Noam Chomsky - Mathematics, Language, and Abstract Objects

[@pragjyotishbhuyangogoi8363]

Chomsky is the king of analogies.

[@waswaswad]

But I am the king of anilingus

[@anthonychristie7781]

Maybe, but if so, Douglas Hofstadter is the emperor of analogies. (N.B. that both king" and "emperor" are analogies in this conversation). See his book: Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, [Douglas Hofstadter (Author), Emmanuel Sander (Author)]... Aslo see his Stanford Lecture on this topic... kzbin.info/www/bejne/pGnQaJ98hpihoM0

[@pragjyotishbhuyangogoi8363]

@@anthonychristie7781 That was quite intriguing and entertaining, thank you!

[@bouipozz]

@@anthonychristie7781 Thanks for that - I wish more people put video suggestions in the comments!

[@aunaprendo9957]

Behold! Plato's man! **throws bloody featherless chicken on the ground** - Diogenes

[@compteprivefr]

Wow he's saying something I used to muse about in my early twenties. That by default our relationship to "physical reality" is already an abstraction because of how limited our senses are. In my room there's a desk a chair and a bed, pretty much just three things. But that's because I can't see all the billions of particles blasting through the room at the same time, from dust particles to radio waves, to light, to sound, static and whatever else there may be. Only because I process the world through my physical body which has roughly the same mass of my furniture that's all I can see. I can imagine life forms with a completely different physical make-up interacting with physical reality in a completely different way, making connections that would be entirely incomprehensible to us. Of course we know that there are particles etc but it took an extremely long amount of time compared to our history to actually discover them, and even then, when we talk about atoms, electrons, protons, thy're just an abstraction from something else that we can't interact with yet. It's impossible to know what reality's "true form" is supposed to be, our senses are too biased and can only process a fraction of it.

[@Zayden.]

You make a great point. The following excerpt on the 'form and content' of knowledge may interest you: www.marxists.org/archive/pilling/works/capital/pilling2.htm

[@minawntr3241]

Great

[@anthonychristie7781]

@@Zayden. Thanks for the interesting link. At the end of this piece is introduced the concept of "essence", with which I guess the author assumes everyone is familiar. "...the movement from the ‘sensed’ to the ‘logical’ was a process in which social man penetrated ever more deeply through the appearance of phenomena, deeper and deeper into their essence." A quick browse around the usual quick-summary websites (Wikipedia, Stanford Encyclopedia of Philosophy) reveals that this is a complicated and contested bit of metaphysics, from Plato through Sartre and beyond and that even Marx may not have been as "married" to this concept as is implied in the piece. Still. V interesting. Thx. I have never forgotten a cheeky handbill plastered on a Philadelphia telephone pole in the mid 70's, proclaiming the slogans; "No Form Without Content! No Fish Without a Dry White Wine!"

[@michaeldebellis4202]

I think what he's saying is even a bit more extreme. That the whole notion that we have of "the physical world" is not scientifically valid. In fact since he gave this lecture there has been additional work in evolutionary psychology that provides evidence that certain concepts such as contact mechanics are innate just as the language faculty is. So that is why we are predisposed to see the world that way but in reality Newton and later work like Maxwell, Einstein, and quantum theory showed that our common sense notion of the physical world, e.g., that things need to come into contact to influence each other is flawed. Newton first did this by demonstrating that "action at a distance" could happen. This was considered ridiculous by the best minds of his time including Newton himself. But eventually we came to accept concepts such as gravitational fields, curved space-time, and quantum probability waves as the true definition of what we used to call physical. But those things behave very differently from our common sense view of physical and Chomsky claims that no one has come up with a coherent alternative. For more on that see his youtube lecture "Newton's contribution to the theory of mind". It's a shame that most philosophers don't understand this basic point and even today many of them waste their time arguing about whether concepts such as "physicalism" are true or not without bothering to provide a coherent definition of physical. I have read a few recent philosophers though who do recognize the problem and attempt a new definition.

