Je suis fasciné par l'énergie qui a été investie dans ce problème, la passion qu'il a déchaînée, et le fait que la résolution fasse la une de Quanta Magazine (...) Pourquoi ? Parce que les valeurs exactes de la fonction castor affairé me paraissent parfaitement inintéressantes
Why care about determining particular values of the Busy Beaver function? Isn’t this just a recreational programming exercise, analogous to code golf, rather than serious mathematical research?
I like to answer that question with another question: why care about humans landing on the moon, or Mars? Those otherwise somewhat arbitrary goals, you might say, serve as a hard-to-fake gauge of human progress against the vastness of the cosmos. In the same way, the quest to determine the Busy Beaver numbers is one concrete measure of human progress against the vastness of the arithmetical cosmos, a vastness that we learned from Gödel and Turing won’t succumb to any fixed procedure. The Busy Beaver numbers are just ... there, Platonically, as surely as 13 was prime long before the first caveman tried to arrange 13 rocks into a nontrivial rectangle and failed. And yet we might never know the sixth of these numbers and only today learned the fifth.
[^] # Re: L'œil amusé d'un théoricien
Posté par patrick_g (site web personnel) . En réponse au lien Des mathématiciens amateurs établissent une preuve du cinquième castor affairé. Évalué à 6.
A cette interrogation il n'y a pas de meilleure réponse que celle de Scott Aaronson :
Why care about determining particular values of the Busy Beaver function? Isn’t this just a recreational programming exercise, analogous to code golf, rather than serious mathematical research?
I like to answer that question with another question: why care about humans landing on the moon, or Mars? Those otherwise somewhat arbitrary goals, you might say, serve as a hard-to-fake gauge of human progress against the vastness of the cosmos. In the same way, the quest to determine the Busy Beaver numbers is one concrete measure of human progress against the vastness of the arithmetical cosmos, a vastness that we learned from Gödel and Turing won’t succumb to any fixed procedure. The Busy Beaver numbers are just ... there, Platonically, as surely as 13 was prime long before the first caveman tried to arrange 13 rocks into a nontrivial rectangle and failed. And yet we might never know the sixth of these numbers and only today learned the fifth.