I'm mainly here to learn about topoï,in order to check the thesis I'm working on.
This thesis is as follows: 1 / There is no change in the way of thinking since man lives in a group. 2 / To prove it, it is necessary to define what are the “thought patterns” of any Subject. 3 / The theory of categories can serve as a universal language model making it possible to identify these different patterns of thinking. 4 / This makes it possible to differentiate 3 levels of reflection, leading to
- The logic and elementary topos of Lawvere,
- A "topological approach", initiated by Évariste Galois and leading to Grothendieck's topos,
- A 3rd level where equivalences or "bridges" are established. 5 / This general scheme would make it possible to consider a "unitary theory" in physics. I leave on my blog the traces of my own evolution in this program. I try as I can, to discuss this subject within the Categorical Logic group led by Anatole Khelif at Paris Diderot. Not being a mathematician at all, I try to find relays to improve my approach. For a short summary of this approach : http://www.entropologie.fr/2021/01/resume-hec.html
English is not a major problem for me, but this discussion is very old, and I made majors evolutions since that time, partially due to this exchange here above !
I have quite move from my first idea, partially due to my discussion with Morgan.
I think I'm now ready to go further into categories theory.
But as this point before a deeper understanding of toposes, I made this article regarding physics : https://www.entropologie.fr/the-speech-of-the-physicist
Regards
Dear Morgan Roger,
Your comments, there is two years ago, helped me to improve my understanding, and change quite seriously my way of thinking. During this two years, I change my way of thinking and finely, I come to this approach of the physics. https://www.entropologie.fr/the-speech-of-the-physicist
After that, I think I'm finally ready to learn more about categories. I starts with "forms and functions" of Saunders Mac Lane: https://www.entropologie.fr/2023/03/saunders-mac-lane-mathematics-form-and-function-from-whole-numbers-to-rational-numbers-4.html and I know that I have a hard work to do to be able to understand effectively what is a topos, but I have time...
Thanks for all your help !
Alain
Pour les curieux :
Je relis actuellement "Mathematics form and function" pour tester ma représentation de l'Imaginaire du Sujet (dans l'idée du triptyque Réel/ Imaginaire / Symbolique de Lacan).
Jusqu'à présent, ça a l'air de fonctionner.
Merci pour tout commentaire ou signalement d'une erreur manifeste : ça m'aiderait dans une démarche qui devrait m'amener aux topos et aux ponts d'Olivia d'ici quelque temps...
https://www.entropologie.fr/2023/04/saunders-mac-lane-real-numbers-relecture-7.html
