When We Cease to Understand the World, Benjamín Labatut (New York Review of Books, 2021). Have you ever sat and stared at the sea? If you’ve been near it, then I’m sure you have. As soon as it hoves into view, our eyes are drawn ineluctably up to that far horizon, that endless undulating plain. Coast-dwelling cultures around the earth have stories and legends about the ocean’s strange magnetism, like some eldritch vista that once beheld deepens and ages the soul, but stare too long and you may never be able to tear your gaze away.
Succinct explanations give immediately useful answers, while multi-layered, tangential explanations give room for the mind to wander and experiment with new connections. Transfixation on the vastness of the sea feels like a infinity of the latter.
It's a wonder mathematics and science education doesn't include more stories about the men who figured things out. I'd started and put down Labatut's book months ago. Thank you for a reminder to pick it back up.
Jane and John, you continually amaze! One of these days you will write a review that doesn’t match my interests or convey impressive insight and understanding in beautiful and witty prose. Until then…
this is really lovely. i've wanted to explain something about the foundational crisis and all that other stuff to non-specialists for ages but never found the right poetic language and this is right on the money
"Were Niagara but a cataract of sand, would you travel your thousand miles to see it? Why did the poor poet of Tennessee, upon suddenly receiving two handfuls of silver, deliberate whether to buy him a coat, which he sadly needed, or invest his money in a pedestrian trip to Rockaway Beach? Why is almost every robust healthy boy with a robust healthy soul in him, at some time or other crazy to go to sea? Why upon your first voyage as a passenger, did you yourself feel such a mystical vibration, when first told that you and your ship were now out of sight of land? Why did the old Persians hold the sea holy? Why did the Greeks give it a separate deity, and own brother of Jove? Surely all this is not without meaning. And still deeper the meaning of that story of Narcissus, who because he could not grasp the tormenting, mild image he saw in the fountain, plunged into it and was drowned. But that same image, we ourselves see in all rivers and oceans. It is the image of the ungraspable phantom of life; and this is the key to it all."
> What all these examples have in common is a disjunction between mundane means of locomotion and fantastical destination. We expect the plodding, step-by-step application of formal reasoning to lead us somewhere reasonable. Occasionally it takes us up a hill, from which we have a beautiful view. But we do not expect it to lead us straight into Hell, or into the freezing depths of the ocean, or into the middle of the Sun. The experience of everyday life teaches us that your destination fits your means of travel. But the experience of doing early twentieth century mathematics or physics is that one minute you’re methodically picking your way up evenly-spaced steps, and the next minute shooting off into the abyss.
I wonder if the Pythagoreans felt this way upon discovering that the legs and hypotenuse if an isosceles right triangle are incommensurable.
I would be very interested to know more about how your faith intersects with philosophical mathematics. I would love to experience the same intuitive understanding of Christianity as you offered here into mathematics
That was very poetic. I'm not really into abstract physics enough to understand what exactly you were going on about (although the black hole example helped a bit), but it was an enjoyable read. I imagine a longer version might explain what the hell they're doing with their large hadron collider?
Historically, the sea was a common theme for oil painters. I vaguely remember walking around a museum in South Street Seaport that was just full of such canvases. It's truly amazing brushwork, and once it was a fairly common talent.
I love this sort of thing. I've always intended to write some sort of fiction based upon this, plus probably something to do with computers and networks → magic (invisible energy that surrounds us and does things, that only the initiated or those favored with their enchantments may intercept? words that change reality? summoning of daemons?! it's right there!)...
...but since I'm afflicted with some sort of paralysis that ensures I lack the energy — or the "gumption", as my mother calls it — to really... like... *DO* anything, it's fairly certain that this too shall come to nothing (...much like my life itself, heh).¹
More cheerfully!:
★ If you've more recommendations for books like this, or Egan's (I loved "Diaspora" for exactly this theme, albeit rendered a bit more optimistically... sort of), I'd love to hear them.
I can only think of two, myself; and I just now realized I have forgotten the one that wasn't Diaspora. Dammit. "Echopraxia" by Watts, maybe, kinda?
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¹(boy, everyone who thought I was gonna do something special sure was wrong; I've entirely ceased answering emails and calls from my former professors: the shame's too great, haha—)
Thank you for writing about Grothendieck. As a physicist who probably isn't as well read as you, the figures I was exposed to in grad school like Dirac or Heisenberg are very different, and I'd long thought that everyone just presumed von Neumann was the smartest guy around. Even though you obviously don't give a very technical treatment here - I get that you're writing for a broad readership - it's opened up a vista for me to be able to look at minds that are more purely mathematical.
I'm extremely disappointed and frustrated with philosophy ( https://thingstoread.substack.com/p/philosophy-is-a-residuum-of-failure ) but I there are hints that it might be possible to actually get somewhere in the discipline with a process like Grothendieck's, who "summoned the ocean, piled up abstractions upon abstractions, the black freezing waters pouring out of his emaciated body, the sea level rising and rising, until the problem, now barely visible at the bottom of an immense underwater canyon, would finally soften up and burst under its terrible pressure..."
So, does contemplating this stuff turn you into a raving looney, or are raving looneys the only people who are willing to contemplate this stuff? Or a bit of both?
Another poem comes to mind:
Tell all the truth but tell it slant —
Success in Circuit lies
Too bright for our infirm Delight
The Truth's superb surprise
As Lightning to the Children eased
With explanation kind
The Truth must dazzle gradually
Or every man be blind —
(Emily Dickinson)
Succinct explanations give immediately useful answers, while multi-layered, tangential explanations give room for the mind to wander and experiment with new connections. Transfixation on the vastness of the sea feels like a infinity of the latter.
