On 05/18/2026 09:03 AM, olcott wrote:
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such a >>>>>>>>>>> fascination with me?I find that 'except' paired with 'yet' covers every
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>>> that that that that that it is so.
instance of
'but.' If you can find an exception to this, please show me. >>>>>>>>>>>>>
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my
part to
disabuse you of the notion. Why not play into it and further >>>>>>>>> befuddle
you? If it were the case that I were not olcott, that is.
Ask your self what his halting decider would say... Look in the >>>>>>>> mirror?
One of the problems of environments of the unmoderated and
pseudonymous
sort is that there are all kinds of trolls. There are plain
rage-bait
and flamer trolls, looky-loos and non-sequitur types, then, also all >>>>>>> sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", then >>>>>>> when I see stuff like either
"smell the new normal, you're living in a dictatorship",
or,
"suffer the children, so your social media and phone get hacked", >>>>>>> then either way the idea of being aware ("woke" wasn't a word
and I'd imagine it would be "awoke" or "woken", or, "woke" will do), >>>>>>> and caring (although, you know, not _too_ caring), that trolls
and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to suspect >>>>>>> trolls in the likely places, and learn to make a troll-filter,
and basically a skeptical if not cynical outlook on the world today, >>>>>>> that there are trolls and trolls, and sometimes it's easiest to
ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic,
give it a howler fallacy it won't let go and the plain obstinance >>>>>>> combined with the stubbornness along with the sort of plain
unwarranted persistence, then it's not always easy to tell the
difference between cranks and trolls, though often it is,
and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these
long-running mostly-empty tit-for-tat nonsense threads get
hijacked by passers-by then into discussions about the issues
at hand, like about the many, many things to do with the
"mathematics" of continuity and infinity, since, despite
the idea of some retro-finitists that their world is a
dot, and not even like AP a giant plutonium atom, there's
much to be done to bring real infinite and continuity into
mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so
it's not just an echo-chamber of trolls and anti-trolls
which is one big troll, is not necessarily a bad thing.
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when all >>>>> possible paths are hit. If you think about its kind of akin to olcotts >>>>> DD. i simply hijack its result. Here is a version that uses random
numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
1 HOME
5 PRINT "ct_dr_fuzz lol. ;^)"
6 P0 = 0
7 P1 = 0
10 REM Fuzzer... ;^)
20 A$ = "NOPE!"
30 IF RND(1) < .5 THEN A$ = "YES"
100 REM INPUT "Shall DD halt or not? " ; A$
110 PRINT "Shall DD halt or not? " ; A$
200 IF A$ = "YES" GOTO 666
300 P0 = P0 + 1
400 IF P0 > 0 AND P1 > 0 GOTO 1000
500 GOTO 10
666 PRINT "OK!"
667 P1 = P1 + 1
700 PRINT "NON_HALT P0 = "; P0
710 PRINT "HALT P1 = "; P1
720 IF P0 > 0 AND P1 > 0 GOTO 1000
730 PRINT "ALL PATHS FAILED TO BE HIT!"
740 GOTO 10
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
1 HOME
5 PRINT "ct_dr_fuzz lol. ;^)"
6 P0 = 0
7 P1 = 0
10 REM Fuzzer... ;^)
20 A$ = "NOPE!"
30 IF RND(1) < .5 THEN A$ = "YES"
100 INPUT "Shall DD halt or not? " ; A$
110 REM PRINT "Shall DD halt or not? " ; A$
200 IF A$ = "YES" GOTO 666
300 P0 = P0 + 1
400 IF P0 > 0 AND P1 > 0 GOTO 1000
500 GOTO 10
666 PRINT "OK!"
667 P1 = P1 + 1
700 PRINT "NON_HALT P0 = "; P0
710 PRINT "HALT P1 = "; P1
720 IF P0 > 0 AND P1 > 0 GOTO 1000
730 PRINT "ALL PATHS FAILED TO BE HIT!"
740 GOTO 10
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens:
