cannot grasp. They appear to suffer a poverty of imagination to investigate the issue adequately.
Think it this way: Emergent processes tend to be describable by simpler math than the underlying processes. As long as we can describe reality by simple equations, we are not yet at the fundamental level.
What is your reason for stating this. All the Giants realize the closer you get to the Source, all the more simple, pure, subtle it becomes, and this is a demonstrable fact from nature itself.
@@echo-offof course they are. Emergence is an epistemic phenomenon, as is math. We use math to describe reality, and we use emergence to make describing reality easier. Two languages to describe the same thing certainly share a connection!
@@uninspired3583 Physical emergent phenomena are not epistemic. Waves on water for example are out there independent to our knowledge about it. These phenomena tend to be well describable by math. To me this connection is unreasonable.
@@echo-off i disagree. The waves are a large collection of fundamental components. Independent of our knowledge, there is no collection, only the fundamental components. What makes the particles in the wave different than the particles of water recently evaporated, they're the same. There's no property in the particles itself that makes it part of the wave or not, it's our knowledge that gives them this property.
I understand the meaning of "Unreasonable Effectiveness" of Mathematics after watching this video more than once. These mathematical geniuses effectively changed my perspective on describing reality. Call me quantumkathmath.
To the extent that meaning can be cognized there is understanding. Certain types of meaning are useful to mathematics. Other types are useful to empirical, science. Modern science combines the meanings of mathematics and the meaning of the "laws of Nature" gleaned from empiricism to make models capable of prediction or calculations that lead to predictions. This method of modern science is called coherentism. To the extent that coherentism is effective (at making predictions or gleaning insights from calculation) it is due, in totality, to mathematical modeling.To the extent that coherentism is not effective it is due to the "reliance" on mathematics and not on empirical observation. The fact that these combinations of meanings is successful is good. This, however, should not overlook the fact that meaning has other...realms of understanding. The greater question to be asked is what is the source of meaning. For long after modern math becomes impotent at giving man control of certain things, the faculty of cognizing meaning may give rise to other, more successful, combinations.
This question would have been worth considering only and only if mathematics that was possible was only the one that happens to fit the laws of our universe and nothing more. But mathematics is a generalized, platonic system, which can model/generate all kinds of possibilities that clearly do not exist in this universe. In fact we should wonder the opposite. How come we do not see all possibilities that mathematics allows and if in fact all those possibilities are instantiated somewhere else because they are possible. So in some sense ineffectiveness of (string theory) mathematics has been demonstrated because modern string theory predicts 10^500 possible universes effectively rendering it's predictive power useless. Which is why the String theory has lost its cache. If you have a system that predicts anything and everything that is possible then it is not really effective right? If your theory about real estate was not compressed but simply enumerated all possible ways market may behave then it is not really effective is it? Sociologically, let us not beat around the bush. People who are theologically inclined tend to get fascinated and interested in this question and a presumed answer "yes", because they hope that some kind of designer has to be there to make mathematics fit the universe we have. Some kind of teleology. Biology, turbulent flows, fractal geometry are difficult because they start straining the simplicity/compactness of mathematics and in some sense we shy away from those precisely for that reason. But in principle more complex mathematics could be possible which can model those system. There are cases like digits of irrational numbers like pi and e and the irregularity of prime numbers etc. show us the limitations of mathematics. Pi is also a definitional number only in Euclidean geometry approximation. The inverse square laws work because we approximate the space to be a 3 dimensional, Euclidean space and area of a sphere grows by square of the distance hence the inverse squared laws like gravity and coulombs law. But GR has already shown that spacetime has curvature near massive objects i.e. spacetime is not Euclidean and we will find that mathematics of true GR metric tensor is no longer simple inverse square law. In other words, we find our mathematical models work, but they work only for spherical cow approximations. So in a nutshell, there is nothing interesting about the fact that parts of mathematics describe our universe and most of the time to the approximations of the universe. And no wonder first we discovered the mathematics that models our universe, but once mathematics matured to an abstract field we now have a more general, widely applicable, sometime abstract mathematics. Big deal.
Well that's a question that never occurred to me. And right this moment, I'm afraid I don't have an answer. I'll think about it and get back to you, maybe next week.
Mathematics is a tool for solving problems. Its effectiveness is a reflection of how mathematicians use it - nothing unreasonable about it. You might equally reflect on the effectiveness of the scientific method.
any structure, objective or subjective, without application of mathematics, becomes either inefficient, in the case of the former or illogical/inconsistent and therefore impossible, in the case of the latter...
In my opinion, the unreasonable mathematical probably is from unpredictable and uncontrollable of the sequences of things like universe, our biological body…because the conditions are continuing to quantize in any seconds and the sequence is changed quickly. Of course, we still can create a simple effective process to more complex process like a manufacturing process or space explorations, but it may be hard to do if the conditions are keeping to change and we can’t recognize the changes.
Everyone that actually works our equations and theories in practice routinely absorbs and fabricates the anomalies . We deem its hidden variables ( trouble shoot) playing musical chairs of super position until we get the answers we desire but unlike in an abstract classroom where you can talk each other into determinant repeated outcomes the actual precision imposed on nature doesn't work this way. We can blame environment and dream up a pantheon of excuses why its random probable odds in everything but in the real world you cant dwell in that mysticism it will not work. The deformaty or phenomenon is scrapped and you accept it and move on while building a record of events because its only a matter of time before the next failure occurs. 😊 Of your lucky you can begin to put probable odds of when nature may fail . Its no such thing as size fits all for infinite repetition
What the heck does Mr. Holt talk about at 19:09? Roger Penrose does not believe that the world is made out of mathematics, neither is Penrose a Platonist in the sense that Holt argues. Holt seems to project the ideas of Max Tegmark(who believes the world is subset of an abstract mathematical world, a silly idea.) onto Sir Roger Penrose.
