Why I Like Math [pdf](southparkwillie.com)
southparkwillie.com
Why I Like Math [pdf]
http://www.southparkwillie.com/SPinfo/mathessayfinal1.pdf
32 comments
> In my experience, the intuitive "experience of the knowledge" was much more striking than the eventual unfolding and application of the logic in that case.
In math applications doesn't matter, just the beauty of the revelation. Understanding how everything in math is connected is the main goal of the field, so understanding more of it is never pointless.
But if we talk about applications then it is that if A and B are the same then all theorems derived for A also works for B and vice versa. This is very important since it automatically multiplies our productivity and learning rate! One such epiphany which many falters on is that x and y doesn't matter, they could be z or µ or whatever. Another which many struggles with but usually overcomes is that 10 + 30 is just as easy to compute as 1 + 3.
In math applications doesn't matter, just the beauty of the revelation. Understanding how everything in math is connected is the main goal of the field, so understanding more of it is never pointless.
But if we talk about applications then it is that if A and B are the same then all theorems derived for A also works for B and vice versa. This is very important since it automatically multiplies our productivity and learning rate! One such epiphany which many falters on is that x and y doesn't matter, they could be z or µ or whatever. Another which many struggles with but usually overcomes is that 10 + 30 is just as easy to compute as 1 + 3.
"Islam was out because that’s not for white people."
For someone who espouses an expertise in mathematics his perspective on religion is quite reductive if not completely wrong in some cases. I guess in addition to math the author is fond of strawman arguments.
For someone who espouses an expertise in mathematics his perspective on religion is quite reductive if not completely wrong in some cases. I guess in addition to math the author is fond of strawman arguments.
I think you might be taking this line too seriously. In this piece I don't think the author is trying to lay out a well-thought-out, validated, and rhetorically-correct argument for his point of view -- if he were trying to do that, you'd be totally right and that line would have no place in it.
But in this case I think the article is pretty clearly more stream of consciousness, just what the author believed at the time, legitimate or not -- and even though it's reductive and just genuinely a pretty bad reason, it's also easy to see how his subconscious might be thinking along the lines of "islam? Nah can't do islam, I'm not brown". Our minds generate totally faulty lines of reasoning like that all the time.
(especially if he came into this with a predisposition towards Buddhism, which I wouldn't be surprised about, since Buddhism tends to be viewed as very "cool" to westerners but Islam not as much)
Edit: ok or it was a joke :p
But in this case I think the article is pretty clearly more stream of consciousness, just what the author believed at the time, legitimate or not -- and even though it's reductive and just genuinely a pretty bad reason, it's also easy to see how his subconscious might be thinking along the lines of "islam? Nah can't do islam, I'm not brown". Our minds generate totally faulty lines of reasoning like that all the time.
(especially if he came into this with a predisposition towards Buddhism, which I wouldn't be surprised about, since Buddhism tends to be viewed as very "cool" to westerners but Islam not as much)
Edit: ok or it was a joke :p
It's a bit of a joke. It was written by Matt Stone after all.
The author is one of the writers of South Park
The easiest way to experience a sensation of quasi-religious vastness from math might be pondering large numbers.
> Weirdly, thinking about Graham’s number has actually made me feel a little bit calmer about death, because it’s a reminder that I don’t actually want to live forever—I do want to die at some point, because remaining conscious for eternity is even scarier. Yes, death comes way, way too quickly, but the thought “I do want to die at some point” is a very novel concept to me and actually makes me more relaxed than usual about our mortality.
https://waitbutwhy.com/2014/11/1000000-grahams-number.html
> Weirdly, thinking about Graham’s number has actually made me feel a little bit calmer about death, because it’s a reminder that I don’t actually want to live forever—I do want to die at some point, because remaining conscious for eternity is even scarier. Yes, death comes way, way too quickly, but the thought “I do want to die at some point” is a very novel concept to me and actually makes me more relaxed than usual about our mortality.
https://waitbutwhy.com/2014/11/1000000-grahams-number.html
It's interesting to consider that people who look for a feeling of one-ness with the world can find it through Mathematics or through religion, even though they are considered almost diametrically opposite approaches to understand the Universe.
In the words of Galileo, "Mathematics is the language with which God has written the universe."
