Lorel

Mon compte Linktree pour retrouver tout mon contenu en ligne 👉 linktr.ee/lorel_sg Ma chaîne TikTok (vidéos toutes les semaines) 👉@lorelsg" target="_blank" rel="nofollow noopener">tiktok.com/@lorelsg Ma chaîne Twitch avec @physaus (vulga) 👉 twitch.tv/sciencesquad_

The Riemann Hypothesis, the Goldbach conjecture, the Twin Prime conjecture... They have all been extensively verified numerically. So for all practical purposes, these are "true" statements. If needed for an actual practical use, they could easily be verified even farther. The mathematical truth of these statements would only be "useful" to mathematicians that seek the truth and those who seek to understand *why* these statements are true. If an AI agent proved these statements but there were no mathematicians to understand and digest the proofs, what would be the point of such a proof? Even in the most optimistic of cases, where a super human mathematician agent exists that could prove or disprove (or declare undecideable) every statement, either there are human mathematicians that are there to understand the proof to explain it to other humans... Or there is simply no point for such a super human agent to exist in the first place.

@LHomme_Qui_Rit @Leophilius Yes you definitely need less epicycles in Copernican heliocentrism (but you still need some)

@lorel_sg @Leophilius Theoretically, wouldn't planetary orbit models need one less epicycle in the heliocentric system to achieve a similar fit?

Ptolemaic geocentrism fit better to the data than Copernicus' heliocentrism

@drmtgr @QuetzaIc0atl C'était surtout ici pour dire que les cas sont multiples, et qu'il serait naïf de uniquement se fier à "fit to the data", et une certaine forme d'élégance mathématique ou théorique peut être un critère intéressant en physique théorique.

@drmtgr @QuetzaIc0atl a été abandonnée pour des lois qui correspondaient mieux aux observations.

@QuetzaIc0atl @drmtgr Oui c'est exactement ce que j'entends par cet exemple

@drmtgr @lorel_sg mais l'exemple qu'il donne ne prouve justement pas que le critère "fit to the data" peut induire en erreur et que l'élégance mathématique *en soi* peut être vertueuse ?

C'est tellement réel

Le gars qui me contredit juste pour me contredire en réponse 😭

@Leophilius You contradict yourself once again 😭 just go read some history of science and come back

@lorel_sg It was actually because heliocentrism was more theoretically virtuous, not because of “elegance”. Scientific models aren't judged on subjective aesthetic values, they're judged on theoretical virtues and beauty is not one of them.

@Leophilius And then came up with a better theory. That's my whole point, mathematical elegancy can be a good argument to favour a theory over another one, as it was for heliocentrism vs geocentrism.

@Leophilius At first it didn't, and we could just have abandoned heliocentrism at that time. Some people rejected heliocentrism because of observational evidences, like Tycho Brahe. But some decided to investigate heliocentrism nonetheway, because it was more mathematically elegant.

@Leophilius Not it isn't, read again. The Copernican model assume circular orbits and constant speed, it explicitly contradicts Kepler's laws.

@lorel_sg Yes it is.

@Leophilius The Copernican model is not in agreement with Kepler's law.

@lorel_sg So the Copernican model better fits to Kepler's laws, or the data we have.

@Leophilius Copernicus' model does need epicycles also. Because Copernicus assumed circular orbits and constant speed. It was only when Kepler proposed elliptic orbits instead of circular ones that the need of epicycles vanished

@lorel_sg Yeah, you had to add epicycles to account for observations, increasing the number of ad hoc hypotheses onto the model to get it to work, where as the Copernican model doesn't need to do this.

@Leophilius And it remained the problem of the non observed parallax of distant stars, which favoured the geocentrism view at that time

@Leophilius It does, the ptolemaic system described very well the observed motion of stars with enough epicycles. Copernicus' model did not as good with circular orbits and constant speed. Copernicus had to add epicycles to his own model to only match the predictions of geocentrism.

Mathematical beauty can be a criteria in theoretical physics

But heliocentrism was more elegant, so we pursued this path and improved it (replacing circular orbits by elliptic ones) and finally it better fit to the data