Ada vs Ruby

On Thu, Apr 17, 2008 at 3:09 PM, Eivind E. [email protected]
wrote:

| formalisms under it that’s providing axioms that we don’t prove, just
| assume.

But a language that is Turing-complete is a complete logical system, is
it not?
Forgive me to add a comment as Eivind has been much clearer than me on
the description of what is the Halting Problem and Completeness. I
also think it was nice to add that your posts are very valuable
usually, I agree indeed.
But your last question can maybe be explained in simple words.

Being turing-complete means in theory that you can solve all problems
that a Turing Machine can solve (given unlimited memory) (1).
E.g.
Ruby being turing-complete means therefore that you can write a Ruby
program of which one can not determine if it will halt or not. But
chances are slim that such a Ruby program is written by chance, and
furthermore it would need infinite memory.

(1) A TM that solves a problem halts and it if halts it can only use a
finite amount of its endless tape, so theoretically Ruby
can do the same thing even if there is no limit of memory that can be
established :slight_smile:

Cheers
Robert


http://ruby-smalltalk.blogspot.com/


Whereof one cannot speak, thereof one must be silent.
Ludwig Wittgenstein

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Robert D. wrote:
|> 1. P e$B"*e(B Q Premise
|> 2. P e$B"*e(B (Q e$B"*e(B e$B"Le(BP) Premise
| De falsum quodlibet, nice try :wink:
| IOW You can prove anything with a wrong premise as false → X is
| always true indeed what you proved was
| false → (P && !P)
| which is correct of course.

Outside of propositional logic, yes. But I did warn that this doesn’t
necessarily apply, too, and provided a link for thorough critique of the
proof by the reader. :slight_smile:

| Is it really called an axiom? An axiom cannot be proven, it should be
| called a Theorem.

Sorry, my mistake. It is a theorem. Still a misnomer since the theorem
is more of a paradox.


Phillip G.
Twitter: twitter.com/cynicalryan

~ “When life gives you a lemon, make lemonade.” -Susie “I say, when
life gives you a lemon, wing it right back and add some lemons of your
own!” -Calvin
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2008/4/17 Phillip G. [email protected]:

| false → (P && !P)
| which is correct of course.

Outside of propositional logic, yes. But I did warn that this doesn’t
necessarily apply, too, and provided a link for thorough critique of the
proof by the reader. :slight_smile:
Oops I missed it, nice trick anyway.

| Is it really called an axiom? An axiom cannot be proven, it should be
| called a Theorem.

Sorry, my mistake. It is a theorem. Still a misnomer since the theorem
is more of a paradox.
I see no paradox in it, the paradox is the proof of the theorem right?
The theorem itself just says that such paradoxes will occur in a
complete system, but I admit it is difficult to accept that as not
being paradoxal itself. :=)
IIRC even Bertrand Russel did not believe Gödel’s theorem and there
were other prominent mathematicians defying it.
Gödel was waaaay ahead of his time.

Cheers
Robert

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http://ruby-smalltalk.blogspot.com/


Whereof one cannot speak, thereof one must be silent.
Ludwig Wittgenstein

On Thu, Apr 17, 2008 at 2:34 PM, Eivind E. [email protected]
wrote:

My claim wasn’t that reasoning about the system is not subject to
Goedel’s incompleteness theorem - it is.

Ah, I see.

It was that the properties
that was described as being a result of Goedel’s incompleteness
theorem was in fact not related to that theorem. That state proving
is impossible in the case of an infinite memory computer and often
infeasible the case of finite memory computers is, to the best of my
knowledge, a fully separate result.

I just looked up Wikipedia on the halting problem[1] - I quote:

“…any finite-state machine, if left completely to itself, will fall
eventually into a perfectly periodic repetitive pattern. The duration
of this repeating pattern cannot exceed the number of internal states
of the machine…”

which agrees with your statement, though the article continues:

Minsky warns us, however, that machines such as computers with e.g. a
million small parts, each with two states, will have on the order of
21,000,000 possible states:

"This is a 1 followed by about three hundred thousand zeroes ...

Even if such a machine were to operate at the frequencies of cosmic
rays, the aeons of galactic evolution would be as nothing compared to
the time of a journey through such a cycle" (Minsky p. 25)

Minsky exhorts the reader to be suspicious – although a machine may
be finite, and finite automata “have a number of theoretical
limitations”:

"...the magnitudes involved should lead one to suspect that

theorems and arguments based chiefly on the mere finiteness [of] the
state diagram may not carry a great deal of significance" (ibid).

When you consider that 1 million bits is about 128K, that is a sobering
thought.

Regards,
Sean

[1] Halting problem - Wikipedia

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Robert D. wrote:

| Oops I missed it, nice trick anyway.

