Relationship of the
Finite to the Infinite

here are six different perspective permutations from which to "observe" the interplay of finite-infinite. We may understand them from their linear analogs. Of these, only three are non-redundant.

  • Line Segment to Line segment
  • Line Segment to Line
  • Point to Line Segment
  • Point to Line
  • Point to Point
  • Line to Line
  • Line Segment to line segment (finite to finite) is simply what we see every day and are, in fact, logically restricted to. (see LP #12)

    Line segment to line represents our common view of infinity. We (as finite lengths) fit into a line an infinite number of times. The same point of view is gotten by imagining ourselves at the point scale relative to a line segment. Here, once again, we fit into infinity an infinite number of times but the universe might now be understood to be comparable to a finished "film in the can". If we could roll out the film and view the individual frames, we could see that each constituted something like one computerized megahertz-clock tick. Each tick being the next level of logical evaluation.

    Point to line represents a relationship of one infinity (the small side) to an infinitely greater (Cantorean ... the large side) infinity which is necessary to display the other relationships.

    Line to line and point to point are simply redundant to the first relationship.

    We cannot pursue any further relationships because all are necessarily redundant and nothing more can be achieved to advance our quantitive understanding.

    I believe that the reader can here understand why it is meaningless to speak of another universe which exists in another time or place. It can have no quantitive bearing on our own.

    Also, one might see why it can be feasible to end up with a hierarchical universe which "ties up" the infinitely fat end of the hierarchy to the point origin of that hierarchy [mentally convert the universe into its line segment analog and fasten the ends] ... and ... why one might think of an infinite space as simply a point turned inside out.

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