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
1 HOME
5 PRINT "ct_dr_fuzz lol. ;^)"
6 P0 = 0
7 P1 = 0
10 REM Fuzzer... ;^)
20 A$ = "NOPE!"
30 IF RND(1) < .5 THEN A$ = "YES"
100 INPUT "Shall DD halt or not? " ; A$
110 REM PRINT "Shall DD halt or not? " ; A$
200 IF A$ = "YES" GOTO 666
300 P0 = P0 + 1
400 IF P0 > 0 AND P1 > 0 GOTO 1000
500 GOTO 10
666 PRINT "OK!"
667 P1 = P1 + 1
700 PRINT "NON_HALT P0 = "; P0
710 PRINT "HALT P1 = "; P1
720 IF P0 > 0 AND P1 > 0 GOTO 1000
730 PRINT "ALL PATHS FAILED TO BE HIT!"
740 GOTO 10
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire,
not so much the being wrong part yet the dream, having the
dreams, I'm all for people having the dream when it's not
frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety
trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain
old "normal normal".
Hm.
There are at least three accounts of programs whether they halt.
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
https://arxiv.org/abs/math/0611740
"The Halting Probability Omega: Irreducible Complexity in Pure
Mathematics", G. Chaitin
"G||del himself did not think that his theorem showed that mathematics
has limitations. In several essays he made it clear that he believed
that mathematicians could eventually settle any significant question by
using their mathematical intuition, their ability to directly perceive
the Platonic world of mathematical ideas, and by inventing or
discovering new concepts and new axioms, new principles.
Furthermore, I share EnriquesrCOs faith in intuition. I think that
excessive formalism and abstraction is killing mathematics. In my
opinion math papers shouldnrCOt attempt to replace all words by formulas, instead they should be like literary essays, they should attempt to
explain and convince.
So let me tell you the story of metamathematics, of how mathematicians
have tried to use mathematical methods to study the power and the
limitations of math itself. ItrCOs a fairly dramatic story; in a previous
era it might have been the subject of epic poems, of Iliads and Odysseys
of verse. IrCOll start with David Hilbert."
"In my opinion this is a fundamental step forward in the philosophy of mathematics because it makes incompleteness seem much more concrete and
much more natural. ItrCOs almost a problem in physics, itrCOs about a machine, you just ask whether or not itrCOs going to eventually stop, and
it turns out thererCOs no way, no general way, to answer that question.
Let me emphasize that if a program does halt, we can eventually discover that. The problem, an extremely deep one, is to show that a program will never halt if this is in fact so. One can settle many special cases,
even an infinity of them, but no finite set of axioms can enable you to settle all possible cases."
Hm, " ... no finite set of axioms ...", ..., how about "no axioms".
"The real numbers are the simplest thing in the world geometrically,
they are just points on a line. But arithmetically, as individuals, real numbers are actually rather unreal. TuringrCOs 1936 uncomputable real is
just the tip of the iceberg, the problem is a lot more serious than that."
Here the iota-values are points _in_ a line, field-reals _on_ a line,
and signal-reals _about_ and _around_ a line.
So, Chaitin doesn't even have three models of continuous domains,
or "repleteness", of concepts like Lebnitz' principle of perfection
and Hilbert's postulate of continuity.
Mathematics really _does_ define continuity:
and there are at least three models of continuous domains.
So, say you want to sample a real number from [0,1] the interval
at uniform random, and all you have is a fair coin that
gives samples from {0, 1} the set.
So, you start flipping coins and marking the result to make
a sequence of 0's and 1's. Each coin toss _refines_ the
sample.
Yet, each coin toss also _begins_ a new sample. So, to sample
one real number, the super-task results sampling infinitely-many
real numbers.
So, the probability of the first sample being a rational value
is, according to the law of large numbers the law of small numbers,
small, and arbitrarily and infinitesimally small. In theories
that are Pythagorean it's almost-all rationals, while in theories
that are Cantorian it's almost-all transcendentals.
Yet, if a sample arrives at a rational, the repeating character
of rationals means that thusly the _one_ sample of a rational
number is automatically _infinitely-many_ samples of rational
numbers.
So, it makes sense to consider that the probability of sampling
a rational number from [0,1] is about 0.5.
This isn't Pythagorean by itself, and isn't Cantorian by itself.