Wait, why is that a silly idea? If we take the Physical Universe we try to understand it and for some reason mathematicss allows us to do that as we discover the maths inherent within it. But such maths is in effect non-existent aka it is abstract or else meta-physical property of the Universe. If we use our human brains, the concept is thus: Super-Set = Metaphysical representation (mathematics) within which a Physical reality is ALSO found (sub-set). Namely it probably is not the only sub-set. So the question is: Why is that a silly idea even if it's wrong? Equally, what does Penrose subscribe to: A cyclic big-bang but that is still a Physical Universe description only.
@@TyrellWellickEcorp that’s interesting… I view language as a more descriptive term… and don’t privilege minds as the creators of languages… DNA is a language.. heck.. transfer RNAs make up a different language.. which can help translate to the language of proteins and amino acids! Lots of languages!
It would be infeasible to continually apply math to every substance, motion, energy, and force before us. Does that mean that math is not applicable to some of those things? Why would math not be applicable? Are there any phenomena describable by substance, motion, energy, and force which would be impossible to evaluate mathematically? What would be the alternative standard and process? Maybe Grant Sanderson knows, or some of his 5.57M subs.
Wigner’s concept of “unreasonable effectiveness” should have been explained first. What is “effectiveness” for Wigner? What does he mean by “unreasonable”?
Some people are simply surprised that math works because they think that math came first. That's simply not the case. Math is an extrapolation of physical observations. Physics came first, we just don't teach that in every school (they did in mine) and some people are not smart enough to figure it out on their own.
I think truly believing humans are special is more naive than truly believing in a god. The question "why?" is something like an error in computing, because it objectively does not matter... until it does matter. That goes for anything, I think 🤔
If the biosphere isn’t “computable” then we wouldn’t be able to say anything concrete about nature or the universe at all. Everything including dna and reality itself is computable at least on a surface level. Nature is fundamentally math, whether we can resolve it to the highest possible resolution has to be a technical limitation. These interviewees are playing word games and are speaking on their own personal philosophy, A hardcore empiricist / physicist knows that even thought itself could be described mathematically in principle. We don’t know where the laws of physics come from, but we DO know that they operate on purely mathematical principle. The Electroweak force , Gravity, they are computational aren’t they?
@@mesplin3 yeah I hear what you’re saying, true that once we have the theory of Quantum Gravity we might gain deeper insight into how/why the laws of physics emerge and there are aspects of Quantum Mechanics (the uncertainty principle) that make nature fundamentally indescribable…. But I tend to think the entire thing (e.g God, the origin of everything physical) should at least be based on some type of Logic. What do you think? Is there some deeper level that we eventually probe that is fundamentally not Logical/math?
@@Okla_Soft Subjective experience seems a decent candidate. As I far as I can tell, logic assumes the existence of something external to the mind. For example, the law of Identity (something is what it is and isn't what it is not) seems to be assumed to exist if one adheres to logic.
Maths does not fundamentally exist, yet here we are within a physical natural universe... as such Nature is not just maths otherwise there would be no physical universe. Or put it another way, you can start with maths but once that takes on material or energetic forms within this universe it generates new properties that are independent of maths also. You can practically construct all science from this angle up to the soft sciences and beyond that. For the record the problem of axioms in maths is also explained by this at the other end.
@@commentarytalk1446 I get what you’re saying, you’re implying that nature has emergent properties that supersede math… I’m telling you that the non-math properties you’re describing are all perceptual and only exist in our minds. An argument can be made that nothing physical exists that is not mathematical. Read Max Tegmark’s “our mathematical universe” From what we can tell, all particles and energy are described by math-give us an example of something in nature that is fundamentally non-mathematical TLDR: The quantum wavefunction describes the entire universe….including subjective thought and experiences The quantum wavefunction is described by the shrodinger equation Everything else emerges from that, so the universe is entirely described by math. Period. I know it’s a stark viewpoint, but everything underlying all soft sciences like psychology and philosophy is just quantum fields i retracting with one another
I don’t see Robert Kuhn as grasping the interesting aspects of mathematics’ non-applicability in biology-it’s not that mathematics can’t be applied in principle to compute the wavefunctions of every element of a complex system or the trajectory of a state of a complex system in a 6N-dimensional phase space-of course it can do that. Because that’s just physics! We understand perfectly how indispensable mathematics is in physics, the whole argument is that mathematics suddenly loses it’s unreasonable effectiveness if instead of physics you try to use it to talk about biology. There is no interesting description of emergent phenomena in the language of mathematics, even if there is in its underlying phenomena.
You have twelve apples in a basket, you give three to your friends. How many apples are left in the basket? What mathematics doesn't tell us is that one friend got a rotten apple! We extract the simple properties before treating them with mathematics, so things go well. But the rest is not described by mathematics, so there is no such "unreasonable effectiveness".
I'm not sure whether the fact that nature conforms to some sort of logic is either reasonable or unreasonable. What is definitely unreasonable is purporting to have knowledge about that. If it says anything at all, it's about the nature of abstract concepts, not about the nature of nature.
Mystics is sort of about exploring the here and now in which we are stuck and getting some deeper insight out of that in reality. It is about looking for a deeper undelying order in which at its core mathematics is of non relevance. Jim Holt in the video stated that mathematics tells us about some aspects of the world and is completely silent on other aspects of the world and he is right about that. Mathematics can only be applied to aspects of reality which are physical construct related.
