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Re: [ontolog-forum] Axiomatic ontology

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Rob Freeman" <lists@xxxxxxxxxxxxxxxxxxx>
Date: Sun, 10 Feb 2008 11:51:18 +0800
Message-id: <7616afbc0802091951l1d9f9638tb817220413fb9e0d@xxxxxxxxxxxxxx>
John,    (01)

You know what I think of arguments about the meaning of words.    (02)

Lets put the word "random" aside for a moment.    (03)

I too think there are many important patterns which can be found on
the Web (and most importantly in natural language.)    (04)

On the other hand I don't think those patterns are predictable. Or
rather, I think that individually they are predictable, but there is
more than one pattern, so you have a choice.    (05)

As Sean says, when he googles his name there is no way to distinguish
between the different people he finds.    (06)

My point just is to turn around our usual attitude to this
unpredictability and argue it is not the bad thing we have always
thought it is. Rather it is the sign of a system which is storing more
information using the same elements.    (07)

In short think we need stop trying to get rid of unpredictability, in
natural language, and on the Web, and recognize it as the sign of a
more compact knowledge representation system than is possible using
elements related predictably.    (08)

And since I believe all cognition works this way, I think we need to
accept that any representation of knowledge as a whole is going to
need to work this way.    (09)

Whether a hologram can be said to be predictable is another question.
But I think Pat's analogy is good. As I recall physically a hologram
is a diffraction pattern. I suspect that diffraction pattern is at
least as complex as the original object.    (010)

Think about it this way. Since a hologram simultaneously codes many
different perspectives of an object, given any individual grain of
photographic emulsion there is no meaningful way to "predict" a
particular perspective. It codes all of them at the same time. In that
sense the interpretation of a grain of emulsion in a hologram is going
to be unpredictable. To actually see a perspective you need to select
one.    (011)

But this "unpredictability" is not a bad thing. It means a hologram
can code much more information than an ordinary photographic plate. In
fact intrigued by Pat's analogy I chased up some vague references to
holographic memories and found that, indeed, technology is starting to
get hip to this. Among others I found this:    (012)

'Although the offices of IBM and Hewlett-Packard are nearby, Longmont,
CO, is decidedly not Silicon Valley chic. But in this Denver suburb, a
radical experiment in data storage is under way. At the headquarters
of InPhase Technologies, where the conference rooms are named after
ski resorts, chief executive Nelson Diaz holds up a clear plastic
disc, about the size of a DVD but thicker, and pops it into a disc
drive...    (013)

But this is no ordinary recording process. The disc has more than 60
times the storage capacity of a standard DVD, while the drive writes
about 10 times faster than a conventional DVD burner. That means the
disc can store up to 128 hours of video content -- almost twice enough
for the full nine seasons of Seinfeld -- and records it all in less
than three hours.    (014)

It's likely to be one of the first commercial systems to use
"holographic storage,"...'
(http://www.technologyreview.com/InfoTech/wtr_14742,294,p1.html)    (015)

And incidentally this:    (016)

"...For physical memory disks such as DVD, the present technique has
reached the upper limit of data density. Computer engineers are trying
to use hologram for the next generation of data storage, because it
may store significantly higher amount of information. In our brain,
the holographic memory may also be able to store more information than
other alternatives."
(http://www.web-books.com/MoBio/free/Learning/Memory.htm)    (017)

>From the same page, this about resolution:    (018)

"The hologram was invented in 1947 by Dennis Gabor to record images in
a medium (e.g., a crystal). It has a very unique feature, namely, any
small part of the medium contains all information about the image.
Therefore, even if the medium is broken into pieces, the entire image
can still be obtained from any piece, except the resolution is
reduced."    (019)

Equate resolution to predictability, and you have a sense for the
"randomness" of any grain of emulsion in a hologram.    (020)

-Rob    (021)

On Feb 10, 2008 6:16 AM, John F. Sowa <sowa@xxxxxxxxxxx> wrote:
> Rob,
> Pat was using the word "random" in a precise technical sense.
> But like any technical term, it can also be used in an open-ended
> variety of metaphorical senses of varying degrees of usefulness.
>  > At the very least we need to think about it more and should
>  > not simply dismiss information sources (like the Web) because
>  > their elements are related randomly (=unpredictably.)
> The info on the web is definitely *not* random, and there are
> very important kinds of patterns that can be found it in.
> The patterns that have been found so far are an insignificant
> fraction of the extremely important patterns that are out there.
>  > It would be interesting to know if it is possible to compress
>  > a hologram without losing resolution. If the analogy of
>  > randomness holds, then it should not be possible.
> A hologram is definitely *not* random.  A hologram is a
> representation in frequency space of an image in a 2-D or 3-D
> Euclidean space.  If you recall from an old math course, a
> sound wave can be represented as a time-varying function f(t).
> The Fourier transform of f(t) is another function F(w), where
> w (actually a lower-case omega) represents frequency.
> Far from being unpredictable, such transformations are very
> widely used for *detecting* many kinds of patterns that are
> easier to find in the transformed frequency coordinates.
> One example is a pure tone of a fixed frequency w1.  For that
> tone, f(t) is very simple:
>     f(t) = A sin(w1 t)
> which is a sine wave of amplitude A.  The Fourier transform of
> that f(t) is even simpler:
>    F(w) is a constant C for w=w1 and 0 for all other values of w.
> This pattern can be compressed to just two numbers, w1 and C, which
> can detect and predict the original pattern with superb accuracy.
> There are the usual caveats about floating-point arithmetic, but
> the usual precision on a digital computer is more than adequate to
> store and reproduce sound and spatial information with a precision
> that is far beyond what the human eyes and ears can detect.
> In short, holograms (and related kinds of transforms, such as
> wavelet transforms) are far from random, and they can be very
> useful for both detecting patterns and reproducing them.
> John    (022)

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