That's not how I see it. Mathematics is not science, even though science has found practical uses for certain types of math. Pure math does not require observation of the real world for proof, only consistency with itself. As a system of symbols independent of the messy real world I see it closer to mysticism than hard science. I am not saying this as a bad thing, only something we need to be honest about.
Well, one can think of, say, natural numbers as a mystical "system of symbols" but I find them extremely close to the real world when I count change in my pocket.
The way I see it, there are three separate endeavors here: understanding the world, understanding various forms of math, and understanding which forms of math are applicable to the real world and why.
Some math may not have any application that we know of in the real world. Maybe there is one but nobody has yet realized what it is. Or maybe the real world will change in the future so that there is one. Or maybe there won't be one and that's OK.
Incidentally, I think understanding how to correctly apply math to a real world problem is a separate skill from understanding the math itself. And just because you're a good at one doesn't mean you're good at the other. It's relatively easy and common to make the error of understanding a situation in a very shallow or inaccurate manner, then applying math which itself is completely valid, then coming to a wrong conclusion that you're very confident of because of how solid the math is. In "P, and P implies Q, therefore Q", it's easy to get so excited about the beauty and wonder of P implies Q that you spend too little time understanding whether P is actually the case. If you've got a hammer, and you're in love with that hammer, you can become blind to whether something actually is a nail.
Some math may not have any application that we know of in the real world. Maybe there is one but nobody has yet realized what it is. Or maybe the real world will change in the future so that there is one. Or maybe there won't be one and that's OK.
Incidentally, I think understanding how to correctly apply math to a real world problem is a separate skill from understanding the math itself. And just because you're a good at one doesn't mean you're good at the other. It's relatively easy and common to make the error of understanding a situation in a very shallow or inaccurate manner, then applying math which itself is completely valid, then coming to a wrong conclusion that you're very confident of because of how solid the math is. In "P, and P implies Q, therefore Q", it's easy to get so excited about the beauty and wonder of P implies Q that you spend too little time understanding whether P is actually the case. If you've got a hammer, and you're in love with that hammer, you can become blind to whether something actually is a nail.
But that's what they they were designed for. The first "numbers" were arguably clay tokens meant to represent goods in storage https://en.wikipedia.org/wiki/History_of_ancient_numeral_sys... Numbers were and are primarily used for accounting purposes. If they didn't accurately represent the change in your pocket then the system would be improved until it did. There's nothing magical about it.
Yet, there are people who see magic in numbers, as others tend to do in other mathematical constructs.
Exactly my point - that viewing magic in math is more akin to religion than science.
Can we state that math is something like religion? The search for The One Truth? I feel oddly connected with the author and his thoughts mirror mine almost completely, I was just not able to word them...
Not really. Religion is based on belief, and math is based on knowledge and logic. (As to the arousal and other "experiences" - that's just a psychological side effect that has nothing to do with anything.)
Conway's Game of Life on a universal scale. Entertainment for Olympus, or a simulation to find an answer / stave off an inevitability?
The laws of physics and mathematics as the author sees them provide the substrate that seems to imply hard determinism; chaos theoreticians revel as the chaos of the now is reduced to causal determinism predicated on initial conditions and the base laws of the system, all interconnected.
But why quantum uncertainty? Why does observed light exhibit particle behavior while unobserved light exhibits wave behavior? Why does observation collapse the waveform? Are the quantum and classical reconcilable into a theory of everything? Einstein would hope so, but who knows what's really going on. In the end, it seems human knowledge is still, ultimately limited, with a vague sense of having experienced an indescribable "oneness" as the big kahuna of the panaceas.
What if it were fractal? What if there was no "end" but just an infinite regression with deeper and deeper questions with ever-escaping answers? An infinite game, consuming disorder, systematizing into local order - life's eternal war waged against entropy, helplessness, meaninglessness until ending and recurring. A tale told by an idiot, full of sound and fury, signifying nothing; pure comedy, where the only thing that seems to make us feel alive is the struggle to survive - whether through religion, philosophy, or mathematics. Still makes for some great art along the way; life as a beauty-generator in the void. /rant
The laws of physics and mathematics as the author sees them provide the substrate that seems to imply hard determinism; chaos theoreticians revel as the chaos of the now is reduced to causal determinism predicated on initial conditions and the base laws of the system, all interconnected.
