## Re: Compressability (was: an structurality index)

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• ... little lamb or &*SAKSJNDKQ . I argued that complexity from a mathematical point of view is in the eye of the beholder. Eray was arguing that a single
Message 1 of 63 , Apr 1, 2005
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wrote:
>
>Lets see if I can catch you up. We started off discussing the
>complexity of strings. So which has more complexity "Mary had a
little >lamb" or "&*SAKSJNDKQ". I argued that complexity from a
mathematical >point of view is in the eye of the beholder. Eray was
arguing that a >single point should be chosen to measure complexity
from.
>

As long as you are limiting the discussion of complexity to the
complexity of strings (composed of a finite alphabet) then the
distinction between patterns and random is arbitrary.

But, What if I could show that "&*SAKSJNDKQ" was a compression
of "Mary had a little lamb". Well, it seems to me that if I could
show such a thing then "&*SAKSJNDKQ" would be more complex (closer
to randomness) than "Mary had a little lamb" but must be less
complex (not fully random) than it could be. Compression cannot
result is total "randomness". Some amount of pattern must remain or
the message is lost forever and can't ever be decompressed.

>
>The reason for this argument on a philosophy of AI group is that
some
>Machine Learning algorithms such as the Levin search assume that a
>single encoding that uses the length of a program that
creates "Mary >had a little lamb" has something fundemental to say
about the nature >of the complexity of "Mary had a little lamb".
>

If we continued along the lines that string A was a compression of
string B and then asked what if we had to continually compress and
decompress such strings. Well it seems to me that eventually we
would learn to deal with the compressed strings as is. IOW string A
would replace string B and the methods of decompression would
eventually be forgotten altogether because they are no longer
needed. Once that happen, another method of compressing the new set
of strings could be developed establishing a new A and B which would
eventually be used to obsolescenceÂ…

IMO that's what it "has something fundemental to say about the
nature of the complexity of "Mary had a little lamb" has to say.

I still think I could be off course from what you guys are talking
about. But, maybe this will shake things up anyway.

JJG

wrote:
>
> --- In ai-philosophy@yahoogroups.com, "John J. Gagne"
> <fitness4eb@c...> wrote:
> >
> > --- In ai-philosophy@yahoogroups.com, "whazateh" <loadquo@g...>
> wrote:
> > >
> >
> > >
> > >If you are using physics why are you still using bits? Why not
go to
> > >the wavelength of a photon? Or are photons not allowed because
> they
> > >travel along all path giving a high volume?
> > >
> >
> > It's obvious to me that you guys are off on some type of tangent
I'm
> > not really followingÂ… but I hope you don't mind my comment on
this
> > one statement.
>
> Lets see if I can catch you up. We started off discussing the
complexity of
> strings. So which has more complexity "Mary had a little lamb" or
> "&*SAKSJNDKQ". I argued that complexity from a mathematical point
of
> view is in the eye of the beholder. Eray was arguing that a single
point
> should be chosen to measure complexity from.
>
> The reason for this argument on a philosophy of AI group is that
some
> Machine Learning algorithms such as the Levin search assume that a
> single encoding that uses the length of a program that
> a little lamb" has something fundemental to say about the nature
of the
> complexity of "Mary had a little lamb".
>
> We then went on to discuss physical systems that could represent
or
> encode strings, because Eray brought it up, and I considered it a
> different field as there is some concrete reason to pick a certain
> language.
>
> He was suggesting a language based on interaction between moving
> parts and the resulting position of said parts. I went on to
suggested one
> based on photons as it might reduce the space complexity,
dependent
> on your interpretation of the electron.
>
> > I would say "why not show how wavelength is converted to bits"?
> > Certainly this will be an algorithmic process of sampling over
time.
> > No? I sure hope this is relevant and if not oh well.
>
> It does bring up an issue, if you require that the string be
represented in
> bits then it is hard, relatively, to convert the photon into bits.
The best I
> can think of is a series of different metal (or programmable
matter) plates
> that bounce the photon between them at 45% angles. Like so
> -- --
> \/\/\
> -- -
> They would be calibrated to have different photoelectric effect
> wavelengths and so act together an analog to digital converter.
Whether
> that counts as temporal algorithmic process is in your court. It
is a hellishly
> complex device (and is beyond our capability at the moment), but
that is
> not what we are worried about, at least not in classical
complexity. We are
> worried about the size of the message, in this case the photon. A
photon
> might not even have infinite degrees of freedom, we don't know
what
> happens when the wave length goes beneath the planck length. And
> there are thermodynamic limits to the least energetic photon you
can
> measure.
>
> But getting back to physical complexity. We could just use qubits,
> although that has the problem that it is hard to create low qubit
systems,
> needing to cool down atoms and the like to near absolute zero so
they
> have fewer vibrational modes. Also we need to specify low qubit
> of the string, else I will want to tack on encoders that translate
from the
> value 1 of a 1 qubit system to the string 3141571 which would
break the
> affect we are looking for. Hmm, now I am not sure that any reader
that did
> the arbitrary conversion would necesarily be any more complex than
that
> did a rational conversion. I shall have to think on it.
>
> Will Pearson
• ... time putting a carriage return at every 60 characters. ... I just figured out that I could set the margins in my word processor. However, there is a
Message 63 of 63 , Apr 10, 2005
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--- In ai-philosophy@yahoogroups.com, Eray Ozkural <erayo@c...> wrote:
> On Apr 9, 2005 7:33 PM, Jim Bromer <jbromer@i...> wrote:
>> I do not mean to be unpleasant, but I am not going to waste my
time putting a carriage return at every 60 characters.
>
> The problem is that yahoo and gmail edit boxes are broken.
> It's just a recommendation that will prevent some unpleasant
> quoting errors. Maybe they'll fix it real soon now. :) I sure
> hope so..
>
> And it doesn't waste time IMO. (Especially if you're using
> an external text editor?)
>
> Regards,
>
> --
> Eray Ozkural (exa), PhD candidate

I just figured out that I could set the margins in my word
processor. However, there is a reason why I decided not to do that a
long time ago and that is because it doesn't work. So until Yahoo
and Microsoft can work it out between them, I am not going to comply
because I have to insert each return indivdually after I paste it
into the Yahoo text box. Sorry.
Jim
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