That empirical intillegence does not compare to Wisdom and mutual relationship with natural order. You're of the few here who comment that I appreciate considering.
Mathematics may be unreasonably effective for describing concrete systems but fails in its effectiveness when trying to describe the failure of progress
The relation between the physical world and mathematics is the same relation between genetic and epigenetic as the last Can acts on the first same thing mathematics is the tool with which we acts on the physical world mathematics is not an abstract thing we think theme as an abstract but we image theme as objects we can Say they are experi_menthal objects like the expérimental physical world objects
"To me its amazing that the world could be described by such a simple equation. I don't have an answer for why the world is so simple". Honestly the way these people think, is extremely irritating to me. Their logic makes no sense. On what grounds are they even arguing that the universe should be complex? He made NO ARGUMENT WHATSOEVER. He just said, you know what, I'm just going to assume that if a universe was made, the overriding probability is that the equations governing its behavior should be staggeringly complex and impossible to describe with math. According to what probabilistic argument? According to what reasoning? According to what comparison between our universe and an ensemble of other universes? According to what model for how complex universes "should be"??? For christ's sake, at least give SOME ANSWER instead of "MUH INTUITION TOLD ME SO". And even to the extent that we can describe electromagnetic behavior using maxwell's laws. What fraction of the universe's true workings do EM fields represent? Maybe with respect to the visible portion its a meaningful part, but with respect to the universe as a whole it might just be the tip of the iceberg, and most of its inner workings are actually impossible to understand. But once again he made no effort to even attempt to quantify whether electromagnetism is a large or small part of the universe. Never mentioned dark energy or dark matter which if real make up 95-99% (I forget which) of the universe. And God knows whatever exists outside our universe or came before it, if such a question could even be framed in a way that makes sense. I'm just so done with this. Robert Kuhn at least did slightly better here. I can't blame him for asking the questions. But this is BEYOND tiresome and frustrating to listen to. I can't stand the lack of intelligence in any of these answers. You may as well have some guy saying "but what if we're in the matrix DUDE and its a simulation!!" while high on weed because its the exact same content
I think a big problem with this channel is that most of the selected guests lean in the hocus pocus direction. Why not interview more chemists, physists, and mathematicians who adhere to the core of their fields of study?
When applied to the true natural universal dynamic of the Universe, mathematics is nothing but an approximation created by and through human mind's logic. Mathematics, locally, in a limited domain of its own internal body of logical associations, can be "rigorously perfect". However, as a totality, mathematics is not itself absolutely complete. Godel proved this, etc. The real dynamic of the the Universe, in its totality, is absolutely causal-iterative, therefore mathematics applied to it is never more than an approximation, at any level of it. For example, the so-called 'Law of conservation of energy' is not actually absolutely true. The ( so-called ) "energetic movement" is never absolutely conserved or absolutely "contained" if correctly applied ( = correctly understood ) to the true natural dynamic of the Universe, therefore the fundamental logic and mathematical apparatus applied to it is an approximation no matter what. Etc. ( there's a humongous number of examples like this in the scientific domain, physics, chemistry , biology, etc ). The abstract logical model, the perfect model, the mathematical model, etc, may appear as being a perfect logical template when applied locally, but when applied to the true universal dynamic is always an approximation, no matter what, no matter how perfectly rigorous is its logical apparatus, etc.
Math can be applied to everything in the universe and we do. Most people do not understand that the relational aspects of languages are basically trivialized math.
@@Corteum What can not be captured by math? My subjective "red" and your subjective "red" form an isomorphism that is guaranteed by the spectral absorption band of the opsins in our eyes, which are mostly detecting the same spectral bands within the same species. See, we even know the physical mechanism that leads to similar, or even identical, color vision. ;-)
@@lepidoptera9337 Math can only deal with objects, not sujects. Subject is aware of the math, as it is aware of sensory information. Computers aren't aware of anything. They can only process information. Humans on the other hand can be aware of the information we process. See if you can compute that, or try computing how to derive subjcts from objects like atoms and molecules, even though they only make up less than 5% of the known mass in the unniverse.
@@Corteum What you call red and what I call red are not subjective. We can (up to color blindness) all agree on that. What red "looks" to you is irrelevant for me since you can't share. It might as well not exist.
Math is a Lot of numbers. Nunber ist means nothing. Nunber is tautology. And math is true ? When equatiion describes reality though numbers are unpredictable reality. Godel axion show is Impossible from axion figure out true. From him math isnt never true absolutetly.
Mathematics hasn’t been able to help with the most fundamental questions of all. Why is there something rather than nothing? Whether the cosmos is material & eternal, or whether there is an eternal god requires an answer which probably won’t be mathematical. If there is a god how it is that there is still requires an explanation
It doesn’t mean anything. This channel just makes things up as they go. Next episode will be called “Math and science plus god if baking a chocolate cake without sprinkles”.
Well, there are no physical objects. Matter is ideas, and the so-called simplicity is false. These clowns don't understand the universe at alll. The universe is infinitely complex. Math doesn't describe the universe. This show is complete bullshit. Gödel proved mathematics can't be part of a true theory, because numbers can act as verbs, nouns, and adjectives, but math can't distinguish between these different meanings. Mathematization discards meanings, but meanings are fundamental. Mathematics is sometimes a useful tool, but using it to determine truth is a wild blunder. It would be understandable before Gödel's theorems, but continuing to pretend math is true is scientific malpractice.
Paul Davis is the most insightful, courageous, and honest.
Whether you believe in god or not, Nihilist or an optimist, just being is awesome. Imagine not having to walk thousands of miles to listen to these intelligent men and women!
