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URL:  http://boards.fool.com/considering-the-state-vector-20553200.aspx

Subject:  Considering the state vector Date:  3/27/2004  9:53 PM
Author:  yttire Number:  233 of 242

Since it is late in the evening and I have nothing better to
do, I am going to give you some background on the idea of
considering the state vector of a system.

First, a very light version:

Lets imagine some friends hanging out and talking. They hang
out together every day, and like to talk about each other.
What are they going to talk about? They are going to talk about
the new things that have happened, about who had had what
happen to them.

Now imagine that one of them is brushing their teeth every
single day. They all talk about this every day, but after
a while, they realize there is really nothing new about it,
and they cease talking about it. They cease talking about it
because there is no new information, there is only repetition.

Now imagine another one of the friends gets up and puts a
ball on the putting green every day. They talk about him
putting, but after a while lose interest in the fact that he
is there in the first place, they start talking about if he
sank his put. They cease talking about
the action, and start talking about the outcome. They talk
about that which is unknown. They talk about that which may
or may not be. They don't talk about what is, unless it is
in the context of how it might change.

In short, they like to talk about that which has a probabilistic
outcome, and do not talk about that which is a definitive
absolute. This is because information is about the unknown,
it is not about the known.


Second, a moderately strong version:

Let us imagine a large domino chain set up on a table. The
domino chain is very intricate and complex, looping around on
itself with lots of interesting patterns. We will simplify
how they fall and claim they fall in a completely deterministic manner.

Now a person walks up to the domino chain and possibly taps
on the lead domino. They may or may not push this domino over.

This system as a whole is in one of a few states: standing up,
in the process of falling over, or already pushed over.

We can imagine looking at the collapsed set of dominos, and
considering that it is a very complex arrangement. However,
they actually only contain 1 piece of information from the point where they were already set up- was the lead domino knocked over, or not?

Thus, a very intricate system (the domino setup) which responds in a very complex way can actually only represent a very small
amount of potentially introduced information. A small bit
of information creates an apparent lot of information, simply
because the initial conditions allow this magnification to
occur. In reality it is not a lot of new information- it is
only a single bit.

Now for a stronger version:

If we examine any system, we can ask "how informed is this
system?". The answer is "It is informed to the degree that
its state is improbable"

Let us ask this of a physical system "How informed is this
system?". The answer is "it is informed to the degree that its
state is improbable."

Now for some almost tautological remarks:

Communication is about the transferring of information. It is,
in essence, the flow of improbability through a system. We
can talk about information flow within a conversation, and we can talk about information flow within a physical system. This may seem a bit absurd, for how can we completely quanity the nature of improbability of a conversation? We can't, but we do know that we act and speak in a physical system, using physical particles.


Is there any physical system for which we completely
understand the interactions of the components on an atomic and subatomic level? Only in highly idealized simulations of perhaps a hydrogen atom. This does not detract from the reality that we can consider a physical system as having a probability of being in a state. It will always be, necessarily, an estimation unless we work with an abstract mathematical model which is highly simplifed.

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