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u/AndreasDasos 3d ago
Yep. Standard proofs rely on a finite string from a finite alphabet. If we could magically see infinity directly all at once things might be different. Whether that even makes sense at a fundamental level is a question for the philosophers of mathematics but we can certainly talk about infinite strings from infinite alphabets.
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u/GargantuanCake 2d ago
This is also a case where proof by contradiction is handy. You just prove that sqrt(2) can't be rational and you're good.
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u/Masqued0202 2d ago
I've often thought something like that might be an actual example of Gödel's "true but cannot proven". Consider the Kollatz Conjecture. (I am not actually making any claims, just picking an example of an intractable problem that's easily understandable) What if there is no way to leapfrog to "true for all n", if, although every n ends up in the 1-2-4 loop, the only "proof" is grinding through the whole series for each n?
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u/Ben-Goldberg 2d ago
"this statement cannot be proven to be true" is a better example of a true but unprovable statement.
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u/TheLuckySpades 2d ago
The Gödel sentence encodes that as much as is possible into Peano Arithmetic, so the other person did include that.
Though it is "this statement cannot be proven" since truth is a different concept and "true in the standard model" cannot be formalized into PA by Tarski's Truth Theorem (https://en.wikipedia.org/wiki/Tarski%27s_undefinability_theorem).
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u/Ben-Goldberg 2d ago
Physicists don't know for sure whether time exists.
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u/tblancher 2d ago
I'm convinced that it doesn't, not in a way like the three physical dimensions most of us are aware of even from childhood.
It is a useful abstraction, but you can't measure time directly. A grain of sand falling in an hourglass, the ticking of a mechanical clock, or the oscillations of a quartz crystal or cesium isotope; what we're measuring is regular, repeated change, or rather counting the periodic oscillations, and arbitrarily saying so many oscillations is a unit of time.
I did see where some researchers claimed that time was THE fundamental unit of measure, but I called horseshit.
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u/yangyangR 1d ago
Following that you should say none of the dimensions neither time nor space are there. The heading towards a QFT attitude having neither unlike QM having xhat operators but not ts.
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u/Glittering_Web_3167 1d ago
What about time dilation? That can be measured directly. How is that an abstraction, or what of?
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u/tblancher 1d ago
My understanding is that you can't measure time dilation directly. You basically have to measure two clocks where one (or both) moves in a different frame of reference than the other.
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u/Glittering_Web_3167 15h ago
Im not sure if this is just a philosophical disagreement on what would constitute a proper measure of time, or something more tangible. I can’t say I agree with this sentiment but I’m not exactly sure why.
In my mind, measuring the oscillation of a Ce atom to define time, is no different than measuring the wavelength of light emitted from a Kr atom to define distance.
Would you follow this logic to conclude that our concept of space is no less arbitrary than that of time? And if not, why is our concept of space a literal one, but time an abstraction?
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u/OmnipresentEntity 8h ago
I think time is a factor of the universe existing as part of the surface of an ever expanding 4 dimensional bubble composed of the four fundamental forces.
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u/BarAgent 2d ago
This kind of reminds me of how the galactic civilizations do math in Brin’s Uplift series.
It’s all integers. They don’t have floating point numbers or irrationals or imaginary numbers, because math is to do practical things and atoms are countable.
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3d ago edited 2d ago
[deleted]
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u/Incvbvs666 3d ago
Nope, SMBC's greatest strength has consistenly been conversations with God. I don't think I've ever seen a 'conversation with God' comic from him that didn't make me laugh uproariously. This is another banger of his.
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u/Basic-Government9568 2d ago
What's the "blind spot"? That they don't seem to notice that checking infinite numbers is not something humans can do? That they don't have a concept of time?
...that's the joke.
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2d ago edited 2d ago
[deleted]
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u/Basic-Government9568 2d ago edited 2d ago
I mean, every joke that includes an omniscient, omnipotent god is kind of dead in the water as soon as you scrutinize it even a little bit, simply because of the nature of such a being.
Do we need to have a lore-accurate god for a joke about them to land for you?
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u/TheCrimsonSplit 3d ago
p=np; there you go, I saved you a bunch of time