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“When we do mathematics, we touch immortality.”

108 points by nature24 10y ago

tluyben2 10y ago
Did not read the article, but that was my feeling when I first touched math and (almost at the same time) wrote my first code. Using Coq, Idris, Haskell, Purescript, Mercury and k give me that sense still. Anything that takes a long and hard time to think about.
ThomPete 10y ago
I think a better way to describe this is that you touch reality. It's important to remember that for all the books written about physics in layman terms, especially quantum physics, there comes a time when words don't cut it and only math allow you to continue the conversation.
FabHK 10y ago
There is the ontological position that mathematical truths are "out there", independent of us, and we are merely "discovering" them. As such, they're eternal, and you could argue then that you "touch immortality". But apart from that, I find this sort of talk unhelpful. It's a bit like Schopenhauer who thought that instrumental classical music gave access to the innermost truth of the universe (I'm paraphrasing from memory here) - what hogwash. Lastly, the headline has not much to do with the article, has it?
- JoeAltmaier 10y ago
  So, the value of PI is a human invention? That's hogwash.
  - cannonpr 10y ago
    Don't you feel it's a bit harsh to summarise the entire debate between idealism and realism as hogwash ?
    - JoeAltmaier 10y ago
      Just echoing the parent post there.
      - FabHK 10y ago
        > Don't you feel it's a bit harsh to summarise the entire debate between idealism and realism as hogwash ? Granted, a bit harsh :-) There's more to be said about it. But remember how Ford Prefect wrote volumes about earth in the Hitchhiker's Guide to the Galaxy, and then it was abridged to "Mostly harmless"? So that was (my) very abridged version of idealism.
  - ThomPete 10y ago
    Who else invented it?
    - JoeAltmaier 10y ago
      That question presupposed it was invented. Its just there. To be discovered. Its not different somewhere else; it wouldn't be different in a different universe.
      - ThomPete 10y ago
        I don't think you are aware of what you are claiming. If something is "out there" as a specific concept as you claim, then it requires a perspective to isolate it as "a thing" which means you are basically claiming there must have been a creator. If there is no creator then there is no perspective other than that of observers like us. Unless you of course claim that the classical physical universe is fundamental not the quantum physical one.
        kordless 10y ago
        I don't think you are aware of what is claiming this. ;) Perspective matters in terms of "proving" something outside of observation, by the assumed fact observation can change perspective. In other words, if all of this is a single entity, it's going to be hard to prove that because bits would exist outside perception due to the cost of it being a recursive operation. One may not know oneself without recursion.
        ThomPete 10y ago
        You are also missing the point. If something exist "out there" as a separate concept then it can only do so because it exist as a discreet entity. Yet QM shows us that the world isn't fundamentally discreet but rather non-local. We can observe because there is a discreet universe to observe within, but that does not make the observable universe the foundation of reality. And so if you want to claim that something exist out there without there being a designer or without our perspective of reality being what turn it into existence then you need to explain how it relates to the entire universe not just the classical one.
  - GavinMcG 10y ago
    This is an odd reading of the parent comment, since "apart from that" indicated that mathematical truths being built in isn't what the commenter disagreed with.
  - omalleyt 10y ago
    The concept of "circle" is a human invention, in that a perfect circle has never been observed in the universe. The value of pi follows immediately as a derivative human invention.
    - justifier 10y ago
      I would argue the 'perfect circle' is inherent in every circle, similarly to how it is inherent in your dismissal of it But if you require a more direct understanding I would say there is a perfect circle in every rotation
      - kordless 10y ago
        The possibility of a perfect circle exists in this universe, but the last digit we are aware of is definitely a posteriori. In other words, the description of a circle is prior knowledge given it allows calculating pi, but the actual values are post observational knowledge, given they must be calculated and continue to be irrational forever. (At least as far as we know.) It would take an infinite amount of power to calculate every digit in pi, given pi itself is irrational, even while describing how to calculate it is rational.
        justifier 10y ago
        You are moving someone else's goalposts I answered where circles are in our universe and you then try to change the original intent of omalleyt's question to mean a symbolic representation of pi > It would take an infinite amount of power to calculate every digit in pi Calculating pi is so simple life without nervous systems does it Now, expressing that value in our limited yet overly verbose base ten symbolic representation would indeed require infinite recursion
        kordless 10y ago