That's a result of modern technology and being fortunate enough to have the amenities that make that possible It's not "just being"
Closer to Truth is at the top of their game. Fantastic.
Thanks for another great video, Robert. The impressive description you make of the topic shows how effective the English language can be at describing nature.
Like mathematics, English is a language that works quite well... Perhaps a video on the "unreasonable effectiveness of English" would also be interesting!
Excellent... ofcourse distinguished Dr. Paul Davis views are best in all aspects... thanks ❤ 26:18 ❤❤
Another totally fascinating video. Wow! This work (Closer to Truth as a whole) is a testament to Robert's impressive hard work and is also a real contribution to our common need to understand nature and our place and destiny in it. Thank you Robert. 👏💯
I listened to David Wallace twice.
Great topic. I think the example of Newton's gravitation being replacd by Einstein's General Relativity shows that mathematics is only giving us an approximate model of what is real and true. Physicists hope to replace GR and Quantum Mechanics with another model that embraces both. Even if they are successful, it is not unreasonable to predict that the "theory of everything" will have gaps that will need to be filled by an even more all-encompassing theory in centuries to come. So the effectiveness of mathematics is its ability to be used in a wide variety of contexts to approximate what we observe and make predictions. One doesn't have to look very far to encounter problems where our mathematics fails us. Consider trying to predict the positions of the planets in a million years, or what the weather will be in a month, or where and when the next 6.0 magnitude earthquake will happen. So Nature is not really built around simple mathematics, either. The series title "Closer to Truth" is perfect, because it expresses the persistance of the gap between Truth and our models of reality.
What you state in a fashion is that math can not make a model more complete then the potential of the model contains intrinic. In other words, math can not rise above the perspective it is used for. It is a tool.
Robert here’s a notion you might be interested to explore: where mathematics cannot predict (based on unknowable-in-advance variables and parameters in complex evolving systems and the “unknowable different uses of a screwdriver” argument), but can retrospectively explain things, THAT IS “the arrow of time” (along with entropy - and likely the two concepts are fundamentally related, as well). Then, the substrate for the mathematics is pure, infinitely-intelligent consciousness that by its very nature posits and calculates absolutely everything that is possibly logically self-consistent (because what else would it do with itself - everyone needs a hobby!) and it sees what unpredictable stuff pops out of it as time passes in the direction of its “arrow”. Some particularly complex mathematical objects (e.g. brains) trap within themselves bit of the consciousness (the radio receiver metaphor) unable to perceive the rest of the total consciousness that gave them their own consciousness, but being conscious, can experience their own interactions with the rest of the calculations that are going on as their own internal qualia, and have (a degree of) free will. This scenario reduces the number of existing entities to (arguably) one - one great consciousness that contains all the platonic ideals, and if you assume its existence, then you remove the mystery of where our consciousness comes from, and you solve the unreasonable effectiveness of mathematics but also those areas where mathematics might not be in principle able to make predictions. Many worlds and multiple universes are just the one consciousness exploring other mathematical calculations. Finally, it gives a hope for an afterlife - death releases the trapped limited individual consciousness, and at the price of losing our individuality, we all after death rejoin the one consciousness and as part of it know all the answers to the mysteries of the universe. Simple summary of key idea: the arrow of time IS where mathematics cannot predict complex systems that evolve. Can you get any of your interviewees to give their take on this?
Oh, and it would account for how information itself seems to be of primal importance, and you could imagine discrete quantisation as pixelation or resolution to simplify the calculations so they need not be calculated to infinite resolutions, and the speed of light as the top speed of information processing. So perhaps the intelligence isn’t infinitely infinite, but is more like one of those infinite sets that nevertheless contain gaps (a simple example is that the set of even numbers is infinite, even though it doesn’t include odd numbers, so in a way, while infinite, its less wealthy infinite than the set of all integers, which is less infinite than the set of all rational and irrational and real and complex numbers, etc). It doesn’t fully resolve the problem of suffering, but opens up all sorts of new ways to think about it.
But are you saying that the individual qualia can be effectively described or defined mathematically? Surely, the ability to make predictions is yet another step along the path of effectiveness and not even a necessary one.
2:56 holy crap I was not expecting such a shrill sounding voice to come out of this guy. He sounds like more like a Disney character than a real person.
Lol, yeah, hes awkward. I imagine he's a brilliant dude though. he kept finding himself agreeing with the idea of mathematics being unreasonably effective. For some reason, he decided to play mental gymnastics to reject the idea outright. I don't think he put too much thought into this before the interview.
Brilliant conversations once again. Thank you
Excellent video with different perspectives and honest answers and provocative questions. Well done.
Excellent 😃
Literally just had a thought similar to the premise of this episode a few days ago, incredible timing.
It's frustrating how many of these academics misunderstand the titular quote and what "in principle means"...you essentially write down the initial positions and momenta of all of the relevant particles. In practice this is impossible, but in principal it is possible.
Brilliant episode 👏🏻🙏
It means that we are good at adapting our logic to the observed phenomena of Nature.
You must have a University degree to come up ith that thought!
@@HermanFickewirth
I have a black belt in making dumplings :)
@19:14: What is said is 100% correct. But to avoid misunderstandings that could arise given the context: Hartry Field did NOT claim that science can be done without math. He claimed SCIENCE can be done WITHOUT NUMBERS (e.g., by using geometry instead).
His book "Science without Numbers" is worth checking out. He succeeds in making his case for one of Newton's laws.
Science can be done without mathematics, but it would be very inefficient.
This video was posted a week ago; why is it being posted again 🤔?
"I don't know the answer to that question." thank god, a honest answer
It doesn't matter that much either way. Just try to enjoy your one extremely short time alive here on Earth.
