David Brown <david.brown@hesbynett.no>: Oct 31 01:59PM +0100
On 30/10/2020 23:50, ijw wij wrote:
> IMOH, a halting deciding algorithm should interest (nearly)every programmer
> and mathematician.
Sorry, but no.
I realise that computation theory underlies all programmers. But the
details - halting problem, computability, Turing machines, and all the
rest are irrelevant to virtually all programmers' work. The same
applies to the workings of processors - from the logic design down to
the laws of quantum mechanics that make them work. They are all part of
the chain of processes that make programming work - but they are at a
completely different part of that chain, and therefore of no particular
interest or relevance to most programmers.
Personally, I /am/ somewhat interested in computability and the
mathematics involved, as I studied it at university. But it has no
relevance to my work as a programmer. I am not particularly interested
in Olcott's ideas, however, since I know they are wrong.
(The impossibility of finding a general halting problem decider is
simple to prove - if he thinks he has found such an algorithm, he is
wrong. He is not the first amateur to think he has done something
impossible in mathematics - there are countless people who think they
have trisected an angle, squared the circle, counted the reals, and so on.)
And since the field of mathematics is so huge, and the halting problem
is only one small part of the (relatively) small field of computation
theory, saying "nearly every mathematician should be interested in a
halting deciding algorithm" is like saying "nearly every sportsperson
should be interested in elephant polo". (If Olott had /really/ proved
Turing wrong, it would be a different matter - and of interest to many
people.)
|
"Alf P. Steinbach" <alf.p.steinbach+usenet@gmail.com>: Oct 31 03:03PM +0100
On 31.10.2020 13:59, David Brown wrote:
> in Olcott's ideas, however, since I know they are wrong.
> (The impossibility of finding a general halting problem decider is
> simple to prove
I would disagree. Because it so happened, I think that was in the
1990's, that Roger Penrose (chair of mathematics department at Oxford
university, England), in either the first or second of his infamous
books about physics and the possibility of artifical intelligence (as I
recall the first titled "The emperor's new mind"), used essentially the
same logic as Turing, but to prove that artificial intelligence is
impossible. Since that's an incorrect conclusion something had to be
wrong in his derivation.
As I recall several things were wrong, not just one critical assumption
or step.
But related to the halting problem: Turing's impossibility proof relied
crucially on the ability to construct a special program that was
undecidable for a given fixed decider machine that /could be numbered/
and henceforth referred to via the number. But if that decider machine
is a human, well, you can't create a fixed undecidable program relative
to the human because the human evolves and changes and has no fixed
completely defining number. And ditto for an artifical intelligence.
So not only was Penrose wrong (which is obvious from his silly result)
but there is necessarily something fishy in Turing's proof (not so
obvious!), because it can't deal with a human as decider.
Namely, Turing did not account for evolving deciders -- I believe a
very simple example could be one that is influenced by random numbers.
> - if he thinks he has found such an algorithm, he is
> wrong.
Well I haven't read what Olcott writes, but see above.
It could well be that Olcott, like I, doesn't contest the validity of
Turing's proof in itself, but contests the assumption that a decider can
always be referred to by a fixed number -- e.g. a human or AI can't.
Turing's proof is still, of course, valid under the assumptions he used.
> should be interested in elephant polo". (If Olott had /really/ proved
> Turing wrong, it would be a different matter - and of interest to many
> people.)
Cheers,
- Alf
PS: Alan Turing might seem to be so great an authority that nothing he
did can be questioned. But remember that Turing had a pretty negative
view of Muslims, that he also had some racist ideas, and that he
believed in telepathy and other extrasensory phenomena. So we're talking
about a flawed genius. But he was crucial for the allied victory in
WWII, and was then wrongfully persecuted due to his sexuality so that he
killed himself, and I believe he was therefore later elevated to near
perfection so that he now can't be questioned -- but actually, flawed.
|
olcott <NoOne@NoWhere.com>: Oct 31 09:57AM -0500
On 10/30/2020 5:50 PM, ijw wij wrote:
> be easy to explain if possible. Not to say it could be implemented in few days.
