BlackBart wrote: ↑Oct 29, 2024 9:40 pm
Euclidean space, which is just a snapshot of projective space, is suitable for the study of mechanics. But life and organic forms are better understood through projective geometry.
Arse gravy.
Projective geometry describes the relationship between geometric objects and their images projected onto a surface. It says nothing about life or organic material.
Nor does it say anything about existence. Infinity just just describes a point where projected parallel lines intersect.
Your crap about parallel lives moving in opposite directions is simply that. Crap.
I suspect we'll be getting quantum deepities next.
Projective geometry is a tool which has many applications.
D'Arcy Thompson has been an inspiration for this type of thinking in many fields such as biology, art & design and engineering.
D'Arcy Thompson (1860–1948) was one of the most celebrated biologists of his day, best known for his On Growth and Form (1917) which was the first successful biophysical explanation of the size and shape of organisms. In particular, his concept of allometric growth and theory of transformations have informed cutting edge research in biometrics and practice in the fields of fine art, urban design and civil engineering. He was a seminal figure in the development of the spatial analysis tradition within geography in the 1960s and 1970s underpinning major contributions by Haggett and Bunge and inspiring Tobler to develop cartograms which liberated map projections from sole reliance on Euclidean geometry. Re-assessing his contribution to geography fifty years later, it is still to be found in Batty's work on the size, shape and scale of cities and in Dorling's World Mapper project. This re-discovery of the importance of geometry within the geographic tradition over the last half century owes much to Thompson who spent the whole of his academic life in the University of St Andrews and (what was later to become) the University of Dundee.
Euclidean geometry confines perspective to a static frame of reference in which angles are fixed. Perspective geometry allows for an infinite variety of viewing perspectives and projected angles.
Projective Geometry: A Short Introduction
Like Goethe before him, D'Arcy Thompson while studying morphology, had the ability to see separate individual organisms and visualize forms transforming into each other. The visualizations in the mind enhanced and completed the sense impressions.
And this is the beauty of projective geometry. It trains the mind to look beyond the senses to a more dynamic and complete portion of reality. The reality envisioned, which the senses alone cannot grasp, is not created by the mind, it is apprehended by the mind.
So when I mentioned lines moving in opposite directions (sorry about the typo that slipped through - "lines" not "lives"), I was talking about a visualization in which one could imagine seeing these lines in the process of extending out to infinity. The Möbius band is a brilliant representation of this with its two edges acting as a shrunken version of those infinitely long parallel lines. An ant walking to the left along one edge will return from the right on which appears to be the opposite edge.
Max Planck: "I regard consciousness as fundamental. I regard matter as derivitive from consciousness. We cannot get behind consciousness. Everything that we talk about, everything that we regard as existing, postulates consciousness."