RLK! That's my boy!!!
I suspect it's mainly selection bias. If geometry wasn't useful for construction, then it wouldn't be used. We would use some other model instead. As an analogy, if screwdrivers weren't useful, then we would use hammers instead.
I find it embarrassingly easy to answer: It means one holds a lacking or wrong view of the relation of mathematics to reality and vice versa.
The effectiveness of mathematics is both reasonable and limited. Talk to Stephen Wolfram about it.
Other embarrassing ideas:
- It seems that many of those that appear in programs like these have some ideas about mathematics - but non whatsoever about computation. Like mathematics is a thing that just happens, viola, results!
- That an astonishing number of thinkers are willing to consider ideas like mathematical platonism.
- The concept (and reality) of computational irreducibility is largely ignored. Likewise, it seems that many have a poor grasp on how readily complexity can come about from the very simplest of rules.
“Reality” is created by sensation, perception,integration, memory, and imagination. “Actuality” is what is, independent of perception.
Maths is excellent at creating abstract representation of reality, like a scluptures work of art.
But knowing/recognising the difference between finding the actual fundamentals/foundations of creation and a near approximation of creation, is where people become fundamentally unstuck.
Thats where tolerance and precision comes in to sort out the wheat from the chaff.
Its the practical engineers argument of a representation thats 'good enough' vs a philosophical search for 'the truth'.
Then comes the subjective prejudicial argument, at what level of tolerance is something considered genuine understanding of creation, rather than a mere approximation of creation, adopted through the process of self delusion ?
Which itself is also utterly dependant upon the genuine reliability of the observational data that its all based upon.
Much of which is now inferred rather than directly observed....if not highly/wilfully selective.
Basically, a simulation of creation, is not an emulation of creation...unless that simulation has zero tolerance for error.
Paul Davies explains so well what the others are blind to or cannot grasp. They appear to suffer a poverty of imagination to investigate the issue adequately.
Abundance of imagination is a bigger human problem than the lack of it. We are hard wired to find patterns, even when they aren't there.
Think it this way: Emergent processes tend to be describable by simpler math than the underlying processes. As long as we can describe reality by simple equations, we are not yet at the fundamental level.
What is your reason for stating this.
All the Giants realize the closer you get to the Source, all the more simple, pure, subtle it becomes, and this is a demonstrable fact from nature itself.
To me it seems that emergence and mathematical elegance of describing a phenomenon are deeply related.
@@echo-offof course they are. Emergence is an epistemic phenomenon, as is math. We use math to describe reality, and we use emergence to make describing reality easier. Two languages to describe the same thing certainly share a connection!
@@uninspired3583 Physical emergent phenomena are not epistemic. Waves on water for example are out there independent to our knowledge about it. These phenomena tend to be well describable by math. To me this connection is unreasonable.
@@echo-off i disagree. The waves are a large collection of fundamental components. Independent of our knowledge, there is no collection, only the fundamental components.
What makes the particles in the wave different than the particles of water recently evaporated, they're the same. There's no property in the particles itself that makes it part of the wave or not, it's our knowledge that gives them this property.
I understand the meaning of "Unreasonable Effectiveness" of Mathematics after watching this video more than once. These mathematical geniuses effectively changed my perspective on describing reality. Call me quantumkathmath.
To the extent that meaning can be cognized there is understanding. Certain types of meaning are useful to mathematics. Other types are useful to empirical, science. Modern science combines the meanings of mathematics and the meaning of the "laws of Nature" gleaned from empiricism to make models capable of prediction or calculations that lead to predictions. This method of modern science is called coherentism.
To the extent that coherentism is effective (at making predictions or gleaning insights from calculation) it is due, in totality, to mathematical modeling.To the extent that coherentism is not effective it is due to the "reliance" on mathematics and not on empirical observation.
The fact that these combinations of meanings is successful is good. This, however, should not overlook the fact that meaning has other...realms of understanding. The greater question to be asked is what is the source of meaning. For long after modern math becomes impotent at giving man control of certain things, the faculty of cognizing meaning may give rise to other, more successful, combinations.
This question would have been worth considering only and only if mathematics that was possible was only the one that happens to fit the laws of our universe and nothing more. But mathematics is a generalized, platonic system, which can model/generate all kinds of possibilities that clearly do not exist in this universe. In fact we should wonder the opposite. How come we do not see all possibilities that mathematics allows and if in fact all those possibilities are instantiated somewhere else because they are possible. So in some sense ineffectiveness of (string theory) mathematics has been demonstrated because modern string theory predicts 10^500 possible universes effectively rendering it's predictive power useless. Which is why the String theory has lost its cache. If you have a system that predicts anything and everything that is possible then it is not really effective right? If your theory about real estate was not compressed but simply enumerated all possible ways market may behave then it is not really effective is it?
Sociologically, let us not beat around the bush. People who are theologically inclined tend to get fascinated and interested in this question and a presumed answer "yes", because they hope that some kind of designer has to be there to make mathematics fit the universe we have. Some kind of teleology.
Biology, turbulent flows, fractal geometry are difficult because they start straining the simplicity/compactness of mathematics and in some sense we shy away from those precisely for that reason. But in principle more complex mathematics could be possible which can model those system. There are cases like digits of irrational numbers like pi and e and the irregularity of prime numbers etc. show us the limitations of mathematics. Pi is also a definitional number only in Euclidean geometry approximation. The inverse square laws work because we approximate the space to be a 3 dimensional, Euclidean space and area of a sphere grows by square of the distance hence the inverse squared laws like gravity and coulombs law. But GR has already shown that spacetime has curvature near massive objects i.e. spacetime is not Euclidean and we will find that mathematics of true GR metric tensor is no longer simple inverse square law. In other words, we find our mathematical models work, but they work only for spherical cow approximations.