> Saying so is because I had just posted a very unpoular question "1/∞!=0..." like
> olcott's post, immediately got enough down vote to deleting it.
bool Aborted_Because_Non_Halting_Behavior_Detected(u32 P, u32 I);
Stops executing and Accepts any and all non-halting inputs and Rejects
any and all halting inputs.
--
Copyright 2020 Pete Olcott
"Great spirits have always encountered violent opposition from mediocre
minds." Einstein
|
olcott <NoOne@NoWhere.com>: Oct 31 09:58AM -0500
On 10/31/2020 7:59 AM, David Brown wrote:
> wrong. He is not the first amateur to think he has done something
> impossible in mathematics - there are countless people who think they
> have trisected an angle, squared the circle, counted the reals, and so on.)
bool Aborted_Because_Non_Halting_Behavior_Detected(u32 P, u32 I);
Stops executing and Accepts any and all non-halting inputs and Rejects
any and all halting inputs.
--
Copyright 2020 Pete Olcott
"Great spirits have always encountered violent opposition from mediocre
minds." Einstein
|
olcott <NoOne@NoWhere.com>: Oct 31 10:00AM -0500
On 10/31/2020 9:03 AM, Alf P. Steinbach wrote:
> WWII, and was then wrongfully persecuted due to his sexuality so that he
> killed himself, and I believe he was therefore later elevated to near
> perfection so that he now can't be questioned -- but actually, flawed.
My related work is a proof that Tarski's undefinability theorem is
incorrect thus enabling truth conditional semantics to finally be
anchored in an actual truth predicate.
--
Copyright 2020 Pete Olcott
"Great spirits have always encountered violent opposition from mediocre
minds." Einstein
|
David Brown <david.brown@hesbynett.no>: Oct 31 05:06PM +0100
On 31/10/2020 15:03, Alf P. Steinbach wrote:
> wrong in his derivation.
> As I recall several things were wrong, not just one critical assumption
> or step.
The halting problem is straightforward to express, and straightforward
to prove - it's a simple enumeration and diagonal argument much like the
proof that the reals are uncountable. Like all mathematics, it of
course relies on axioms.
"Artificial intelligence" is a far more nebulous and abstract concept.
You need a book to define what you mean by it, before trying to prove
anything about it.
And surely you are not suggesting that because one smart person
published a "proof" that you say turned out to be wrong (I don't know
enough to say if it really was wrong or not), then this casts doubt on a
completely different proof of a completely different hypothesis by a
completely different person?
> crucially on the ability to construct a special program that was
> undecidable for a given fixed decider machine that /could be numbered/
> and henceforth referred to via the number.
Yes. For any given computation model, programs can be numbered. (If
you are happy to assume the Church-Turing hypothesis, then each of these
models is equivalent. If you are not happy with that assumption, then
you can prove the halting problem for each of them with the same method.)
If you could find a computation model that cannot be enumerated, then
the proof would not apply. (But neither does the hypothesis.) No
realisable non-Turing computation model has been found.
> is a human, well, you can't create a fixed undecidable program relative
> to the human because the human evolves and changes and has no fixed
> completely defining number. And ditto for an artifical intelligence.
Humans are limited. "Mathematician with pen and paper executing a
finite set of algorithms" is one of the enumerable computation models
that is equivalent to a Turing machine. The same would apply to
artificial intelligence (however it is defined).
> So not only was Penrose wrong (which is obvious from his silly result)
> but there is necessarily something fishy in Turing's proof (not so
> obvious!), because it can't deal with a human as decider.
As I say, I don't know Penrose's argument here enough to comment -
except that it depends totally on the definition used for "artificial
intelligence".
> Namely, Turing did not account for evolving deciders -- I believe a
> very simple example could be one that is influenced by random numbers.
Random deciders can sometimes give you the answer for something that is
uncomputable - but since it is not deterministic it cannot solve the
problem in general.
