Topological Meditations

To the infant’s developing mind, topology comes before geometry. In general, deeper and more fundamental logical operations are developed earlier than more specific rules and applications. The history of mathematics, which is generally taken as a process of moving towards deeper and more general levels of thought, could also be thought of as a process of excavation which attempts to uncover the earliest operations of thought in infancy. According to this argument, the very first operations exist at a pre-conscious level [i.e. ‘pre-intellectualizing’ level in the conscious and intuitive infant] so that the more fundamental a logical operation happens to be, the earlier it was developed by the infant and the deeper it has become buried in the mind.” – F. David Peat,

My feeling is that ‘topology’ plays an important role in shaping our understanding of ‘realty’, yet it is IMPLICIT in the language we use, helping to shape our understanding UNCONSCIOUSLY.  For example, we commonly employ the word GROWTH as if it refers to a reality, but the ‘growth’ on some thing (e.g. a town) on the surface of a sphere is NOT POSSIBLE since the concept of ‘growth’ is innately incomplete in its failure to capture the simultaneous reciprocal shrinking of the undeveloped land.  Only if the growing town were on a plane of infinite extent would the term GROWTH (which is one-sided in that refers to the thing-in-itself that is ‘growing’) be appropriate.  In the case that the surrounding undeveloped land is shrinking by the same amount the town is growing, we would have to use a terms like TRANSFORMATION rather than GROWTH to capture this.

Such understanding is in the realm of TOPOLOGY and while we are born with this tool of understanding at the ready, … it is, in our WESTERN CULTURE, soon ‘trained out of us’ as we are taught language which orients us to name-instantiated things-in-themselves.  This is the realm of GEOMETRY rather than TOPOLOGY and as is the thesis explored in this note, the reduction of TOPOLOGY to the GEOMETRY OF THINGS, is a WESTERN CULTURE CRAZY-MAKER.

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