Stuart Kauffman - Why the ‘Unreasonable Effectiveness’ of Mathematics?

[@Ndo01]

A brilliant mind. Mathematics can account for interactions in the physical world but not for emergence of phenomena. So phenomena must come first. Math itself is an emergent phenomena, how does it account for itself? The argument of infinite affordances is great. If there are indeed infinite affordances then we only need to ask "Can you count to infinity given an infinite amount of time, in principle?".

[@wakabaloola]

the answer is yes, I mean the Feynman path integral does that (explores the most likely outcome out of an infinity of options) on a daily basis

[@Ndo01]

@@wakabaloola Well of course if you ask "jump ahead infinite eons, what number are you at?" The answer would be infinite. That is a representation of infinity as an endpoint from a macro perspective. Counting and finding the probability of something is not the same thing. A probability can be 0.99 recurring, but you could never count how many 9's there are. The 0.99r is just a representation that contains an infinite set within itself.

[@wakabaloola]

@@Ndo01 i don't understand what you are counting or wanting to count. but emergence is certainly very interesting, and in my opinion it is also certainly within the reach of mathematics, in principle

[@Ndo01]

@@wakabaloola Counting anything, like the possible paths a particle can take. You can represent the probability of possible paths without actually counting them. Maths can be used to represent probabilities of interactions within a system, but cannot predict what those interactions will manifest without first 'looking' at the higher order of manifestations of what new things have emerged. You have to understand the entire 'nature' of two things to predict what their interactions will bring about. You can't just take the predictions made in the lower interactions to predict the interactions in the higher one, because it is actually impossible to know how the same particle will behave in every possible context that emerges.

[@wakabaloola]

@@Ndo01 the number of paths a particle can take is uncountably infinite, so only ranges make sense. anyway, it is worth mentioning that the reason we can predict anything at all relies precisely on the fact that there is a Wilsonian mechanism at play, so we don't need to know everything at all scales in order to make a prediction about what happens at a specific range of scales. e.g., in principle we can derive the emergent phenomenon of confinement from QCD, despite the fact that quarks might move around freely at high energies. since this is one of the millennium problems this is hard, but in principle possible. of course, to apply this line of reasoning to the kind of things in the video is hard, we don't know what one might imagine doing with a screwdriver, that's hard to predict, but in principle it is possible.

[@Robinson8491]

Interestingly I am reading something similar explained in Henri Bergson's (1889!) book Time and Free Will, where he speaks about the difference of the experience of time the way mathematics in physics reduces it to quantity, and the actual experience of time which is irreducible. The discrepancy between physical determinism which Robert Lawrence Kuhn is (like most peope) thinking about, which is based on quantity, while biological development cannot be reduced to a quantitative metric. Even if it is difficult for us to see it and we are very stubborn to see everything in our deterministic view, this is something Bergson explains very well and makes very good arguments for. Interesting to see this today! He uses literally a similar example of what it means to predict something in time, to predict something in the future, and that there is a specific difference between predicting for instance a solar eclipse and an action of a person, and exactly why this is so. Very compelling!

[@Robinson8491]

Dynamic versus static, that is a description of the issue according to Bergson. Mathematics is static, and consciousness is dynamic. So too would biology be dynamic according to Stuart Kauffman, that is the issue. And mathematics is just a description of something static. Empty basically.

[@y37chung]

The key point he is struggling to say is "free will" (whether that is fundamental or apparent, doesn't matter), once you have free will, the amount of things that you can do with just a boring table appears infinite (at least insanely large) and each option cannot be mapped easily to a fitness function. The exact evolutionary detail in every planck time moment of a complex system cannot be written in Math, but there are "quasi/abstract-laws" that emerge at a larger scale and that can be described mathematically.

[@stevenverrall4527]

While mathematics can describe many aspects of complex systems, it struggles mightily to predict their evolution. Mathematics can describe what is, but not what will be. I say this as a mathematical physicist.

