hi all, especially olcott!
first off, why is usenet so annoying to access? jeez... sorry if
i mess up any conventions. and no edits if i make a typo! such 20th century technology 😮💨
second, olcott could you please tell me the gist of your ideas?
i stumbled onto your name about 10 years ago when i first started contemplating the halting problem. i wrote it down in a document noting that you've been cranking on this since at least 2004! i promptly forgot about
it until a few days ago going thru my archives, and i'm pleasantly surprised to see you're still active working on this, albeit here in some obscure part of computing history...
third, has anyone here (especially olcott) actually read turing's original arguments on the matter? the decision paradox described by turing, involving whether some input machine is "satisfactory" or not, is slightly different than your basic halting paradox, and comes with an additional constraint
that any resolution to said paradox must abide by. namely: if the resolution to
the paradox allows for expressing the computation of the antidiagonal (β) across the sequence of computable numbers .../then ya done goofed!/
if you haven't, i /highly/ recommend carefully reading thru the first two pages
of §8 from /on computable numbers/. they were the /first/ words turing wrote about computing, after defining the underlying model of computing as theory, where he lays down the foundation for undecidability within computing:
https://www.astro.puc.cl/~rparra/tools/PAPERS/turing_1936.pdf#page=17
or you can read my thesis on the matter:
https://www.academia.edu/143540657
hi all, especially olcott!
first off, why is usenet so annoying to access? jeez... sorry if
i mess up any conventions. and no edits if i make a typo! such 20th century technology 😮💨
second, olcott could you please tell me the gist of your ideas?
i stumbled onto your name about 10 years ago when i first started contemplating the halting problem. i wrote it down in a document noting that you've been cranking on this since at least 2004! i promptly forgot about
it until a few days ago going thru my archives, and i'm pleasantly surprised to see you're still active working on this, albeit here in some obscure part of computing history...
third, has anyone here (especially olcott) actually read turing's original arguments on the matter? the decision paradox described by turing, involving whether some input machine is "satisfactory" or not, is slightly different than your basic halting paradox, and comes with an additional constraint
that any resolution to said paradox must abide by. namely: if the resolution to
the paradox allows for expressing the computation of the antidiagonal (β) across the sequence of computable numbers .../then ya done goofed!/
if you haven't, i /highly/ recommend carefully reading thru the first two pages
of §8 from /on computable numbers/. they were the /first/ words turing wrote about computing, after defining the underlying model of computing as theory, where he lays down the foundation for undecidability within computing:
https://www.astro.puc.cl/~rparra/tools/PAPERS/turing_1936.pdf#page=17
or you can read my thesis on the matter:
https://www.academia.edu/143540657
On 9/17/2025 2:18 PM, dart200 wrote:
Here is the essence of my work and its validation by Claude AI https://philpapers.org/archive/OLCHPS.pdf Four other LLM models also
hi all, especially olcott!
first off, why is usenet so annoying to access? jeez... sorry if i mess
up any conventions. and no edits if i make a typo! such 20th century
technology 😮💨
second, olcott could you please tell me the gist of your ideas?
i stumbled onto your name about 10 years ago when i first started
contemplating the halting problem. i wrote it down in a document noting
that you've been cranking on this since at least 2004! i promptly
forgot about it until a few days ago going thru my archives, and i'm
pleasantly surprised to see you're still active working on this, albeit
here in some obscure part of computing history...
third, has anyone here (especially olcott) actually read turing's
original arguments on the matter? the decision paradox described by
turing, involving whether some input machine is "satisfactory" or not,
is slightly different than your basic halting paradox, and comes with
an additional constraint that any resolution to said paradox must abide
by. namely: if the resolution to the paradox allows for expressing the
computation of the antidiagonal (β) across the sequence of computable
numbers .../then ya done goofed!/
if you haven't, i /highly/ recommend carefully reading thru the first
two pages of §8 from /on computable numbers/. they were the /first/
words turing wrote about computing, after defining the underlying model
of computing as theory, where he lays down the foundation for
undecidability within computing:
https://www.astro.puc.cl/~rparra/tools/PAPERS/turing_1936.pdf#page=17
or you can read my thesis on the matter:
https://www.academia.edu/143540657
agree.
This is the summation of 22 years worth of work since 2004. 25% of all
of the postings on comp.theory since 2004 are mine.
I bypass the whole diagonal argument and delve directly into the
semantics of the algorithm specifications.
Here is the essence of my work and its validation by Claude AI https://philpapers.org/archive/OLCHPS.pdf
Four other LLM models also agree.
This is the summation of 22 years worth of work since 2004.
25% of all of the postings on comp.theory since 2004 are mine.
