Travis B. wrote: ↑Fri May 01, 2026 11:22 am
The key thing is that
math is an abstraction divorced from any particular thing in the physical world. One can express math countless different ways in the physical substrate, yet the math remains the same regardless. By your logic, math itself is inseparable from the physical world, and hence the rules of math should change depending on whether you are drawing equations in sand or doing computations on a computer.
mmm... but already this happens from time to time, as with the case of parallel lines. we could say that they're different mathematical entities, parallel-lines-in-a-plane and parallel-lines-in-a-sphere, but that wasn't apparent till it was: i don't think there's any transcendental math for there to be objetively different mathematical entities beyond language and thoughts that humans utter and think and so, from that perspective, the rules of math can and do change all the time: we used to think the square root of minus one was a silly notion, and now we know better. we used to think zero was silly, now we know better.
but of course not all changes in material reality should be expected to affect the math of material entities either: the hipotenuse of a square triangle with sides 3 and 4 in fact is 5 whether the triangle is made of wood or stone or bone, cause that mathematical relation is not a predicate that applies to like different materials, but i don't know, to space itself or something. as with parallels, maybe in different spaces the famous theorem doesn't obtain. maybe it doesn't obtain in spheres or negative curvature spaces or sth i honestly dunno.
zompist wrote: ↑Fri May 01, 2026 3:29 pmI'll grant you this quibble, but not the general point that a computer can't be made of toast. It happens that you can compute using silicon, or vacuum tubes, or brains, or punch cards and tinker toys. If you can make a NAND gate you can make any computational device. Some substrates would be unutterably slow or clumsy, but that's an engineering problem, not a philosophical obstacle.
i meean, sure, you could glue toast in this or that way to make a sort of Babbage machine buuuut, at that point would we even say we're running doom on toast? i'd say we're running it on a mechanical computer that's made *of* toast, and a lot of PVA, and what'd you use for bearings? steel probably. we're running doom on toast at this point only technically, but i'm on board with the general idea that a computer can, in principle, be made of whatever materials.
Sure, human things are "things" based on convention, which can be arbitrary or incoherent. You can certainly argue that any actual heap of sand doesn't have a precisely measurable size or number of grains....
sure but this all boils down to facts about material reality: it turns out that there's objective ways to reckon certain things, cause it turns out there's actually quantized stuff in material-reality-as-such. or at least so say our best models, sure, but you don't need to come up with an entire new class of entities, actually-existing-transcendental-ideal-things for that. The andromedans would arrive at many of the same mathematical conclusions as we have, in essence, but that's because they have a lot of things in common with us: material, real, observable things, like light, protons, space, fields, etcetera. we share the same material reality, and we're both clever thingamabobs, so we arrive a similar observations, we'd expect this.
I think there is:
Code: Select all
0 = {}
1 = {0}
2 = {0, 1}
3 = {0, 1, 2}
4 = {0, 1, 2, 3}
5 = {0, 1, 2, 3, 4}
6 = {0, 1, 2, 3, 4, 5}
i don't think i get it. we can all write things down, that doesn't mean those things are actually existing things in reality, does it?
I guess this may be more of a yellow dress / purple dress kind of thing. I get where mathematical realism comes from, the fact that math works is remarkable and wonderful but, then again, you'd expect smart apes to figure out some regularities in the material reality they find themselves in, wouldn't you? that's kinda what being smart is all about. the effectiveness of it all doesn't entail or suggest, i don't think, the existence of a transcendental realm of math, or a transcendental god who created said realm, or any of it... or at least, i honestly don't see how it does.