[@Primitarian]

@@michaeldebellis4202 This is exactly what he means. Newton was part of the English empiricist tradition, wherein nothing is real except bodies bumping into each other. This was in contrast to the rationalism of Newton's rival Leibniz, who denied the empiricist presupposition. Turns out, as Newton himself came to concede, the empiricists were wrong, at least when it came to gravity (and later with things like curved space time and quantum entanglement). Thus physicists since Newton have realized that physical reality at bottom appears to be entirely a mental construct, even if the prevailing assumption of the Anglo-Saxon culture has been, even to this day, that reality is fundamentally physical and not mental.

[@davidrestrepomartina8150]

I would definitely give you some years of my life so that you could live longer Dr Chomsky!

[@lqacwaz470]

so would i!

[@SoundsSilver]

Can I have some?

[@coreycox2345]

@@SoundsSilver Maybe.

[@stoyanfurdzhev]

Close to divinisation.

[@SoundsSilver]

@@Abhiraj_Jana Listen man I'll take an hour or two if he's giving it away

[@RameenFallschirmjager]

As a software developer I benefit and learn a lot from this great man.

[@youwaisef]

There's always that cougher..

[@truthobservatory6767]

There is a saying I like, ‘humans are eagles raised to believe they were chickens’

[@okoyoso]

There are reasons why proofs are written in English (or another natural language) as opposed to formal logic. Certain connotations are ignored in math (eg. iff), which I presume is what he was arguing, but others are useful if not important because they communicate some kind of viewpoint on, for instance, the importance of the exact subject matter or lack thereof or maybe some kind of intuition. I assume here that by 'technical', he means formal (ie. rigorous).

[@Adamml321]

8:20 There's actually plenty of mathematics to be done about biology!

[@duxnihilo]

nope

[@okoyoso]

@@duxnihilo Many graduate programs now have classes on biomathematics. It's a growing area, and there is plenty of mathematics to be done, not to mention that its development is encouraged by DARPA in their list of 23 problems.

[@duxnihilo]

@Language and Programming Channel That's a number.

[@8beef4u]

yes but it's not mathematics like in quantum mechanics. It's describes behavior but isn't purported to be truth like in qm or gr, at least in their respective domains

[@lkd982]

"... and the answer is:". Thanks again Chomsky

[@lve5571]

Mr. Noam breaking the norms as normal.

[@norbis3939]

Of course all of our notions of the world are abstract, but notions become more concrete the more closely they refer directly to reality. If you're interacting with a stone, the reality of the stone is concrete. Then your concept of the stone is referentiallly concrete, in that it is referring to a thing that is concrete. Although the concept is of course in some sense an abstraction, its nature of referring to a concrete thing allows us to categorize the concept of the "stone" as concrete.

[@FRAMEINTOFOCUS]

To simplify what he's saying and -- correct me if i am wrong: the world had has no meaning but only a symbolic meaning in to which we identify the world. And chickens are not like people.

[@mikethebreeze]

I think because through physics we know physical reality doesn't exist it's an abstract concept

[@mikethebreeze]

So hence all scientific experiments are abstract eg no 2 flies are identical so we pretend they are to gain a control. But Mike no genius. Basically mathematics can never be used as a language because it's not complex enough

[@Tesla_Death_Ray]

+Bernie Bro He's saying it doesn't make sense to talk about physical and non-physical because we don't have a coherent definition of physical.

[@FRAMEINTOFOCUS]

oooooooooooooooooooh like plato and the cave!!!!!!!!!! and descartes! and like the early idealist! Ok Im done. Thanks.