All realisable computation is limited. There are a number of physical
constraints on calculations - no computation system (human, electronic,
quantum computer, artificial intelligence, etc.) can break these
constraints. (Even as we refine physical theories to go beyond quantum
mechanics, these will not be be broken - in the same way that more
nuanced theories of gravity do not allow bricks to float.) There are
limits to calculation speed, information density, computation energy,
and so on. This means programs are countable, regardless of the way
they are computed.
>> - if he thinks he has found such an algorithm, he is
>> wrong.
> Well I haven't read what Olcott writes, but see above.
He thinks that not only has he found an algorithm, but he has a program
that implements it (I think - I haven't read his stuff in detail either).
> Turing's proof in itself, but contests the assumption that a decider can
> always be referred to by a fixed number -- e.g. a human or AI can't.
> Turing's proof is still, of course, valid under the assumptions he used.
As I showed above, that assumption is valid for any realisable method of
computation (in particular, on the model used by Olcott - programs on
real computers).
Anyway, the whole point of Turing's proof is that if you take the set of
all possible programs in some countable model of computation, then the
halting decider for those programs is not in that set. It does not say
that there is no such thing as a halting decider - it says that a
halting decider is not a computable function. If you are going to
imagine the possibility of "hyper-computers" that can evaluate
incomputable numbers, then maybe it could be a halting decider for
computable functions. (But you can't create such a machine.)
> - Alf
> PS: Alan Turing might seem to be so great an authority that nothing he
> did can be questioned.
We are talking about mathematics here, not American politics or TV
fashion shows. Authorities are /always/ questioned in mathematics and
science. There is no greater aim for a mathematician or a scientist
than to prove a famous theorem wrong.
And the uncomputability of the halting problem is simple enough to prove
that anyone studying computation theory will prove it to their own
satisfaction in their first year at university. It's not something we
have to take on trust.
> view of Muslims, that he also had some racist ideas, and that he
> believed in telepathy and other extrasensory phenomena. So we're talking
> about a flawed genius.
Find me a genius (or anyone else) that is not flawed, and perhaps that
argument would not be so laughable.
> WWII, and was then wrongfully persecuted due to his sexuality so that he
> killed himself, and I believe he was therefore later elevated to near
> perfection so that he now can't be questioned -- but actually, flawed.
There is no doubt that Turing was an interesting person, who lived an
interesting life. But his work on computability is famous and important
because of what it is, not because of who Turing was. And his proofs
are correct if and only if they are correct - not because he was gay!
|
olcott <NoOne@NoWhere.com>: Oct 31 11:28AM -0500
On 10/31/2020 11:06 AM, David Brown wrote:
> that anyone studying computation theory will prove it to their own
> satisfaction in their first year at university. It's not something we
> have to take on trust.
Refutation of halting problem proofs for high school students
https://groups.google.com/d/msg/comp.theory/wjjjtn39rEc/ah0QIayJBQAJ
--
Copyright 2020 Pete Olcott
"Great spirits have always encountered violent opposition from mediocre
minds." Einstein
|
David Brown <david.brown@hesbynett.no>: Oct 31 05:38PM +0100
On 31/10/2020 17:28, olcott wrote:
>> have to take on trust.
> Refutation of halting problem proofs for high school students
> https://groups.google.com/d/msg/comp.theory/wjjjtn39rEc/ah0QIayJBQAJ
If that's the quality of your claims, then I'm glad I haven't wasted
effort on reading your posts. But I'm willing to suppose there is more
to it than that - write a proper paper and publish it on a blog, not here.
|
olcott <NoOne@NoWhere.com>: Oct 31 11:52AM -0500
On 10/31/2020 11:38 AM, David Brown wrote:
> If that's the quality of your claims, then I'm glad I haven't wasted
> effort on reading your posts. But I'm willing to suppose there is more
> to it than that - write a proper paper and publish it on a blog, not here.
That is the gist of my proof.
