--
"Intuition is not something that is given. I've trained my intuition
to accept as obvious shapes which were intially rejected as absurd,
and I find everyone else can do the same."
- Benoit Mandelbrot, on Fractals
Logic is an axiomatic system. To me, computation is the process of
following a procedure to manipulate symbols to produce other symbols.
Prolog is for the purpose of computation, specifically following
procedures to satisfy logical and arithmetic expressions.
Computation isn't an axiomatic system, so it is hard to compare with
logic. I guess you could say that an ESP experiment would be a non-
logical computation. You could also have a deterministic but
completely arbitrary or absurb computation.
Sent via Deja.com http://www.deja.com/
Before you buy.
It depends on what you mean by "computation". What mathematicians
call "Theory of Computation" was born in fact as a branch of Logic,
and concerned concepts such as Turing machines and recursiveness.
Algorithms, computability, efficiency, complexity, etc., are concepts
that can be defined and developed in purely logic terms.
Miguel A. Lerma
As well as what he means by "logic." Like any other crackpot, he doesn't
try to define his terms.
Actually vague definitions are a major difference between "thought" and
"computation", as was being discussed in a recent thread. Computation
applies some well-defined operations to well-defined input and produces
some output. OTOH thought applies some poorly defined operations to
poorly defined input and produces some output. Perhaps Mr.Kagalenko's
need for nice definitions are indicative of his facility for computation
rather than thought.
Yes, It seems to me that, calculation is a method of decision. There
are 3 main methods of decision for Logic...deduction, natural eduction,
and calculation.
The Truth Table method is Logical Calculation, and has use in finite
domains. Even higher order quantification theory, can be resolved to
truth tables within finite domains. In non-finite domains deduction has
broader application.
Bad answer. If you felt like some sort of aggressive reply to the
word "crackpot" that might be appropriate - I don't think many people
here think the word crackpot applies to you, people sometimes think
you're wrong about things and sometimes think your points are a bit
silly or off-topic, but you _don't_ insist in the truth of sttaements that
are demonstrably false. _I_ certainly would not call you a crackpot.
But you lose credibility when you denigrate the guy's need
for precise definitions and suggest this indicates hes stupid or
something. This is sci.math. (Um, this is sci.math, _and_ questions
like "what is computation" and "what is logic" are not like boldly
going into unexplored territory where precise definitions would
not be expected. If he'd shown a need for a precise definition
of "thought" that might be different, even. But the subject was
not "thought". If you want to discuss the relation between
logic and computation as you claimed then asking for precise
definitions is extremely appropriate.)
> --
> "Intuition is not something that is given. I've trained my intuition
> to accept as obvious shapes which were intially rejected as absurd,
> and I find everyone else can do the same."
>
> - Benoit Mandelbrot, on Fractals
>
I assumed that he meant Mathematical Logic. The question
seemed to me a perfectly legitimate one.
Miguel A. Lerma
Thank you. (Phew!)
> But you lose credibility when you denigrate the guy's need
> for precise definitions and suggest this indicates hes stupid or
> something. This is sci.math. (Um, this is sci.math, _and_ questions
> like "what is computation" and "what is logic" are not like boldly
> going into unexplored territory where precise definitions would
> not be expected. If he'd shown a need for a precise definition
> of "thought" that might be different, even. But the subject was
> not "thought". If you want to discuss the relation between
> logic and computation as you claimed then asking for precise
> definitions is extremely appropriate.)
I agree that precise definitions are appropriate in sci.math. But
unfortunately I can't always express myself or think in terms of precise
definitions. I assumed that most people here understood I meant
propositional or predicate logic. Also computation is usually understood
in terms of Turing machines or String rewriting or Pascal programs etc.
I think these are _already_ well defined and I don't need to repeat
those definitions.
>> But you lose credibility when you denigrate the guy's need
>> for precise definitions and suggest this indicates hes stupid or
>> something. This is sci.math. (Um, this is sci.math, _and_ questions
>> like "what is computation" and "what is logic" are not like boldly
>> going into unexplored territory where precise definitions would
>> not be expected. If he'd shown a need for a precise definition
>> of "thought" that might be different, even. But the subject was
>> not "thought". If you want to discuss the relation between
>> logic and computation as you claimed then asking for precise
>> definitions is extremely appropriate.)
>
>I agree that precise definitions are appropriate in sci.math. But
>unfortunately I can't always express myself or think in terms of precise
>definitions. I assumed that most people here understood I meant
>propositional or predicate logic.