[@patrickirwin3662]

Best contribution to the "Closer to Truth" program in quite a while. Haven't worked it out yet but there's something like a Gödel incompleteness thing going on here. I wish he had defined "function." and "task," as in an infinitely long list of possible functions or tasks for a screwdriver. I cannot imagine either word being used in this context except insofar as the screwdriver serves the end of a purposive agent. Do the "particles" in the standard model perform tasks? Do they serve a function? Does the uncanny ability of mathematics --generated by nothing but mental axioms and inductive logic-- to describe and predict the physical world so accurately break down precisely where the animate demarcated from the inanimate? Great conversation.

[@Ndo01]

Agreed. I think Godel is incredibly relevant here. René Magritte's "This is not a pipe." Taoism's "The Tao that can be spoken is not the eternal Tao." They're all basically saying the same thing. It is interesting to think that it makes no sense for particles to have function or use for tasks without an agent, and yet they give rise to agents that give them function and tasks. There is a seemingly infinitely wide step from no-agent to agent, so to me this implies there is always an agent. I'm not even a theist, but I don't know how else to bridge that gap. There is a great book and lecture series on KZbin called Godel, Escher, Bach that goes more into this if you haven't already seen it.

[@claudiochianese9850]

I think Stuart Kauffman is my favourite scientist ever.

[@georgegrubbs2966]

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."

[@stevenverrall4527]

I am a mathematical physicist. I am fully aware that mathematics cannot predict the things most important to humanity. These include technological and economic development, wars and other major historical shifts, and climate change. On civilizational timescales, natural evolution is so slow that it is unimportant. However, humanity can selectively breed and genetically modify organisms in desirable ways--but with unforseen outcomes. The unforseen outcomes of bioengineering are indeed troubling. The nuclear industry is heavily regulated, as should be bioengineering to a much larger degree than at present.

[@quakers200]

Stuff has properties that are fairly consistent. Water boils. Freezes, has weight, reacts with other stuff all on a consistent basis that we can measure and we measure with numbers. Of course there is complexity that is nearly impossible to predict. We don't know what an individual water molecule will do. The pattern of frost on a window pane is not predictable.

[@JRBNinetynine-mf6gy]

Imagine, a molecule unless in the 'company' of another, ~ both remain dead, inert, the same, but together, bingo, some unknown it seems causes, this and that and then this, them, ~, life as we know it! This, is where, evolutionary biology, theology, philosophy, mysticism, science, neuro science, and quantum physics meet. I'm guessing!

[@alephnull7410]

Finally someone who doesn’t subscribe to the “Universe is made of mathematics” dogma. It is preposterous that physicists maintain the final word on the universe through quantification despite many fundamental open questions.

[@alephnull7410]

@The Truth of the Matter let’s not forget that mathematics is fundamentally abstract. Any relation to the physical world is as a “descriptor” and not as a fundamental aspect of the physical world.

[@Ndo01]

@The Truth of the Matter What maths formulates the existence of maths and how it works?

[@Ndo01]

​@The Truth of the Matter I suppose we should just throw out all ontological questions then. Not thinking about it that way doesn't get you anywhere either. A question can't be circular reasoning. It can be infinitely regressive. That's a problem for the thing in question, not the question itself. The physical world has a behavior that can be represented and modelled by math. The representation however cannot fully encapsulate the reality as shown by Godel's incompleteness theorem. Math is only necessarily fundamental if the universe is entirely physical in nature along with consciousness. But if it isn't entirely physical, it would account from the unbridgeable chasm between representation and reality.

[@alephnull7410]

@The Truth of the Matter Can this “prime equation at the dawn of reality” (?), or any mathematical object, be understood by our senses? You contend that mathematics can extend as a body into the physical world and not as representation. Then what is the number “2”? What is that which inherently holds the quality of “two-ness”?

