Items filtered by date: January 2024

Coordinate Systems and Spacetime

“It does not do harm to the mystery to know a little about it. For far more marvelous is the truth than any artists of the past imagined!”
(Richard Feynman)¹

Although the article contains many and deep mathematical connections, it also includes many interpretations and explanations, which may make the old/new concepts of number and infinity in mathematics understandable to those who are not involved in mathematics, and reveal the mystical beauty of mathematical connections.

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¹ Richard Feynman, The Feynman Lectures on Physics Vol. I Ch. 3 / Footnote 3-4 Astronomy

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From my Diary, 23.01.2024.

I listened to the latest conversation¹ of the podcast Mindenségit! with brain researcher Balázs Hangya while doing housework today.

I would like to highlight one topic in the discussion, the one that science has no real theories on yet, so I will write a few words about consciousness.

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¹ Balázs Hangya: Brain research, brain function, learning, consciousness, emotions / Mindenségit!
https://www.youtube.com/watch?v=e7U04VjmfHE 

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Is the existence of transcendental numbers an actual existence?

Contents

1. Introduction
   1. The potential and the actual existence
   2. The intensive and the extensive infinite
2. The new concept of qualitative infinity
3. Duality of extensive and intensive infinity in qualitative infinity
4. The actual existence of transcendental numbers
   1. The actual existence of transcendental numbers in positional numeral systems
   2. The actual existence and geometry
   3. Continuity and infinity
   4. An artificial intelligence (AI) answer to the question of the actual existence of transcendental numbers
5. The idealization of "arbitrarily large finite" with potential infinity
6. Summary

Appendix A- Elementary properties of two-element numbers
Appendix B - Two-element numbers and homogeneous coordinates
Appendix C - Axiomatisation of set theory with the new qualitative infinite

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