        I'm not aware of a means by which goal posts can exist in a philosophical debate around rational vs. irrational thinking. Both types of thinking are valid, but I can see how and why some tend to argue for absolute rationality at all times.
  - jknoepfler 10y ago
    The means of systematizing, expressing, reasoning about, computing with, and teaching about pi are human inventions. Does pi amount to more than the sum of its human parts? You can say "hogwash," but that's not contributing much to a question that requires a careful answer
  - lacker 10y ago
    A circle is a human invention. There are no perfect circles in the universe. Euclidean geometry is a human invention. In the real world, spacetime is curved. Real numbers are a human invention. The universe does not seem to be built of numbers with infinite precision. I would go further and say that the number "two" is a human invention. The universe could carry on just fine without any life anywhere having the concept of "two". But the case is certainly stronger for calculus and geometry being human inventions, than it is for number theory.
    - raattgift 10y ago
      > In the real world, spacetime is curved Why is curved spacetime (in the sense of an infinitely differentiable pseudo-Riemannian manifold with a Lorentzian metric) not a human invention while Euclidean geometry (a limiting case of such a manifold) is? > The universe does not seem to be built of numbers with infinite precision What's your definition of spacetime? It's not that of General Relativity, if you deny infinitesimals. I think you're stuck either with accepting curvature and infinitesimals and the involvement in pi in the relationships between a set of points at a small fixed spacelike distance from an origin, or you're stuck with denying curvature as anything other than a coarse approximation of some manifold with a non-Lorentzian taxicab-like metric. Minimum lengths (abolishing infinitesimals) have been proposed theoretically, and we can readily parameterize with a minimum length equations like the Dirac equation or the Klein-Gordon equation or like the Lagrangian of the Standard Model, and in doing so we see pretty plainly that the Lorentz transformations of Special Relativity must be modified. One concrete modification is the theory of Doubly Special Relativity whose length cutoff is the Planck length. It predicts an energy-dependent speed of light, and that is contradicted by evidence (gamma rays do not win races with infrared rays in near vacuum). Other similar deformations of Special Relativity have been advanced, and they also conflict with experiment and observation, unless the minimum length goes to zero, or other physical quantities are (counter-)parameterized pushing the observation-and-experiment conflict elsewhere. (One programme for this sort of research is the Standard Model Extension). > The universe could carry on just fine without any life anywhere having the concept of "two" The universe could carry on just fine without any life period. Indeed, it almost certainly did in our distant past. However, there is pretty conclusive evidence that there were quadratic relations among various physical quantities in the earlier universe, notably the inverse square laws for electrostatics and gravitation. It seems extreme to blame that on humans...
  - FabHK 10y ago
    No, as I meant to say with the "apart from that" - mathematical truths are clearly interpersonally verifiable and arguably "out there" to be discovered, not invented. I'm disagreeing with the overly poetic language of "touching immortality" etc. (and German idealism... but that's another topic)
- visarga 10y ago
  > Schopenhauer who thought that instrumental classical music gave access to the innermost truth of the universe So I get you haven't appreciated Mahler and Bruckner. I can understand your position if you haven't. /s
- snarfy 10y ago
  It's true of any idea, not just mathematics. Ideas are discoveries, not inventions. This philosophy goes all the way back to Plato. https://en.wikipedia.org/wiki/Theory_of_Forms https://en.wikipedia.org/wiki/Theory_of_Forms
  - eastWestMath 10y ago
    Well yes, Platonism is true if you presuppose that Platonism is true.
- coldtea 10y ago
  >But apart from that, I find this sort of talk unhelpful. It's a bit like Schopenhauer who thought that instrumental classical music gave access to the innermost truth of the universe (I'm paraphrasing from memory here) - what hogwash. How do you know it's hogwash?
  - kurthr 10y ago
    Well, I'd say that Schopenhauer's statement requires a higher level of verification than someone calling him out for BS. If you're asking for a proof, I'd say that the fact that multiple equally sophisticated musical schema are present across the world in different cultures that he didn't acknowledge (and only _instrumental_ music??). The point that I think you inadvertently bring up is that an appreciation of mathematics is so far only human (and we tend to focus on the ones that are useful to us right now)... perhaps when we meet alien life we'll actually know how universally interesting our little parts truly are. In any case, they are still mostly consistent sets of postulates, theorems, and axioms.
  - FabHK 10y ago
