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
i guess we'll see where the paper ultimately leads for sure, but things
are cooking rLiN+A
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
You can't do much advanced computing on an Apple laptop operating from your kitchen table.
i guess we'll see where the paper ultimately leads for sure, but things
are cooking rLiN+A
As an IT professional, I can say without the least hesitation, there's not many machines that can compare with a Cray.
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.
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 rLiN+A
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?
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?-a 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 rLiN+A
your
kitchen table.
That is a matter of perspective.-a 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.
On 8/12/26 7:34 PM, Ross Finlayson wrote:
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 >>>> your
i guess we'll see where the paper ultimately leads for sure, but
things
are cooking rLiN+A
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
On 08/12/2026 10:15 PM, dart200 wrote:
On 8/12/26 7:34 PM, Ross Finlayson wrote:
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?-a 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 >>>>> your
i guess we'll see where the paper ultimately leads for sure, but
things
are cooking rLiN+A
kitchen table.
That is a matter of perspective.-a 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
Why would you do that?
It's kind of like driving a car, and knowing the limits,
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.
It's like the very notion of analysis, making
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, 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.--
On 8/13/26 10:12 AM, Ross Finlayson wrote:
On 08/12/2026 10:15 PM, dart200 wrote:
On 8/12/26 7:34 PM, Ross Finlayson wrote:
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
i guess we'll see where the paper ultimately leads for sure, but >>>>>>> things
are cooking rLiN+A
from
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
Why would you do that?
because erroneously proving a limit that does not actually exist will artificially limit our potential to wield computing as an applied technique
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,
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.
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
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, making
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.
i'm not proposing a reduction in power to computing, if anything this
would be an expansion in descriptive power
Mirimanoff points out that a model of finite ordinals is extra-ordinary,
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.
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
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.
On 08/13/2026 06:29 PM, dart200 wrote:
On 8/13/26 10:12 AM, Ross Finlayson wrote:
On 08/12/2026 10:15 PM, dart200 wrote:
On 8/12/26 7:34 PM, Ross Finlayson wrote:
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?-a 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 rLiN+A
your
kitchen table.
That is a matter of perspective.-a 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
Why would you do that?
because erroneously proving a limit that does not actually exist will
artificially limit our potential to wield computing as an applied
technique
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,
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.
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
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, making
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.
i'm not proposing a reduction in power to computing, if anything this
would be an expansion in descriptive power
Mirimanoff points out that a model of finite ordinals is extra-ordinary, >>> 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.
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
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.
Hm. Thanks for writing.
Agreeably, accounts of the _unbounded_, of the _finite_, keep
things "sensible, fungible, and tractable", and that accounts
of _completions_, in the _infinite_, are due descriptions by
super-classical results like what give the geometric series,
or Zeno's arguments either way _both existing_ when induction
either way makes a counter-development/counter-example to the other,
this is about "weak and strong induction", that induction and infinite induction it's usual given account of the base case then inductive case,
is "weak", since it's _completion_, doesn't have an "actual
infinite".
For the theory of computation, a usual idea is that there are
"Turing machines" and then "Zeno machines", then, that like
there are the "digital" and "analog", the "discrete" and "continuous",
that it's independent number theory which of large, larger, and largest
laws of large numbers apply, for inductive, infinite, and continuum limits.
There are at least three kinds of limits, then that if infinite limits
and continuum limits require the "strong induction", i.e., weak
induction plus also another reason why the completion occurs,
then makes for "completeness" and "measure" after "density".
The unbounded readily gives density, it's agreeable.
I suppose it's been called "non-standard", like "non-standard models
of integers" or "non-standard models of probability", yet, that's
because the entire linear curriculum mostly doesn't have an account
of deductive analysis at all, since, trivially enough, it's provides
a direct and immediate counter-development and counter-example to
any plain course of the naive (or weak) induction at all, which has
been known since antiquity about why the ancients said truth was
"discovered" instead of "invented".