It's a wonder mathematics and science education doesn't include more stories about the men who figured things out. I'd started and put down Labatut's book months ago. Thank you for a reminder to pick it back up.
Jane and John, you continually amaze! One of these days you will write a review that doesn’t match my interests or convey impressive insight and understanding in beautiful and witty prose. Until then…
this is really lovely. i've wanted to explain something about the foundational crisis and all that other stuff to non-specialists for ages but never found the right poetic language and this is right on the money
From "Loomings," the first chapter of Moby Dick:
"Were Niagara but a cataract of sand, would you travel your thousand miles to see it? Why did the poor poet of Tennessee, upon suddenly receiving two handfuls of silver, deliberate whether to buy him a coat, which he sadly needed, or invest his money in a pedestrian trip to Rockaway Beach? Why is almost every robust healthy boy with a robust healthy soul in him, at some time or other crazy to go to sea? Why upon your first voyage as a passenger, did you yourself feel such a mystical vibration, when first told that you and your ship were now out of sight of land? Why did the old Persians hold the sea holy? Why did the Greeks give it a separate deity, and own brother of Jove? Surely all this is not without meaning. And still deeper the meaning of that story of Narcissus, who because he could not grasp the tormenting, mild image he saw in the fountain, plunged into it and was drowned. But that same image, we ourselves see in all rivers and oceans. It is the image of the ungraspable phantom of life; and this is the key to it all."
There is much more like it in the chapter.
> What all these examples have in common is a disjunction between mundane means of locomotion and fantastical destination. We expect the plodding, step-by-step application of formal reasoning to lead us somewhere reasonable. Occasionally it takes us up a hill, from which we have a beautiful view. But we do not expect it to lead us straight into Hell, or into the freezing depths of the ocean, or into the middle of the Sun. The experience of everyday life teaches us that your destination fits your means of travel. But the experience of doing early twentieth century mathematics or physics is that one minute you’re methodically picking your way up evenly-spaced steps, and the next minute shooting off into the abyss.
I wonder if the Pythagoreans felt this way upon discovering that the legs and hypotenuse if an isosceles right triangle are incommensurable.
I would be very interested to know more about how your faith intersects with philosophical mathematics. I would love to experience the same intuitive understanding of Christianity as you offered here into mathematics
That was very poetic. I'm not really into abstract physics enough to understand what exactly you were going on about (although the black hole example helped a bit), but it was an enjoyable read. I imagine a longer version might explain what the hell they're doing with their large hadron collider?
It's just a singularity.
A more mundane example is 1/r^2 which appears as the force from a point charge in classical electrostatics.
Also, Grothendieck worked in a social group of mathematicians.
He built on their ideas. One was Deligne, who is a friend of mine.
He wasn't some weird super mind working in isolation.
I think G's mental illness had more to do with growing up in an internment camp than with abstract math.
Who (or what) created the paintings shown in this post?
Historically, the sea was a common theme for oil painters. I vaguely remember walking around a museum in South Street Seaport that was just full of such canvases. It's truly amazing brushwork, and once it was a fairly common talent.
I love this sort of thing. I've always intended to write some sort of fiction based upon this, plus probably something to do with computers and networks → magic (invisible energy that surrounds us and does things, that only the initiated or those favored with their enchantments may intercept? words that change reality? summoning of daemons?! it's right there!)...
...but since I'm afflicted with some sort of paralysis that ensures I lack the energy — or the "gumption", as my mother calls it — to really... like... *DO* anything, it's fairly certain that this too shall come to nothing (...much like my life itself, heh).¹
More cheerfully!:
★ If you've more recommendations for books like this, or Egan's (I loved "Diaspora" for exactly this theme, albeit rendered a bit more optimistically... sort of), I'd love to hear them.
I can only think of two, myself; and I just now realized I have forgotten the one that wasn't Diaspora. Dammit. "Echopraxia" by Watts, maybe, kinda?
-------------------------
¹(boy, everyone who thought I was gonna do something special sure was wrong; I've entirely ceased answering emails and calls from my former professors: the shame's too great, haha—)
Thank you for writing about Grothendieck. As a physicist who probably isn't as well read as you, the figures I was exposed to in grad school like Dirac or Heisenberg are very different, and I'd long thought that everyone just presumed von Neumann was the smartest guy around. Even though you obviously don't give a very technical treatment here - I get that you're writing for a broad readership - it's opened up a vista for me to be able to look at minds that are more purely mathematical.
I'm extremely disappointed and frustrated with philosophy ( https://thingstoread.substack.com/p/philosophy-is-a-residuum-of-failure ) but I there are hints that it might be possible to actually get somewhere in the discipline with a process like Grothendieck's, who "summoned the ocean, piled up abstractions upon abstractions, the black freezing waters pouring out of his emaciated body, the sea level rising and rising, until the problem, now barely visible at the bottom of an immense underwater canyon, would finally soften up and burst under its terrible pressure..."
So, does contemplating this stuff turn you into a raving looney, or are raving looneys the only people who are willing to contemplate this stuff? Or a bit of both?
I work in this stuff and most research mathematicians, even the Fields Medalists and Abel prize winners are not at all deranged.
In fact, quite the opposite.
Well that was a grand read to start the week.