    There is this story related by George Orwell (when he was in Burma) of an opium addict (Indian army officer?) that was convinced that the had discovered the innermost truth of the universe while smoking opium, this profound beautiful infinite insight, but could never remember it when he was sober again. Finally one day he managed to write it down. It said: "The banana is great, but the skin is greater." [1] Basically I believe that instrumental music conveys no deeper truth (for starters, it hardly conveys anything without significant training on behalf of the listeners. Program music like Berlioz' Symphonie fantastique is called program music after all because Berlioz himself handed out a program, notes, explaining (in words) what was going on in the symphony (the artiste falls in love unhappily and poisons himself with opium and has nightmares). Now, you can immerse yourself in profound romantic feelings when listening to it, or find delight in the unexpected deviation from the rounded binary form in a minuet & trio, or "suffer" from a deceptive cadence, but that's because it's previously been communicated and learned, with words and examples. Plus it's not exactly "secrets of the universe" stuff.) Wagner's Gesamtkunstwerk operas also include words, and to understand them, it helps to get an explanation and interpretation (with words). Of course some people claim to have had deep insights under the influence of psychedelics, and some people claim to have had deep insights from classical music. What I'm basically saying is that the claim is not enough, you must also be able to communicate this deep insight. And basically I claim the insight must be communicated in words. And then the words carry the insight. Not drugs or music. Visual arts or music (or drugs?) can support that communication, but they can't replace it. Of course, you could just say, well, there is all this insight in the music, and Schopenhauer got it, and you get it, and I don't, and you cannot communicate it in words, you can just communicate it in music, and so it's there, but I don't get it. That's a bit like what postmodernists like to do when someone challenges the scholarship of their papers - "you just don't get it". And that I call hogwash, I suppose, for now. It might be instructive to listen to an hour of Cantonese opera, and see what insights are gained. [1] https://www.theguardian.com/books/2004/may/06/classics.georgeorwell https://www.theguardian.com/books/2004/may/06/classics.georg...
danidiaz 10y ago
“Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold.” —Hermann Weyl
zentropia 10y ago
For me when I see some physics equations is a mystic experience.
vinchuco 10y ago
Immortality, meanwhile, rolls its eyes. Still, it's interesting to see what motivates people to learn something (or to stay away from it). Better put: >"When you take a course in Euclidean geometry is not the teacher putting a... learning program into you? ...You enter the course and cannot do problems; the teacher puts into you a program and at the end of the course you can solve such problems. ...Are you sure you are not merely "programmed" in life by what by chance events happens to you?" - Hamming I'm curious as to how different mathematics would be for two otherwise identical civilizations but with distinct average lifespans. In alternate Earths where lifespan is 40 or 200 years, what's the state of mathematics in 2017?
- everybodyknows 10y ago
  As Hamming describes, it was very much for me: 8th grade plane geometry feels now like an intellectual awakening. The satisfaction of proving "pons asinorum", by Euclid's method, followed by vexation at learning I had overlooked the much simpler reflexive approach.
lngnmn 10y ago
Which, along with infinity, does not exist. The ability to produce an infinite series of numbers (by adding another one) does not constitute a proof of existence of anything infinite outside one's mind. Good philosophers, like Leibniz and the Indian tradition, which includes early Buddhists, have postulated this, but popular memes are much stronger. The ability to notice some inherent patterns of natural phenomena, such as the ratio of a circle's circumference to its diameter, does yield this ratio to be immortal, or any other inferred constant. Math does not exist outside people's minds (contrary to the popular discourse from the Zen And Art Of Motorcycle Maintenance). Only a few of what we call conservative forces and different forms of what we call energy (or matter if you like) which are different aspects of the same That, to which human categories are inapplicable.
- keiferski 10y ago
  Once, just once, I would love to open the comments of a philosophy-related HN article and not see a middlebrow dismissal [1] as the top comment. [1] https://news.ycombinator.com/item?id=4693920 https://news.ycombinator.com/item?id=4693920
  - Ar-Curunir 10y ago
    It's a slight variant of the Dunning-Kruger effect; people have just a little knowledge of some field, and can therefore dismiss entire decade's worth of thought on the matter.
    - lngnmn 10y ago
      What is wrong with dismissing entire decade's worth of superstitions, astrology, alchemy, metaphysics and theology?
  - lngnmn 10y ago
    This has nothing to do with philosophy, which was and still is the endeavor to unveil what is - to see things as they are.
- justifier 10y ago
swayvil 10y ago
Mathematics touches immortality like fractals touch infinity and circles are endless.
hzhou321 10y ago
