The Unreasonableness of Math Is Context Independence
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The Unreasonableness of Math Is Context Independence
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Re: The Unreasonableness of Math Is Context Independence
#2Except for the corner cases. So the trivial one is "angles in a triangle add up to 180" which works in a plane but not on the surface of a sphere so navigation has to use more than trivial trigonometry functions for accuracy at scale.
The context is sometimes everything.
Re: The Unreasonableness of Math Is Context Independence
#3Math is not context-independent.
The meta-mathematical assumptions (axioms) are the context. Different axioms produce different truths; or if you want - they produce different Mathematical universes [1].
Maths is relative like Physics is relative - it depends on your frame of reference [2].
1. https://en.wikipedia.org/wiki/Universe_(mathematics)
2. http://math.andrej.com/2012/10/03/am-i-a-constructive-mathem...
Re: The Unreasonableness of Math Is Context Independence
#4I chased 2-3 linked articles deep am still wondering what is meant by reasonable here. Or "reasonably effective."
Is that just an example of the ineffective reasonability of essays?
My best guess at this point is that reasonable is what a person expects. And if that's so, it's subjective. And math abstracts realities into imperfect but objective simulacra. So I think the claim is that math is made of abstract rules. A tautology? A deepity? I must be missing something.
Re: The Unreasonableness of Math Is Context Independence
#5I chased 2-3 linked articles deep am still wondering what is meant by reasonable here. Or "reasonably effective." Is that just an example of the ineffective reasonability of essays? My best guess at this point is that reasonable is what a person expects. And if that's so, it's subjective. And math abstracts realities into imperfect but objective simulacra. So I think the claim is that math is made of abstract rules.…
It's a play on the "unreasonable effectiveness of math" essay right?
I took it to mean the "unreasonable" ingredient which makes math so effective is context independence - since that's something which is not so easily attainable in other fields.
Re: The Unreasonableness of Math Is Context Independence
#6IMO math seems effective because everything that works is called math. So yeah, that quote from the beginning is right, it's selection.
There are many different math concepts used to describe the world, everything from calculus to graph theory, geometry, and so on. These things have a two way relationship with the real world: they don't necessarily have to correspond with anything real, like Hardy's quote about his number theory work that eventually ended up appearing in cryptography, but if something in the real world happens ahead of it, math will expand to swallow it.
Think of a scientific theory that isn't described with some kind of math. I'm not sure it can be done. My sense is that whatever you think of, even if it's completely new, will be called math. For instance general relativity relied on some quite new concepts at the time, but nobody would point at it and say it wasn't math.
Re: The Unreasonableness of Math Is Context Independence
#7I chased 2-3 linked articles deep am still wondering what is meant by reasonable here. Or "reasonably effective." Is that just an example of the ineffective reasonability of essays? My best guess at this point is that reasonable is what a person expects. And if that's so, it's subjective. And math abstracts realities into imperfect but objective simulacra. So I think the claim is that math is made of abstract rules.…
It's the E.P. Wigner thing in the first link, it's a famous essay and a bit of an HN evergreen, along with a related Hamming piece:
https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...
it's also a meme-ish title thing, sort of like 'considered harmful'
https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...
Re: The Unreasonableness of Math Is Context Independence
#8IMO math seems effective because everything that works is called math. So yeah, that quote from the beginning is right, it's selection. There are many different math concepts used to describe the world, everything from calculus to graph theory, geometry, and so on. These things have a two way relationship with the real world: they don't necessarily have to correspond with anything real, like Hardy's quote about his n…
What? I'm sorry but this is utter bullshit. Math is not just anything that works. Every hot new theory is assumed to "work" in the era which it is produced, and not everything is called "math". There has been no significant "wrong" result in the entire history of math since ancient times, nor has any significant result been jettisoned from the field of math, whereas every other field or discipline of study has been wrong at some point. If math was just "anything that works", then we'd be regularly purging stuff from the "math" label, but I can't think of anything that was called "math" in history and not called "math" now.
Re: The Unreasonableness of Math Is Context Independence
#9Except for the corner cases. So the trivial one is "angles in a triangle add up to 180" which works in a plane but not on the surface of a sphere so navigation has to use more than trivial trigonometry functions for accuracy at scale. The context is sometimes everything.
That's not a corner case, that's just more advanced math. No one ever claimed that triangulation on a plane is the same as triangulation on the surface of a sphere.
Re: The Unreasonableness of Math Is Context Independence
#10Except for the corner cases. So the trivial one is "angles in a triangle add up to 180" which works in a plane but not on the surface of a sphere so navigation has to use more than trivial trigonometry functions for accuracy at scale. The context is sometimes everything.
That's not a corner case. Either you defined "triangle" and "angles" to mean a plane triangle and angles, or that is not a theorem. Within the theory you're looking at, the definitions are not part of the context, they are part of the theory itself. So you're not depending on the context.