we did not even start talking about extra dimensions...

Well, the expanding-universe theory is in the standard model. The big bang. So expanding infinitely, at the speed of light. Space extends, a bit like an inflating balloon. Dark energy increases the extension. Gravity propagates changes through waves, ripples in spacetime at the speed of light.

True. I did not mention I was talking about the standard model. In the multiverse model? Who knows. The infinite universe model, or the quantum vacuum energy model... I'm just implicitly using Occam's razor 🙈because it's the simplest that corresponds with our observations.

No. Since in the universe, we tend to assume time is infinite (hard to believe :-)) but matter is finite. In a Turing machine, both time and memory (matter) are infinite. With these, the Turing machine is more powerful.

The universe is way too constrained, and is probably less powerful than a Turing machine. After all, Turing machines have infinite memory (and existing compute that we know doesn't). To get to the level of Turing machines we may have to accept the multiverse?

I feel bad for disagreeing all the time. In a computer you get inaccuracies if the mantissa does not have enough bits. It can be very small, but a mantissa will never be able to represent π, of course. These effects become noticeable in long iterations or vector ops, as the errors then propagate.

but according to your discreteness theory, things themselves are countable infinite? And yes, you can take R as the set of symbols... but doesn't that dilute the definition of "symbol" beyond anything useful.

What were we talking about again?

so you mean randomness.

One should not confuse inaccuracy and uncertainty. The former means the observer measures values that differ systematically from the true value. The latter quantifies the range of possible values due to measure limits or variability. You can still measure a probability density.

back to this. My starting point, yes why should there not be more than we can name?
But your statement on countable infinity of symbols assumes discrete symbols. So, e.g., you see two handwritten A's as identical. If you don't, it's uncountable. So.... what is a symbol?

It's just numbers! So: in your computed simulation: yes.

Now you can discuss what happens if you use analogue computers. Or optical ones. They're not so popular, for obvious reasons. There, one could argue, their accuracy / granularity ends with the granularity of the underlying, physical system.

You mean, *can* have large effects. Now we're off to chaos theory, fun!

But we cannot determine this, right, according to Heisenberg's uncertainty principle? And following that principle, randomness is built into the system.

Gravity -- the curvature of spacetime -- follows these laws.

Well... yes and no. Of course this is true, but, at the same time you can scale up the world, in your simulation. Which then allows you to let your word describe a state at any granularity.

only in most standard models; not in string theory. And again: both are just theories, neither of them has been "proven", and probably never will?

Michel, are you sure? I think the standard model is in your mind when you say this. But even in that model, space and time are often taken continuously (except in quantum gravity). Or EM waves. In string theory, spacetime is continuous. *Either way*: both are just theories.

Anke Kranendonk, Kapitein Kees?
Anna Woltz, Gips -- wellicht nog iets te moeilijk voor B2
Wellicht een vertaalde Dahl, De Heksen ofzo, maar ja, wie leest nou vertaalde boeken?