>> “the math that’s being taught has no relevance to my life" I think our math education do fail in that way. Math essentially is a logic system where you set up premises and derive and make sure everything is consistent. That can be applied to real life such as accounting and physics, or it can be applied to an artificial game -- number theory is such a case. Our education emphasize on the latter part, and it is quite irrelevant to real life, and it is hard. I am in mid-life now and on reflection, fractions, for example, had zero use for my life, and I am in the career of scientific computing. What we need is a concept level of understanding of mathematics -- realizing that the key idea of mathematics is basically consistency. Most importantly, the math required in the real life is not hard -- it is necessarily intuitive. What the education we receive is the technical gaming part of mathematics, e.g. how to actually find the roots of quadratic equation. I don't really remember the formula now, but I now have an intuitive understanding of the quadratic curves and the meaning of roots. And the same goes for quintic equations. It is not hard at all. I roughly sketch out the curve and I immediately have a rough idea of where the roots are. And at work, it is simply an exercise in programming. It is hard following the way in our education, though. The purpose of education is to show them that knowledge exists, but not the knowledge itself. Knowledge itself is misleading. It is more important to recognize what you don't know than to remember what you know. To clarify, I personally do not hate math. And I respect the discipline of mathematics. However, doing math (the way our education system assumes) is just like doing music or art, or playing star craft, it is not for everyone. PS: on further reflection, not only useless, the concept of rational number has been quite damaging in our understanding of the real world.
- justifier 10y ago
  I was thinking about education last night and here is the idea I am developing.. I encourage ongoing criticism Students study varied subject matter but only one subjects' grade 'matters' and can be chosen by the student Personally, I think our maths education suffers from a lack of freedom.. I do think it can be for anyone but only because I believe anyone can bring to it whatever they'd like, whereas education tells you what areas need to be studied and how is competition the foil of expression?
  - 10y ago
jayeshsalvi 10y ago
Despite Gödel's incompleteness theorems?
Bluestrike2 10y ago
God, some of those quotes about how some early math teaching techniques hurt people's appreciation and understanding of the subject are depressing. I still remember the anxiety and even embarrassment caused by timed drills in elementary school that seemed to harshly pit student against student. It took me until college to realize that I was just coasting through math courses and not really investing myself in the subject. Perhaps in an effort to avoid those long-ago memories? Everything started to click in college. Interestingly enough, it was my enjoyment of programming and study of philosophy that really helped to push me. That, and sitting in a calculus class and realizing that I had to either dive in or be royally screwed. It's a shame that such stories are so common.
- captain_clam 10y ago
  Dear god, the timed drills. I distinctly recall the tremendous anxiety evoked by the ultra-competitive nature of those drills in elementary school, and especially the subsequent feelings of failure when comparing my performance to that of my peers. It must have been that bitter flavor of failure that first inured me against mathematics...it didn't help that the rest of my K-12 education never even attempted to demonstrate the enormous beauty of maths. In fact, until I discovered calculus on my own terms between high school and college, I understood mathematics to be nothing more than the practice of applying rote formulas to arbitrary equations. There was no rhyme or reason to the quadratic equation...it was just one of many "rules" pulled from the mathematical "rulebook," and math was simply the practice of recognizing when this arbitrary rule applied, and then applying it. Therefore, for most of my life, math was not seen as a creative or exploratory discipline, and in fact the very opposite: One's ability in math was completely contingent on their memorization of rules and simply following them. It was purely robotic, the domain of tightly-wound, uninspired automatons. It was for squares, not free-spirited creative souls like myself! Though I am disappointed to think of the heights and wonders I could have visited by now, had I been given a proper introduction at a younger age, I am no less excited by the wonders ahead of me, and the many years I have left to explore them. :)
imh 10y ago
Can we get a title change? About half of the people seem to be commenting on the HN title instead of the article content.
ivan_ah 10y ago
It's surprising to see so few math haters in the hexagon (the thin outer shell). I'm guessing there is a self-reporting bias, since if you hate math you wouldn't really want to fill in this survey... It's also interesting to note that many of the haters direct their hate towards rote learning tasks like arithmetic calculations and memorizing multiplication tables, which makes me think that they don't really hate math but rather the way it is taught. I'd hate math too if I saw it as following procedures blindly! Perhaps with better computer math tools[1], future students won't be forced to learn "manual labour" math tasks, and instead focus on "white collar" tasks like modelling and abstraction. [1] SymPy is the best computer algebra system ever: https://minireference.com/static/tutorials/sympy_tutorial.pdf https://minireference.com/static/tutorials/sympy_tutorial.pd...