Approximation algorithms abound, to be sure, and approximations
always have a nominally non-zero error term, and modeling the error term
or modeling the error bounds of approximations, include for
where the error term gets away from the approximation itself.
Then, the "as-if" or "almost", like the "almost-all",
"almost-everywhere", "almost-periodic", "almost-analytic", the sorts
of "almost-approximate", that's naturally enough more of a
"what-if" than an "as-if".
So, "modeling the error bounds" is usually what's involved in
analysis since here the study of things is called "dynamical
modeling" not "chaos theory", since math is not indeterministic,
then about singularity theory that singularities in a singularity
theory are branches in a multiplicity theory, just taking the extra-book-keeping when there's enough scratch-space to write
out the numerical method or approximative algorithm, or making
an account of how mathematics does that in actual numerical resources,
or for the usual accounts of incompleteness (or, inconsistency if
you'd rather not have incompleteness) of the ordinary, and somehow
the completeness and the consistency in the extra-ordinary,
of the infinite and continuous.
So, Church-Turing thesis is prolly not fritzed, though that
it is though merely a "fragment" or the "ordinary", and,
in the extra-ordinary then thusly, it's _independent_, the ordinary.
(The "standard" in one sense of the ordinary is "non-standard"
the other, like "standard infinitesimals" or "standard integers",
one giving a clock-arithmetic the other a field-arithmetic,
and only agreeing about the measure of [0,1].)
On 8/14/26 7:27 AM, Ross Finlayson wrote:
On 08/13/2026 06:29 PM, dart200 wrote:
On 8/13/26 10:12 AM, Ross Finlayson wrote:
On 08/12/2026 10:15 PM, dart200 wrote:
On 8/12/26 7:34 PM, Ross Finlayson wrote:
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?-a 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 rLiN+A
your
kitchen table.
That is a matter of perspective.-a 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
Why would you do that?
because erroneously proving a limit that does not actually exist will
artificially limit our potential to wield computing as an applied
technique
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,
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.
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
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, making
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.
i'm not proposing a reduction in power to computing, if anything this
would be an expansion in descriptive power
Mirimanoff points out that a model of finite ordinals is extra-
ordinary,
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.
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
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.
Hm. Thanks for writing.
Agreeably, accounts of the _unbounded_, of the _finite_, keep
things "sensible, fungible, and tractable", and that accounts
of _completions_, in the _infinite_, are due descriptions by
super-classical results like what give the geometric series,
or Zeno's arguments either way _both existing_ when induction
either way makes a counter-development/counter-example to the other,
this is about "weak and strong induction", that induction and infinite
induction it's usual given account of the base case then inductive case,
is "weak", since it's _completion_, doesn't have an "actual
infinite".
For the theory of computation, a usual idea is that there are
"Turing machines" and then "Zeno machines", then, that like
there are the "digital" and "analog", the "discrete" and "continuous",
that it's independent number theory which of large, larger, and largest
laws of large numbers apply, for inductive, infinite, and continuum
limits.
There are at least three kinds of limits, then that if infinite limits
and continuum limits require the "strong induction", i.e., weak
induction plus also another reason why the completion occurs,
then makes for "completeness" and "measure" after "density".
The unbounded readily gives density, it's agreeable.
I suppose it's been called "non-standard", like "non-standard models
of integers" or "non-standard models of probability", yet, that's
because the entire linear curriculum mostly doesn't have an account
of deductive analysis at all, since, trivially enough, it's provides
a direct and immediate counter-development and counter-example to
any plain course of the naive (or weak) induction at all, which has
been known since antiquity about why the ancients said truth was
"discovered" instead of "invented".
Approximation algorithms abound, to be sure, and approximations
always have a nominally non-zero error term, and modeling the error term
or modeling the error bounds of approximations, include for
where the error term gets away from the approximation itself.
Then, the "as-if" or "almost", like the "almost-all",
"almost-everywhere", "almost-periodic", "almost-analytic", the sorts
of "almost-approximate", that's naturally enough more of a
"what-if" than an "as-if".
