u/Negative_Gur9667

I have been thinking about this after hearing Terence Tao's latest statement regarding the rapid development of LLMs. He argues that something should only count as a proof if it can be understood by at least one human.

Considering how quickly LLMs are improving, it is not unreasonable to assume that we will soon run out of proofs that a human can actually comprehend.

What happens when we encounter new problems with proofs that are thousands of pages long, making them far too complex for any human to grasp in a lifetime?

If these proofs are verified in Lean and lead to significant breakthroughs, should we simply dismiss them?

How should we handle these new kinds of proofs?

Deep in the forest lived a fox who was widely known as a master chef. His kitchen always smelled of the most refined spicesand his dishes were considered true masterpieces of culinary art. But the fox had an ironclad principle - the absolute foundation of every single one of his meals was meat. With this ingredient, he conjured up the most incredible creations.

One day, a hare hopped past the fox's kitchen. He stopped, sniffed curiously, and observed the artfully arranged plates standing on the counter.

Dear Fox, said the hare, "your dishes look truly masterful and delicious. Tell me, can you also make me a nice, tasty salad?"

The fox smiled confidently, adjusted his Chefs hat, and nodded. "Yes, I certainly can. But I will, of course, need some kind of meat for that. What kind would you like as a base?"

The hare gently shook his head. 'But I don't eat meat at all. I would like something entirely without meat.'

The fox's eyes widened, and he stared at the hare in sheer disbelief. He put his kitchen knife aside and raised a paw instructively. "I am sorry, but that makes no sense! Without meat, you cannot make a juicy steak, age a delicious salami, or braise a perfect roast. I cannot prepare food without this wonderful meat, that is simply impossible. Just consider: without meat, we would not have all these magnificent and sublime dishes that I am able to prepare here every day!"

The Hare let his ears droop and slowly turned away. He was deeply disappointed, as he would have been very happy to eat something good without meat for once. The fox did not understand the problem. All these opulent dishes, the steak, the salami, and the roast, did not interest the hare at all. He did not even miss them. He would much rather have eaten other great things that manage entirely without this one ingredient.

Hey everyone, ​I want to discuss the philosophical motivations behind each of the ZFC axioms. ​Axioms are mathematically true by definition, but what philosophical worldview actually justifies them? For example, does the Axiom of Infinity require strict Platonism, or is it just about our cognitive ability to imagine such concepts? What about the philosophical reasoning behind the Axiom of Choice or Regularity? ​I'd love to hear your thoughts on the reasoning that grounds these axioms, or get recommendations for philosophers who have deeply explored the "why" behind ZFC.

Ich setze die Hysterie mal in Relation.

Pro Jahr stirbt im Durchschnitt eine Person in Deutschland an einem terroristischen Anschlag (auf 10 Jahre gerechnet).

Es ist 3 bis 4 mal wahrscheinlicher, vom Blitz getroffen zu werden, 400 mal wahrscheinlicher zu ertrinken und 150 mal wahrscheinlicher, 6 Richtige im Lotto zu haben.

Ich würde gerne wissen welche Argumente ihr dagegen habt.

In 1961, physicist Rolf Landauer proved that information is inherently physical. The absolute minimum amount of energy required to change or erase a single bit of information is directly tied to the surrounding temperature. This is known as Landauer's principle.

In quantum physics the minimum amount of physical mass or matter required to store a binary 0 or 1, the limit is a single fundamental particle.

The minimum physical volume required to store a bit, theoretical physics provides an absolute limit known as the Bekenstein bound.

The brain and the universe are pysical, therefore it would require infinite particles, energy and space to have an actual infinite object.

This means in reality we can only imagine 0.999... to exist as a function just like n+1 is the function that generates all numbers.

These functions can not end but we can imagine they end just like we can imagine invisible clothes.

Working on actual infinite real numbers is like tailors working on invisible clothes.

In the famous story "The Emperor's New Clothes" neither the emperor nor his officials can see any clothes, but they pretend to see them so they do not look foolish. The emperor walks in a public procession wearing nothing at all until a small child shouts out the truth: "The king is naked!"

The emperor and his officials are todays mathaticians, nobody wants too look like a fool so they all agree they are seeing invisible numbers.

And the child is SPP.

□

Es gibt Menschen hier auf Reddit, die komplett toxisch sind. Einige wollen immer recht haben, und wenn sie falsch liegen, drehen sie alles so lange, bis es doch irgendwie passt.

Andere interpretieren alles Mögliche in einen harmlosen Satz. Am schlimmsten sind die politischen Debatten. Die meisten sind einfach komplett ignorant und empathielos dem anderen gegenüber. Besonders an den politischen Rändern sind Diskussionen unmöglich. Zum Beispiel ist Kritik an Israels Regierung auf der rechten Seite direkt Antisemitismus, und auf der anderen Seite die Sorgen der AxD-Wähler (man darf das Wort hier nicht mal sagen, lol) ernst zu nehmen, macht einen direkt zum Steigbügelhalter für das Dritte Reich.

Kaum jemand ist offen für etwas, will diskutieren oder abwägen. Viele wollen nur Bestätigung, und die anderen haben immer etwas nicht verstanden, weil sie angeblich dumm sind.

Ich blockiere neuerdings sofort solche Leute, wenn ich sie erkenne, und es ist wirklich viel besser geworden. Es lohnt sich sogar, auch mal etwas zugespitzt zu sagen, weil dann all diese Personen aus ihren Löchern gekrochen kommen.