So in a nutshell, there is nothing interesting about the fact that parts of mathematics describe our universe and most of the time to the approximations of the universe. And no wonder first we discovered the mathematics that models our universe, but once mathematics matured to an abstract field we now have a more general, widely applicable, sometime abstract mathematics. Big deal.
Meth exists because of math.
Well that's a question that never occurred to me.
And right this moment, I'm afraid I don't have an answer.
I'll think about it and get back to you, maybe next week.
it means because the sky is blue infinite subgroups must exist, the Rayleigh effect gives a well defined group with a bijected dispersion
skipto 20:28
Stewart is in the "its all bs, you can't do it" phase of life. Lol
25:00 Idk, Doc.
I'm thinking it might depend upon the source of one's bafflement at any given spacetime event...lol
Go Bluejays!!
It means that the Universe and Reality seem to be relational ordered, as mathematics is a language about relations.
Like the requirements of a bus driver to programme the coordinates to drive down the road to brake at the same old bus stops
Hey please interview John Searle asap, he' has only limited days left.
Mathematics is a tool for solving problems. Its effectiveness is a reflection of how mathematicians use it - nothing unreasonable about it. You might equally reflect on the effectiveness of the scientific method.
any structure, objective or subjective, without application of mathematics, becomes either inefficient, in the case of the former or illogical/inconsistent and therefore impossible, in the case of the latter...
In my opinion, the unreasonable mathematical probably is from unpredictable and uncontrollable of the sequences of things like universe, our biological body…because the conditions are continuing to quantize in any seconds and the sequence is changed quickly.
Of course, we still can create a simple effective process to more complex process like a manufacturing process or space explorations, but it may be hard to do if the conditions are keeping to change and we can’t recognize the changes.
Audio cuts out for a second some times
Yes, the attention to quality has gone down quite a bit in the last several episodes.
Everyone that actually works our equations and theories in practice routinely absorbs and fabricates the anomalies .
We deem its hidden variables ( trouble shoot) playing musical chairs of super position until we get the answers we desire but unlike in an abstract classroom where you can talk each other into determinant repeated outcomes the actual precision imposed on nature doesn't work this way.
We can blame environment and dream up a pantheon of excuses why its random probable odds in everything but in the real world you cant dwell in that mysticism it will not work.
The deformaty or phenomenon is scrapped and you accept it and move on while building a record of events because its only a matter of time before the next failure occurs. 😊
Of your lucky you can begin to put probable odds of when nature may fail .
Its no such thing as size fits all for infinite repetition
Math is one on of the languages of consciousness to quantify aspects of reality.
I come here for answers, not questions.
Answers are merely new questions in hiding.
There are no answers to these questions
What the heck does Mr. Holt talk about at 19:09? Roger Penrose does not believe that the world is made out of mathematics, neither is Penrose a Platonist in the sense that Holt argues. Holt seems to project the ideas of Max Tegmark(who believes the world is subset of an abstract mathematical world, a silly idea.) onto Sir Roger Penrose.
Wait, why is that a silly idea?
If we take the Physical Universe we try to understand it and for some reason mathematicss allows us to do that as we discover the maths inherent within it. But such maths is in effect non-existent aka it is abstract or else meta-physical property of the Universe.
If we use our human brains, the concept is thus: Super-Set = Metaphysical representation (mathematics) within which a Physical reality is ALSO found (sub-set). Namely it probably is not the only sub-set.
So the question is: Why is that a silly idea even if it's wrong?
Equally, what does Penrose subscribe to: A cyclic big-bang but that is still a Physical Universe description only.
Well you can watch the second most viewed Closer To Truth episode to hear Penrose’s answer.
According to my calculatios bring in the ba nk audit report
It means people are surprised that math describes math
(Bc math is the only way we can tell if math is reasonable… natural observations embedded or not…)
Math is a language in and of itself. Languages always come from minds.
@@TyrellWellickEcorp that’s interesting… I view language as a more descriptive term… and don’t privilege minds as the creators of languages… DNA is a language.. heck.. transfer RNAs make up a different language.. which can help translate to the language of proteins and amino acids! Lots of languages!
It would be infeasible to continually apply math to every substance, motion, energy, and force before us. Does that mean that math is not applicable to some of those things? Why would math not be applicable? Are there any phenomena describable by substance, motion, energy, and force which would be impossible to evaluate mathematically? What would be the alternative standard and process? Maybe Grant Sanderson knows, or some of his 5.57M subs.
Wigner’s concept of “unreasonable effectiveness” should have been explained first. What is “effectiveness” for Wigner? What does he mean by “unreasonable”?
Some people are simply surprised that math works because they think that math came first. That's simply not the case. Math is an extrapolation of physical observations. Physics came first, we just don't teach that in every school (they did in mine) and some people are not smart enough to figure it out on their own.
I think truly believing humans are special is more naive than truly believing in a god. The question "why?" is something like an error in computing, because it objectively does not matter... until it does matter. That goes for anything, I think 🤔
If the biosphere isn’t “computable” then we wouldn’t be able to say anything concrete about nature or the universe at all. Everything including dna and reality itself is computable at least on a surface level.
Nature is fundamentally math, whether we can resolve it to the highest possible resolution has to be a technical limitation.
These interviewees are playing word games and are speaking on their own personal philosophy,
A hardcore empiricist / physicist knows that even thought itself could be described mathematically in principle.
We don’t know where the laws of physics come from, but we DO know that they operate on purely mathematical principle. The Electroweak force , Gravity, they are computational aren’t they?