It's them together according to accounts of paradox-free reason,
not "non-classical logics where we ignore contradiction",
which is _hypocrisy_ and furthermore _fallacious_,
since "infinity" and "continuity" are "absolute" and "replete".
"LetrCOs start with BorelrCOs know-it-all number, but now letrCOs use the Nth binary digit to tell us whether or not the Nth computer program ever
halts. So now BorelrCOs number is an oracle for the halting problem. For example, there is a bit which tells us whether or not the Riemann
hypothesis is true, for that is equivalent to the statement that a
program that systematically searches for zeros of the zeta function that
are in the wrong place, never halts.
It turns out that this number, which IrCOll call TuringrCOs number even though it does not occur in TuringrCOs paper, is wasting bits, it is
actually highly redundant. We donrCOt really need N bits to answer N cases
of the halting problem, a much smaller number of bits will do. Why?
Well, consider some large number N of cases of the halting problem, some large number N of individual programs for which we want to know whether
or not each one halts. Is this really N bits of mathematical
information? No, the answers are not independent, they are highly
correlated. How? Well, in order to answer N cases of the halting
problem, we donrCOt really need to know each individual answer; it
suffices to know how many of these N programs will eventually halt. Once
we know this number, which is only about log_2 N
bits of information, we can run the N programs in parallel until exactly
this number of them halt, and then we know that none of the remaining programs will ever halt. And log_2 N is much, much less than N for all sufficiently large N. In other words, TuringrCOs number isnrCOt the best possible oracle for the halting problem. It is highly redundant, it uses
far too many bits.
Using essentially this idea, we can get the best possible oracle number
for the halting problem; that is the halting probability +-, which has no redundancy, none at all.
So, now that there's readily equipped a notion of uniform sampling
that results "oracle numbers", always _infinitely-many_ just to get one,
then Chaitin's quote is equipped some context that makes
quite a fresh reading.
This goes for all y'all.
On 05/18/2026 09:44 AM, Ross Finlayson wrote:
On 05/18/2026 09:03 AM, olcott wrote:
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such a >>>>>>>>>>>> fascination with me?I find that 'except' paired with 'yet' covers every >>>>>>>>>>>>>> instance of
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>>>> that that that that that it is so.
'but.' If you can find an exception to this, please show me. >>>>>>>>>>>>>>
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my >>>>>>>>>> part to
disabuse you of the notion. Why not play into it and further >>>>>>>>>> befuddle
you? If it were the case that I were not olcott, that is.
Ask your self what his halting decider would say... Look in the >>>>>>>>> mirror?
One of the problems of environments of the unmoderated and
pseudonymous
sort is that there are all kinds of trolls. There are plain
rage-bait
and flamer trolls, looky-loos and non-sequitur types, then, also >>>>>>>> all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", then >>>>>>>> when I see stuff like either
"smell the new normal, you're living in a dictatorship",
or,
"suffer the children, so your social media and phone get hacked", >>>>>>>> then either way the idea of being aware ("woke" wasn't a word
and I'd imagine it would be "awoke" or "woken", or, "woke" will >>>>>>>> do),
and caring (although, you know, not _too_ caring), that trolls >>>>>>>> and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to suspect >>>>>>>> trolls in the likely places, and learn to make a troll-filter, >>>>>>>> and basically a skeptical if not cynical outlook on the world
today,
that there are trolls and trolls, and sometimes it's easiest to >>>>>>>> ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic,
give it a howler fallacy it won't let go and the plain obstinance >>>>>>>> combined with the stubbornness along with the sort of plain
unwarranted persistence, then it's not always easy to tell the >>>>>>>> difference between cranks and trolls, though often it is,
and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these
long-running mostly-empty tit-for-tat nonsense threads get
hijacked by passers-by then into discussions about the issues
at hand, like about the many, many things to do with the
"mathematics" of continuity and infinity, since, despite
the idea of some retro-finitists that their world is a
dot, and not even like AP a giant plutonium atom, there's
much to be done to bring real infinite and continuity into
mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so
it's not just an echo-chamber of trolls and anti-trolls
which is one big troll, is not necessarily a bad thing.
