Several times I have felt that we have a big fundamental problem re: ‘levels of abstraction’. I have experienced it in communication using natural/formal languages, writing/designing software and in personal relationships. It appears that we not only have the obvious problem of two people with different levels of abstraction for a given thought at a given time, but also the fact that our intuitive understanding of ‘levels of abstraction’ is ‘discrete’ as opposed to ‘continuous’, which is more likely to be the reality.
What I mean by discrete vs. continuous is perhaps best expressed by a simple example: thinking about integral pairs that satisfy ‘y=x’ vs. thinking about a straight line on a graph.
For example, we can see a car as 1) a box, or 2) a box with glass windows, 3) ... with steering wheel, brakes, gears etc. …n) (further deeper physical/mechanical view) m) (further deeper atomic view) etc. In all cases above we have discrete views. How should we learn to think about the continuity and furthermore, how should we express it?
Furthermore, discrete ‘is an abstraction for’ continuous. So talking about continuous abstractions equates to not-so-abstract abstractions. Hmm... total nonsense?
Versatility with levels of abstractions creates beauty, for example -- a painting that appears something when seen 10 feet away, something else, much richer and finer, when seen from a foot and something else yet again when seen closely; or a musical note with different pitches; or a relationship between a Father and a Son, where the father can be a Father or a Friend. Fractal nature of Nature?
Thursday, July 13, 2006
Typo!
Thanks to Megha for letting me know.
I have a typo in the blog url - 'adyathm' should be 'adhyatm or adhyātma'.
My simple understanding of the term ‘adhyātma' is non-materialism or spiritual and is an antonym for 'bhautik or bhautika' or materialism. Both words come from Sanskrit language and are also present in Hindi language.
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