Well, we don't have a theory of quantum gravity yet...
But I'm mostly just playing devil's advocate. I agree with most of what you said.
@@mesplin3 yeah I hear what you’re saying, true that once we have the theory of Quantum Gravity we might gain deeper insight into how/why the laws of physics emerge and there are aspects of Quantum Mechanics (the uncertainty principle) that make nature fundamentally indescribable….
But I tend to think the entire thing (e.g God, the origin of everything physical) should at least be based on some type of Logic.
What do you think? Is there some deeper level that we eventually probe that is fundamentally not Logical/math?
@@Okla_Soft Subjective experience seems a decent candidate. As I far as I can tell, logic assumes the existence of something external to the mind. For example, the law of Identity (something is what it is and isn't what it is not) seems to be assumed to exist if one adheres to logic.
Maths does not fundamentally exist, yet here we are within a physical natural universe... as such Nature is not just maths otherwise there would be no physical universe. Or put it another way, you can start with maths but once that takes on material or energetic forms within this universe it generates new properties that are independent of maths also. You can practically construct all science from this angle up to the soft sciences and beyond that.
For the record the problem of axioms in maths is also explained by this at the other end.
@@commentarytalk1446 I get what you’re saying, you’re implying that nature has emergent properties that supersede math…
I’m telling you that the non-math properties you’re describing are all perceptual and only exist in our minds.
An argument can be made that nothing physical exists that is not mathematical.
Read Max Tegmark’s “our mathematical universe”
From what we can tell, all particles and energy are described by math-give us an example of something in nature that is fundamentally non-mathematical
TLDR:
The quantum wavefunction describes the entire universe….including subjective thought and experiences
The quantum wavefunction is described by the shrodinger equation
Everything else emerges from that, so the universe is entirely described by math. Period.
I know it’s a stark viewpoint, but everything underlying all soft sciences like psychology and philosophy is just quantum fields i retracting with one another
Would math exist without a conscious mind to interpret it? That’s the fundamental question
I wonder if there will ever be an equation that describes what it's like to be a bat.
I don’t see Robert Kuhn as grasping the interesting aspects of mathematics’ non-applicability in biology-it’s not that mathematics can’t be applied in principle to compute the wavefunctions of every element of a complex system or the trajectory of a state of a complex system in a 6N-dimensional phase space-of course it can do that. Because that’s just physics! We understand perfectly how indispensable mathematics is in physics, the whole argument is that mathematics suddenly loses it’s unreasonable effectiveness if instead of physics you try to use it to talk about biology. There is no interesting description of emergent phenomena in the language of mathematics, even if there is in its underlying phenomena.
I would suggest you look into computational genetics or protein folding or medical trials. There is plenty of math there.
My attempts to imagine a yet undetected new colour is futile then….?
You have twelve apples in a basket, you give three to your friends. How many apples are left in the basket?
What mathematics doesn't tell us is that one friend got a rotten apple! We extract the simple properties before treating them with mathematics, so things go well. But the rest is not described by mathematics, so there is no such "unreasonable effectiveness".
Logic can differentiate rotten apples from good ones as well. You just did it. ;-)
I'm not sure whether the fact that nature conforms to some sort of logic is either reasonable or unreasonable. What is definitely unreasonable is purporting to have knowledge about that. If it says anything at all, it's about the nature of abstract concepts, not about the nature of nature.
Normally, I don’t mind math videos, but I don’t understand this topic. So. I’m calling the police.
“Unreasonable Effectiveness” of Mathematics Mean?
its unreason is its reason 1 goes to 2 and unreason is there is no last number
Does mathematics scare the mystics when it can successfully simplify complexity?
Mystics is sort of about exploring the here and now in which we are stuck and getting some deeper insight out of that in reality. It is about looking for a deeper undelying order in which at its core mathematics is of non relevance. Jim Holt in the video stated that mathematics tells us about some aspects of the world and is completely silent on other aspects of the world and he is right about that. Mathematics can only be applied to aspects of reality which are physical construct related.
A truly mathematical universe with hardcoded laws would seem to point towards an intelligent designer.
Why is the pencil so effective at making drawings of reality?
Because the pencil is reality?
7:56
What does the "Unreasonable effectiveness" of mathematics mean in the context of the ongoing collapse of our industrial civilization?
That empirical intillegence does not compare to Wisdom and mutual relationship with natural order.
You're of the few here who comment that I appreciate considering.
Mathematics may be unreasonably effective for describing concrete systems but fails in its effectiveness when trying to describe the failure of progress
@@realLsf How effective is mathematics in describing such concrete systems as biological organisms or evolution?
All i can say about health advice is that i wont see in the next century
The relation between the physical world and mathematics is the same relation between genetic and epigenetic as the last Can acts on the first same thing mathematics is the tool with which we acts on the physical world mathematics is not an abstract thing we think theme as an abstract but we image theme as objects we can Say they are experi_menthal objects like the expérimental physical world
objects
""...the human mind has somehow evolved to mirror the nature of reality.." is a profound comment.
Probably lions, earthworms and my pet cat, Ginger, have evolved to mirror reality. What else could natural selection produce?
@@longcastle4863 exactly...
Physics is statistics
No, physics is not statistics. :-)
@@lepidoptera9337 yes it is. And predicts - just as statistics
@@matterasmachine No, it doesn't. ;-)
My usual reaction after the first few lines. You've lost me
To say the biosphere is not describable mathematically seems absurd. Start with simpler laws and iterate n times.
"To me its amazing that the world could be described by such a simple equation. I don't have an answer for why the world is so simple".