I can actually demonstrate this proof on the basis of an operating
system that I created that executes UTM equivalent virtual machines
where the x86 language is the description language of these virtual
machines.
x86 language ≡ von Neumann architecture ≡ UTM ≡ RASP Machine
x86utm shows all of the detailed steps of exactly how a machine that is
equivalent to the Peter Linz H correctly decides halting on a machine
that is equivalent to the Peter Linz Ĥ.
http://www.liarparadox.org/Peter_Linz_HP(Pages_315-320).pdf
The paper that I write will be my very first attempt at writing an
academic quality paper so my biggest fear it that it will be rejected
out-of-hand without review entirely on the basis of style versus
substance issues. It is for this reason that I seek preliminary reviews
of this work on USENET.
--
Copyright 2020 Pete Olcott
"Great spirits have always encountered violent opposition from mediocre
minds." Einstein
|
ijw wij <wyniijj@gmail.com>: Oct 31 10:00AM -0700
olcott 在 2020年10月31日 星期六下午10:57:41 [UTC+8] 的信中寫道：
> Copyright 2020 Pete Olcott
> "Great spirits have always encountered violent opposition from mediocre
> minds." Einstein
What I saw are just pseudo-codes(very suspicious). I need at least full
documentation of each function and variable in a compilable header
file to understand. The example programs are BAD.
void H_Hat(u32 P)
{
if (!Halts(P, P)) // If it does not halt then
HALT // halt
else // if it halts then
HERE: goto HERE; // loop forever
}
void H(u32 P, u32 I)
{
if (Non_Halting_Detected_While_Running_it(P, I))
{
Stop running it.
Report Non Halting Detected. // Does not halt
}
else
Report that it already stopped running. // H
|
ijw wij <wyniijj@gmail.com>: Oct 31 10:35AM -0700
David Brown 在 2020年10月31日 星期六下午8:59:23 [UTC+8] 的信中寫道：
> the chain of processes that make programming work - but they are at a
> completely different part of that chain, and therefore of no particular
> interest or relevance to most programmers.
I am only interested in the halting algorithm, not others.
At least, I know compiler implementors and language designers will
be happy to know such algorithm even it is not entirely functional.
> wrong. He is not the first amateur to think he has done something
> impossible in mathematics - there are countless people who think they
> have trisected an angle, squared the circle, counted the reals, and so on.)
Agree.
> should be interested in elephant polo". (If Olott had /really/ proved
> Turing wrong, it would be a different matter - and of interest to many
> people.)
Halting problem is not a small thing, many can be derived from it.
I, as app. programmer, do not really calculate O(f), but the idea being
in the head is importantly essential. Without knowing it, lots of time
can be wasted and unaware of bad codes written.
|
olcott <NoOne@NoWhere.com>: Oct 31 12:35PM -0500
On 10/31/2020 12:00 PM, ijw wij wrote:
> }
> else
> Report that it already stopped running. // H
The pseudo code was so that high school students can get the gist of the
idea of the basic design.
Here is the executable code that runs in my x86utm operating system:
void H_Hat(u32 P)
{
if (Aborted_Because_Non_Halting_Behavior_Detected(P, P))
MOV_EAX_1 // Execution of P(P) has been aborted
else
{
MOV_EAX_0 // P(P) has halted
HERE: goto HERE;
}
HALT
}
void H(u32 P, u32 I)
{
if (Aborted_Because_Non_Halting_Behavior_Detected(P, I))
MOV_EAX_1 // Execution of P(I) has been aborted
else
MOV_EAX_0 // P(I) has halted
HALT
}
int main()
{
u32 P = (u32)H_Hat;
H(P, P);
HALT
}
It implements virtual machine equivalents to the Peter Linz H and Ĥ.
I have known all of the details or exactly how the above H decides the
above H_Hat() since 2018-12-13 @ 7:00 PM these details are posted in the
comp.theory USENET group.
Please respond to comp.theory if you can.
--
Copyright 2020 Pete Olcott
"Great spirits have always encountered violent opposition from mediocre
minds." Einstein
|
David Brown <david.brown@hesbynett.no>: Oct 31 06:44PM +0100
On 31/10/2020 18:35, ijw wij wrote:
> I am only interested in the halting algorithm, not others.
> At least, I know compiler implementors and language designers will
> be happy to know such algorithm even it is not entirely functional.