[@Tesla_Death_Ray]

Bernie Bro Weirdo

[@Young.Supernovas]

I revere Chomsky greatly, but a few of the things he says here are wrong. For instance, he says you "disguard with language altogether," when doing mathematics, which is true in a sense, but also not true in another sense. Advanced mathematics involves far more words and complete sentences than high school calculus, because it's proof-based, and you need to explain to the reader what your line of reasoning is. You can't just write symbols when proving a theorem -- you need to explain what they mean. He is correct, however, to make the distinction between human language and mathematics, and that formal logical truths are, "supposed to be understood as something else entirely." What he said that was really kind of ridiculous was that, to mathematicians, "there's really only a few numbers -- 1, 2, maybe 3, and infinity." That's hilariously absurd. There's not only infinitely many numbers, but infinitely many *types* of numbers -- rational, irrational, real, imaginary, finite, transfinite and infinitesimal. All of which mathematicians use regularly. I understand his point -- mathematicians tend to idealize, more so than any scientist, even physicists. Physicists are to engineers what mathematicians are to physicists, in that way. There's the joke, "consider a spherical cow. But he said a lot of silly shit on his way to making that point. 😂

[@GCBrin]

@@seansanyal1895 Chomsky's quite aware of mathematical biology, particularly its roots in Turing. He's not saying mathematics is a waste of time or something, he's saying that it's not the same as natural language. It isn't an infinite array of hierarchically structured expressions (definition of natural, as opposed to formal language). A lot of his background is in mathematics. EDIT; the joke about there only being a few numbers I think is about proofs by induction. And it is a joke, not an argument made in earnest.

[@BuGGyBoBerl]

@@seansanyal1895 i thin you misunderstand his point regarding math. he makes a distinction between applied math and theroretical "real" math and points out that "real" math stops when it gets complicated. look at applied math, ie the case where math interacts with reality. numerical/statistical math etc. try solving these problems analytically. math focuses on somewhat simple ideas and doesnt focus on very complex/complicated cases. other sciences use these findings to apply the math.

[@shwetanktewari7762]

Mathematicians do not use numerals much - may be 1, 2 and infinity. All the work they do is in abstract symbols. (Let x be a Natural Number, etc )

[@gurjotsingh8934]

Why isn't there physical?

[@rogercarl3969]

I disagree that one studies abtracta in order to get to reality. It can get to the physical world but the abstract realm is a world unto itself.

[@Lavl-dq2tk]

we can't talk about difference between physical and mental because we have no notion of the physical; mathematics has some, but don't share that many properties with language

[@stoyanfurdzhev]

Have another try.

[@قتقبتقتقيت]

the mathematics is in every domain's of sceinces of course with this language's ho reserve and protect of course all the sceince in different domains we have action and reactoin between the languageand sceince

[@creeperkinght1144]

It is, but consider how mathematics is applied every field of science, and to what degree. You have to take different amount of levels of empirical compromise or restriction depending on what field your integrating with. Say for example, genetics and physics. The nature of how the fundamental and elementary concepts of mathematics can have very much different amounts of abstract impulses to us in both groups and level of brevity of what should be consider of be accepted and what we can't based our restrictions of our minds. Like the process of using mathematics to study allelic dynamics across periods of time in evolution have different implications compared to say defining and keeping consistent track of redshift observations in astrophysics. The point is to consider how humans should consider each abstract group of ideas, in this case the fields of science, and how they interact with other, and how relevant the abstract and approaches to increasing or decreasing said ideas while having to keep the most rationale consistency as possible for the most efficient results. This, like Chomsky said, is why we have experiments. It's to define the abstract outlines of our observation of reality and accept the levels of accuracy and acceptance that certain concepts fit better or worse in certain scenarios, regardless of the end results, detrimental or beneficial, as nature cannot be restricted, as it is everywhere and everything. One that thinks that they can restrict and contain nature in a controlled environment is no different than building a dam out of paper for an ocean.

[@MT-nt7qc]

Love Chomsky but disagree about his comments on Mathematics being given up "when it gets complicated". Mathematics often predates theorems in physics. Love ya anyway though

[@BuGGyBoBerl]

well you apply math then. ofc you need math for all kinds of things and ofc it gets complicated take a look at applied math and "real math". real math quickly stops when it gets too complicated as analytical solutions dont really turn up while applied math like numerical math or statistics does its work. imagine solving these (usually solved numerical etc) analytical. crazy. i think his point wasnt that math cant be complicated etc.