Begin practicing expressing yourself with precision. You'll never
be able to write a functional, architectural or design spec
without being very, very, very precise. Engineers will
implement exactly what you write :-).
>Also computation is usually understood
>in terms of Turing machines or String rewriting or Pascal programs etc.
Sigh! Has computing really come down to this?
>I think these are _already_ well defined and I don't need to repeat
>those definitions.
Ah, no :-). And you also posted this in sci.physics.
/BAH
Subtract a hundred and four for e-mail.
>david_...@my-deja.com wrote:
>>
>> In article <3975443C...@home.com>,
>> Rajarshi Ray <raja...@home.com> wrote:
>> > Michael Kagalenko wrote:
>> > >
>> > > Miguel A. Lerma (le...@math.nwu.edu) wrote
>> > > ]Rajarshi Ray (raja...@home.com) wrote:
>> > > ]: What is the difference between logic and computation? I read that
>> > > ]: computation can be subsumed by logic (according to the inventors of the
>> > > ]: Prolog language). So is computation a limited form of logic??
>> > > ]
>> > > ]It depends on what you mean by "computation".
>> > >
>> > > As well as what he means by "logic." Like any other crackpot, he doesn't
>> > > try to define his terms.
>> >
>> > Actually vague definitions are a major difference between "thought" and
>> > "computation", as was being discussed in a recent thread. Computation
>> > applies some well-defined operations to well-defined input and produces
>> > some output. OTOH thought applies some poorly defined operations to
>> > poorly defined input and produces some output. Perhaps Mr.Kagalenko's
>> > need for nice definitions are indicative of his facility for computation
>> > rather than thought.
>>
>> Bad answer. If you felt like some sort of aggressive reply to the
>> word "crackpot" that might be appropriate - I don't think many people
>> here think the word crackpot applies to you, people sometimes think
>> you're wrong about things and sometimes think your points are a bit
>> silly or off-topic, but you _don't_ insist in the truth of sttaements that
>> are demonstrably false. _I_ certainly would not call you a crackpot.
>
>Thank you. (Phew!)
>
>> But you lose credibility when you denigrate the guy's need
>> for precise definitions and suggest this indicates hes stupid or
>> something. This is sci.math. (Um, this is sci.math, _and_ questions
>> like "what is computation" and "what is logic" are not like boldly
>> going into unexplored territory where precise definitions would
>> not be expected. If he'd shown a need for a precise definition
>> of "thought" that might be different, even. But the subject was
>> not "thought". If you want to discuss the relation between
>> logic and computation as you claimed then asking for precise
>> definitions is extremely appropriate.)
>
>I agree that precise definitions are appropriate in sci.math. But
>unfortunately I can't always express myself or think in terms of precise
>definitions. I assumed that most people here understood I meant
>propositional or predicate logic. Also computation is usually understood
>in terms of Turing machines or String rewriting or Pascal programs etc.
>I think these are _already_ well defined and I don't need to repeat
>those definitions.
Well phew back at you (I mean that in a nice way). Seeing
I had a reply from you my stomach started churning a bit, but here
you are just explaining something about what was written. Fabulous.
I agree as well that what you meant by "logic" was clear.
I didn't say anything was unclear about it. Whether it was a good
idea to open my mouth or not, my only point was regarding your
statement "Perhaps Mr.Kagalenko's need for nice definitions
are indicative of his facility for computation rather than thought."
If you'd just given a nice definition in response to what he said
I don't think I would have said anything. If you'd simply claimed
that the definition of "logic" was clear that would have been
fine too. Just about any comment whatever about what had
been said would have slipped through.
It's not even quite that I don't think it's appropriate for
you to say something nasty about Mr. Kagalenko the way you
did, instead of restricting your comments to what he said.
I've thought similar things about various posts from, um,
various people, but here you might even claim he started it,
calling you a crackpot. All I wanted to say was you should
chose your insults more carefully: What you said about
his "need for precise definitions" sounds like you don't
feel that definitions are important. Even if we agree that
there was no need for _explicit_ definitions _here_ because
the terms you were using had well-known meanings,
you don't want to sound like a "need for precise definitions"
is a bad thing. Insisting you're not required to
define your terms _is_ a very strong indicator of
crackpottery. (Not that you were insisting that, I
didn't say you were. But your reply comes close to
sounding that way.)
> [...]
