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Re: [ontolog-forum] Axiomatic ontology

To: "Rob Freeman" <lists@xxxxxxxxxxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Fri, 8 Feb 2008 11:21:10 -0600
Message-id: <p06230902c3d23ac06eb7@[]>
At 6:48 PM +0800 2/8/08, Rob Freeman wrote:
On Feb 8, 2008 2:21 PM, Pat Hayes <phayes@xxxxxxx> wrote:
> I take it to be obvious that a random sequence cannot encode information
> about anything other than itself. Right?

I think I understand what you are suggesting. I think you are
suggesting that while a random string is very complex, it can't
actually code anything. If I drop my coffee on the floor the mess
might be complex to describe, but it won't tell me anything.

I think that is intuitive, and the way we normally see randomness. But
I'm not sure that its true, not for all random systems, anyway.

Maybe it comes down to the way the random pattern is created. Say you
code one signal. Then you code another using the same elements. The
second one will interfere with the first one a little, but it need not
obliterate it. If you push enough signals on eventually the overall
pattern might appear random.

But if you can extract information from it, it isn't in fact random. The definition of a random sequence is that no matter how much of it you have, there is no way even in principle to compute any information about the next item. This is why their information capacity is as high as it can get, because you can't compress them into a smaller package. But this also means that you can't in any sense parse them: you can't find any structure in them to utilize to say something about something else. They are entirely used up being themselves. All they can do, as it were, by way of communication, is to exhibit themselves and then stop.

I had better stop this conversation myself, as I am getting to the point where I have no confidence that I know what I am talking about :-)

In fact from the point of view of each
individual element it will be random, because there will be no way to
decide given only a single element, which pattern it belongs to (it
will belong to many.) But combinations of elements will still reveal
patterns. The key is using combinations to select, when individually
the distribution is random.

I think there is an important distinction between appearing random and actually being random. You seem here to be talking about something like a hologram (?)

What will happen is you will get a whole lot of patterns using the
same elements. And because they use the same elements you won't be
able to form more than one at a time. But they will all be there.
Different combinations will "resonate". And because you can have many
more combinations of n elements than n, you will be able to have many
more "resonances" for a given number of elements than you have
elements (if the distribution for each element is random.)

It is that "more combinations for n elements than n" that gives you
the extra storage space. (Some suggest it is this kind of "larger than
itself" ability which might give the mind its ability to comprehend
the universe, when the mind is itself smaller than the universe.)

BTW This "not being able to form more than one at a time" starts looks
a lot like an uncertainty principle, or at least Chaitin's Omega.
Which is what I thought you might be alluding to.

No, and indeed I don't know that term. I will go and find out more about it, thanks for the pointer.



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