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when all >>>>>> possible paths are hit. If you think about its kind of akin to
olcotts
DD. i simply hijack its result. Here is a version that uses random >>>>>> numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
1 HOME
5 PRINT "ct_dr_fuzz lol. ;^)"
6 P0 = 0
7 P1 = 0
10 REM Fuzzer... ;^)
20 A$ = "NOPE!"
30 IF RND(1) < .5 THEN A$ = "YES"
100 REM INPUT "Shall DD halt or not? " ; A$
110 PRINT "Shall DD halt or not? " ; A$
200 IF A$ = "YES" GOTO 666
300 P0 = P0 + 1
400 IF P0 > 0 AND P1 > 0 GOTO 1000
500 GOTO 10
666 PRINT "OK!"
667 P1 = P1 + 1
700 PRINT "NON_HALT P0 = "; P0
710 PRINT "HALT P1 = "; P1
720 IF P0 > 0 AND P1 > 0 GOTO 1000
730 PRINT "ALL PATHS FAILED TO BE HIT!"
740 GOTO 10
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
1 HOME
5 PRINT "ct_dr_fuzz lol. ;^)"
6 P0 = 0
7 P1 = 0
10 REM Fuzzer... ;^)
20 A$ = "NOPE!"
30 IF RND(1) < .5 THEN A$ = "YES"
100 INPUT "Shall DD halt or not? " ; A$
110 REM PRINT "Shall DD halt or not? " ; A$
200 IF A$ = "YES" GOTO 666
300 P0 = P0 + 1
400 IF P0 > 0 AND P1 > 0 GOTO 1000
500 GOTO 10
666 PRINT "OK!"
667 P1 = P1 + 1
700 PRINT "NON_HALT P0 = "; P0
710 PRINT "HALT P1 = "; P1
720 IF P0 > 0 AND P1 > 0 GOTO 1000
730 PRINT "ALL PATHS FAILED TO BE HIT!"
740 GOTO 10
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens:
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
1 HOME
5 PRINT "ct_dr_fuzz lol. ;^)"
6 P0 = 0
7 P1 = 0
10 REM Fuzzer... ;^)
20 A$ = "NOPE!"
30 IF RND(1) < .5 THEN A$ = "YES"
100 INPUT "Shall DD halt or not? " ; A$
110 REM PRINT "Shall DD halt or not? " ; A$
200 IF A$ = "YES" GOTO 666
300 P0 = P0 + 1
400 IF P0 > 0 AND P1 > 0 GOTO 1000
500 GOTO 10
666 PRINT "OK!"
667 P1 = P1 + 1
700 PRINT "NON_HALT P0 = "; P0
710 PRINT "HALT P1 = "; P1
720 IF P0 > 0 AND P1 > 0 GOTO 1000
730 PRINT "ALL PATHS FAILED TO BE HIT!"
740 GOTO 10
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire,
not so much the being wrong part yet the dream, having the
dreams, I'm all for people having the dream when it's not
frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety
trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain
old "normal normal".
Hm.
There are at least three accounts of programs whether they halt.
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
https://arxiv.org/abs/math/0611740
"The Halting Probability Omega: Irreducible Complexity in Pure
Mathematics", G. Chaitin
"G||del himself did not think that his theorem showed that mathematics
has limitations. In several essays he made it clear that he believed
that mathematicians could eventually settle any significant question by
using their mathematical intuition, their ability to directly perceive
the Platonic world of mathematical ideas, and by inventing or
discovering new concepts and new axioms, new principles.
Furthermore, I share EnriquesrCOs faith in intuition. I think that
excessive formalism and abstraction is killing mathematics. In my
opinion math papers shouldnrCOt attempt to replace all words by formulas,
instead they should be like literary essays, they should attempt to
explain and convince.
So let me tell you the story of metamathematics, of how mathematicians
have tried to use mathematical methods to study the power and the
limitations of math itself. ItrCOs a fairly dramatic story; in a previous
era it might have been the subject of epic poems, of Iliads and Odysseys
of verse. IrCOll start with David Hilbert."
