Regularity

[Detlef Morgenstern]

Gerry,

Thanks for your comments. Slight differences between our views are natural:
You prioritised making a functioning prototype (for which one must narrow
the focus), whereas I felt not bound by this goal as first priority and
tried instead to dig deeper "to the roots" (but - cannot present a running
machine at the time being).

You wrote:

> How can we have a "simple, abstract and, at the same time,
> comprehensive explanation of what "regularity" means?"
> when kinds of knowledge are so diverse?

This seeming diversity is a result of diverse aggregation principles at
higher aggregation levels. I believe (still cannot prove this) that there is
something common in all knowledge. To find this "atomic substance" of
knowledge one must resolve it to finest possible granularity (not losing
functionality!).

[How can we have a simple, abstract and, at the same time, comprehensive
explanation of what "substance" means, when kinds of physical objects are so
diverse?...]

> This idea goes hand-in-hand with the working hypothesis
> that *all* kinds of knowledge might be analysed in terms
> of the principle which is used in all 'standard' methods for
> compression: "identify relatively large patterns which
> repeat 'relatively often'..."

I wish you could widen this hypothesis. As I tried to show in "Regularity",
there might exist regularities (I think, you agree, knowledge can be treated
being something regular) which cannot been found looking for repeated
occurrence of patterns only. And there may arise some problems from the
attempt modelling such "functional" knowledge on machines which are
specialised in repeated patterns. If the structure of a model does not match
the structure of the process to be modelled, it is an awful procedure to
reflect the process in the model "turning knobs" only.

> In this kind of material, a regularity is anything that
> repeats 'relatively often'.

"Repeated occurrence of entities in space/time" is a sub-set of regularity.
It will result in a specialised class of functions
An ... Fn (see "Regularity") and in a specialised kind of detector.
(It might be attractive reflecting on how this function class could be
described mathematically. Certainly, some NN's mathematical apparatus would
match.)

Humans highly prioritise this "repetitive" regularity for biological
reasons. Our vision, e.g., will isolate a moving object from the background
by its repeated occurrence in the scene. Subconsciously, we prefer this kind
of regularity because we must not "think" about it, it was "built in" by
evolution or is learnt early in life.

Detecting "functional" regularity, which I suggest to not ignore, is much
more difficult. We do not have a tuned detector at hand (as in the case of
repetitive regularity). Our compression daemon must tune a detector instance
(induce the rule) for a given environment snapshot. This takes massively
longer than detecting repetitive regularities, applying pre-configured
detectors. You feel tired after a while because it consumes large amounts of
"CPU". That's why it takes a lot of self-discipline to force oneself to this
kind of cognitive activity.

I wish I could see a way making an SP machine induce
XYZ   Z=X+Y
---
54
21
76

("inventing" addition) from
XYZ
---
549
213
76D

Best wishes,

Detlef