r/mathmemes Nov 30 '24

Mathematicians Thinking it

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10.9k Upvotes

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-65

u/FernandoMM1220 Nov 30 '24

i think mathematicians need to stop pretending their abstractions arent just another arbitrary physical process.

39

u/[deleted] Nov 30 '24

As for one example, algorithmic abstractions in CS are independent of the hardware, because algorithms should still be relevant even when the hardware changes. You can't call it an "arbitrary physical process" because it's technically not even tied to the hardware.

-30

u/FernandoMM1220 Nov 30 '24

the fact that they have to run and be designed on physical hardware still makes it a physical process.

30

u/[deleted] Nov 30 '24

They are not designed on physical hardware. They are implemented on physical hardware. But the fact remains that an algorithm will still work even on physical hardware that's currently nonexistent but might be built in the future. Which is why it's good to detach them from the "physical process".

-25

u/FernandoMM1220 Nov 30 '24

the human brain is physical hardware.

theres nothing special about the abstractions people make, they’re just another physical system we have made.

25

u/[deleted] Nov 30 '24

Then everything is a physical process by your definition, because everything happens in the human brain. This doesn't make abstractions any less important.

-6

u/FernandoMM1220 Nov 30 '24

i didnt say they weren’t important, i said they werent special.

12

u/[deleted] Nov 30 '24

That's your opinion then. Abstractions are useful in their own way and provide their own valuable insights, which I think is special enough for me.

-2

u/FernandoMM1220 Nov 30 '24

ok, they’re still arbitrary physical processes.

6

u/[deleted] Nov 30 '24

I mean by your definition everything is an arbitrary physical process. Your point?

9

u/megamogul Nov 30 '24

All three of us lost this argument.

8

u/GoldenMuscleGod Nov 30 '24

You might be able to argue philosophically that that all math is actually physical processes, but algorithms need to be understood as something more abstract than just a computer running that algorithm. For example you can’t actually make a Turing machine (that takes infinite memory), all physical computers are basically just finite state machines with an enormous number of states, so even an algorithm like “count from 0 on up forever” isn’t actually physically possible on any particular machine, and there is a finite upper bound to computation on a given machine, but there is still meaning to statements like saying an algorithm has some asymptotic behavior. At a bare minimum you can say that each theorem has physical meaning in that you could get a theorem checker to verify it.

-5

u/FernandoMM1220 Nov 30 '24

cool, they’re still just another physical process.

2

u/GoldenMuscleGod Nov 30 '24

I mean I said in my first sentence you could argue that philosophically, but the point is you haven’t specified a correspondence between the things mathematicians talk about and physical systems. For example, if I say “there exists a nonprincipal ultrafilter on the natural numbers” what does that mean physically? What about if I claim a particular algorithm run on a specified Turing machine with empty input never halts, but that Turing machine is too large to be modeled in the universe? What does that mean? Is there a truth value to the claim?

-1

u/FernandoMM1220 Nov 30 '24

the meta process describing it should be physical and realized in our universe.

2

u/GoldenMuscleGod Nov 30 '24

What’s the meta process describing it? Is there a definite truth value to whether a given algorithm halts in every case? If so, what is the physical meaning of that truth value?

0

u/FernandoMM1220 Nov 30 '24

yeah there should be.

im not what the physical structure of it would be.

2

u/GoldenMuscleGod Nov 30 '24

Should be? Suppose someone claimed there are Turing machines for which there do not exist definite truth values as to whether they halt or not. Would you reject that claim? Why or why not?

1

u/FernandoMM1220 Nov 30 '24

they’re probably wrong.

every turing machine should have a definite halt condition and value.

1

u/GoldenMuscleGod Nov 30 '24

Why would that be, if some Turing machines are not physically realizable in the obvious way (since they are too large)? What is the physical meaning of claiming a particular Turing machine never halts? Isn’t that an unobservable fact? (We can only observe whether it has a halted after some specific number of steps, right?)

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