On 08/12/2026 10:15 PM, dart200 wrote:because erroneously proving a limit that does not actually exist will artificially limit our potential to wield computing as an applied techniqueOn 8/12/26 7:34 PM, Ross Finlayson wrote:Why would you do that?On 08/07/2026 10:18 AM, Johann 'Myrkraverk' Oskarsson wrote:>On 06/08/2026 5:29 AM, Dude wrote:>>>
dart200 <user7160@newsgrouper.org.invalid> posted:
>upon picking apart the abject nonsense that is recursive
undecidability,
so that i can discuss what undecidability _actually_ looks like within
computing,
>
i find myself stumbling into a proof that turing machines as a
model are
not capable of computing everything that can be computed mechanically
>
Have you considered how to model the /Antikythera Mechanism/ on a Turing
machine, as a subject for your thesis? I believe that's been done, so
the question is, what exactly is it about mechanical computing that
cannot be done on Turing machines?
>>>You can't do much advanced computing on an Apple laptop operating from
i guess we'll see where the paper ultimately leads for sure, but
things
are cooking ✌️
>
your
kitchen table.
That is a matter of perspective. The fruit laptop on the kitchen table
can be thought of as a terminal, or even just a typewriter, for the
Cray.
>>>
As an IT professional, I can say without the least hesitation, there's
not
many machines that can compare with a Cray.
>
I'm an I.T. professional who's never used a Cray, so I can't comment on
that.
>>>
Cray Computers are optimized for massive mathematical arrays rather
than
standard scalar math. Crays are heavily utilized in nuclear research,
aerospace design, codebreaking, and global satellite weather
prediction.
>
So if I understand Finseth's book about how to code an Emacs correctly,
a Cray supercomputer would be massively hampered were you to implement a
text editor on one.
>
So, which text editor do yo prefer, when coding a Cray?
Maybe if you read Finsler and Boffa then it would be more clear
why Church-Turing thesis is in a model of computation that simply
doesn't necessarily include "Zeno machines" and the like, while
it's so for the finite and bounded, in the unbounded.
>
Finsler and Boffa make some various accounts of "infinity"
and the "extra-ordinary" that numbers naturally have that
are usually ignored or plain banned in "ordinary" models.
>
theoretical mathematician do have a tendency to try wacky shit when it
comes infinite ...
>
turing for example tried to extend logical systems into transfinite
ordinals in an attempt to get around incompleteness. no idea what kind
of axiom would realistically come past an infinite amount of them, but
this unfortunately didn't work so it doesn't really matter eh?
>
i plan to propose a limit to the incompleteness within computing, which
in turn may in fact make it complete. or at least trivialize
incompleteness to the point of irrelevancy
>
like specifically when it comes to our practical application of computing, we do not prove what our computations do. we might test various inputs/outputs combos, but this is quite a bit inferior to proving semantics across their entire input possibility space (and not just brute forcing that proof)
It's kind of like driving a car, and knowing the limits,i'm not sure how framing currently intractable problems as actually tractable (without limiting the domain!) risks driving over some kind of existential cliff in this case
since one never knows the limits, yet is always finding the limits,
incompleteness is simply beyond a limit, and not being cognizant
of it, if not quite sure where it is, risks hitting its wall,
or driving over its cliff.
undecidability within computing is entirely founded in the problems of computing the semantic properties of computations, unlocking those kinds of problems as actually tractable seems like possibly a huge boon to the advancement of computing
It's like the very notion of analysis, makingi'm not proposing a reduction in power to computing, if anything this would be an expansion in descriptive power
restriction-of-comprehension keeps some things simple, other things
un-available to reason. Somebody else needn't adopt that restriction,
and then it's like a rooster locking itself in the coop.
Mirimanoff points out that a model of finite ordinals is extra-ordinary,i have a hard time parsing what u mean even with gemenigpts help, but please do remember the /theory of computing/ is inherently limited to the cardinality of natural numbers, as mechanical computations must be mapped to the finite machine description which compute them
Russell wishes it away, the "Russell-ian retro-thesis",
it's natural that infinity is "in", and that models of ordinals
or integers start as both bounded-fragments and
extraordinary-extensions, the "standard" model not even existing except as
a limit of those.
The classical expositions of the super-classical, usually considered
to start with Zeno's account of infinite-divisbility and summability
and motion in time, and the geometric series, gives reasons why that
for infinitary-analysis, that's about the only place to start that
isn't wacky, and it makes of itself accounts of why induction fails
where deduction succeeds, and about complementary duals, and the
great account of structure and geometry and arithmetic, and continuity
and infinity, up-front.
Then, that there are more models of laws of large numbers, and--
that naive induction is basically finitistic and only knows a
law of small numbers, or "weak" induction, compared to the "strong"
induction which is given an account by the existence of a space
and its structure, that the "a priori" of "strong induction" is
due classical-expositions of super-classical results after the
double-reductio and the ad-infinitum instead of the ad-absurdam,
about the "ab-absurdam", that numbers and forms always have those.
Then, retro-finitism or ultra-finitism is naive, and incomplete.
arising us out of the computing dark ages,
please excuse my pseudo-pyscript,
~ the lil crank that could
| Date | Sujet | # | Auteur | |
| 16 Jul 26 |  ct thesis is prolly fucked | 9 | dart200 | |
| 5 Aug 26 |  Re: ct thesis is prolly fucked | 8 | Dude | |
| 13 Aug 26 |  Re: ct thesis is prolly fucked | 7 | Ross Finlayson | |
| 13 Aug 26 | Re: ct thesis is prolly fucked | 6 | dart200 | |
| 13 Aug 26 | Re: ct thesis is prolly fucked | 5 | Ross Finlayson | |
| 14 Aug 26 | Re: ct thesis is prolly fucked | 4 | dart200 | |
| 14 Aug15:27 | Re: ct thesis is prolly fucked | 3 | Ross Finlayson | |
| 15 Aug22:38 | Re: ct thesis is prolly fucked | 2 | dart200 | |
| 17 Aug01:43 |  Church-Turing (ct) thesis | 1 | Ross Finlayson |
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