[@briancamus8131]

There are many unsolved hypotheses and problems in mathematics that can't be solved yet because not enough knowledge/literature (that would assist mathematicians with finding an answer) has been established within the relevant specialized subfields. And when mathematicians hit that wall, they quit and hope to return when more mathematical tools are available.

[@michaeldebellis4202]

I think he was kind of kidding. His point was that in terms of complexity mathematics is to some extent "simpler" than a science like biology or psychology where you have so many factors that make research difficult. Ethical issues, separating genetic from evolutionary causes, etc. In that sense there is a beautiful simplicity and purity to mathematics. I think it's a shame that the way it is often taught emphasizes number crunching so much and doesn't communicate the elegance of the theories. I always thought I hated math but when I had some time and really studied it, I found I loved it. But certainly plenty of mathematicians didn't give up when it gets complicated. A good example is Turing who was a big influence on Chomsky's work. Turing approached a problem that mathematicians had been working on for a long time with no progress called the Entscheidungsproblem. Everyone expected that there would eventually be an algorithm devised that solved the problem but Turing proved that on the contrary no such algorithm was possible (and he did it when he was an insanely young age like 21 or so). And in the process he also defined the mathematical model of the Turing machine which later was the theoretical foundation for all programmable digital computers from then to now.

[@calibratingform]

​@@briancamus8131 Exactly. Mathematicians don't quit when an important problem becomes "complicated"; they quit when the problem becomes hopelessly impossible to solve with the current techniques available. Some of these problems get solved decades (or even hundreds of years) later after human understanding has evolved. Others have been more-or-less proven to be genuinely impossible to solve, so of course there's no point in working further on such things.

[@calibratingform]

​@@BuGGyBoBerl I don't disagree with you, but I'm curious as to what problems you're referring to. Are you referring to numerical versus explicit closed-form (what you call "analytic") solutions of differential equations? In many cases, it's not really that finding explicit solutions is "too complicated"; it's that it's completely hopeless. For example, there are simple differential equations which can be proven to have infinitely many solutions, yet (at the same time) not a single solution is expressible as an explicit formula with elementary functions. It's not that such an equation is difficult to solve analytically; it's provably impossible. Pure mathematicians do, in fact, still study many of the differential equations that arise in engineering, physics, economics, etc., but they're typically concerned with whether solutions exist (abstractly) and if so, how many are there and how smooth are they. These are highly complicated problems, but the point is that (a) they're occasionally solvable with current techniques, and (b) despite their complexity, their solutions (i.e., proofs) are often of little use to engineers, who are content with numerical approximations.

[@lucasrandel8589]

wait did he just ignore the hard problem of consciousness? Or am I misunderstanding wich part of Whitehead he's talking about?

[@IDidactI]

He says the "hard problem" doesn't really exist because it presupposes a mind-body distinction which he maintains is basically illusory, because there's no notion of "physical", not since Newton.

[@lucasrandel8589]

@@IDidactI it doesn't presuppose anything. There's something that it's like to be my mind and that's not the same as the 'mystical' force of gravity

[@IDidactI]

@@lucasrandel8589 It quite literally presupposes a mental-physical distinction. But to posit that distinction your helping yourself to a notion of physical. The problem is, there is no notion of physical. If you're just stipulating - the physical is by definition whatever isn't mental - then the "hard problem" is just a direct consequence of your stipulation.

[@lucasrandel8589]

@@IDidactI but that's just semantics. You can say 'anger' and whatever organization of matter and energy in the brain that occur parallel to that anger are just 'different aspects of the world'. They are still in totally different conceptual domains.