So, "modeling the error bounds" is usually what's involved in
analysis since here the study of things is called "dynamical
modeling" not "chaos theory", since math is not indeterministic,
then about singularity theory that singularities in a singularity
theory are branches in a multiplicity theory, just taking the
extra-book-keeping when there's enough scratch-space to write
out the numerical method or approximative algorithm, or making
an account of how mathematics does that in actual numerical resources,
or for the usual accounts of incompleteness (or, inconsistency if
you'd rather not have incompleteness) of the ordinary, and somehow
the completeness and the consistency in the extra-ordinary,
of the infinite and continuous.
So, Church-Turing thesis is prolly not fritzed, though that
it is though merely a "fragment" or the "ordinary", and,
ross, i'm not using a model of hypercomputation to usurp the ct thesis.
as we don't actually know how to mechanically implement those, they
cannot be used by a human to compute something a turing machine cannot,
and therefore do not refute it.
recall that the ct thesis is thus:
-a| A function is effectively calculable by a human being
-a| _iff_ it can be computed by a turing machine.
the ct thesis claims actual mechanical computation that a human can do
is limited to what can be expressed within the turing machine model. refuting the ct thesis involves demonstrating a mechanical process that utilizes an idealized human agent to compute something which a turing machine simply cannot express.
the refutation is not algorithmically novel or hard, it's more due to
the fact that the human operation exists outside what can be directly referenced by the turing machine model. yes, we can simulate the human operation within the turing machine model, and that simulation will be limited by what turing machines can express, but a human agent
mechanically doing that same thing just is not. i'm sure u won't be convinced by my paragraphs here, the full argument will be in a paper
i'm finishing up.
the refutation is again, not algorithmically hard, it's moreso tied to
the same self-referential paradox which stumped turing into establishing limits to turing machine computation in the first place, back on the
1936 paper /on computable numbers/
in the extra-ordinary then thusly, it's _independent_, the ordinary.
(The "standard" in one sense of the ordinary is "non-standard"
the other, like "standard infinitesimals" or "standard integers",
one giving a clock-arithmetic the other a field-arithmetic,
and only agreeing about the measure of [0,1].)
On 16/08/2026 5:38 AM, dart200 wrote:
On 8/14/26 7:27 AM, Ross Finlayson wrote:
On 08/13/2026 06:29 PM, dart200 wrote:
On 8/13/26 10:12 AM, Ross Finlayson wrote:
On 08/12/2026 10:15 PM, dart200 wrote:
On 8/12/26 7:34 PM, Ross Finlayson wrote:
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 rLiN+A
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
Why would you do that?
because erroneously proving a limit that does not actually exist will
artificially limit our potential to wield computing as an applied
technique
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,
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.
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
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, making
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.
i'm not proposing a reduction in power to computing, if anything this
would be an expansion in descriptive power
Mirimanoff points out that a model of finite ordinals is extra-
ordinary,
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.
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
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.
Hm. Thanks for writing.
Agreeably, accounts of the _unbounded_, of the _finite_, keep
things "sensible, fungible, and tractable", and that accounts
of _completions_, in the _infinite_, are due descriptions by
super-classical results like what give the geometric series,
or Zeno's arguments either way _both existing_ when induction
either way makes a counter-development/counter-example to the other,
this is about "weak and strong induction", that induction and infinite
induction it's usual given account of the base case then inductive case, >>> is "weak", since it's _completion_, doesn't have an "actual
infinite".
For the theory of computation, a usual idea is that there are
"Turing machines" and then "Zeno machines", then, that like
there are the "digital" and "analog", the "discrete" and "continuous",
that it's independent number theory which of large, larger, and largest
laws of large numbers apply, for inductive, infinite, and continuum
limits.
There are at least three kinds of limits, then that if infinite limits
and continuum limits require the "strong induction", i.e., weak
induction plus also another reason why the completion occurs,
then makes for "completeness" and "measure" after "density".
