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Sitaram · Site Admin Joined: 14 Sep 2005 Posts: 1079

I am adding each of my posts here to a post at my message board,... so I can develop these thoughts (which are not solely my thoughts of course), in some lasting form that many may reference

if we bog down in picking nits, and showing how clever we are, then we shall surely never see the forest for the trees, though we may possibly succeed in doting every i and crossing every t

It does us little good to be perfect spellers and grammarians if we never achieve anything profound with our language

The greatest blessing AND the greatest tragedy of human nature is that we have the ability to imagine a perfection that is beyond anything which could possibly be actualized.

Einstein once said that it would never be possible for someone to inductively arrive at a theory of relativity or quantum through experienced phenomena (my own words, paraphrasing).

The point i am trying to make... has to do with the potential of human imagination, and the nature of model theory.

Only a few people will understand what I am getting at, and they will understand because they have a certain foundation in their studies.

If one considers the ancient work on astronomy by Ptolemy, "The Almagist", where Ptolemy frequently uses the expression "Sonzein ta phainomena" (saving the phenomena/observations/appearance).

You see, the laws of physics do not predict the existence of rabbits, yet the nature of rabbits in no way defies or violates the laws of physics.

When Einstein said that one could not possibly INDUCTIVELY arrive at a theory such as relativity through observation and experience,... it relates to the rabbit statement, as well as Ptolemy's "saving the phenomena", and mathematical model theory.

Another thing we must study carefully is Wallace Stevens essays on imagination, "The Necessary Angel", which will shed some light on mathematics, as a product of imagination, and the "disconnectedness" between the physical phenomenal world, the possible world of imagination, and model theory.

Socrates, in Plato's dialogue, "The Meno", attempts to use geometry, and the human powers of induction and deduction, to demonstrate that the soul is immortal, having a prior existence, by questioning an illiterate slave boy to demonstrate that mathematical knowledge resides within that slave boy.

Socrates, and all thinkers up until the 19th century, assumed that there was only ONE kind of geometry, namely Euclidean.

Plato posted a sign at the entrance to his Academy saying something like "Let none enter here who have not mastered Euclid's Elements of Geometry".

I realize this next statement will seem a non sequitur, but one essential question pertaining to our inquire: "Is the nature of reality digital or analog" , that is may phenomena be precisely represented by numbers, or is there some analog incommensurability?

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