[@IDidactI]

It is in a sense a semantic point, but it’s an important one, because the whole notion that mind/brain dichotomy is a special, unique “hard problem” is based on a semantic mistake. I happen to think when you clear away the semantic issue, it’s still an interesting problem; it’s just that it’s the same kind of problem that action at a distance represented to mechanical philosophy. I got started into philosophy via the “hard problem” as it happens. David Charmers’ book was formative reading for me when I was 16 or so and I took it very seriously. Despite taking Chomsky’s point on it now, I’ve never sided with those materialists who seem to want to deny the data of subjective experience. So I do think there’s a problem for how to think about “quaila” or what have you, it’s just a matter of de-escalating the rhetoric as far as I’m concerned. The fact is, we don’t have a unified intelligible model of the traditional nominally “physical” domain, never mind the mental, and the problem of consciousness, is in my view not ontologically distinct from the other sorts of explanatory difficulties that arise in science. Posing the question as about mental-physical reduction is sort of like posing the question of gravity-physical reduction, or electromagnetism-physical reduction.

[@stevenhines5550]

What are we going to do when he's gone?

[@Footnotes2Plato]

Wasn't the point of Whitehead's later foray into metaphysics to come up with a new definition of "physical" in light of quantum and relativity theories that allowed us to make sense, in ORGANIC terms, of the relation between what we used to call "mental" and "physical"?

[@Jedi_Mind_]

Matt !!!

[@Objectivityiskey]

His epistemology follows from floating abstractions devoid of concreter examples. This is how I know he's full of tihs.

[@jackevans9574]

Can you use less pompous words next time?

[@Objectivityiskey]

@@jackevans9574 What about my words make you think they are pompous?

[@jackevans9574]

@@Objectivityiskey I dont know sorry

[@stevenhines5550]

It's all very spiritual. I always knew it was. WHY o WHY did I have to fuck my life up so badly? There was a time, maybe when I was six or seven, that I actually had the potential to develop along profound philosophical lines and, maybe, even reach a point where I could have qualified to hold a conversation with someone such an exquisite and profound intellect. Then some awful shit happened and I started bailing out and taking shortcuts in all my endeavors. No victimization here, just a preface to this: when I started getting my shit together I started attending community college and banging out all the requisite liberal arts courses I had this one hateful psych professor who insisted that what I have come to understand as materialism and behaviorism and logical positivism were valid and that free will and human rights we're a pleasant story we liked to tell ourselves and that all things were determined by coercion. It was, in effect, a retraumatization. I basically intuitively grasped, even then - that something had changed since the 17th century and that human will and human rights and dignity were inextricably entwined with non-duality and a basic inseparability from divine mystery. I wish I had access to Chomsky then for solace in the face of mean and ignorant psychology professors with a grudge against humanity.

[@michaeldebellis4202]

Chomsky is probably one of the most influential people in terms of both my approach to science and how I try to live my life. I flew to Tucson and got an AirB&B a few years ago just to attend a class he gave at Univ. of AZ on Linguistics. It was amazing. I used to exchange emails with him every once in a while. But I try not to anymore, he's really old (I think 91) but still keeps such a busy schedule. But IMO it is never too late to keep on learning. I had to retire early due to Multiple Sclerosis and for a while I thought it was the end of the world because so much of my life revolved around my work in computer science. But then I started auditing classes at Berkeley and it was amazing. They are incredibly open to just letting people come and participate in classes without paying. You don't get a grade but if you want to learn and interact with smart people it is amazing. I just get kind of high off of being on the campus of a good university, especially a place like Berkeley, there are so many brilliant people and the students treat someone older than their parents just like any other student. They even provide me with access to the online system for finding papers, posting discussions, etc. And I think most universities have a similar policy.

[@naturphilosophie1]

I'm not sure if Whitehead draws a distinction between mental and physical in Process and Reality. I read his concept of prehension, lure for feeling, and his philosophy of time as an attempt to get around what chomsky correctly understands as a false problem. I do think Whitehead has issues with going beyond Hegelian dialectic. Being/becoming, infinite/finite etc.. these categories can be seen as opposites, but this is really a false polarity. Whitehead and Dewey were influenced by Hegelian ideas that were put into question by many, nietzsche to name one.

