“When we do mathematics, we touch immortality.”

https://www.quantamagazine.org/20161020-science-math-education-survey/?code=3048

by nature24 • 9 years ago

108 87 9 years ago

tluyben2• 9 years 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.

ThomPete11• 9 years 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.

FabHK4• 9 years 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?

JoeAltmaier4• 9 years ago

So, the value of PI is a human invention? That's hogwash.

cannonpr• 9 years ago

Don't you feel it's a bit harsh to summarise the entire debate between idealism and realism as hogwash ?

ThomPete11• 9 years ago

Who else invented it?

GavinMcG• 9 years 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.

omalleyt2• 9 years 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.

jknoepfler• 9 years 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• 9 years 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.

FabHK4• 9 years 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• 9 years 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• 9 years 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

eastWestMath• 9 years ago

Well yes, Platonism is true if you presuppose that Platonism is true.

coldtea2• 9 years 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• 9 years 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.

FabHK4• 9 years 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.georg...

danidiaz• 9 years ago

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

zentropia• 9 years ago

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

vinchuco• 9 years 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• 9 years 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.

lngnmn5• 9 years 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• 9 years 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

Ar-Curunir• 9 years 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.

lngnmn5• 9 years 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.

justifier6• 9 years ago

Did you click the link or simply start soap boxing?

It's a survey, and the link text is a quote of one of the surveyors which I only found by clicking view comments then ctrl-f'ing 'immort' which took me far down the list to find this:

Shane Magrath, 48, from Australia, has loved math since grades 9-12

“One day the universe will be a cold black emptiness. However that which is mathematically true will remain vibrantly true even if the universe fades to darkness. When we do mathematics we touch immortality.”

You rely too much on proof by assertion to support your ideology

does not constitute a proof of existence of anything infinite outside one's mind.

You argue a lack of rigor but refuse to uphold your dismissal to your own projected standards

You even claim there are texts to support your position but choose to leave out a link for others to review

I am comfortably an opposing opinion to your opinion but one of the things that confuses me about those that share it with you is the 'outside the mind' element

Can you elaborate on how mathematical phenomena only exist inside the mind and if so how that proves mathematics fails to exist immortally

sethrin2• 9 years ago

You're correct to say that mathematics is not empirical, but why you think that somehow invalidates it is obscure. Judging by your last paragraph, your position is more informed by mysticism than a knowledge of epistemology. Mathematics may not be "real" but the truths it produces are the product of inarguable logic -- it is because it does not depend on the real world that we can say that mathematics is 'touching immortality'.

lngnmn5• 9 years ago

it is because it does not depend on the real world

Nothing does not depend on the real world, to begin with. Especially, products of the mind conditioned by senses and a language.

danharaj• 9 years ago

This dismissal seems to implicitly accept Cartesian dualism, maybe? There's not much difference between a human engaging in mathematical reasoning and say, a computer enumerating proofs. Mathematical reasoning is a form of computation. Computation comprises physically realizable processes that are equivalent in a certain way. It is this equivalence between computational (and hence physical) processes which allows us to talk about mathematics as something "outside" of the human mind which itself is only one sort of computational physical process. As far as mathematics is concerned, the human mind isn't privileged. So if mathematics doesn't exist outside of people's minds, it certainly doesn't exist within it either. But then what are we talking about?

Computation is a finitary process, but its behavior is informed by infinity. Even if infinity doesn't "exist" in the sense that we could ever observe and comprehend it, we can see its shadow everywhere.

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.

I have to disagree. The fact that there are patterns to notice is a deep mystery of the world and prefigures mathematical truth. Things are different in some ways but the same in other ways. Trivial, but fundamental. The fact that we can find mathematics everywhere relies on this fact.

lngnmn5• 9 years ago

Math, as the science of patterns, captures some patterns of what is. There is absolutely nothing extraordinary about it. There is some necessary order, which physicists and philosophers are truing to grasp, and the language of choice to describe physics is math. But it is only a systematized and logically structured observations of what is.

What is a deep mystery for me, is that life, it seems, does not have the notion of counting at all, at least on the level of cell biology. It is uses "pure functional" molecular structures as "code and data" and message-passing as its "language", but this is quite another topic.

This, BTW, is a hint to justify the principle that what cannot exist without an observer does not exist in principle. There is, obviously the notion of a distance, but not necessarily of space. There is notion of a process as a result of applied forces, but not necessarily of duration and time. Time is a derivative. Derivatives does not exist, physical phenomena do.

swayvil• 9 years ago

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

hzhou321• 9 years 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.

justifier6• 9 years 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?

baobrain• 9 years ago

Could you elaborate?

For example, What would motivate a student to put towards any effort in their non-main courses if it doesn't affect their grade?

Edit: clarity and accuracy

jayeshsalvi• 9 years ago

Despite Gödel's incompleteness theorems?

Bluestrike2• 9 years 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• 9 years 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• 9 years 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• 9 years 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.pd...

“When we do mathematics, we touch immortality.”

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