"In my opinion this is a fundamental step forward in the philosophy of
mathematics because it makes incompleteness seem much more concrete and
much more natural. ItrCOs almost a problem in physics, itrCOs about a
machine, you just ask whether or not itrCOs going to eventually stop, and
it turns out thererCOs no way, no general way, to answer that question.
Let me emphasize that if a program does halt, we can eventually discover
that. The problem, an extremely deep one, is to show that a program will
never halt if this is in fact so. One can settle many special cases,
even an infinity of them, but no finite set of axioms can enable you to
settle all possible cases."
Hm, " ... no finite set of axioms ...", ..., how about "no axioms".
"The real numbers are the simplest thing in the world geometrically,
they are just points on a line. But arithmetically, as individuals, real
numbers are actually rather unreal. TuringrCOs 1936 uncomputable real is
just the tip of the iceberg, the problem is a lot more serious than
that."
Here the iota-values are points _in_ a line, field-reals _on_ a line,
and signal-reals _about_ and _around_ a line.
So, Chaitin doesn't even have three models of continuous domains,
or "repleteness", of concepts like Lebnitz' principle of perfection
and Hilbert's postulate of continuity.
Mathematics really _does_ define continuity:
and there are at least three models of continuous domains.
So, say you want to sample a real number from [0,1] the interval
at uniform random, and all you have is a fair coin that
gives samples from {0, 1} the set.
So, you start flipping coins and marking the result to make
a sequence of 0's and 1's. Each coin toss _refines_ the
sample.
Yet, each coin toss also _begins_ a new sample. So, to sample
one real number, the super-task results sampling infinitely-many
real numbers.
So, the probability of the first sample being a rational value
is, according to the law of large numbers the law of small numbers,
small, and arbitrarily and infinitesimally small. In theories
that are Pythagorean it's almost-all rationals, while in theories
that are Cantorian it's almost-all transcendentals.
Yet, if a sample arrives at a rational, the repeating character
of rationals means that thusly the _one_ sample of a rational
number is automatically _infinitely-many_ samples of rational
numbers.
So, it makes sense to consider that the probability of sampling
a rational number from [0,1] is about 0.5.
This isn't Pythagorean by itself, and isn't Cantorian by itself.
It's them together according to accounts of paradox-free reason,
not "non-classical logics where we ignore contradiction",
which is _hypocrisy_ and furthermore _fallacious_,
since "infinity" and "continuity" are "absolute" and "replete".
"LetrCOs start with BorelrCOs know-it-all number, but now letrCOs use the Nth
binary digit to tell us whether or not the Nth computer program ever
halts. So now BorelrCOs number is an oracle for the halting problem. For
example, there is a bit which tells us whether or not the Riemann
hypothesis is true, for that is equivalent to the statement that a
program that systematically searches for zeros of the zeta function that
are in the wrong place, never halts.
It turns out that this number, which IrCOll call TuringrCOs number even
though it does not occur in TuringrCOs paper, is wasting bits, it is
actually highly redundant. We donrCOt really need N bits to answer N cases >> of the halting problem, a much smaller number of bits will do. Why?
Well, consider some large number N of cases of the halting problem, some
large number N of individual programs for which we want to know whether
or not each one halts. Is this really N bits of mathematical
information? No, the answers are not independent, they are highly
correlated. How? Well, in order to answer N cases of the halting
problem, we donrCOt really need to know each individual answer; it
suffices to know how many of these N programs will eventually halt. Once
we know this number, which is only about log_2 N
bits of information, we can run the N programs in parallel until exactly
this number of them halt, and then we know that none of the remaining
programs will ever halt. And log_2 N is much, much less than N for all
sufficiently large N. In other words, TuringrCOs number isnrCOt the best
possible oracle for the halting problem. It is highly redundant, it uses
far too many bits.
Using essentially this idea, we can get the best possible oracle number
for the halting problem; that is the halting probability +-, which has no
redundancy, none at all.
So, now that there's readily equipped a notion of uniform sampling
that results "oracle numbers", always _infinitely-many_ just to get one,
then Chaitin's quote is equipped some context that makes
quite a fresh reading.
This goes for all y'all.
"But, but, but,
my "language oracle"
didn't tell me that
"oracle numbers" are "real numbers"
and that "P(Halts)" is alike P(Rational)".
