[bubblyworld]

Wild, well, I'm a lowly math PhD so that's where my interests lie =)

I'm _not_ suggesting we replace R with Q. I'm suggesting that you bake in the desired accuracy of your computational approximation as an input. This is how Turing evades self-referential problems in his conception of computational reals, and also perhaps how you evade your criticisms with CM requiring infinite precision.

Similarly - I think it's reasonable in a computational context to assume linearity up to an error bound that is provided as an input. Of course things become non-computable if you ask for exact linearity. Equality itself is non-computable!

Either way I think we agree about physics. I don't believe the universe is describable as a computable function. Merely that we can approximate it to arbitrary degrees of accuracy =P

[mjburgess]

I think we teach people only what we can write in finite formula, and compute in finite time.

This is imv, much like teaching people what's under a street light just because everything else is in darkness.

I think, philosophically, we can build inferential telescopes that point to the vast (epistemic) blackness, inside say, a proton, or a cell, or the chaos in water.

As an ameliorative, or therapeutic project, I think people who build computational models too much should meditate on the number of protons flowing free in a drop of water, and what properties their interactions might bring about. And whether it would ever be possible to know them.

[bubblyworld]

Poetic. Perhaps you're right.

[calf]

I've read this thread exchange with interest, but what about the results that quantum computers are simulatable by classical computers? See David Deutsch 1985. This would reduce the issue of infinite Hilbert spaces to simulation using quantum computers, and in turn, Deutsch's result which says classical Turing machines can actually simulate quantum computers.

[mjburgess]

You can always make local arguments that, say, some g can be substituted with some c.

The issue is broader than that. It concerns the premises of vast areas of physics -- you have to show they are more likely false than true.

This isnt an argument saying no c can be found for any given g, it's saying, "g-c gaps have empirical consequences we havent observed" and if we did, physics would be foundationally wrong

[calf]

When they assert theorems like "classical TMs can simulate quantum TMs" they mean the simulation is gapless. Otherwise they use the term approximation.