Is it possible to talk about the boundaries of what can be computed without considering an automaton with infinite memory, or accepting that there are undecidable languages? If a bound is placed on time and space available to the automaton then does the algorithm complexity need to be taken into account?

On Friday, August 11, 2023 at 2:42:18 PM UTC-7, Kevin S wrote:
> Is it possible to talk about the boundaries of what can be computed without considering an automaton with infinite memory, or accepting that there are undecidable languages? If a bound is placed on time and space available to the automaton then does the algorithm complexity need to be taken into account?

Pretty much all "computability theory" is already "ultra-finitist".

I.e., "since the tape's unbounded, we can't really unbounded our program, too",m
but nature has one, and for any given large bound, there's an arbitrarily larger integer.

Now, one way to think of that is that it helps explain related rates and asymptotic
complexity. Another is that the entire lesson is that thinking is futile, along with a
grab-bag of results after undecide-ability and incompleteness, that there's no true theory.

.... Which some reject.

On Friday, August 11, 2023 at 2:49:07 PM UTC-7, Ross Finlayson wrote:
> On Friday, August 11, 2023 at 2:42:18 PM UTC-7, Kevin S wrote:
> > Is it possible to talk about the boundaries of what can be computed without considering an automaton with infinite memory, or accepting that there are undecidable languages? If a bound is placed on time and space available to the automaton then does the algorithm complexity need to be taken into account?
> Pretty much all "computability theory" is already "ultra-finitist".
>
> I.e., "since the tape's unbounded, we can't really unbounded our program, too",m
> but nature has one, and for any given large bound, there's an arbitrarily larger integer.
>
> Now, one way to think of that is that it helps explain related rates and asymptotic
> complexity. Another is that the entire lesson is that thinking is futile, along with a
> grab-bag of results after undecide-ability and incompleteness, that there's no true theory.
>
> ... Which some reject.

It's similar when there's been constructed "vector machines" or what that have basically
"we don't really know what went in or how it comes out, it's not just plausibly deniable
but all the theory says it's so. It's right though, because empirically we haven't been sued
out of existence".

On Friday, August 11, 2023 at 2:54:49 PM UTC-7, Ross Finlayson wrote:
> On Friday, August 11, 2023 at 2:49:07 PM UTC-7, Ross Finlayson wrote:
> > On Friday, August 11, 2023 at 2:42:18 PM UTC-7, Kevin S wrote:
> > > Is it possible to talk about the boundaries of what can be computed without considering an automaton with infinite memory, or accepting that there are undecidable languages? If a bound is placed on time and space available to the automaton then does the algorithm complexity need to be taken into account?
> > Pretty much all "computability theory" is already "ultra-finitist".
> >
> > I.e., "since the tape's unbounded, we can't really unbounded our program, too",m
> > but nature has one, and for any given large bound, there's an arbitrarily larger integer.
> >
> > Now, one way to think of that is that it helps explain related rates and asymptotic
> > complexity. Another is that the entire lesson is that thinking is futile, along with a
> > grab-bag of results after undecide-ability and incompleteness, that there's no true theory.
> >
> > ... Which some reject.
> It's similar when there's been constructed "vector machines" or what that have basically
> "we don't really know what went in or how it comes out, it's not just plausibly deniable
> but all the theory says it's so. It's right though, because empirically we haven't been sued
> out of existence".

Don't get me wrong, if I use an argument of the troll uses, not all of which I do, I use it in full effect.

That the troll uses arguments I might use doesn't mean I don't use them.

Here, the troll is a broken arguer, that you reduce to three terms to set it, its truth,
then any other formula you feed it, it picks the finder, arguments you use.

Then, the rest fills out with only complaining and attacking anything else.

You give it input until it's satisfied, then next time it'll have a case or a drop.

On 8/11/2023 2:42 PM, Kevin S wrote:
> Is it possible to talk about the boundaries of what can be computed without considering an automaton with infinite memory, or accepting that there are undecidable languages? If a bound is placed on time and space available to the automaton then does the algorithm complexity need to be taken into account?

Well, the Mandelbrot set has a boundary, yet is infinite at the same time...