Yet, ..., _yet_: doesn't it?
"Marcia, Marcia, Marcia, ...."
On 05/18/2026 09:51 AM, Ross Finlayson wrote:
On 05/18/2026 09:44 AM, Ross Finlayson wrote:
On 05/18/2026 09:03 AM, olcott wrote:
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such a >>>>>>>>>>>>> fascination with me?I find that 'except' paired with 'yet' covers every >>>>>>>>>>>>>>> instance of
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>>>>> that that that that that it is so.
'but.' If you can find an exception to this, please show me. >>>>>>>>>>>>>>>
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my >>>>>>>>>>> part to
disabuse you of the notion. Why not play into it and further >>>>>>>>>>> befuddle
you? If it were the case that I were not olcott, that is. >>>>>>>>>>>
Ask your self what his halting decider would say... Look in the >>>>>>>>>> mirror?
One of the problems of environments of the unmoderated and
pseudonymous
sort is that there are all kinds of trolls. There are plain
rage-bait
and flamer trolls, looky-loos and non-sequitur types, then, also >>>>>>>>> all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", then >>>>>>>>> when I see stuff like either
"smell the new normal, you're living in a dictatorship",
or,
"suffer the children, so your social media and phone get hacked", >>>>>>>>> then either way the idea of being aware ("woke" wasn't a word >>>>>>>>> and I'd imagine it would be "awoke" or "woken", or, "woke" will >>>>>>>>> do),
and caring (although, you know, not _too_ caring), that trolls >>>>>>>>> and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to
suspect
trolls in the likely places, and learn to make a troll-filter, >>>>>>>>> and basically a skeptical if not cynical outlook on the world >>>>>>>>> today,
that there are trolls and trolls, and sometimes it's easiest to >>>>>>>>> ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic, >>>>>>>>> give it a howler fallacy it won't let go and the plain obstinance >>>>>>>>> combined with the stubbornness along with the sort of plain
unwarranted persistence, then it's not always easy to tell the >>>>>>>>> difference between cranks and trolls, though often it is,
and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these >>>>>>>>> long-running mostly-empty tit-for-tat nonsense threads get
hijacked by passers-by then into discussions about the issues >>>>>>>>> at hand, like about the many, many things to do with the
"mathematics" of continuity and infinity, since, despite
the idea of some retro-finitists that their world is a
dot, and not even like AP a giant plutonium atom, there's
much to be done to bring real infinite and continuity into
mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so
it's not just an echo-chamber of trolls and anti-trolls
which is one big troll, is not necessarily a bad thing.
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when all >>>>>>> possible paths are hit. If you think about its kind of akin to
olcotts
DD. i simply hijack its result. Here is a version that uses random >>>>>>> numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
