very nice thought and very nice written.

As per suggestion, I will post here:

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This is a summary of a philosophical and mathematical work by a former teacher and mentor of mine. The work attempts to describe mathematical structures based on philosophical concepts that could potentially be applied in physics. I first encountered this work as a mathematics student, but at that time, I couldn't understand most of it. With this publication, I hope to attract interested readers to this work.

Abstract:
"UrEins and Algebra - The Concept of the ONE.
Implications of the Concept of the ONE.

This work was jointly created between the years 2000 and 2006. It is a philosophical-mathematical work with possible outlooks on physics. Philosophically, it resolves the contradiction between the views of Parmenides and Heraclitus, on which Western metaphysics failed, as Georg Picht elaborated extensively in his posthumously published work "On Time". Additionally, it meets Picht's further demands to make at least one step out of the crisis of Western philosophy. Parmenides speculated and argued with the concept of the ONE, in which everything should be united. Heraclitus, on the other hand, claimed that only "movement in being" was essential, and there was no "rest in the ONE."
The "movement in being" corresponds to "water" and also "fire". This movement is also referred to as Heraclitean Logos. It should be noted that even today, the view is still largely held that there is "rest" in the ONE and no "movement."
Picht's work "On Time" is incredibly important for criticizing Western philosophy because he makes further demands, but cannot fulfill them. It seems to us that in general language, this appears almost impossible. What Picht calls "being in time," that overarching mode in which past, present, and future are summarized as a possibility, is the mode of reflection that is embedded in the cosmos. Being embedded in the cosmos also means "being embedded in the past, present, and future." For with the view into the spatial cosmos, we also look into the past and recognize dynamic processes there that point to the future. Moreover, it is considered an unsolved philosophical problem what the present is, which transforms an unknown future into unalterable past. This requires a philosophical justification of the "ticking" of time, which must be considered not yet found. We propose a suggestion for this. Although time is measured with clocks in physics, the "ticking" of time, as well as space in its three dimensions, are simply assumed and described mathematically above the continuum of real numbers. Of course, there are already conjectures that space and time could be quantized.
Beginning a "lattice theory" of space is being tested for elementary particle physics.
In our work, the mode of reflection according to Picht will be expanded with the linguistic possibilities of mathematics. However, it will not be done in such a way that mathematics is added as a language from the "outside" to expand the mode of reflection. Rather, essential parts of algebra arise from the mode of reflection. Permutations as mappings play the fundamental role. Finite groups are introduced as a result. From these, finite rings and finite algebraic fields, called Galois fields, are constructed through endomorphisms of finite, commutative groups as mappings. The concept of mapping is central. This meets Picht's demand to break the boundaries of Western metaphysics. A curious view of possible physics of space, time, and photons emerges, but not yet of matter.
The method outlined is open to extensions.
AUTHORS: Dieter Beckmann, born 1941 Studied mathematics and physics from 1962 to 1969 Teaching activity from 1969 to 2005.
Klaus Pullmann, born 1934 Studied mathematics and physics from 1954 to 1960. Teaching activity from 1961 to 1996."
pdf in Archive (It is written in German.)
https://archive.org/details/Ureinsundalgebra