I bypass the whole diagonal argument and delve directly
into the semantics of the algorithm specifications.
let αn be the n-th computable sequence, and let φn(m) be the m-th figure in αn.
Let β be the sequence with 1-φn(m) as its n-th. figure. Since β is computable,
there exists a number K [== β computation] such that 1-φn(n) = φK(n) for all n.
Putting n = K, we have 1 = 2φK(K), i.e. 1 is even. This is impossible.
olcott <polcott333@gmail.com> posted:
Here is the essence of my work and its validation by Claude AI
https://philpapers.org/archive/OLCHPS.pdf
Four other LLM models also agree.
llms can be made to agree 1=2 given enough prompting, unfortunately. we really should
be evaluating llms not based on what they can prove, but on what they can't be
prompted to prove. that would show truly critical reasoning. the bubble popping for
2020s AI will be quite spectacular.
also, that result fundamentally contradicts itself. the analyser simulated its own
behavior as a matter of infinite recursion ... but then uses that to return
a result???
and if that is the result then shouldn't HHH(DD) -> 0, so Halt_Status = 0, and the
if statement triggering the goto HERE loop does not run, causing DD() to halt ...
meaning HHH(DD) should have been 1. the result is just completely nonsensical.
oh dear olcott. but look i have a resolution to this paradox and u definitely are the
right track to a degree, i do hope you'll hear me out fully.
(is there a guide somewhere for usenet markup conventions? like for fixed-width)
This is the summation of 22 years worth of work since 2004.
25% of all of the postings on comp.theory since 2004 are mine.
unfortunately time spent =/= correctness. while i'm sure there is plenty of value
in the work you did do, even beyond priming you for this engagement, i'm also sure
that ur missing something about the original argument for exactly why turing established undecidability in computing in the first place. i'm just hoping your
time spent indicates a willingness to continue engagement, and that if i do swing
you over, others will 👀👀👀
I bypass the whole diagonal argument and delve directly
into the semantics of the algorithm specifications.
the diagonal that turing is discussing not "by-passable". he's talking about an
/actual diagonal/ computed across the sequence of computable numbers: for every r-th
machine that can "satisfactorily" compute a number, the diagonal computation will
find it's r-th digit and this becomes the r-th digit on the diagonal.
the problem turing is worried about is that if such a diagonal is computable, it
can be used to "diagonalize" the computable numbers like cantor did with the reals.
turing presumes that if one can compute a diagonal across the computable numbers,
then this computation could be used to create an anti-diagonal where each digit
is the opposite from the true diagonal ... meaning it would be a computable number that can't exist on the total list of computable numbers. contradiction!
turing even gives a succinct formal proof for this problem:
let αn be the n-th computable sequence, and let φn(m) be the m-th figure in αn.
Let β be the sequence with 1-φn(m) as its n-th. figure. Since β is computable,
there exists a number K [== β computation] such that 1-φn(n) = φK(n) for all n.
Putting n = K, we have 1 = 2φK(K), i.e. 1 is even. This is impossible.
the reason that turing goes on in the next page to show how computing the direct diagonal (β') results in an undecidable paradox is to provide a reason why
the computation of β can't be computed. he does so with a decision paradox that
isn't /exactly/ like the halting paradox, but very much quite similar.
if you resolution for decision paradoxes doesn't also show that β isn't, then it's not gunna work. i don't think you've yet had awareness of this problem,
let alone found a resolution to decision paradoxes that also avoids computing a β.
On 9/17/2025 6:02 PM, dart200 wrote:
The way that the diagonal *is* bypassed is my newest work that is not provided anywhere else besides here:
olcott <polcott333@gmail.com> posted:
Here is the essence of my work and its validation by Claude AI
https://philpapers.org/archive/OLCHPS.pdf Four other LLM models also
agree.
llms can be made to agree 1=2 given enough prompting, unfortunately. we
really should be evaluating llms not based on what they can prove, but
on what they can't be prompted to prove. that would show truly critical
reasoning. the bubble popping for 2020s AI will be quite spectacular.
also, that result fundamentally contradicts itself. the analyser
simulated its own behavior as a matter of infinite recursion ... but
then uses that to return a result???
and if that is the result then shouldn't HHH(DD) -> 0, so Halt_Status =
0, and the if statement triggering the goto HERE loop does not run,
causing DD() to halt ... meaning HHH(DD) should have been 1. the result
is just completely nonsensical.
oh dear olcott. but look i have a resolution to this paradox and u
definitely are the right track to a degree, i do hope you'll hear me
out fully.
(is there a guide somewhere for usenet markup conventions? like for
fixed-width)
This is the summation of 22 years worth of work since 2004.