Yeah, abstract logic allows for neat stunts (and a lot of sales for
aspirin, too). :stuck_out_tongue:

| I see no paradox in it, the paradox is the proof of the theorem right?
| The theorem itself just says that such paradoxes will occur in a
| complete system, but I admit it is difficult to accept that as not
| being paradoxal itself. :=)
| IIRC even Bertrand Russel did not believe Gödel’s theorem and there
| were other prominent mathematicians defying it.
| Gödel was waaaay ahead of his time.

Well, the theorem is counter-intuitive in its nature, and paradoxical.

After all, any consistent system should be provable, but isn’t. But if
it isn’t provable, it isn’t consistent, but yet it is.

The theorem is, in a way, its own proof. :stuck_out_tongue:


Phillip G.
Twitter: twitter.com/cynicalryan

~ - You know you’ve been hacking too long when…
…you think “grep keys /dev/pockets” or “grep homework /dev/backpack”
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On Thu, Apr 17, 2008 at 7:35 PM, Phillip G.
[email protected] wrote:

After all, any consistent system should be provable, but isn’t. But if
it isn’t provable, it isn’t consistent, but yet it is.
No Gödel is not talking about consistent systems, he has only (that is
a strange adjective in this context, but you know how I mean it)
proven that all complete systems are inconsistent.

Eivind can you explain this better? Or am I wrong after all? I really
liked how you put things last time, felt kind of, gosh that is exactly
what I should have sayed…

Cheers
Robert

On Thu, Apr 17, 2008 at 12:13 PM, Robert D. [email protected]
wrote:

| IOW You can prove anything with a wrong premise as false → X is

were other prominent mathematicians defying it.
Gödel was waaaay ahead of his time.

Cheers
Robert

Fascinating conversation! It comes up every once in a while in
database talk lists.

Formal logic system proves that it cannot prove everything that’s true
within the system (It’s not talking about itself, is it? :).

I love it!

Todd

On Apr 17, 12:16 am, “Arved Sandstrom” [email protected]
wrote:

…Having said that, it seems to me that the better correctness of programs in
SPARK or Ada compared to C/C++, say, would also be due to the qualities of
organizations that tend to use/adopt these languages…

I think there’s a lot to be said for this. Organizations that choose
bad tools when better tools are available show that at some level they
are not properly serious, and/or not properly informed (which points
again to not being properly serious).

Mike

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Robert D. wrote:
| On Thu, Apr 17, 2008 at 7:35 PM, Phillip G.
| [email protected] wrote:
|
|> After all, any consistent system should be provable, but isn’t. But if
|> it isn’t provable, it isn’t consistent, but yet it is.
| No Gödel is not talking about consistent systems, he has only (that is
| a strange adjective in this context, but you know how I mean it)
| proven that all complete systems are inconsistent.

Even so, it is still a paradox. :wink:


Phillip G.
Twitter: twitter.com/cynicalryan

~ “I suppose the secret to happiness is learning to appreciate the
moment.”

  • -Calvin
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Eleanor McHugh wrote:

reality in which our processes must survive. Thus we must leave
Games With Brains
http://slides.games-with-brains.net


raise ArgumentError unless @reality.responds_to? :reason

Well, yes. And it’s also classical Zen Buddhism - we kill the Buddha we
meet on the road to avoid being distracted from the road. All
idealizations and representations fail, and we must endeavor not to be
taken in. When formalisms are complete enough not to fail, they become
clones - copies, not representations. Psychologically, this is why
thinking too much betrays the thinker. The dialectic between
representation (formalism) and reality is ongoing and unavoidable, if
one wishes to minimize crashes of all sorts.

What utterly fascinates me is that this clearly seems to be true in
cockpits AND people’s love lives. That makes it a very good truth
indeed. My earlier expressed appreciation derives precisely from my
delight at seeing the same truth I know well in my home environment
emerging here in a very different (for me) environment. “Delight” is the
precisely correct description of my reaction to seeing this, although it
does not well represent the reality of that reaction. (!)

t.

Tom C., MS MA, LMHC
Private practice Psychotherapist
Bellingham, Washington, U.S.A: (360) 920-1226
<< [email protected] >> (email)
<< TomCloyd.com >> (website & psychotherapy weblog)
<< sleightmind.wordpress.com >> (mental health issues weblog)
<< directpathdesign.com >> (web site design & consultation)

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Tom C. wrote:

| For what it’s worth, in my profession (clinical applied psychology/
| psychotherapy), it’s written into our professional ethics that decisions
| are always to be made by people, not by some testing device, instrument,
| or technology. Sometimes we merely review and approve, but that human is
| required to be there. Very few people object to this, especially after a
| little reflection.

It is a sad state of affairs, if this has to be written down and people
have to think about this, before it makes sense to them.