The unbounded readily gives density, it's agreeable.
I suppose it's been called "non-standard", like "non-standard models
of integers" or "non-standard models of probability", yet, that's
because the entire linear curriculum mostly doesn't have an account
of deductive analysis at all, since, trivially enough, it's provides
a direct and immediate counter-development and counter-example to
any plain course of the naive (or weak) induction at all, which has
been known since antiquity about why the ancients said truth was
"discovered" instead of "invented".
Approximation algorithms abound, to be sure, and approximations
always have a nominally non-zero error term, and modeling the error term >>> or modeling the error bounds of approximations, include for
where the error term gets away from the approximation itself.
Then, the "as-if" or "almost", like the "almost-all",
"almost-everywhere", "almost-periodic", "almost-analytic", the sorts
of "almost-approximate", that's naturally enough more of a
"what-if" than an "as-if".
So, "modeling the error bounds" is usually what's involved in
analysis since here the study of things is called "dynamical
modeling" not "chaos theory", since math is not indeterministic,
then about singularity theory that singularities in a singularity
theory are branches in a multiplicity theory, just taking the
extra-book-keeping when there's enough scratch-space to write
out the numerical method or approximative algorithm, or making
an account of how mathematics does that in actual numerical resources,
or for the usual accounts of incompleteness (or, inconsistency if
you'd rather not have incompleteness) of the ordinary, and somehow
the completeness and the consistency in the extra-ordinary,
of the infinite and continuous.
So, Church-Turing thesis is prolly not fritzed, though that
it is though merely a "fragment" or the "ordinary", and,
ross, i'm not using a model of hypercomputation to usurp the ct
thesis. as we don't actually know how to mechanically implement those,
they cannot be used by a human to compute something a turing machine
cannot, and therefore do not refute it.
recall that the ct thesis is thus:
| A function is effectively calculable by a human being
| _iff_ it can be computed by a turing machine.
the ct thesis claims actual mechanical computation that a human can do
is limited to what can be expressed within the turing machine model.
refuting the ct thesis involves demonstrating a mechanical process
that utilizes an idealized human agent to compute something which a
turing machine simply cannot express.
So, why not use my earlier example of the /Antikythera mechanism/ as a counter example. If I get it right, it's an actual mechanical calcula-
tor, and as such, cannot be implemented in a /turing machine/ except as
a simulation of such.
Now, simulation isn't reality. /The map is not the territory/. I know mathematical types have a hard time with this concept, so bear with me
for now if you're confused.
I'm also confused about the theoretical argument about what is and isn't calculable by a turing machine. I live in the real world, and I use
real machines.
Basically, what I'm getting at, a human operating the /Antikythera
mechanism/ is indeed calculating something that /cannot/ be done by
a turing machine, and therefore refutes the /ct thesis/ above.
Now, I know proof by counter example is not pleasant to experience, so
I don't begrudge you being upset, but please find another topic for a
thesis, or just present the /Antikypthera mechanism/ as a counter ex-
ample, and be done with it.
the refutation is not algorithmically novel or hard, it's more due to
the fact that the human operation exists outside what can be directly
referenced by the turing machine model. yes, we can simulate the human
operation within the turing machine model, and that simulation will be
limited by what turing machines can express, but a human agent
mechanically doing that same thing just is not. i'm sure u won't be
convinced by my paragraphs here, the full argument will be in a paper
i'm finishing up.
the refutation is again, not algorithmically hard, it's moreso tied to
the same self-referential paradox which stumped turing into
establishing limits to turing machine computation in the first place,
back on the 1936 paper /on computable numbers/
in the extra-ordinary then thusly, it's _independent_, the ordinary.
(The "standard" in one sense of the ordinary is "non-standard"
the other, like "standard infinitesimals" or "standard integers",
one giving a clock-arithmetic the other a field-arithmetic,
and only agreeing about the measure of [0,1].)
I didn't graduate as a /math major/ so I don't move in the infinite
social circles.
Have a nice day!
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