25% of all of the postings on comp.theory since 2004 are mine.
unfortunately time spent =/= correctness. while i'm sure there is
plenty of value in the work you did do, even beyond priming you for
this engagement, i'm also sure that ur missing something about the
original argument for exactly why turing established undecidability in
computing in the first place. i'm just hoping your time spent indicates
a willingness to continue engagement, and that if i do swing you over,
others will 👀👀👀
I bypass the whole diagonal argument and delve directly into the
semantics of the algorithm specifications.
the diagonal that turing is discussing not "by-passable". he's talking
about an /actual diagonal/ computed across the sequence of computable
numbers: for every r-th machine that can "satisfactorily" compute a
number, the diagonal computation will find it's r-th digit and this
becomes the r-th digit on the diagonal.
the problem turing is worried about is that if such a diagonal is
computable, it can be used to "diagonalize" the computable numbers like
cantor did with the reals. turing presumes that if one can compute a
diagonal across the computable numbers, then this computation could be
used to create an anti-diagonal where each digit is the opposite from
the true diagonal ... meaning it would be a computable number that
can't exist on the total list of computable numbers. contradiction!
turing even gives a succinct formal proof for this problem:
let αn be the n-th computable sequence, and let φn(m) be the m-th
figure in αn.
Let β be the sequence with 1-φn(m) as its n-th. figure. Since β is
computable, there exists a number K [== β computation] such that
1-φn(n) = φK(n) for all n.
Putting n = K, we have 1 = 2φK(K), i.e. 1 is even. This is impossible.
the reason that turing goes on in the next page to show how computing
the direct diagonal (β') results in an undecidable paradox is to
provide a reason why the computation of β can't be computed. he does so
with a decision paradox that isn't /exactly/ like the halting paradox,
but very much quite similar.
if you resolution for decision paradoxes doesn't also show that β
isn't,
then it's not gunna work. i don't think you've yet had awareness of
this problem, let alone found a resolution to decision paradoxes that
also avoids computing a β.
Halt deciders only report on the actual behavior that their actual input finite string actually specifies.
There never has been an actual input that does the opposite of whatever
its halt decider decides. All of the conventional proofs incorrectly
conflate the behavior of an actual Turing Machine (not its description)
with the behavior that the input specifies.
typedef int (*ptr)();
int HHH(ptr P);
int DD()
{
int Halt_Status = HHH(DD);
if (Halt_Status)
HERE: goto HERE;
return Halt_Status;
}
DD simulated by HHH specifies:
HHH simulates DD that calls HHH(DD)
that simulates DD that calls HHH(DD)
that simulates DD that calls HHH(DD)
that simulates DD that calls HHH(DD)
that simulates DD that calls HHH(DD)
that simulates DD that calls HHH(DD)...
until HHH aborts its simulation and rejects its input or until
out-of-memory error.
This single page sums up 22 years of work: https://claude.ai/share/da9e56ba-f4e9-45ee-9f2c-dc5ffe10f00c Every
rebuttal involves provably false assumptions.
On Wed, 17 Sep 2025 18:16:45 -0500, olcott wrote:
On 9/17/2025 6:02 PM, dart200 wrote:
The way that the diagonal *is* bypassed is my newest work that is not
olcott <polcott333@gmail.com> posted:
Here is the essence of my work and its validation by Claude AI
https://philpapers.org/archive/OLCHPS.pdf Four other LLM models also
agree.
llms can be made to agree 1=2 given enough prompting, unfortunately. we
really should be evaluating llms not based on what they can prove, but
on what they can't be prompted to prove. that would show truly critical
reasoning. the bubble popping for 2020s AI will be quite spectacular.
also, that result fundamentally contradicts itself. the analyser
simulated its own behavior as a matter of infinite recursion ... but
then uses that to return a result???
and if that is the result then shouldn't HHH(DD) -> 0, so Halt_Status =
0, and the if statement triggering the goto HERE loop does not run,
causing DD() to halt ... meaning HHH(DD) should have been 1. the result
is just completely nonsensical.
oh dear olcott. but look i have a resolution to this paradox and u
definitely are the right track to a degree, i do hope you'll hear me
out fully.
(is there a guide somewhere for usenet markup conventions? like for
fixed-width)
This is the summation of 22 years worth of work since 2004.
