Dynamic Euclidean Surfaces are more than “Euclidean”

Motion sequents are not a new idea. There is a connection to Newton's fluxions, and an influence by Hamilton's "pure time" conception. a link through Newton takes us back to the indo-greek atomic/atem theoretical analysis. There is certainly a link to notions of the calculus of infinitesimals both differential and integrational, So i am confident i bring nothing new to the table other than my own Dickensian style.

When i look at a brick wall, i see a sequence of bricks and cement, the cement joining the bicks into a series of bricks. This series is on the face of it a spatial arrangement with no sequents apparent.
And yet i know the brick wall stands as a result of sequents and continues standing through a balance of sequents.

A series of sequents creates a sequence of motions and those sequences of motions connect every brick in ths wall into a spatial series which i perceive as a sequence of bricks. By this i am able to perceive every structure as a series of sequents. What is of note is the way i filter the series of sequents to apprehend a strucure.

Clearly i apprehend structures in many ways involving relative motion sequences, and these ways exhibit a kind of "glue' sticking various spatial structures together, within certain limits of relative motions, and dependent on observer apprehension and processing status.

Much that seems stable and fixed to me is in fact in convoluted motion beyond a level of distinction/perception and those motion sequents are infinitesimally small compared to the computational surfaces produced by the perceptual processing systems. These surfaces are scale emergent, as discussed, and provide only one of an infinite number of ways of computing a surface.

Whatever aggregation structures we devise the scale emergent factor needs to be observed. In general we approach this notion through the notion of limits. Limit relations enable us dynamically to tie emergent factors, properties to a scale process , in other words to the choosing of a unity.

It cannot escape notice that by infinitesimal motion sequents Euclidean geometry and greek indian trigonometry can be applied resulting in an emergent spatiometry which is more than Euclidean, and which is dynamic. In this sense Newton's theory of fluxions explores these consequences, and Hamilton provides a way to algebraically and fundamentally ground and make sense of these motion sequent results.


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