Compiler implementers and language designers would be /very/ interested
in hearing of an algorithm that could tell if a program was going to
hang or not - /if/ such an algorithm existed, and it could be
implemented to run in a sensible time frame. Beyond that, they don't care.
> I, as app. programmer, do not really calculate O(f), but the idea being
> in the head is importantly essential. Without knowing it, lots of time
> can be wasted and unaware of bad codes written.
If I understand you correctly, you mean that you even though you don't
go through detailed proofs of the efficiency of your code, you still
think a little about the theoretical aspects when you write code.
That's a good thing, yes.
|
ijw wij <wyniijj@gmail.com>: Oct 31 11:53AM -0700
David Brown 在 2020年11月1日 星期日上午1:44:47 [UTC+8] 的信中寫道：
> go through detailed proofs of the efficiency of your code, you still
> think a little about the theoretical aspects when you write code.
> That's a good thing, yes.
I mean the halting problem (or algorithm) is a key algorithm.
The influence extends to 'design' and software decision making.
Other fields are the same. I can just come up with a recent one occurred to me.
For example, is 0.333...=1/3? (0.333... is derived from common division method)
0.333... equal to 1/3 or not is a halting problem to me.
I categorize this as a halting problem, since the repeating 3 never terminates,
undecidable-ness is then translated to 'false'.
[My View] In common division methods, 0.333... can repeat forever is because
there exists non-zero remainder. If 0.333... terminating to 1. then remainder=0.
See, like it or not, the influence can be broad.
|
olcott <NoOne@NoWhere.com>: Oct 31 01:59PM -0500
On 10/31/2020 1:53 PM, ijw wij wrote:
> [My View] In common division methods, 0.333... can repeat forever is because
> there exists non-zero remainder. If 0.333... terminating to 1. then remainder=0.
> See, like it or not, the influence can be broad.
Or you could simply represent it internally as an actual fraction and
not as an infinitely repeating decimal.
--
Copyright 2020 Pete Olcott
"Great spirits have always encountered violent opposition from mediocre
minds." Einstein
|
ijw wij <wyniijj@gmail.com>: Oct 31 12:05PM -0700
ijw wij 在 2020年11月1日 星期日上午2:54:14 [UTC+8] 的信中寫道：
> [My View] In common division methods, 0.333... can repeat forever is because
> there exists non-zero remainder. If 0.333... terminating to 1. then remainder=0.
> See, like it or not, the influence can be broad.
Sorry, some typos:
"undecidable-ness in "0.333...=1/3 could then be translated to 'false' "
"If 0.333... terminates to 1/3"
|
ijw wij <wyniijj@gmail.com>: Oct 31 12:16PM -0700
olcott 在 2020年11月1日 星期日上午2:59:34 [UTC+8] 的信中寫道：
> Copyright 2020 Pete Olcott
> "Great spirits have always encountered violent opposition from mediocre
> minds." Einstein
That original problem was to PROVE: lim(n->∞) 1/n≠ 0
But limit is not defined by me, so changed to prove ∞/1≠ 0 (∞ is defined)
A related problem is: 0.999...=1?
|
David Brown <david.brown@hesbynett.no>: Oct 31 08:16PM +0100
On 31/10/2020 19:53, ijw wij wrote:
>> think a little about the theoretical aspects when you write code.
>> That's a good thing, yes.
> I mean the halting problem (or algorithm) is a key algorithm.
No, it isn't. The halting problem is about finding an algorithm that
can decide if other programs ever stop. Even if such an algorithm
existed, it would have no particular use except as an aid to finding
bugs in code. The halting problem is not about determining if the code
you are writing at the moment will hang.
> Other fields are the same. I can just come up with a recent one occurred to me.
> For example, is 0.333...=1/3? (0.333... is derived from common division method)
> 0.333... equal to 1/3 or not is a halting problem to me.
It is not a "halting problem". That's just mathematics, and the
definition of the notation you are using. Yes, 0.33... equals 1/3.
Let x = 0.33.....
Then 10x = 3.33.....
So 10x - x = 3, i.e., 9x = 3, and so x = 1/3.