This reminds me of the late Joseph Weizenbaum’s shock he felt, when
people accepted ELIZA as more than a toy, which led to his seminal work
“Computer Power and Human Reason”[0], arguing my case better than I ever
could.

This quote encompasses it, methinks:
“I want them [teachers of computer science] to have heard me affirm that
the computer is a powerful new metaphor for helping us understand many
aspects of the world, but that it enslaves the mind that has no other
metaphors and few other resources to call on. The world is many things,
and no single framework is large enough to contain them all, neither
that of man’s science nor of his poetry, neither that of calculating
reason nor that of pure intuition.”[1]

It is sad that we, as human beings, so eagerly submit ourselves to the
seeming rule of computers (SkyNET and its counterparts in
science-fiction, anyone?).

| Cross-validation of process, eh?

Yes, indeed.

[0] Computer Power and Human Reason - Wikipedia
[1] http://www.smeed.org/1735


Phillip G.
Twitter: twitter.com/cynicalryan

Use the good features of a language; avoid the bad ones.
~ - The Elements of Programming Style (Kernighan & Plaugher)
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Tom C. wrote:

| Well, yes. And it’s also classical Zen Buddhism - we kill the Buddha we
| meet on the road to avoid being distracted from the road. All
| idealizations and representations fail, and we must endeavor not to be
| taken in. When formalisms are complete enough not to fail, they become
| clones - copies, not representations. Psychologically, this is why
| thinking too much betrays the thinker. The dialectic between
| representation (formalism) and reality is ongoing and unavoidable, if
| one wishes to minimize crashes of all sorts.

Or, on a wider scale, the difference and conflict between perception,
perception of self, and reality (which can be objective, or not), in all
its forms.

After all, every thing we create reflects our self, on one level or
another, be these things physical or not.

I think Plato’s Allegory of the Cave applies, too.

“The things which we perceive as real are actually just shadows on a
wall. Just as the escaped prisoner ascends into the light of the sun, we
amass knowledge and ascend into the light of true reality: where ideas
in our minds can help us understand the form of ‘The Good’.” [0]

| What utterly fascinates me is that this clearly seems to be true in
| cockpits AND people’s love lives. That makes it a very good truth
| indeed. My earlier expressed appreciation derives precisely from my
| delight at seeing the same truth I know well in my home environment
| emerging here in a very different (for me) environment. “Delight” is the
| precisely correct description of my reaction to seeing this, although it
| does not well represent the reality of that reaction. (!)

Well, it is not all that surprising, considering that humans are
involved in all of this. :wink:

I share the delight, in a way, from my philosophical background, myself.

[0] Allegory of the cave - Wikipedia

P.S.: My random quote add on for Thunderbird worries me in its
randomness, producing quotes that somehow relate to the email I’m going
to write…


Phillip G.
Twitter: twitter.com/cynicalryan

Zen: the sound of the ax chopping. Chopping logic.
~ – Edward Abbey
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On Fri, Apr 18, 2008 at 7:36 AM, Phillip G.
[email protected] wrote:

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This quote encompasses it, methinks:
“I want them [teachers of computer science] to have heard me affirm that
the computer is a powerful new metaphor for helping us understand many
aspects of the world, but that it enslaves the mind that has no other
metaphors and few other resources to call on. The world is many things,
and no single framework is large enough to contain them all, neither
that of man’s science nor of his poetry, neither that of calculating
reason nor that of pure intuition.”[1]
That pretty much is why I find Gödel’s theorem all save paradoxical.
It showed me, fortunately I was young enough to fully except it as a
truth, that formalism cannot do anything (as does the halting
problem). Without these knowings I might as well still think the
contrary, which would indeed reduce my own awareness of the greater
picture.

Now not to become too serious, I deduce from Gödel’s theorem that if a
human being would fully understand the nature of the human brain at
least one of the following things would happen
(1) 42 becomes nil
(2) Life, the universe and evertyhing would vanish immediately.
(42) All of Doug Adam’s works will be put on the index.
(SSSSSSSSSS0) I will try to find the error in Gödel’s proof.

Cheers
Robert


http://ruby-smalltalk.blogspot.com/


Whereof one cannot speak, thereof one must be silent.
Ludwig Wittgenstein

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Phillip G. wrote:

achieve (since we, as human beings, aren’t perfect).
Unfortunately, I can only assume that it was so, since I cannot find a
new, and very different from the “throw away” capsules used before, with


Phillip G.
Twitter: twitter.com/cynicalryan

“…no amount of software nor hardware can replace judgment calls made
by human beings. Technology can only
assist in making decisions.”

For what it’s worth, in my profession (clinical applied psychology/
psychotherapy), it’s written into our professional ethics that decisions
are always to be made by people, not by some testing device, instrument,
or technology. Sometimes we merely review and approve, but that human is
required to be there. Very few people object to this, especially after a
little reflection.

Cross-validation of process, eh?

t.