108 points by nature24 10y ago

Did not read the article, but that was my feeling when I first touched math and (almost at the same time) wrote my first code. Using Coq, Idris, Haskell, Purescript, Mercury and k give me that sense still. Anything that takes a long and hard time to think about.

ThomPete 10y ago

I think a better way to describe this is that you touch reality. It's important to remember that for all the books written about physics in layman terms, especially quantum physics, there comes a time when words don't cut it and only math allow you to continue the conversation.

FabHK 10y ago

There is the ontological position that mathematical truths are "out there", independent of us, and we are merely "discovering" them. As such, they're eternal, and you could argue then that you "touch immortality". But apart from that, I find this sort of talk unhelpful. It's a bit like Schopenhauer who thought that instrumental classical music gave access to the innermost truth of the universe (I'm paraphrasing from memory here) - what hogwash. Lastly, the headline has not much to do with the article, has it?

JoeAltmaier 10y ago
So, the value of PI is a human invention? That's hogwash.
- cannonpr 10y ago
  Don't you feel it's a bit harsh to summarise the entire debate between idealism and realism as hogwash ?
  - JoeAltmaier 10y ago
    Just echoing the parent post there.
    - FabHK 10y ago
      > Don't you feel it's a bit harsh to summarise the entire debate between idealism and realism as hogwash ? Granted, a bit harsh :-) There's more to be said about it. But remember how Ford Prefect wrote volumes about earth in the Hitchhiker's Guide to the Galaxy, and then it was abridged to "Mostly harmless"? So that was (my) very abridged version of idealism.
- ThomPete 10y ago
  Who else invented it?
  - JoeAltmaier 10y ago
    That question presupposed it was invented. Its just there. To be discovered. Its not different somewhere else; it wouldn't be different in a different universe.
    - ThomPete 10y ago
      I don't think you are aware of what you are claiming. If something is "out there" as a specific concept as you claim, then it requires a perspective to isolate it as "a thing" which means you are basically claiming there must have been a creator. If there is no creator then there is no perspective other than that of observers like us. Unless you of course claim that the classical physical universe is fundamental not the quantum physical one.
      - kordless 10y ago
        I don't think you are aware of what is claiming this. ;) Perspective matters in terms of "proving" something outside of observation, by the assumed fact observation can change perspective. In other words, if all of this is a single entity, it's going to be hard to prove that because bits would exist outside perception due to the cost of it being a recursive operation. One may not know oneself without recursion.
        ThomPete 10y ago
        You are also missing the point. If something exist "out there" as a separate concept then it can only do so because it exist as a discreet entity. Yet QM shows us that the world isn't fundamentally discreet but rather non-local. We can observe because there is a discreet universe to observe within, but that does not make the observable universe the foundation of reality. And so if you want to claim that something exist out there without there being a designer or without our perspective of reality being what turn it into existence then you need to explain how it relates to the entire universe not just the classical one.
- GavinMcG 10y ago
  This is an odd reading of the parent comment, since "apart from that" indicated that mathematical truths being built in isn't what the commenter disagreed with.
- omalleyt 10y ago
  The concept of "circle" is a human invention, in that a perfect circle has never been observed in the universe. The value of pi follows immediately as a derivative human invention.
  - justifier 10y ago
    I would argue the 'perfect circle' is inherent in every circle, similarly to how it is inherent in your dismissal of it But if you require a more direct understanding I would say there is a perfect circle in every rotation
    - kordless 10y ago
      The possibility of a perfect circle exists in this universe, but the last digit we are aware of is definitely a posteriori. In other words, the description of a circle is prior knowledge given it allows calculating pi, but the actual values are post observational knowledge, given they must be calculated and continue to be irrational forever. (At least as far as we know.) It would take an infinite amount of power to calculate every digit in pi, given pi itself is irrational, even while describing how to calculate it is rational.
      - justifier 10y ago
        You are moving someone else's goalposts I answered where circles are in our universe and you then try to change the original intent of omalleyt's question to mean a symbolic representation of pi > It would take an infinite amount of power to calculate every digit in pi Calculating pi is so simple life without nervous systems does it Now, expressing that value in our limited yet overly verbose base ten symbolic representation would indeed require infinite recursion
        kordless 10y ago
        I'm not aware of a means by which goal posts can exist in a philosophical debate around rational vs. irrational thinking. Both types of thinking are valid, but I can see how and why some tend to argue for absolute rationality at all times.
- jknoepfler 10y ago
  The means of systematizing, expressing, reasoning about, computing with, and teaching about pi are human inventions. Does pi amount to more than the sum of its human parts? You can say "hogwash," but that's not contributing much to a question that requires a careful answer
- lacker 10y ago
  A circle is a human invention. There are no perfect circles in the universe. Euclidean geometry is a human invention. In the real world, spacetime is curved. Real numbers are a human invention. The universe does not seem to be built of numbers with infinite precision. I would go further and say that the number "two" is a human invention. The universe could carry on just fine without any life anywhere having the concept of "two". But the case is certainly stronger for calculus and geometry being human inventions, than it is for number theory.
  - raattgift 10y ago