[@naturphilosophie1]

Yes, I would agree it does refute the idea of opposing values or categories on a conceptual and ontological level. Some clarity on this issue might be gained by looking closely at the difference between Whitehead and Hegel with regard to negation. Whitehead certainly did not adhere to the view that there is both the physical and spiritual, or the physical and mental as two opposing categories, as Chomsky thinks. Whitehead doesn't think categories can help us at this stage, rather there is some irreducible mystery in the world.

[@thisismyname9569]

Is a brick an essential object according to Whitehead?

[@aLby_doira]

chickens fly like eagles, and humans don't fly at all...silly martians...

[@JuanRodriguez-tr6st]

3:23

[@feelwang]

Love when he uses words like junk or useless mass. Guess because it is more junky and more useless when he says it

[@NothingMaster]

I’ve always loved Chomsky’s non-political talks/lectures. He is exceptionally brilliant when he stays away from temporal political discourse.

[@edwardjones2202]

Actually you've got it the wrong way round. As a Philosopher he is first class but not peerless - Kripke, Quine, Dummett, Putnam and more have all at least matched him. As a political analyst, nobody in the 20th or 21st century can match the breadth of his knowledge, the unifying penetration of his vision and the relentless energy of his activism.

[@abtinshahidi4390]

🧠🚀🧠❤️🐐🚀🧠

[@joshbone9600]

"Nobody does mathematics of biology for example..." I don't think this is true

[@coeruleum7563]

Yes, you can get entire books on this topic like Mathematical Biology by Chasnov. I heard it's a widely-demanded field as well. I respect many of Chomsky's opinions on other things but this video probably has the highest concentration of outright wrong opinions I've heard from him.

[@jeewillikers]

I think his point is that the vast majority of biology has little to no mathematics attached, at most you have some statistical techniques that can be applied to things like populations and genetic traits, but these techniques are only fancy ways of describing what we see. Real science goes beyond inductive generalizations and seeks to discover the deeper principles underlying observed phenomena. This puts biology in contrast to more "fundamental" areas of inquiry like physics, which has a rich theoretical framework built on objects of pure mathematical abstraction; the types of mathematics underlying something like general relativity provide an explanatory basis that can rest solely on mathematical objects and structure itself, whereas things like population statistics can only be understood in relation to the high-level concepts used in everyday (normal) use of language. That's not to say there hasn't been plenty of deep principles discovered in biology, only that we still rely on non-mathematical concepts to explore these principles. Most of the actual mathematics is really in sub-biological inquiry like biochemistry or pharmokinetics, and even those provide little to nothing in the way of deep explanatory principles, at least not like in physics.

[@johnmaisonneuve9057]

It doesn’t seem to understand the argument.

[@mattconrad]

I think what Chomsky is saying here is that, long-ago, mankind somehow achieved what no other species before him could do and that is to eventually breach the mental barrier which had kept him imprisoned since the dawn. Our mental faculties are essentially what separate us from the other animals; that is, our unique awareness of the relationship between us and our environment. The mission of the sciences thus far has been to aggregate information in an effort to better understand our world, and the intellectual's sharpest tool has always been his ability for abstraction; for a physicist, that could mean creating a better model of the phenomenon of gravity as Einstein did with Newton's theory, and what physicists may improve upon in the 21st Century (as Einstein's theory literally breaks down in the event of a black hole).

[@felixlipski3956]

ok platon

[@grgarciaxiv]

I think Chomsky's reputation carries this answer wherein his logic does not. He clearly doesn't give very much thought to mathematics based on his reductionist argument for metaphor. In addition, he endorses a Kantian view of matter/reality but fails to follow through with any comparably complex insight on what kind of "thing" maths is. There's some truth to saying maths is abstract; there's no truth in saying that it's fundamentally simple-- that's manifestly untrue.

[@AnthonyKComedy]

Sounds like hate to me.

[@rysw19]

Compared to the phenomena of the world, math is extremely simple. We don’t have the capacity to hold precise representations of any significant (or even insignificant) chunk of the world in our heads. Simple doesn’t mean easy.

