From Geometry to Culture: How the Theorems of Pappus and Desargues May Change Your Thinking

[@topologielacanienne]

Theoretically groundbreaking. Dr. Kunze-thank you once again.

[@boundarylanguage]

You are kind … maybe there is something original in the idea of the perfect shadow. I'd appreciate your thoughts.

[@santerisatama5409]

When I started to wonder the seemingly mysterious defintions "Point has no part" and "Line is length without width" that Elementa starts with, I had to wait patiently for small eternities for the intuitive answers to lighten up in this participatory perspective to the Spiritus Mundi. The answer I received was, to put it in short form theoretical language, that the first definitions speak from ontology of holistic mereology, in which forms are projective animated decompositions observed from participatory perspectives of mathematicians learning the Protean shapeshifting art of intuitive geometry. Why Protean art? The first action required to intuit the meanings is to transform yourself to the shape of a flatlander perspective. To break the spell of a rigid identity of a static form, and to become aware of the ability of bodily awareness and attention to change and project form. In my native language Finnish, our word for self, "itse", has also the ancient meaning "shadow". Euclids definition of line does not exclude the potential/potency/exponent (Gr. dynamis) that a line can have depth when it doesn't have width from the ideal perspective and form into which mathematicians project their attention, their eye of the mind.

[@jaybro321]

This is the best kind of applied mathematics

[@boundarylanguage]

Thanks but I think I just pointed out a few obvious things. I'm still working on the meaning of the zig-zags.

[@santerisatama5409]

@@boundarylanguage Zig-Zags?! Are you aware of the top down constructs of the Stern-Brocot type, in which we can define continued fractions as zig-zag paths? With minimal alphabet of < and >, we can both replace R/L notation of zig-zag paths along binary tree and/or taxicab-norm, as well as construct the whole number theory in top down manner: < > < > < > etc. Define < and > as the numerator elements of tallying, and as the denominator element. Numerically the result of this tri-tally of the operator language looks like: 1/0 1/0 1/0 0/1 1/0 1/0 1/1 0/1 1/1 1/0 etc. The fun and fascinating aspect of this notational parsimony is that the words have at least the dual interpretation of a) multisets for tally operation that generates totally ordered coprime fractions and b) string instruction for a zig-zag path. So far I haven't seen any simple computationally reducible relation between the a) and b) interpretations of the words. The Dyck pair generator < > can be studied also in the inverse from of > < of inwards movement, as well as full combinatorics of both as generator strings for concatenating mediants that preserve the reversibility condition of chiral reflection, which we can interprete also as "Pure Dirac notation" that drops out the unnecessary or less necessary stuff from holistic perspective of constructing. Semantical motivation of stumbling on this construction was interpreting the operators < and > as relational pair of verbs in object independent manner. Thus the first concatenation stands semantically for duration ("both increasing and decreasing"), and the whole construct can be interpreted temporally as mereology of duration, following the intuitions of Bergson's philosophy of time. A very simple observation is that and >< are simple bit rotations of each other - both ways - as well as Boolean inverses of each other. This form of Wheel of Time seems also deeply linked with Aristotle's Wheel Problem and it's trochoids. Especially if and when we conjecture that the syntropic operator pair is connected by tautochrone cycloid arc.

[@AdarshKumar-fr8xg]

Sir, I have been reading projective geometry along with kashmir shaivism, bergson and merleau ponty. I want to know more about this discipline. How can I contact you?

[@boundarylanguage]

Hi, I have an email, [e-mail], and a website, boundarylanguage.psu.edu; I have a busy fall however, so I hope I have time to get back to you.

[@santerisatama5409]

Bergson was mentioned in my couple comments to this wonderful presentation, maybe you are interested to check them up. Bergson comment was in response to Kunze wondering about zig-zags in a subthread.

[@Anabsurdsuggestion]

Brilliant video.

[@sticlavoda5632]

This is interesting, but I struggle with the Lacanian words used to explain these notions. I find parallels in Renaissance philosophers (I know some things of Ficino, of Pico della Mirandolla, Paracelsus, etc.), in the likes of Kant, in the understanding of Fichte, in Bergson at times, in the Neoplatonists and in Schopenhauer. But I find it enormously difficult to follow because some explanation which you offer, due to my poor understanding of mathematics and english, can relate a multitude of different understandings I correlate with all these thinkers. And because I do not quite know how to put whichever thing I understand into the words necessary (not on account of some limit of english, but certainly on account of some limit nonetheless), I am finding it difficult to even signify what it is that is unclear at this time. I know superficially some phenomenologists such as Jean-Luc Marion. Is there perhaps a chance you can explain in a paragraph or so what is needed to further my understanding? I wanted to study Giambatistta Vico, and because I already am reading through a lot of things and at a snail's pace, I wanted to find an explanation. Your explanation of him stumped me with it's approach, and I was positively impressed. But I only know some introductions of Lacan, I know nothing of Freud (and you referenced him at some point, so it may be that this is where I stand to lose grasp of your work). I think I am young and uncultivated. Excuse me!

[@sticlavoda5632]

The only real philosophy I have been able to properly read through is from Schopenhauer. And I think I read through Camus well but he bores me always and I abandon his literature books halfway. His enormously famous "Myth of Sisyphus" (appropriate for people younger, because it concerns things simply -and by an intellectualist slight-of-hand provides an uninitiated reader a sense of understanding there where there is none) was hallucinating and mesmerizing. But I got nothing from it. And I think he unintentionally glorifies Kierkegaard a lot (who I hold very dear to me) besides Chestov and the like, in that precisely all he claims against them for his reasoning... is their greatest contribution. Maybe the limit on me is a Christian understanding? Maybe it is constantly and without reason questioning where "appears" the position of Apophatic divinity in any such a system. Or it may be a matter of age. Either way, I hope that you can help, or otherwise the years.

[@jameson9334]

𝓅𝓇𝑜𝓂𝑜𝓈𝓂

[@zzasdfwas]

wtf is this? I was expecting math but got a bunch of rambling mysticism.