    > In the real world, spacetime is curved Why is curved spacetime (in the sense of an infinitely differentiable pseudo-Riemannian manifold with a Lorentzian metric) not a human invention while Euclidean geometry (a limiting case of such a manifold) is? > The universe does not seem to be built of numbers with infinite precision What's your definition of spacetime? It's not that of General Relativity, if you deny infinitesimals. I think you're stuck either with accepting curvature and infinitesimals and the involvement in pi in the relationships between a set of points at a small fixed spacelike distance from an origin, or you're stuck with denying curvature as anything other than a coarse approximation of some manifold with a non-Lorentzian taxicab-like metric. Minimum lengths (abolishing infinitesimals) have been proposed theoretically, and we can readily parameterize with a minimum length equations like the Dirac equation or the Klein-Gordon equation or like the Lagrangian of the Standard Model, and in doing so we see pretty plainly that the Lorentz transformations of Special Relativity must be modified. One concrete modification is the theory of Doubly Special Relativity whose length cutoff is the Planck length. It predicts an energy-dependent speed of light, and that is contradicted by evidence (gamma rays do not win races with infrared rays in near vacuum). Other similar deformations of Special Relativity have been advanced, and they also conflict with experiment and observation, unless the minimum length goes to zero, or other physical quantities are (counter-)parameterized pushing the observation-and-experiment conflict elsewhere. (One programme for this sort of research is the Standard Model Extension). > The universe could carry on just fine without any life anywhere having the concept of "two" The universe could carry on just fine without any life period. Indeed, it almost certainly did in our distant past. However, there is pretty conclusive evidence that there were quadratic relations among various physical quantities in the earlier universe, notably the inverse square laws for electrostatics and gravitation. It seems extreme to blame that on humans...
- FabHK 10y ago
  No, as I meant to say with the "apart from that" - mathematical truths are clearly interpersonally verifiable and arguably "out there" to be discovered, not invented. I'm disagreeing with the overly poetic language of "touching immortality" etc. (and German idealism... but that's another topic)
visarga 10y ago
> Schopenhauer who thought that instrumental classical music gave access to the innermost truth of the universe So I get you haven't appreciated Mahler and Bruckner. I can understand your position if you haven't. /s
snarfy 10y ago
It's true of any idea, not just mathematics. Ideas are discoveries, not inventions. This philosophy goes all the way back to Plato. https://en.wikipedia.org/wiki/Theory_of_Forms https://en.wikipedia.org/wiki/Theory_of_Forms
- eastWestMath 10y ago
  Well yes, Platonism is true if you presuppose that Platonism is true.
coldtea 10y ago
>But apart from that, I find this sort of talk unhelpful. It's a bit like Schopenhauer who thought that instrumental classical music gave access to the innermost truth of the universe (I'm paraphrasing from memory here) - what hogwash. How do you know it's hogwash?
- kurthr 10y ago
  Well, I'd say that Schopenhauer's statement requires a higher level of verification than someone calling him out for BS. If you're asking for a proof, I'd say that the fact that multiple equally sophisticated musical schema are present across the world in different cultures that he didn't acknowledge (and only _instrumental_ music??). The point that I think you inadvertently bring up is that an appreciation of mathematics is so far only human (and we tend to focus on the ones that are useful to us right now)... perhaps when we meet alien life we'll actually know how universally interesting our little parts truly are. In any case, they are still mostly consistent sets of postulates, theorems, and axioms.
- FabHK 10y ago
  There is this story related by George Orwell (when he was in Burma) of an opium addict (Indian army officer?) that was convinced that the had discovered the innermost truth of the universe while smoking opium, this profound beautiful infinite insight, but could never remember it when he was sober again. Finally one day he managed to write it down. It said: "The banana is great, but the skin is greater." [1] Basically I believe that instrumental music conveys no deeper truth (for starters, it hardly conveys anything without significant training on behalf of the listeners. Program music like Berlioz' Symphonie fantastique is called program music after all because Berlioz himself handed out a program, notes, explaining (in words) what was going on in the symphony (the artiste falls in love unhappily and poisons himself with opium and has nightmares). Now, you can immerse yourself in profound romantic feelings when listening to it, or find delight in the unexpected deviation from the rounded binary form in a minuet & trio, or "suffer" from a deceptive cadence, but that's because it's previously been communicated and learned, with words and examples. Plus it's not exactly "secrets of the universe" stuff.) Wagner's Gesamtkunstwerk operas also include words, and to understand them, it helps to get an explanation and interpretation (with words). Of course some people claim to have had deep insights under the influence of psychedelics, and some people claim to have had deep insights from classical music. What I'm basically saying is that the claim is not enough, you must also be able to communicate this deep insight. And basically I claim the insight must be communicated in words. And then the words carry the insight. Not drugs or music. Visual arts or music (or drugs?) can support that communication, but they can't replace it. Of course, you could just say, well, there is all this insight in the music, and Schopenhauer got it, and you get it, and I don't, and you cannot communicate it in words, you can just communicate it in music, and so it's there, but I don't get it. That's a bit like what postmodernists like to do when someone challenges the scholarship of their papers - "you just don't get it". And that I call hogwash, I suppose, for now. It might be instructive to listen to an hour of Cantonese opera, and see what insights are gained. [1] https://www.theguardian.com/books/2004/may/06/classics.georgeorwell https://www.theguardian.com/books/2004/may/06/classics.georg...