> Begin practicing expressing yourself with precision. You'll never
> be able to write a functional, architectural or design spec
> without being very, very, very precise. Engineers will
> implement exactly what you write :-).
<RANT OFFTOPIC=true> Heh, I wish :) In my experience, when it comes to
software, what often passes for a "spec" is a vague description of a
program with some pictures in it, leaving lots of guesswork,
mind-reading, and design choices to the software engineer. Not that I
mind making design choices in some instances, but this often places
the engineer in a catch-22 situation: you do exactly what the "spec"
says (to your best interpretation, which shouldn't even be an issue),
and you get a system that, well, doesn't work very well; or you make
your own design choices, and risk being told that the choices were
wrong. </RANT>
(note followups)
--
J. Antonio Ramirez R.
Remove hybrid silverware from email address.
That's still too vague. Does he mean a logistical system, or semantical
system (in the sense those terms used in Church's intro to logic) ?
]The question
]seemed to me a perfectly legitimate one.
And to me, it seems muddleheaded crackpot nonsense, just like the rest
of Rajarshi Ray's posts.
No, they aren't. You are just a clueless crackpot.
] Computation
]applies some well-defined operations to well-defined input and produces
]some output. OTOH thought applies some poorly defined operations to
]poorly defined input and produces some output.
While "applies some poorly defined operations to poorly defined input and
produces some output" appears to be very accurate description of your own
thought process, same is not true for the general case. In other words, not
everyone is an undereducated crackpot like yourself.
] Perhaps Mr.Kagalenko's
Sure. And you're brain works just like the Pentium III processor, albeit
much slower. You're welcome to bathe in your muddy ignorance. Just don't
expect others to join you.
> ] Computation
> ]applies some well-defined operations to well-defined input and produces
> ]some output. OTOH thought applies some poorly defined operations to
> ]poorly defined input and produces some output.
>
> While "applies some poorly defined operations to poorly defined input and
> produces some output" appears to be very accurate description of your own
> thought process, same is not true for the general case. In other words, not
> everyone is an undereducated crackpot like yourself.
Then it seems the more 'educated' you get, the more you begin to think
like a silicon chip...(shudder)...and I was getting excited about grad
school! :-(
> ] Perhaps Mr.Kagalenko's
> ]need for nice definitions are indicative of his facility for computation
> ]rather than thought.
--
"Intuition is not something that is given. I've trained my intuition
to accept as obvious shapes which were initially rejected as absurd,
Then start training him; he is just a kid. Now, it might turn
out that he's as untrainable as [pronoun deleted]. And, if
he is, <shrug> then we'll just have to wait and see if he
perpetuates the myth of C.S.
I don't call that a spec. I call that a marketing wish list.
I had a very good friend whose nickname was TW. He kept a diary
of his experiences when he was handed the prints of a piece of
hardware so he could write a device routine. Now one would think
that the prints would have been the definitive spec. Hah!
He called it, "Tony in RH20 Land -or- I Should Have Listened When
Mother Told Me There Was A Great Future In Encyclopedia Sales".
A copy of it is somewhere in http://www.inwap.com/pdp10/. The
original didn't have all those typos.
Computation has physical constraints on space (memory) and time.
Difficulties arise in maintaining a strictly logical formalism
when these constraints display their dualism and yield paradoxes.
Then analogic must be employed as well. Analogic is not as
well formalized as logic. It tends to get left to "creativity",
or "experience", or "AI"; but analogic is formalizable. There
are rules for making acausual (alogical) comparisons.
In general these rules are difficult to approach logically.
It's sort of like teaching someone to ride a bicycle, something
that is too complex to be described in a "computational" sense.
So learning to ride a bicycle is not taught logically (you don't
say: "IF you do this AND do that and... THEN you can ride.")
There is a science for analogy as there is for logic, but
usually it's considered too subjective to call a "science";
because it's not logical. That's not a good reason though.
There's a rational for analogies; because we use them so
often in the arts and sciences. Being rational isn't always
just a matter of logic. Sometimes we step outside the box
and look in, or cross lines to make acausual comparisons:
some things are very similar and have similar sub-components,
knowing something about one reveals something about the other
but there is no logical/causual connection between them.
They're just similar; analogues.
That's a powerful tool that's just beginning to be better
understood. Especially in the area of analog computing and
hybrid analog/digital computers like quantum computers.
> There is a science for analogy as there is for logic, but
> usually it's considered too subjective to call a "science";
> because it's not logical. That's not a good reason though.
