Sunday, May 15, 2011

THE NATURE OF THE PROOF

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THE NATURE OF THE PROOF Part I

The proof is part of Information Theory, about data transfer, about
learning, in particular mechanical learning.

By learning we do not mean a noun, we do not mean knowledge, which
is gained from learning.

Learning is a causal PROCESS by which both theoretical and certain
knowledge is gained.

Learning is a change in state in the learner, caused by
the learned about.

If there is no change in state in the learner, nothing is learned.

Theoretical knowledge is born of generalizing from direct or
indirect observations or instances.

Certain knowledge is a description of the direct observations
themselves.

A direct observation is simply the process of looking at the thing
itself.

An indirect observation is the process of learning about an object
by looking at another object causally related to, or the effect of, the
first.

Since there is no, and cannot be any, direct observation in the
physical or mechanical universe, all observations made of or in the
physical universe are theoretical in nature.

Direct observations produce perfect certainties.

Indirect observations produce theories made of evidence and models.

Very quickly if we are trying to learn about A by looking at B,
then B is the evidence, A is the model for the existence of B, and the
theory is the postulated causal relation between A and B.

The above presents us with he need to define the following terms.

Causation, learning, machine and certainty.

Causation means that changes in state in one object NECESSARILY
result in changes in state of a second different object a moment later.

The 'moment later' results from the fact that the speed of cause is
finite at the speed of light.

Light itself is a form of causal messenger wave.

The causing object is called the referent, and the affected object
is called the symbol.

Throw a light switch and the light bulb turns on.

The switch is the referent, and light bulb is the symbol.

We can theoretically judge (learn about) the state of the switch (A) by
looking at the state of the light bulb (B).

We say the state of the symbol TRACKS the state of the referent.

Notice the process of learning about the state of the switch from
the state of the lightbulb DEPENDS absolutely on there being a valid
causal pathway between switch and light bulb.

Without causation, meaning in the absence of valid causal pathways
between referent and symbol, there can be no learning.

Notice that using MORE causal pathways to verify the first
causal pathway between switch and light, begs the question of
whether the second set of cuasal pathways are valid.

Thus we can state that

Causal pathways can not be used to validate other causal pathways
with certainty.

MORE CAUSAL PATHWAYS DO NOT A MORE CERTAIN CAUSAL PATHWAY MAKE.

Learning is any change in state in the LEARNER that is causally
related to and thus symbolizes the nature of the LEARNED ABOUT, where
the learner and the learned about are TWO DIFFERENT OBJECTS.

The change in state in the learner is a SYMBOL OF FINAL AUTHORITY
for the learned about which is the ORIGINAL REFERENT.

A machine is defined as any system of objects interacting via cause
and effect across a space time distance.

Machines learn by being an effect, by BEING the second object, the
learner, which is changing state as a causal result of the learned
about, namely the external physical universe impinging upon the machine.

In the mechanical world, all learning is symbolic in nature,
because the learner is a different object than the learned about.

For example a learning machine can take a video picture of a cow
out in the physical universe.

The picture of the cow is not a cow, but contains high DATA CONTENT
about the cow.

Further the data in the picture also looks like a COW!

We call the fact of high geometric similarity between the cow and
its picture, high GEOMETRICITY.

Notice a picture of a cow may look exactly like a cow, but its
still a symbol for the real thing.

Thus as a symbol, the picture of cow has both high data content and
high geometricity relative to the original referent.

One could however scan that picture into an encrypted data stream
that didn't at all look like a cow but yet retained recoverable data
about the cow. Or one could write a book about the cow or its picture
describing it in words.

Both the encryped data stream and the book are symbols for the cow.

In both of these symbols they still have high data content but very
low geometricity.

As data flows from the original referent to a symbol of final
authority through a causal pathway of many hops, the geometricity may
change from high to low and back again many times, but the data content
is hopefully conserved as it travels its path.

Since each causal hop adds in its own component of change into each
symbol along the way, some times the data from the original referent can
be covered in so many other changes that it becomes unrecoverable.

Have you ever received a fax of a perfectly good picture or text
that was none the less badly marred or unreadable in sections because of
added effects from the sending fax machine?

Digitization and protocols for transmission and retransmission, of
data helps greatly in this problem of data decay,

But in the natural physical universe, most data pathways are
analogue in nature, and thus original data can get covered by so many
other effects added later in the chain, that the original data falls
below the noise floor of the transmission and becomes unrecoverable.

Homer

- ------------------------------------------------------------------------
Homer Wilson Smith The Paths of Lovers Art Matrix - Lightlink
(607) 277-0959 KC2ITF Cross Internet Access, Ithaca NY
homer@lightlink.com In the Line of Duty http://www.lightlink.com

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