danidiaz 10y ago

“Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold.” —Hermann Weyl

zentropia 10y ago

For me when I see some physics equations is a mystic experience.

vinchuco 10y ago

Immortality, meanwhile, rolls its eyes. Still, it's interesting to see what motivates people to learn something (or to stay away from it). Better put: >"When you take a course in Euclidean geometry is not the teacher putting a... learning program into you? ...You enter the course and cannot do problems; the teacher puts into you a program and at the end of the course you can solve such problems. ...Are you sure you are not merely "programmed" in life by what by chance events happens to you?" - Hamming I'm curious as to how different mathematics would be for two otherwise identical civilizations but with distinct average lifespans. In alternate Earths where lifespan is 40 or 200 years, what's the state of mathematics in 2017?

everybodyknows 10y ago
As Hamming describes, it was very much for me: 8th grade plane geometry feels now like an intellectual awakening. The satisfaction of proving "pons asinorum", by Euclid's method, followed by vexation at learning I had overlooked the much simpler reflexive approach.

lngnmn 10y ago

Which, along with infinity, does not exist. The ability to produce an infinite series of numbers (by adding another one) does not constitute a proof of existence of anything infinite outside one's mind. Good philosophers, like Leibniz and the Indian tradition, which includes early Buddhists, have postulated this, but popular memes are much stronger. The ability to notice some inherent patterns of natural phenomena, such as the ratio of a circle's circumference to its diameter, does yield this ratio to be immortal, or any other inferred constant. Math does not exist outside people's minds (contrary to the popular discourse from the Zen And Art Of Motorcycle Maintenance). Only a few of what we call conservative forces and different forms of what we call energy (or matter if you like) which are different aspects of the same That, to which human categories are inapplicable.

keiferski 10y ago
Once, just once, I would love to open the comments of a philosophy-related HN article and not see a middlebrow dismissal [1] as the top comment. [1] https://news.ycombinator.com/item?id=4693920 https://news.ycombinator.com/item?id=4693920
- Ar-Curunir 10y ago
  It's a slight variant of the Dunning-Kruger effect; people have just a little knowledge of some field, and can therefore dismiss entire decade's worth of thought on the matter.
  - lngnmn 10y ago
    What is wrong with dismissing entire decade's worth of superstitions, astrology, alchemy, metaphysics and theology?
- lngnmn 10y ago
  This has nothing to do with philosophy, which was and still is the endeavor to unveil what is - to see things as they are.
justifier 10y ago

swayvil 10y ago

Mathematics touches immortality like fractals touch infinity and circles are endless.