[@davefischer2344]

lol i love 7:50

[@PeteUtonic]

Poor understanding from Chomsky.

[@BuGGyBoBerl]

not really

[@adamguerrero5293]

I'd really like to use his "humans and chickens fly" to the transtrenders thinking "I was assigned male at birth but i feel like a female"

[@viggosimonsen]

With due respect for Mr Chomsky whom I admire a lot, he is talking nonsense here. First of all, what is this thing about there being no distinction between physical and mental categories since Newton? It is simply nonsense. And secondly, it is not true that mathematics and linguistics share no properties. They actually share a lot. They both have syntax, grammar and semantics. They both consist of operators and operands in some general sense. It is a strange statement to come from a professor of linguistics. One has to assume that he knows very little about mathematics

[@OisinNolanChannel]

He literally invented half of the mathematics used to anaylse language - the man knows what he's talking about. He acknowledged in the video that maths and language share some properties, but as he explained that doesn't make maths a language in itself. It is a bit of a definitions game, but here he's clearly talking about natural language. If maths was indeed a natural language, thousands of papers in subjects like formal semantics would be void.. unless of course you have made some discovery that these semanticists are missing out on.

[@noisepuppet]

He didn't say they share no properties. He said they share a lot of properties. So that's the opposite of what you quote him as saying. Due respect might take the form of quoting what he actually said before dismissing him as talking nonsense. He also mentioned at least one specific way in which they differ. A moment's reflection should reveal more examples to anyone who's seriously interested in the question. Considering what a person says in this way, seeing if maybe you can think of further examples, or not, might also constitute evidence of due respect. The differences between mathematics and natural languages are hardly obscure, after all, and Chomsky is hardly the first or only thinker to notice them. Having performed these minimal gestures of respect, you can of course feel free to wave his performance away as nonsense. Or you can do so before the fact, as here. I realize that the danger of considering what he actually said is that you might find that he has a point, the integration of which can be a bother, but it's not a grave concern. Most intelligent people have ways of navigating such hazards and coming out with all their previous views intact, and you do seem intelligent.

[@cloud-w2v]

I think that in a formal sense, there ought to be a distinction between the notion of mathematics and the *language* of mathematics (i.e., mathematics ≠ language of mathematics). Indeed, physicists and engineers often mistakenly prescribe mathematics as simply a descriptive language. Mathematicians, on the other hand, tend to think of mathematics as separate from the language of mathematics. That is to say, mathematics is the study of ALL (abstract) systems -- which generalizes, for instance, music theory (study of the systems of music), linguistics (study of the system of languages both symbolically and sonically), physics (study of physical systems), and more; the language of mathematics allows us to "codify" mathematical ideas into a concrete form (enabling the stimulation of our visual and auditory senses) -- in a way that allows us to actually think about and make sense of mathematics.

[@MassDefibrillator]

"First of all, what is this thing about there being no distinction between physical and mental categories since Newton? It is simply nonsense." He gives a 2 hour talk completely dedicated to this idea called "the machine, the ghost and the limits of understanding". The premise is pretty straight forward: natural science has had to internalise the mathematical theory and accept that these theories are not meant to be models of the reality in order to progress. The last attempt by science to try to look for physical reality was with the search for the ether. Now, we just accept that general relativity describes a "medium" that isn't supposed to really be there.

[@viggosimonsen]

@@MassDefibrillator GR does not describe a medium - it describes a space topology, based on mass distribution. And its predecessor SR was exactly the logical conclusion of the failed attempt to detect the Ether (and the relative speed of light)

[@djtan3313]

That's why, in history, cultures other than whites never paid too much heed to mathematics...

[@ocek2744]

You realize Algebra is an arabic term, and you're ignoring the vast number of Chinese mathematicians.

[@jake_runs_the_world]

Lmao what

[@edwardjones2202]

Terence Tao has paid a bit of attention to maths