Welcome to the "philosophical" section of the Around toposes Forum!
This section is specifically devoted to discussions on conceptual aspects of topos theory and of the unifying methodologies based on the 'bridge' technique. Don't hesitate to pose speculative questions and to engage in discussions about the inter-disciplinary role of toposes.
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I'll represent the Subject as a Grothendieck"s topos. It is a fundamentally non-Platonic philosophical approach.
Refer to this article on my blog (written in French)
https://www.entropologie.fr/2024/05/schema-de-presentation-au-cle-du-22/05/2024.html
Dear Professor Caramello,
Going by 'X is what X does' or, in terms of our universal mapping properties, X is what X is good for (which may be operationalized as: X is that which wouldn't be but for X), biology is, if any, not like physics, which appears hellbent on killing us without doing anything, so to speak. Biology goes to great lengths spending enormous amounts of energy establishing the gradients (e.g., ionic gradients across neuronal membranes), but for which we would be brain dead. Physics, uses the very gradients to dissipate the gradients (cf. water flows downhill) and biology fights back again and again until it gives up, and physics declares victory in equality embodied in our dead body. There is more to the primal war of the worlds (physics vs. biology), which I can elaborate on in terms of pieces/connected components and souls (yes, I said soul; objects have souls, according to Professor F. William Lawvere), and with the express purpose of establishing the evil that is physics 😉 I must hasten to add that physics may not be doing anything out of the ordinary in the sense of converting everything into one of its kind (dead/pure matter) as if straightening the crooked timber of humanity.
Given that I can no longer resist the call of morning coffee, I am rushing to wind it up: unlike physics, with its shortest distance paths and minimum energy configurations, mathematics, more like me, takes the most convoluted route, which may have something to do with their nefarious actively concealed agenda of appearing to be more smart than they are (cf. https://conceptualmathematics.substack.com/p/crooked-timber-of-mathematics).
Summing up, we have two dualities
(i) Physics vs. Biology
and
(ii) Mathematics vs. Physics
within a trinity: Biology, Mathematics, and Physics.
Thanking you, yours truly, poison venkata rayudu