hzhou321 10y ago

>> “the math that’s being taught has no relevance to my life" I think our math education do fail in that way. Math essentially is a logic system where you set up premises and derive and make sure everything is consistent. That can be applied to real life such as accounting and physics, or it can be applied to an artificial game -- number theory is such a case. Our education emphasize on the latter part, and it is quite irrelevant to real life, and it is hard. I am in mid-life now and on reflection, fractions, for example, had zero use for my life, and I am in the career of scientific computing. What we need is a concept level of understanding of mathematics -- realizing that the key idea of mathematics is basically consistency. Most importantly, the math required in the real life is not hard -- it is necessarily intuitive. What the education we receive is the technical gaming part of mathematics, e.g. how to actually find the roots of quadratic equation. I don't really remember the formula now, but I now have an intuitive understanding of the quadratic curves and the meaning of roots. And the same goes for quintic equations. It is not hard at all. I roughly sketch out the curve and I immediately have a rough idea of where the roots are. And at work, it is simply an exercise in programming. It is hard following the way in our education, though. The purpose of education is to show them that knowledge exists, but not the knowledge itself. Knowledge itself is misleading. It is more important to recognize what you don't know than to remember what you know. To clarify, I personally do not hate math. And I respect the discipline of mathematics. However, doing math (the way our education system assumes) is just like doing music or art, or playing star craft, it is not for everyone. PS: on further reflection, not only useless, the concept of rational number has been quite damaging in our understanding of the real world.

justifier 10y ago
I was thinking about education last night and here is the idea I am developing.. I encourage ongoing criticism Students study varied subject matter but only one subjects' grade 'matters' and can be chosen by the student Personally, I think our maths education suffers from a lack of freedom.. I do think it can be for anyone but only because I believe anyone can bring to it whatever they'd like, whereas education tells you what areas need to be studied and how is competition the foil of expression?
- 10y ago

jayeshsalvi 10y ago

Despite Gödel's incompleteness theorems?

Bluestrike2 10y ago

God, some of those quotes about how some early math teaching techniques hurt people's appreciation and understanding of the subject are depressing. I still remember the anxiety and even embarrassment caused by timed drills in elementary school that seemed to harshly pit student against student. It took me until college to realize that I was just coasting through math courses and not really investing myself in the subject. Perhaps in an effort to avoid those long-ago memories? Everything started to click in college. Interestingly enough, it was my enjoyment of programming and study of philosophy that really helped to push me. That, and sitting in a calculus class and realizing that I had to either dive in or be royally screwed. It's a shame that such stories are so common.

captain_clam 10y ago
Dear god, the timed drills. I distinctly recall the tremendous anxiety evoked by the ultra-competitive nature of those drills in elementary school, and especially the subsequent feelings of failure when comparing my performance to that of my peers. It must have been that bitter flavor of failure that first inured me against mathematics...it didn't help that the rest of my K-12 education never even attempted to demonstrate the enormous beauty of maths. In fact, until I discovered calculus on my own terms between high school and college, I understood mathematics to be nothing more than the practice of applying rote formulas to arbitrary equations. There was no rhyme or reason to the quadratic equation...it was just one of many "rules" pulled from the mathematical "rulebook," and math was simply the practice of recognizing when this arbitrary rule applied, and then applying it. Therefore, for most of my life, math was not seen as a creative or exploratory discipline, and in fact the very opposite: One's ability in math was completely contingent on their memorization of rules and simply following them. It was purely robotic, the domain of tightly-wound, uninspired automatons. It was for squares, not free-spirited creative souls like myself! Though I am disappointed to think of the heights and wonders I could have visited by now, had I been given a proper introduction at a younger age, I am no less excited by the wonders ahead of me, and the many years I have left to explore them. :)

imh 10y ago

Can we get a title change? About half of the people seem to be commenting on the HN title instead of the article content.

ivan_ah 10y ago

It's surprising to see so few math haters in the hexagon (the thin outer shell). I'm guessing there is a self-reporting bias, since if you hate math you wouldn't really want to fill in this survey... It's also interesting to note that many of the haters direct their hate towards rote learning tasks like arithmetic calculations and memorizing multiplication tables, which makes me think that they don't really hate math but rather the way it is taught. I'd hate math too if I saw it as following procedures blindly! Perhaps with better computer math tools[1], future students won't be forced to learn "manual labour" math tasks, and instead focus on "white collar" tasks like modelling and abstraction. [1] SymPy is the best computer algebra system ever: https://minireference.com/static/tutorials/sympy_tutorial.pdf https://minireference.com/static/tutorials/sympy_tutorial.pd...