Regularity

[Sergio Navega]

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From: Detlef Morgenstern <detlef_morgenstern at bigfoot.de>
>Dear Sergio,
>
>Let me cite your homepage (about the driving force of disagreement in
>newsgroups):
>"If two people agree with each other, then their thread will extinguish
>very fast."
>
>Here we are with some practising disagreement.
>

Thanks for the disagreement ;-)

>--- Sergio Navega <snavega at attglobal.net> wrote:
>> First, I propose to reduce all the aspects related to 'data'
>> in the universe as belonging to one of three categories:
>>
>> a) The totally randomic data
>The 'degree of randomness' depends on the observer, his expectations, the
>hidden (built-in) knowledge in his sensorial mechanism.
>Is this 'totally randomic': "100101100001110110110011"?
>

Obviously no. It is here that we can see the advantage of
Algorithmic Information Theory in providing a criterion for
this kind of question. But the point is better touched below.

>> b) The totally regular data
>Is there an objective (observer independent) measure of regularity?
>

Obviously, no. The very same data can be said to be "random" or
completely regular, it depends on the observer. Does this mean we'll
never find an objective observer? I guess so.

>> Examples of item a) are white noise: set your radiotelescope to an
>> unpopulated area of the sky (difficult to find!) and you'll listen
>> to that characteristic 'sssshhhhh'.
>One can code any information in a way that it will resemble white noise.
>How can you be sure, there is no hidden (coded) transmission mixed into the
>thermal noise?


I can't. No one can. But let's review the things from a different
viewpoint.

When you choose to code something, no matter the final result, you're
applying a method over a specific data. You're the transmitter, the
one who codes the data according to a specific method. The input is
a "chicken", the output is 'scrambled eggs'.

The receiver will easily decode the message if it is allowed access
to the same method you used. But a receiver that does not know the
method may, in most of the cases and with considerable effort, be
able to "infer" what the method was, based on the application of
some techniques over the data together with previous knowledge
about the nature of that data. This is the principle of
cryptography (and the "hacker" activities).

Now suppose that there isn't an intentional transmitter. Suppose
that the data occurs freely in nature and that there's no preconceived
method to discover. We're left with the task of apprehending as
much as possible about the universe given this data. My main
point is that this capturing cannot be done in a single pass,
neither in multiple pass over the same data. What appears to
be necessary is the progressive refinement of feature detectors
that will discover the "obvious patterns" present in one instance
of the data and then use these feature detectors in future
instances of received data.

>
>> Examples of item b) are the regular signals of a rotating pulsar
>> or a binary star: you have that characteristic 'rat  rat  rat'
>> signal with extremely regular intervals. Again, taken in isolation
>> this regularity is unable to carry any information.
>At least, we learn something about the revolution speed. And that, at the
>time the pulse left the pulsar, the pulsar was still rattling, hence
>existed.

But in order to infer this, you're using previous knowledge. You
already knew that the presence of the pulse implied in the existence
of the object, you already knew that rotation speed can be derived
from the rhythm of pulses. Try to do any kind of inference from
that regular sequence of pulses *without* using any prior knowledge:
there's nothing to get from that. We only get meaningful things
when we notice things in the order/disorder boundary.

>
>> This is also what I think explains our curiosity. We're easily
>> bored by "known" circumstances. But when we listen to an unusual
>> sound, or when our computer does something unexpected, or when
>> someone shows us an 'yellow apple', then our attention is grabbed.
>> We become 'desperate' to find a way to look at the event from a
>> point of view that cancels the unexpectedness.
>This is a mechanism which proved to be efficient for the evolution of the
>human species. It assists filtering the incoming information stream. But,
>in my opinion, it has nothing to do with an objective measure of 'what is
>information'.

Well, I guess that my previous text left the impression that I was
looking for ways to define or measure information objectively. I agree
with Gerry that Shannon's and Chaitin's visions are adequate. I just
wanted to reason about the circumstances we're faced when we try to
make sense of the universe around us.

>
>> As a simple example, recall when you move to a new house. Usually,
>> this house "clicks and squeaks" in very specific ways. During
>> the first night in which you're at that house, every click will
>> raise your attention. This occurs until some days latter, when
>> these clicks will be "stored" in our perceptual mechanisms
>> associated with regular and "explainable" things (the click
>> of the wood of the door; the click of the aluminum window, etc)
>> and this transforms it into a "known" pattern, unable to raise
>> our attention anymore (we finally sleep unconcerned). Moreover,
>> the perceptual work of deciphering future instances of these
>> clicks goes from the conscious to unconscious, denoting the
>> its lack of importance . Only "new" clicks will jump from
>> the unconscious and "wake" the conscious mind, indicating a
>> potentially important information on its way.
>With 'potentially important' you describe the selection criterion: It is
>the 'value' of information in a given framework of values of the observer.
>But again - it is no observer independent measure.
>
>Referencing our induction thread: If it all depends on the observer, can
>there be any 'objective' induction at all?
>

On the rigorous view of 'objective', of course not (unless we're
talking about mathematical truth). But we can't forget one
important thing: we all share the same world! So I can have a
completely different vision of what a river is, but it is
*comparable*, or slightly similar to your vision of a river.
It is not mathematically equal, it is just similar.

Interestingly, it is exactly this comparableness of our concepts
that allows communication through language. If our concepts were
exactly the same, we would have nothing new to inform to each
other. If they were not similar (if they were totally different),
then you'd understand nothing of what I say (and vice versa).
Language is meaningful mainly among slightly different agents,
not more, not less.

Regards,
Sergio Navega