> I categorize this as a halting problem, since the repeating 3 never terminates,
> undecidable-ness is then translated to 'false'.
It is not a "halting problem" because the notation has a simple and
well-defined meaning.
You would have been better to pick an irrational number as an example,
such as 1.41421356... (the square root of two), where it not only does
not terminate but there is no obvious pattern to the digits. It would
still not be a "halting problem" - we /know/ it does not terminate, so
there is no problem.
> [My View] In common division methods, 0.333... can repeat forever is because
> there exists non-zero remainder. If 0.333... terminating to 1. then remainder=0.
> See, like it or not, the influence can be broad.
I'm sorry, I don't think you understand what you are saying.
But I /do/ know it is unrelated to C++, and also unrelated to getting
Olcott to act like a rational human being, so this should be the end of
this thread.
|
ijw wij <wyniijj@gmail.com>: Oct 31 12:50PM -0700
David Brown 在 2020年11月1日 星期日上午3:17:13 [UTC+8] 的信中寫道：
> existed, it would have no particular use except as an aid to finding
> bugs in code. The halting problem is not about determining if the code
> you are writing at the moment will hang.
That's appearance. Halting Problem is a logic problem, applicable to all
decision problems.
> Let x = 0.33.....
> Then 10x = 3.33.....
> So 10x - x = 3, i.e., 9x = 3, and so x = 1/3.
[Snippet from the original proof]
+-------------------+
| Prop4: 0.999⋯≠1 ? |
+-------------------+
A major issue of this proposition should be the interpretation of 0.999⋯
(or "⋯ "). The answer from the understanding of number says that we should look
for the way this number is constructed.
1. From subtracting minute quantity. Such numbers are many.
a= 1-1/∞ = 0.999⋯
b= 1-2/∞ = 0.999⋯
c= 1-1/10^∞ = 0.999⋯
d= 1-2/100^∞= 0.999⋯
Similar proof of Prop3 shows that lim(n→∞) {(1+k/n)^n}= e^k, that is
(0.999⋯^n) is always some number less than 1, never (1^n)=1.
Therefore, 0.999⋯ is not unique to represent a specific number (in the
example above, a≠b≠c≠d≠1. Density property remains valid).
2. From formal recursive construction
Let X= 0.999⋯
<=> 10X= 9.999⋯
<=> 10X= 9 + 0.999⋯
==> 10X= 9 + X (invalid)
<=> 9X= 9
<=> X= 9/9 =1
The focus is the line marked 'invalid', where the right hand side X
refers to the 0.999⋯ multiplied by 10 and subtract 9, which is not the
0.999⋯ in the proposition. This step uses unproven(or yet to prove)
equation is therefore invalid. But wait... if the "0.999⋯" does possess the
x10-9 invariant property, then X=0.999⋯ =1 is correct. But note that this
0.999⋯ is not equal to the 0.999⋯ from subtracting minute quantity from 1.
QED.
> > undecidable-ness is then translated to 'false'.
> It is not a "halting problem" because the notation has a simple and
> well-defined meaning.
I glimpsed a your argument with others (I am not really an English speaker, reading all the posted are difficult to me)
We have different definitions of "decider" or "the halting problem"
> > there exists non-zero remainder. If 0.333... terminating to 1. then remainder=0.
> > See, like it or not, the influence can be broad.
> I'm sorry, I don't think you understand what you are saying.
Surely I do. I am just afraid the opposite.
If I could post the original text file somewhere.
> But I /do/ know it is unrelated to C++, and also unrelated to getting
> Olcott to act like a rational human being, so this should be the end of
> this thread.
1+1=3 not related to C++? (kidding but truely related)
I expect to learn/teach something from and to olcoot
|
"Alf P. Steinbach" <alf.p.steinbach+usenet@gmail.com>: Oct 31 09:16PM +0100
On 31.10.2020 17:06, David Brown wrote:
> finite set of algorithms" is one of the enumerable computation models
> that is equivalent to a Turing machine. The same would apply to
> artificial intelligence (however it is defined).
Mathematician don't prove theorems (an endeavor similar to proving
halting or not) by executing fixed finite set algorithms.