25% of all of the postings on comp.theory since 2004 are mine.
unfortunately time spent =/= correctness. while i'm sure there is
plenty of value in the work you did do, even beyond priming you for
this engagement, i'm also sure that ur missing something about the
original argument for exactly why turing established undecidability in
computing in the first place. i'm just hoping your time spent indicates
a willingness to continue engagement, and that if i do swing you over,
others will 👀👀👀
I bypass the whole diagonal argument and delve directly into the
semantics of the algorithm specifications.
the diagonal that turing is discussing not "by-passable". he's talking
about an /actual diagonal/ computed across the sequence of computable
numbers: for every r-th machine that can "satisfactorily" compute a
number, the diagonal computation will find it's r-th digit and this
becomes the r-th digit on the diagonal.
the problem turing is worried about is that if such a diagonal is
computable, it can be used to "diagonalize" the computable numbers like
cantor did with the reals. turing presumes that if one can compute a
diagonal across the computable numbers, then this computation could be
used to create an anti-diagonal where each digit is the opposite from
the true diagonal ... meaning it would be a computable number that
can't exist on the total list of computable numbers. contradiction!
turing even gives a succinct formal proof for this problem:
let αn be the n-th computable sequence, and let φn(m) be the m-ththe reason that turing goes on in the next page to show how computing
figure in αn.
Let β be the sequence with 1-φn(m) as its n-th. figure. Since β is
computable, there exists a number K [== β computation] such that
1-φn(n) = φK(n) for all n.
Putting n = K, we have 1 = 2φK(K), i.e. 1 is even. This is impossible. >>>
the direct diagonal (β') results in an undecidable paradox is to
provide a reason why the computation of β can't be computed. he does so >>> with a decision paradox that isn't /exactly/ like the halting paradox,
but very much quite similar.
if you resolution for decision paradoxes doesn't also show that β
isn't,
then it's not gunna work. i don't think you've yet had awareness of
this problem, let alone found a resolution to decision paradoxes that
also avoids computing a β.
provided anywhere else besides here:
Halt deciders only report on the actual behavior that their actual input
finite string actually specifies.
There never has been an actual input that does the opposite of whatever
its halt decider decides. All of the conventional proofs incorrectly
conflate the behavior of an actual Turing Machine (not its description)
with the behavior that the input specifies.
typedef int (*ptr)();
int HHH(ptr P);
int DD()
{
int Halt_Status = HHH(DD);
if (Halt_Status)
HERE: goto HERE;
return Halt_Status;
}
DD simulated by HHH specifies:
HHH simulates DD that calls HHH(DD)
that simulates DD that calls HHH(DD)
that simulates DD that calls HHH(DD)
that simulates DD that calls HHH(DD)
that simulates DD that calls HHH(DD)
that simulates DD that calls HHH(DD)...
until HHH aborts its simulation and rejects its input or until
out-of-memory error.
This single page sums up 22 years of work:
https://claude.ai/share/da9e56ba-f4e9-45ee-9f2c-dc5ffe10f00c Every
rebuttal involves provably false assumptions.
But HHH rejects its input by reporting non-halting to DD which will then
halt proving that HHH is incorrect.
/Flibble
The behavior of main-->DD-->HHH(DD) is not in the scope of HHH.
The behavior of main-->DD-->HHH(DD) is not in the scope of HHH.
You are smart enough to know what an argument to a function is.
DD() is not an argument to the function HHH.
A finite string
of x86 machine code is the actual argument.
On 18/09/2025 00:23, olcott wrote:
<snip>
The behavior of main-->DD-->HHH(DD) is not in the scope of HHH.
If you say so.
You are smart enough to know what an argument to a function is.
Are you?
DD() is not an argument to the function HHH.
DD() is a function call.
DD, however, is very much an argument to the function HHH,
A finite string
of x86 machine code is the actual argument.
Not according to C rules, it isn't.
What HHH gets is a function pointer, DD by name.
DD is an argument to HHH, and to claim otherwise is flat out bullshit.
You don't like it? Take it up with ISO.
On 9/17/2025 7:13 PM, Richard Heathfield wrote:
On 18/09/2025 00:23, olcott wrote:
<snip>
The behavior of main-->DD-->HHH(DD) is not in the scope of HHH.
If you say so.
You are smart enough to know what an argument to a function is.
Are you?
DD() is not an argument to the function HHH.
DD() is a function call.
DD, however, is very much an argument to the function HHH,
A finite string
of x86 machine code is the actual argument.
Not according to C rules, it isn't.
What HHH gets is a function pointer, DD by name.
DD is an argument to HHH, and to claim otherwise is flat out
bullshit. You don't like it? Take it up with ISO.
It is as a matter of verified fact
| Sysop: | DaiTengu |
|---|---|
| Location: | Appleton, WI |
| Users: | 1,070 |
| Nodes: | 10 (0 / 10) |
| Uptime: | 159:54:40 |
| Calls: | 13,734 |
| Calls today: | 2 |
| Files: | 186,966 |
| D/L today: |
826 files (296M bytes) |
| Messages: | 2,418,695 |