Honestly the way these people think, is extremely irritating to me. Their logic makes no sense. On what grounds are they even arguing that the universe should be complex? He made NO ARGUMENT WHATSOEVER. He just said, you know what, I'm just going to assume that if a universe was made, the overriding probability is that the equations governing its behavior should be staggeringly complex and impossible to describe with math.
According to what probabilistic argument? According to what reasoning? According to what comparison between our universe and an ensemble of other universes? According to what model for how complex universes "should be"??? For christ's sake, at least give SOME ANSWER instead of "MUH INTUITION TOLD ME SO". And even to the extent that we can describe electromagnetic behavior using maxwell's laws. What fraction of the universe's true workings do EM fields represent? Maybe with respect to the visible portion its a meaningful part, but with respect to the universe as a whole it might just be the tip of the iceberg, and most of its inner workings are actually impossible to understand. But once again he made no effort to even attempt to quantify whether electromagnetism is a large or small part of the universe. Never mentioned dark energy or dark matter which if real make up 95-99% (I forget which) of the universe. And God knows whatever exists outside our universe or came before it, if such a question could even be framed in a way that makes sense.
I'm just so done with this. Robert Kuhn at least did slightly better here. I can't blame him for asking the questions. But this is BEYOND tiresome and frustrating to listen to. I can't stand the lack of intelligence in any of these answers. You may as well have some guy saying "but what if we're in the matrix DUDE and its a simulation!!" while high on weed because its the exact same content
I think a big problem with this channel is that most of the selected guests lean in the hocus pocus direction. Why not interview more chemists, physists, and mathematicians who adhere to the core of their fields of study?
Robert your fits are always so hard
Tankyo luk for anser.we got it. Edukate your brane peeple.
The effectiveness of mathematics is very reasonable. Nature, and the mathematics that describes it,are fundamentally about dynamical relations.
And what if the universe were empty, static, or didn't physically exist? What's dynamic that math is about then?
Why so determined not to acknowledge God?
All is Brahman
Brahman is absolute
When applied to the true natural universal dynamic of the Universe, mathematics is nothing but an approximation created by and through human mind's logic.
Mathematics, locally, in a limited domain of its own internal body of logical associations, can be "rigorously perfect". However, as a totality, mathematics is not itself absolutely complete. Godel proved this, etc.
The real dynamic of the the Universe, in its totality, is absolutely causal-iterative, therefore mathematics applied to it is never more than an approximation, at any level of it.
For example, the so-called 'Law of conservation of energy' is not actually absolutely true.
The ( so-called ) "energetic movement" is never absolutely conserved or absolutely "contained" if correctly applied ( = correctly understood ) to the true natural dynamic of the Universe, therefore the fundamental logic and mathematical apparatus applied to it is an approximation no matter what.
Etc. ( there's a humongous number of examples like this in the scientific domain, physics, chemistry , biology, etc ).
The abstract logical model, the perfect model, the mathematical model, etc, may appear as being a perfect logical template when applied locally, but when applied to the true universal dynamic is always an approximation, no matter what, no matter how perfectly rigorous is its logical apparatus, etc.
It just means that math cannot be applied to everything in the universe. Because not everything in the universe is mathematically quantifiable.
Math can be applied to everything in the universe and we do. Most people do not understand that the relational aspects of languages are basically trivialized math.
@@lepidoptera9337 We do things like consciousness. Subjectivity. Things that cannot be captured by purely mathematicaly descriptions.
@@Corteum What can not be captured by math? My subjective "red" and your subjective "red" form an isomorphism that is guaranteed by the spectral absorption band of the opsins in our eyes, which are mostly detecting the same spectral bands within the same species. See, we even know the physical mechanism that leads to similar, or even identical, color vision. ;-)
@@lepidoptera9337 Math can only deal with objects, not sujects. Subject is aware of the math, as it is aware of sensory information. Computers aren't aware of anything. They can only process information. Humans on the other hand can be aware of the information we process. See if you can compute that, or try computing how to derive subjcts from objects like atoms and molecules, even though they only make up less than 5% of the known mass in the unniverse.
@@Corteum What you call red and what I call red are not subjective. We can (up to color blindness) all agree on that. What red "looks" to you is irrelevant for me since you can't share. It might as well not exist.
Math is a Lot of numbers. Nunber ist means nothing. Nunber is tautology. And math is true ? When equatiion describes reality though numbers are unpredictable reality. Godel axion show is Impossible from axion figure out true. From him math isnt never true absolutetly.
Man, now that gibberish really comes from a over-educated brain. I hope you don't blow a fuse.
Mathematics hasn’t been able to help with the most fundamental questions of all. Why is there something rather than nothing? Whether the cosmos is material & eternal, or whether there is an eternal god requires an answer which probably won’t be mathematical. If there is a god how it is that there is still requires an explanation
Relativity. ;-)
It doesn’t mean anything. This channel just makes things up as they go. Next episode will be called “Math and science plus god if baking a chocolate cake without sprinkles”.
Don't worry carlz, it is Verboten to even whisper the possibility that a great creator mind stands behind all we see.!
Well, there are no physical objects. Matter is ideas, and the so-called simplicity is false. These clowns don't understand the universe at alll. The universe is infinitely complex. Math doesn't describe the universe. This show is complete bullshit. Gödel proved mathematics can't be part of a true theory, because numbers can act as verbs, nouns, and adjectives, but math can't distinguish between these different meanings. Mathematization discards meanings, but meanings are fundamental. Mathematics is sometimes a useful tool, but using it to determine truth is a wild blunder. It would be understandable before Gödel's theorems, but continuing to pretend math is true is scientific malpractice.
Yes, you failed both in math and physics. So what, though? So nothing. :-)