>
> There's a rational for analogies; because we use them so
> often in the arts and sciences. Being rational isn't always
> just a matter of logic. Sometimes we step outside the box
> and look in, or cross lines to make acausual comparisons:
> some things are very similar and have similar sub-components,
> knowing something about one reveals something about the other
> but there is no logical/causual connection between them.
> They're just similar; analogues.
>
> That's a powerful tool that's just beginning to be better
> understood. Especially in the area of analog computing and
> hybrid analog/digital computers like quantum computers.
I think Einstein called these "thought experiments"; but there is so much room
for errors that many of them are misconstrued.
Gramp
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Good comments but I think you may place too severe
limits on what is called logical. There are logical
computations which use complex numbers to represent
statistical logic and we can expect them to eventually
include quaternions and higher counting aggregates.
As you say, the question is the complexity, understood
and under control in the description? What are the
pictures? the patterns of relations? the structures
being counted? This seems to be an unlimited process
that we are well on the way to unlocking. If you look
at the projective geometry patterns that William Rowan
Hamilton used for all his developments you can see what
I'm talking about. In his work the reason for the
harmony and the excitment of patterns is very clear.
This applies to all physical and human description.
Possibly it will someday be considered just another
aspect of rational logic? and not separate analogic?
Good seeing. JD
-------------------------------------------------------------------
'Decoherence' is just as much a problem for quantum computers
as it is for grade school students.
Somehow they learn to deal with it.
There's a boom now in brain research. See for instance
ERP P3 P300. It's a sort of an event manager in the brain
something like the event interrupt in Windows or X.
It's been used to electrically interface with the brain
like a PC port amoung other things.
The web is doing quite abit to make analogic as powerful
a tool as logic.
http://www.google.com/search?q=ERP+P3+P300
Connecting the dots doesn't have to happen serially like
a logical trajectory of causual chaining. It can be done
parallely in an acausual manner much like a histogram
is the acausual compilation of many batched events (when
phases are included, the histogram is a spectrum and Time
enters the picture, but the batched events in a histogram
are treated as simultaneous in time or as "timeless").
Acausual or analogical effects are very useful:
http://www.google.com/search?q=SIRDS
There is an underlying logic to the layout of the dots
but the perception of them is governed by correlations
and not dependancies. Correlations are not 'logical',
especially in quantum physics where they can yeild
rather "illogical" (some people use the word "wierd") effects
like quantum entanglements etc.
But the same "analogical" correlations can be studied and
understood in SIRDS and in it's many manifestations such
as Rorschach tests etc:
http://www.bestweb.net/~ca314159/rorld2.gif
Joseph Campbell's "power of myth" series suggested that
there was alot to learn from analogies. His influence
by Jung and his influence on Hollywood (Lucas etc)
revitalize a broader based natural philosophy began
many millenia ago.
Historically though, the power of analogic was considered
too dangerous for mere mortals to possess, and it was disguised
in mythos and religious decoherence.
Nowadays that same power threatens to break our best codes,
the ones that maintain "order"; quantum cryptanalysis.
"Throw away your watches and clocks."
Definitely.
Analogic and logic are duals with
analogic being the more speculative/subjective,
and logic be the more pragmatic/objective.
Logic is more fundamental. The same is said about
"particles" in physics; particles are more fundamental
than "waves"; but the two go together and make-up a
'strange' subjective-objective thing called a "quantum".
It's not that strange though.
Analogic and logic can be treated as functional domains
like the spectral* and temporal domains in signal processing.
*also called the spatial-domain (as in spatial filtering) or
frequency domain (in statistics, signal processing) and by
many other names in other fields. Analogy reveals the
underlying logic of synonyms, homonyms etc.
Idioms though, are noise:
http://babelfish.altavista.com/
making translation difficult. They are somewhat analogous to
decoherence in that the meanings get confused as in data
collisions, or state tunnelling, or other non-orthogonalities...
Nowadays "language independant" systems are very popular
in computing, but in a more physical and mathematical
sense they've always been popular in terms of invariants
and characteristic functions,...
More sophisticated though is a protocol independance that
surpasses even Einstein's relativity theory and Sapir-Whorf's
linguistic relativity conjecture in its objective and subjective
applications. Linguistic effects, not only applies to natural
languages but also computer languages and physical languages
such as signal processing... even to the language of nature
itself as we speak to it in designing experiments as questions
and it answers us in measurements and more sophisticated
effects like optical illusions.