Tom C., MS MA, LMHC
Private practice Psychotherapist
Bellingham, Washington, U.S.A: (360) 920-1226
<< [email protected] >> (email)
<< TomCloyd.com >> (website & psychotherapy weblog)
<< sleightmind.wordpress.com >> (mental health issues weblog)
<< directpathdesign.com >> (web site design & consultation)

2008/4/18 Sylvain COURTECUISSE [email protected]:

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LOL we will not tell anybody that you tried - unsucessfully BTW - to
unsubscribe from this group (which indeed is a shame :wink:
But please try to send this to the administration address of this
mailing list.

HTH
Robert


http://ruby-smalltalk.blogspot.com/


Whereof one cannot speak, thereof one must be silent.
Ludwig Wittgenstein

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Robert D. wrote:

| That pretty much is why I find Gödel’s theorem all save paradoxical.
| It showed me, fortunately I was young enough to fully except it as a
| truth, that formalism cannot do anything (as does the halting
| problem). Without these knowings I might as well still think the
| contrary, which would indeed reduce my own awareness of the greater
| picture.

We humans are neither consistent, nor logical, though. We are still
guided by imperatives that we have little control over, for example
(fear, lust, greed, envy, gluttony…). We can control them, but only if
we a) are aware of them, and b) have the intellect (Freud’s super-ego)
to keep them in check. :wink:

Not to mention that Godel’s Incompleteness Theorem applies to abstract
concepts more than human nature. Machines and abstract systems are in
conflict with human nature, necessitating process for interaction (from
social rules, ethics [distinct from morals, which are more on a
meta-level], software development methodologies, what have you) in a
meaningful and consistent terms.

The game of Chinese whispers (Stille Post in Germany) demonstrates this
quite efficiently, as well as the Mythical Man-Month: Adding people to a
late project makes it later, since communication increases to the square
of the team size).

Alas, process has the problem of creating friction and stifles
creativity, if taken to the extreme. The balance has to be found between
human nature and process, and this is a constant struggle.

Too much process stifles creativity and the wellbeing of those
participating in the process, and no process endangers the success of
the task at hand (whatever that task may be).

| Now not to become too serious, I deduce from Gödel’s theorem that if a
| human being would fully understand the nature of the human brain at
| least one of the following things would happen
| (1) 42 becomes nil
| (2) Life, the universe and evertyhing would vanish immediately.
| (42) All of Doug Adam’s works will be put on the index.
| (SSSSSSSSSS0) I will try to find the error in Gödel’s proof.

Which are probable events, just not likely. :stuck_out_tongue:


Phillip G.
Twitter: twitter.com/cynicalryan

Don’t sacrifice clarity for small gains in “efficiency”.
~ - The Elements of Programming Style (Kernighan & Plaugher)
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On Fri, Apr 18, 2008 at 9:41 AM, Phillip G.
[email protected] wrote:

| picture.
social rules, ethics [distinct from morals, which are more on a
human nature and process, and this is a constant struggle.

Too much process stifles creativity and the wellbeing of those
participating in the process, and no process endangers the success of
the task at hand (whatever that task may be).
I completely agree with you on this, but the interesting thing is that
Gödel’s theorem is just such a realistic one in a real world far away
from the abstractions of an ideal world, because it showed that even
the abstract, logical world was not ideal as soon
as something got complex enough to be “interesting”. That is why his
theorem was that much contested I suppose.
When you say paradox, do you as a matter of fact contest the theorem?
Maybe this is simply my wrong interpretation of the term?
Which are probable events, just not likely. :stuck_out_tongue:
Well I am glad you like my humor :wink:
Cheers
Robert


http://ruby-smalltalk.blogspot.com/


Whereof one cannot speak, thereof one must be silent.
Ludwig Wittgenstein

On Fri, Apr 18, 2008 at 11:03 AM, Phillip G.
[email protected] wrote:

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Robert D. wrote:

Look at this definition of paradox:

“a statement or proposition that seems self-contradictory or absurd but
in reality expresses a possible truth.”[0]

I merely state, that Godel’s Incompleteness Paradox would be closer to
the truth of Godel’s assertion, than the term theorem can transport. :slight_smile:

ok, if I were a Romulan I would say that this is acceptable :wink:
Really enjoyed the discussion.

Cheers
Robert


http://ruby-smalltalk.blogspot.com/


Whereof one cannot speak, thereof one must be silent.
Ludwig Wittgenstein

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Robert D. wrote:

| ok, if I were a Romulan I would say that this is acceptable :wink:
| Really enjoyed the discussion.

So do I. :slight_smile:

A nice exchange, and so very polite, too.


Phillip G.
Twitter: twitter.com/cynicalryan

Rule of Open-Source Programming #4:

If you don’t work on your project, chances are that no one will.
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