Points and numbers

From: Hal Ruhl <hjr.domain.name.hidden>
Date: Tue, 05 Dec 2000 20:55:51 -0800

Numbers within numbers and points within points explored.

1) Numbers within numbers:

Take a binary coded number such as EX = 11001001101 as an example. This is
a counting number. EX contains the counting numbers 0 and 1. The 0's and
1's are still counting numbers simply because we are still using them as
counters - how many 1's in EX, how many 2's in EX, how many 4's in EX etc.
So EX is a compound number - a number containing numbers.

2) Points within points:

We represent numbers with a physical isomorphism to points on a line.

Take a line of unit length and hang it in 3 space. Each point on the line
will be associated with at least the following numbers:

a) Its x coordinate
b) Its y coordinate
c) Its z coordinate
d) Its distance from one end of the line.
e) Its distance from the other end of the line.

One could argue that in addition to these it is also associated with its
coordinates in any other system for encoding an N dimensional space.

However, for the moment let us ignore that.

This leaves us with just "d" and "e" - the numbers derived from the
geometric object with which we have associated the point.

Now take another unit length line and intersect the first line with it at
the point in question. If the intersection is asymmetric this point is now
associated with four numbers:

d) Its distance from one end of line 1.
e) Its distance from the other end of line 1.
f) Its distance from one end of line 2.
g) Its distance from the other end of line 2.

How can the single point retain all these identities?

Is it better to suppose there are actually four lines each with its own set
of points and these points nest with each other in various ways?

In any event lets continue to add unit length lines intersecting this same
point without repeating any other intersection parameter. Eventually we
can associate the point with as many numbers as we care to. Is this a
suitable isomorphism for all those numbers or do we as I might suggest
simply nest the points so each number has its own point - its own isomorphism?

If we continue to a countably infinite number of lines do we have an

How about if we just go the other way and eliminate all lines and all
neighbor points. Go all the way down to just one point. That is postulate
a naked point. Absent any relation at all it is as devoid of selection as
a point that has all lines intersecting at it. So it is isomorphic to all
numbers or rather is an infinitely nested point.

Given the above is the correct postulate: "There exists a naked point."?

The naked point contains multiply nested points and we select just those
that are isomorphic to FAS as the states of universes. The sorting dynamic
I use as the basis of my model then becomes just points changing their
nesting level.

A space without space, a dynamic without change.

Any comments on any of this speculation?


Received on Tue Dec 05 2000 - 18:15:47 PST

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