1 HOME
5 PRINT "ct_dr_fuzz lol. ;^)"
6 P0 = 0
7 P1 = 0
10 REM Fuzzer... ;^)
20 A$ = "NOPE!"
30 IF RND(1) < .5 THEN A$ = "YES"
100 REM INPUT "Shall DD halt or not? " ; A$
110 PRINT "Shall DD halt or not? " ; A$
200 IF A$ = "YES" GOTO 666
300 P0 = P0 + 1
400 IF P0 > 0 AND P1 > 0 GOTO 1000
500 GOTO 10
666 PRINT "OK!"
667 P1 = P1 + 1
700 PRINT "NON_HALT P0 = "; P0
710 PRINT "HALT P1 = "; P1
720 IF P0 > 0 AND P1 > 0 GOTO 1000
730 PRINT "ALL PATHS FAILED TO BE HIT!"
740 GOTO 10
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
1 HOME
5 PRINT "ct_dr_fuzz lol. ;^)"
6 P0 = 0
7 P1 = 0
10 REM Fuzzer... ;^)
20 A$ = "NOPE!"
30 IF RND(1) < .5 THEN A$ = "YES"
100 INPUT "Shall DD halt or not? " ; A$
110 REM PRINT "Shall DD halt or not? " ; A$
200 IF A$ = "YES" GOTO 666
300 P0 = P0 + 1
400 IF P0 > 0 AND P1 > 0 GOTO 1000
500 GOTO 10
666 PRINT "OK!"
667 P1 = P1 + 1
700 PRINT "NON_HALT P0 = "; P0
710 PRINT "HALT P1 = "; P1
720 IF P0 > 0 AND P1 > 0 GOTO 1000
730 PRINT "ALL PATHS FAILED TO BE HIT!"
740 GOTO 10
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens:
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
1 HOME
5 PRINT "ct_dr_fuzz lol. ;^)"
6 P0 = 0
7 P1 = 0
10 REM Fuzzer... ;^)
20 A$ = "NOPE!"
30 IF RND(1) < .5 THEN A$ = "YES"
100 INPUT "Shall DD halt or not? " ; A$
110 REM PRINT "Shall DD halt or not? " ; A$
200 IF A$ = "YES" GOTO 666
300 P0 = P0 + 1
400 IF P0 > 0 AND P1 > 0 GOTO 1000
500 GOTO 10
666 PRINT "OK!"
667 P1 = P1 + 1
700 PRINT "NON_HALT P0 = "; P0
710 PRINT "HALT P1 = "; P1
720 IF P0 > 0 AND P1 > 0 GOTO 1000
730 PRINT "ALL PATHS FAILED TO BE HIT!"
740 GOTO 10
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire,
not so much the being wrong part yet the dream, having the
dreams, I'm all for people having the dream when it's not
frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety
trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain
old "normal normal".
Hm.
There are at least three accounts of programs whether they halt.
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
https://arxiv.org/abs/math/0611740
"The Halting Probability Omega: Irreducible Complexity in Pure
Mathematics", G. Chaitin
"G||del himself did not think that his theorem showed that mathematics
has limitations. In several essays he made it clear that he believed
that mathematicians could eventually settle any significant question by
using their mathematical intuition, their ability to directly perceive
the Platonic world of mathematical ideas, and by inventing or
discovering new concepts and new axioms, new principles.
Furthermore, I share EnriquesrCOs faith in intuition. I think that
excessive formalism and abstraction is killing mathematics. In my
opinion math papers shouldnrCOt attempt to replace all words by formulas, >>> instead they should be like literary essays, they should attempt to
explain and convince.
So let me tell you the story of metamathematics, of how mathematicians
have tried to use mathematical methods to study the power and the
limitations of math itself. ItrCOs a fairly dramatic story; in a previous >>> era it might have been the subject of epic poems, of Iliads and Odysseys >>> of verse. IrCOll start with David Hilbert."
"In my opinion this is a fundamental step forward in the philosophy of
mathematics because it makes incompleteness seem much more concrete and
much more natural. ItrCOs almost a problem in physics, itrCOs about a
machine, you just ask whether or not itrCOs going to eventually stop, and >>> it turns out thererCOs no way, no general way, to answer that question.
Let me emphasize that if a program does halt, we can eventually discover >>> that. The problem, an extremely deep one, is to show that a program will >>> never halt if this is in fact so. One can settle many special cases,
even an infinity of them, but no finite set of axioms can enable you to
settle all possible cases."
Hm, " ... no finite set of axioms ...", ..., how about "no axioms".
"The real numbers are the simplest thing in the world geometrically,
they are just points on a line. But arithmetically, as individuals, real >>> numbers are actually rather unreal. TuringrCOs 1936 uncomputable real is >>> just the tip of the iceberg, the problem is a lot more serious than
that."
Here the iota-values are points _in_ a line, field-reals _on_ a line,
and signal-reals _about_ and _around_ a line.
So, Chaitin doesn't even have three models of continuous domains,
or "repleteness", of concepts like Lebnitz' principle of perfection
and Hilbert's postulate of continuity.
Mathematics really _does_ define continuity:
and there are at least three models of continuous domains.
So, say you want to sample a real number from [0,1] the interval
at uniform random, and all you have is a fair coin that
gives samples from {0, 1} the set.
So, you start flipping coins and marking the result to make
a sequence of 0's and 1's. Each coin toss _refines_ the
sample.
Yet, each coin toss also _begins_ a new sample. So, to sample
one real number, the super-task results sampling infinitely-many
real numbers.
