Let’s Count to Infinity
Recently, I stopped by a little café and ordered a cup of cappuccino. The waitress asked what size I preferred. I replied, “Infinitely large.” She said, “Sure!” and walked away. A few minutes later, I received this.
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Smart. Very smart, no doubt about it. She deserves a promotion and a tip. I got infinite coffee.
And then I started thinking about how we misuse mathematics and the scientific disciplines.
The amazing thing is — this universe just doesn’t accept the idea of infinity. Every time someone walks up to a physicist and says “infinite,” the physicist smirks and reaches for a pen or a tablet. “Let me show you just how wrong you are.”
But in this physical universe live some very strange beings. Not only do they accept infinity — they operate with it like it’s no big deal. Take the Hilbert Hotel paradox, for example. These beings will calmly explain how a hotel already filled with an infinite number of guests can still accommodate another infinite number. And this example? Created for children, no less — to help them understand how the mathematics of infinity works.
Mathematics, by the way — just an unbelievable thing. Something that simply shouldn’t exist in a physical universe made of space, energy, mass, and time. And yet these beings wield it effortlessly. Not only that — they post videos about it on YouTube like it’s nothing. Math is a marvelous science. It’s basically a prank on the physical universe. It never belonged to the physical world. It was created by other beings living in this universe. Beings who know that their love can be eternal, their coffee infinite, and their determination inexhaustible.
Even the fact that we have digits and numbers already violates one of the fundamental laws of the universe: you cannot count forever. Every third-grader sits there, amazed — how is it even possible to count to infinity?
See, concepts like Schrödinger’s Cat, the Hilbert Hotel, and the like — those are just us mocking the universe, saying, “Look, I can do this — and you can’t.”
If there are any mathematicians here who feel like solving a problem, just for fun, try this:
An LLM model contains 40 terabytes of data. It’s trained on 200 billion parameters. Calculate the total number of possible responses this model can produce. The number will be enormous — but still finite. Increase the number of parameters by a hundred orders of magnitude, feed the model 600 times more data, and what do you get? A finite number. The responses of an LLM model can be counted.
But would you like a problem that cannot be solved without the word “infinite”? Here you go:
Count how many ideas a human can invent.
Infinitely many.
We can create languages, universes, spaces, circumstances — entire worlds that no one has ever seen. And no matter what task can be solved in the physical universe, your essence will always be one infinity greater.
And after that, it’s honestly funny to hear people talk about the possibility of creating “true” artificial intelligence. How can it be true if it’s made from a universe that can’t even produce infinity?
It’s amusing and kind of adorable listening to people breathlessly proclaim that “such-and-such LLM can score 95% on some synthetic test.”
Don’t forget how important the exact sciences are. Don’t forget that we mastered them thanks to mathematics. And don’t forget the difference between what belongs to reason — and what belongs to the object.