[@alephnull7410]

@The Truth of the Matter What you are stating is what I speak of except the use of the phrase “a logic”. The use of logic implies reasoning and only “minds” can conduct reasoning. Your second comment seems to take wild jumps by suggesting this “logic that supersedes all things” would somehow be part of the fabric of reality? Do you mean the physical world? How? You seem to be agreeing with my idea of this problem concerning mathematics that Kant stated as synthetic a priori but then you want to answer it by bringing it into the physical world and that cannot be inductively done.

[@beenay18]

the biology he is talking about is too complex for mathematics capability we have now. but mathematics is being used in lots of things like genetics at present. actually its being used almost everywhere in biology too where the present mathematical processing capability is sufficient.

[@beenay18]

@@DJWeiWei it just means that new discoveries are yet to be made and theories to be postulated and mathematical models are yet to be formulated. It does not mean that making predictions in biology using maths is impossible. Actually mathematics and computers along with research in biology have made many things possible in biology which were unimaginable just some years ago.

[@ofinterest2007]

I like Dr. Kauffman's argument of "affordance" (sp?). But I don't think one has to necessarily go there. Mathematics is a tool created in an environment that has properties. These properties are discovered while also informing our creation and modification of our toolset. To then get ones head so far up into "the place where the sun doesn't shine" that one can't fathom how a tool created in a relative microcosm can also have discovered applications of that tool that also applies to the macrocosm is just plain silly. IMO. Given a different universe with different properties-- if such can exist--then I'm sure the created toolset would be different.

[@melissaflanary7]

I would love to learn if any willing to teach

[@alijassim7015]

So basically he is saying that we cannot predict the biosphere because we do not have the perfect knowledge. That is all to his claim, as he put it after 8:10... Whether I agree or not, I am not really sure.

[@___Truth___]

Yes, but that's all. He's also saying in principle we cannot sufficiently deduce what can also emerge in the grand scheme of things in life, the economy, and the universe at large since the nature of how things come into fruition depends on how things are preceding it and how things arw preceeding that thing e.t.c, where at every point the scope of what's possible to come into existence changes with how things are developing in real-time and in principle

[@uremove]

Hmmm... very interesting debate. Isn’t this a problem of complexity? With hindsight, I think you could pick out the variables that would enable you to calculate a mathematical probability function of “Patrick becoming a filter feeder”. It might include a sequence of contingency probabilities such as the probability of adhesion, a probability of catching food, of Patrick surviving to reproduce, of adaptations in future generations etc. etc. The required contingencies may not be linear, which is where it becomes mind bogglingly complex! I think the end result might look something like the Drake equation.. but longer.

[@DanielRMueller]

It seems to argument here is that you cannot create the "world formula" and use it derive "Patrick becomes a filter feeder". The filter feeder thingy is just not part of the theory, it does not contain variables that track the existence or function of the filter feeder. From the math of the world formula, it's just a mass of particles doing something. Only when you leave the math of the world formula behind can you recognize that this particular mass of particles is actually describe this phenomena as filter feeder and start reasoning about it. With just the world formula, it's just an arrangement of particles moving through spacetime. There might be other arrangements of particles that are also filter feeders, but you wouldn't be able to notice it from the "world formula". At least that's my interpretation.

[@y37chung]

You would need the phenomenon of "Patrick becoming a filter feeder" to exist first and observe it. Only then you can pick out (pre-state) the relevant variables. What he is arguing is that Math cannot truly be used to predict forward (real unknowns). It only describes.

[@dsc4178]

It may be hubris to think math can explain everything.

[@danfarley320]

All he has demonstrated is that many biological processes occur in ways we cannot yet describe by mathematics, in the same way all of physics can be. This doesn't in anyway invalid the original statement, which is why mathematics provides such a good description of the universe. Or to put it another way, why does the universe (at least the aspects we can so far model), conform to abstract mathematical principles that are only conceptualize within minds?

[@markbricklin3096]

He's right!