Penrose assumed something of the sort and ended up with a contradiction,
that intelligence (he added the qualifier "artificial", but define
/that/) is mathematically impossible.
Essentially he proved that he isn't intelligent, just via the kind of
assumption you mention -- which is not how intelligent systems behave.
> As I say, I don't know Penrose's argument here enough to comment -
> except that it depends totally on the definition used for "artificial
> intelligence".
I don't recall that he ever defined AI. The main assumption was just
that an AI would be a computational process that, when presented with
some halting problem as input, could be assigned a fixed defining
number. And he carefully avoided applying the same proof to humans.
Perhaps at some level he realized the futility of defining a human's
ongoing and evolving thinking process by a single fixed number.
I.e. quite silly, childish, but it did not amount to a scandal; e.g. he
was not fired.
I believe the scientific community treated those books as more like
religious statements, and forgave him. He extrapolated from the (to him)
impossibility of AI that humans, or in particular mathematicians like
himself, had to rely on some special quantum mechanical effects in order
to tap into a non-computability that his envisioned AIs could not
access, for otherwise his AI impossibility proof would apply to humans.
His main candidate for that hidden effect was tied to quantum wave
function collapse, as I recall a "missing half" of the QM math.
Perhaps a bit less mystic than US philosopher John Searle who concluded
that only biological brains can be intelligent, but not much less!
This is a guy that along with two others got the Nobel prize in physics
this year, 2020.
But he's not the first crackpot to get the Nobel.
> Random deciders can sometimes give you the answer for something that is
> uncomputable - but since it is not deterministic it cannot solve the
> problem in general.
A proof of that assertion would be interesting when "cannot" is replaced
with the more reasonable (and only meaningful) "cannot with any
probability arbitrarily close to but less than 1".
[snip]
Cheers,
- Alf
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"daniel...@gmail.com" <danielaparker@gmail.com>: Oct 31 03:23PM -0700
On Saturday, October 31, 2020 at 4:16:23 PM UTC-4, Alf P. Steinbach wrote:
> On 31.10.2020 17:06, David Brown wrote:
> > On 31/10/2020 15:03, Alf P. Steinbach wrote:
.
> >> recall the first titled "The emperor's new mind"), used essentially the
> >> same logic as Turing, but to prove that artificial intelligence is
> >> impossible.
No, that wasn't what Penrose was trying to do. Penrose was attempting to
refute the idea of "strong AI" that a computer program could exhibit consciousness.
That was a big topic in the 1990's.
>>> Since that's an incorrect conclusion something had to be
> >> wrong in his derivation.
Daniel Dennett is one of the most well known proponent of strong AI.
I recall reading his book Consciousness Explained from cover to cover,
including illustrations of the mind/body problem with sketches of Casper
the ghost, hoping to learn something. But I don't think anywhere in the
book that consciousness was actually explained.
In any case, I'm pretty convinced that none of the programs that I
write will ever exhibit consciousness.
> > "Artificial intelligence" is a far more nebulous and abstract concept.
> > You need a book to define what you mean by it, before trying to prove
> > anything about it.
The idea of consciousness and what it would mean for a computer
program to exhibit consciousness is hard to define. Dennett argues
that human consciousness is an illusion, and what it really is can be
realized in a machine. Dennett can be read as denying the existence of
consciousness, but the problem is, even though we don't know
what it is, we can all experience it.
Daniel
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olcott <NoOne@NoWhere.com>: Oct 31 05:57PM -0500
> consciousness, but the problem is, even though we don't know
> what it is, we can all experience it.
> Daniel
comp.ai.philosophy › Is strong AI possible?
https://groups.google.com/forum/#!msg/comp.ai.philosophy/q3YDGZ9fnIM/Jw22XeHTAjYJ
Six years ago I came up with a possible measure of the functional
equivalent of consciousness.
An AI mind could have a [will of its own] as soon as it has a
sufficiently populated goal hierarchy.
--
Copyright 2020 Pete Olcott
"Great spirits have always encountered violent opposition from mediocre
minds." Einstein
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