But why quantum uncertainty? Why does observed light exhibit particle behavior while unobserved light exhibits wave behavior? Why does observation collapse the waveform? Are the quantum and classical reconcilable into a theory of everything? Einstein would hope so, but who knows what's really going on. In the end, it seems human knowledge is still, ultimately limited, with a vague sense of having experienced an indescribable "oneness" as the big kahuna of the panaceas.
What if it were fractal? What if there was no "end" but just an infinite regression with deeper and deeper questions with ever-escaping answers? An infinite game, consuming disorder, systematizing into local order - life's eternal war waged against entropy, helplessness, meaninglessness until ending and recurring. A tale told by an idiot, full of sound and fury, signifying nothing; pure comedy, where the only thing that seems to make us feel alive is the struggle to survive - whether through religion, philosophy, or mathematics. Still makes for some great art along the way; life as a beauty-generator in the void. /rant
I'm not religious, I'm not against atheism, but I think it's unfortunate that math and science have become so strongly associated with atheism. We tend to forget that many of the most influential scientists and mathematicians were mystics who had experiences similar to Matt's (Pythagoras and Newton being two prominent examples).
Some people need these transcendent experiences or else their lives feel empty. Nothing wrong with finding it through math or science instead of organized religion.
Some people need these transcendent experiences or else their lives feel empty. Nothing wrong with finding it through math or science instead of organized religion.
". . . these Magic-Eye moments single-handedly define faith for me."
A Unix fortune today gave me this great quote by German philosopher and theologian Paul Tillich:
"Doubt is not the opposite of faith; it is an element of faith."
The broader paragraph, on what kinds of certitude we seek in life and the judgments we must make upon them, is striking:
"The affirmation that Jesus is the Christ is an act of faith and consequently of daring courage. It is not an arbitrary leap into darkness but a decision in which elements of immediate participation and therefore certitude are mixed with elements of strangeness and therefore incertitude and doubt. But doubt is not the opposite of faith; it is an element of faith. Therefore, there is no faith without risk. The risk of faith is that it could affirm a wrong symbol of ultimate concern, a symbol which does not really express ultimacy (as, e.g., Dionysus or one’s nation). But this risk lies in quite a different dimension from the risk of accepting uncertain historical facts. It is wrong, therefore, to consider the risk concerning uncertain historical facts as part of the risk of faith. The risk of faith is existential; it concerns the totaliy of our being, while the risk of historical judgments is theoretical and open to permanent scientific correction. Here are two different dimensions which should never be confused. A wrong faith can destroy the meaning of one’s life; a wrong historical judgment cannot. It is misleading, therefore, to use the word 'risk' for both dimensions in the same sense."
Matt Stone's essay resonates here I think . . . mathematics goes beyond historical judgments and gets to existential concerns too.
A Unix fortune today gave me this great quote by German philosopher and theologian Paul Tillich:
"Doubt is not the opposite of faith; it is an element of faith."
The broader paragraph, on what kinds of certitude we seek in life and the judgments we must make upon them, is striking:
"The affirmation that Jesus is the Christ is an act of faith and consequently of daring courage. It is not an arbitrary leap into darkness but a decision in which elements of immediate participation and therefore certitude are mixed with elements of strangeness and therefore incertitude and doubt. But doubt is not the opposite of faith; it is an element of faith. Therefore, there is no faith without risk. The risk of faith is that it could affirm a wrong symbol of ultimate concern, a symbol which does not really express ultimacy (as, e.g., Dionysus or one’s nation). But this risk lies in quite a different dimension from the risk of accepting uncertain historical facts. It is wrong, therefore, to consider the risk concerning uncertain historical facts as part of the risk of faith. The risk of faith is existential; it concerns the totaliy of our being, while the risk of historical judgments is theoretical and open to permanent scientific correction. Here are two different dimensions which should never be confused. A wrong faith can destroy the meaning of one’s life; a wrong historical judgment cannot. It is misleading, therefore, to use the word 'risk' for both dimensions in the same sense."
Matt Stone's essay resonates here I think . . . mathematics goes beyond historical judgments and gets to existential concerns too.