So, the probability of the first sample being a rational value
is, according to the law of large numbers the law of small numbers,
small, and arbitrarily and infinitesimally small. In theories
that are Pythagorean it's almost-all rationals, while in theories
that are Cantorian it's almost-all transcendentals.
Yet, if a sample arrives at a rational, the repeating character
of rationals means that thusly the _one_ sample of a rational
number is automatically _infinitely-many_ samples of rational
numbers.
So, it makes sense to consider that the probability of sampling
a rational number from [0,1] is about 0.5.
This isn't Pythagorean by itself, and isn't Cantorian by itself.
It's them together according to accounts of paradox-free reason,
not "non-classical logics where we ignore contradiction",
which is _hypocrisy_ and furthermore _fallacious_,
since "infinity" and "continuity" are "absolute" and "replete".
"LetrCOs start with BorelrCOs know-it-all number, but now letrCOs use the Nth
binary digit to tell us whether or not the Nth computer program ever
halts. So now BorelrCOs number is an oracle for the halting problem. For >>> example, there is a bit which tells us whether or not the Riemann
hypothesis is true, for that is equivalent to the statement that a
program that systematically searches for zeros of the zeta function that >>> are in the wrong place, never halts.
It turns out that this number, which IrCOll call TuringrCOs number even
though it does not occur in TuringrCOs paper, is wasting bits, it is
actually highly redundant. We donrCOt really need N bits to answer N cases >>> of the halting problem, a much smaller number of bits will do. Why?
Well, consider some large number N of cases of the halting problem, some >>> large number N of individual programs for which we want to know whether
or not each one halts. Is this really N bits of mathematical
information? No, the answers are not independent, they are highly
correlated. How? Well, in order to answer N cases of the halting
problem, we donrCOt really need to know each individual answer; it
suffices to know how many of these N programs will eventually halt. Once >>> we know this number, which is only about log_2 N
bits of information, we can run the N programs in parallel until exactly >>> this number of them halt, and then we know that none of the remaining
programs will ever halt. And log_2 N is much, much less than N for all
sufficiently large N. In other words, TuringrCOs number isnrCOt the best >>> possible oracle for the halting problem. It is highly redundant, it uses >>> far too many bits.
Using essentially this idea, we can get the best possible oracle number
for the halting problem; that is the halting probability +-, which has no >>> redundancy, none at all.
So, now that there's readily equipped a notion of uniform sampling
that results "oracle numbers", always _infinitely-many_ just to get one, >>> then Chaitin's quote is equipped some context that makes
quite a fresh reading.
This goes for all y'all.
"But, but, but,
my "language oracle"
didn't tell me that
"oracle numbers" are "real numbers"
and that "P(Halts)" is alike P(Rational)".
Yet, ..., _yet_: doesn't it?
"Marcia, Marcia, Marcia, ...."
Eve Plumb's famous rendition of "Marcia Marcia Marcia"
was considered in her exasperation one of the greatest
or most memorable moments from "Brady Bunch", which was
a prime-time and later syndicated television show,
among other lines like "Mom always said don't play
ball in the house" and "Pork chops: and apple sauce".
(That and that "freaky tiki" bit, ....)
So, it's one of the great mysteries of syndicated television,
about Mrs. Brady, the lovely lady, and three very lovely girls,
besides whether Florence Henderson had a glass eye,
is that they're always referred to as "the Brady's", yet,
presuming that Mike Brady adopted the Brady girls and they
took his name: _who is the father on Marcia Brady's
birth certificate_? And, is it even one person?
It's similarly for the Brady boys: "Mom always said,
don't play ball in the house", _who is this person_.
"Enquiring minds want to know", was the tagline of
what was a super-market tabloid in the '80's considered
to be the worst of yellow and trash journalism at the
time, vis-a-vis, "Weekly World News".
| Sysop: | Amessyroom |
|---|---|
| Location: | Fayetteville, NC |
| Users: | 65 |
| Nodes: | 6 (0 / 6) |
| Uptime: | 62:50:05 |
| Calls: | 862 |
| Files: | 1,311 |
| D/L today: |
10 files (20,373K bytes) |
| Messages: | 264,051 |