[@mehrdadassar2542]

I think this man did not understand that the mathematics that works at the fundamental level is absolutely different from that which applies in the effective and low energy world.

[@jamesruscheinski8602]

Something more fundamental than mathematics?

[@dosomething3]

What about the unreasonable effectiveness of the English language?

[@danielm5161]

Is the English language really that effective though? One thing learning how to program a computer has taught me is how comparably crappy English is. Words are slippery and have different meanings to different people. It's one reason politics is such a clusterfuck. Say "Capitalism" to one person and they think free market sustenance and to another person means greedy oppressive slavery. Same word with completely different meanings depending on the brain that is conceptualizing it.

[@ThalesPo]

English is not very effective. Pretty crappy, actually.

[@gerhardris]

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.

[@livesimple-ub9qd]

Do math not meth

[@tedarcher9120]

Why not both

[@totheknee]

Mathematic (or as the Brits say, Mathematics) is a descriptive language, not a prescriptive one. I wonder if this has a part to play in its reasonable uselessness? But I suspect Kauffman is using word play here. "You can't get to the relevant variables that have to do with the biosphere." We can produce a computer simulation of genetic evolution, and new functions emerge. Yet the CPU is solely performing mathematical operations. Whatever the CPU did to get the emergent property, just write that down and you have the relevant variables. Same with AI generated images.

[@keramatebrahimi943]

Relevant matter is quantum physics.

[@JRBNinetynine-mf6gy]

Remember my name, hm, in case I forget it! Very pleased to read some these comments. IMO, in a community spirit, respectful etc. It seems we have massive acceleration in change in, scientific understanding, communication between homosapiens, list,... We don't don't know what, they say, check, 95 percent of the universe, universes, is,... ...ditto, what is in the oceans on Earth,... And we don't know what we don't know. The tendency to hang on to what is familiar, what was safe, is very 'homosapiens', most usually with good reason. Science though, and new thinking, understanding just a little bit more about what we know we don't understand, however, requires something else. A fact of science is a almost always, one proved true, along comes, not true, either, well not entirely or not at all. Newton, no,...so Einstein, Einstein no,.. ...various,... Darwin doubted his own (..., in fact the work of a good few others,..) work, many have since disproved it by observing bugs, they evolve intelligently, and simply by basic mathematics, statistics, ... In yet many remain, er, stuck in a past. Kouffman, seems to be knocking down doors, and moving us on big time. IMO.

[@reenatai75]

I didnt understand athing

[@alephnull7410]

@rubiks6 Actually very important ,yet unpopular, opinions regarding what mathematics actually “is” can be heard in between the lines of this conversation. Unfortunately it’s not about Tesla, SpaceX, simulation theory, or extraterrestrials, so nobody cares.

[@christopherwalsh3101]

I've this channel, but this video is horrible! What is going g on in his Patrick and rock story?? Cut this interview!

[@patrickirwin3662]

It's too long and corny, sure, he's a codger and a geezer, but the critique of mathematics' applicability to all problems is quite sound and not trivial.

[@senjinomukae8991]

This guy is very confused, thinks he's thought of something clever, but actually he's just taking a high level view of an end result that has some human 'meaning' for us, and then saying it's not mathematical. Yes it is. Everything probably is, whether or not we can compute it, or whether it can even be computed, it's still mathematical.

[@wakabaloola]

that's not what he's saying

[@claudiochianese9850]

Sure, the guy who pretty much invented complexity science is confused.

[@stevenverrall4527]

You are just upset that our Universe is a real complex system that can't be simulated.

[@y37chung]

Mathematical models need to pre-state the relevant variable existing. e.g., F=ma these are all pre-stated variables, but a written equation as such cannot give rise to new relevant variables (even if in reality it could, by observation). Else you must write out all the astronomical number of relevant variables in the same equation first (if you can do this, you are God, you don't need math to predict things anyway, which is a logical paradox)