That is an enviable feeling to get from Math. It's true that enlightenment may come in many forms. Also, purpose and meaning is desperately needed even from the most sane and rational of us. For the lucky, religion is enough source for meaning and happiness. For others it may take a little more than that.
"Mathematics for Human Flourishing" [1] is a beautiful, inspiring book on deeply human perspective on mathematics.
[1] https://www.amazon.com/Mathematics-Human-Flourishing-Francis...
[1] https://www.amazon.com/Mathematics-Human-Flourishing-Francis...
That is an enviable feeling to get from Math. It's true that enlightenment may come in many forms. Also, purpose and meaning is desperately needed even from the most sane and rational of us. For the lucky, religion is enough source for meaning and happiness. For others it may take a little more than that.
Reminds me of this, https://www.businessinsider.com/steven-strogatz-interview-on..., interview with Steven Strogatz, when he gets onto the idea (and dangers) of what beauty means in maths.
Also, this https://plus.maths.org/content/andrew-wiles-what-does-if-fee... from Andrew Wiles, when he mentions that maths, the actual doing of it at least, isn't so much the cold hard logic of formal equations, that's just how it's communicated. It's the sitting down and trying to grapple with some mathematical ideas when it becomes more akin to musical experience.
iirc, there's a passage in Godel, Escher, Bach where Hofstadter actually works through a mathematical calculation and compares its cadences with musical experience. And there's the poems of Rebecca Elson (Theories of Everything, Explaining Relativity) that do the best job, for me, of describing what is actually appealing about maths.
Like this article, they all emphasise the joy of just sitting down and playing with mathematical ideas. That that is where the understanding and fun really is, though difficult to communicate directly. It's not so much the technical bits of learning formulae and grinding results out of them that, at least when I was at school, was all we ever really did.
Also, this https://plus.maths.org/content/andrew-wiles-what-does-if-fee... from Andrew Wiles, when he mentions that maths, the actual doing of it at least, isn't so much the cold hard logic of formal equations, that's just how it's communicated. It's the sitting down and trying to grapple with some mathematical ideas when it becomes more akin to musical experience.
iirc, there's a passage in Godel, Escher, Bach where Hofstadter actually works through a mathematical calculation and compares its cadences with musical experience. And there's the poems of Rebecca Elson (Theories of Everything, Explaining Relativity) that do the best job, for me, of describing what is actually appealing about maths.
Like this article, they all emphasise the joy of just sitting down and playing with mathematical ideas. That that is where the understanding and fun really is, though difficult to communicate directly. It's not so much the technical bits of learning formulae and grinding results out of them that, at least when I was at school, was all we ever really did.
Lovely! Here's a different take, by a 5th grader :-)
https://leosstemhacks.wordpress.com/2019/08/31/i-like-math-a-poem/This reads 95% like a personal statement for some university program - I was very surprised to see Matt Stone’s name at the end.
This essay made me think a lot of Douglas Adams' "The Hitchhikers Guide to the Galaxy"
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I can see by the way you write, you have read enough Buddhist texts.
One thing I would clarify is that Buddhism, as taught by Buddha, doesn’t have beliefs. It has hypotheses that are proved causally and tasted experiential you during deep attention and awareness. The word used by Buddha is “Ehipassiko”, translated as come and see for yourself.
Carry on with your journey of mathematics and I wish you all the success!
One thing I would clarify is that Buddhism, as taught by Buddha, doesn’t have beliefs. It has hypotheses that are proved causally and tasted experiential you during deep attention and awareness. The word used by Buddha is “Ehipassiko”, translated as come and see for yourself.
Carry on with your journey of mathematics and I wish you all the success!
I thought this was interesting--that the revelatory experience can end up being so subjective and limited in the goes-nowhere-from-here sense, yet it feels so darn amazing at the time. I wondered if it was similar to seeing a Tetris happen for the first time. An emotional reward in the sense of rewarding an organizational triumph of the mind. And seeing it with the intuition is one of those things our mind loves to count as actually seeing it in real life.
(I've also experienced this as a practicing religious person; in religion though, the subjectivity can quickly become a bummer because the question of one's worthiness or lack of discipline is nearly always up for discussion, especially when you ask why the results were disappointing or something like that)