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]]>https://www.quantamagazine.org/20160630-infinity-puzzle-solution/ ]

The idea of infinity was invented this way: if n is the largest number, (n+1) is larger. However, this assumes that, having used n symbols, we can find still another. So what are the “symbols” going to be? If they are fermions, there is clearly a finite number within the event horizon. Thus there is a number n so that (n+1) does not exist.

https://patriceayme.wordpress.com/2011/10/10/largest-number/

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Excuse me, how to you construct “infinity” from the usual axioms? Or a “potential infinity”? How can one “assume” something, “infinity”, that one has not defined? Absent a construction of “infinity”, or “potential infinity”, it cannot lead to contradiction.

Nor can introducing “infinity” as an axiom lead to a contradiction.

Another objection is that, indeed, assuming “infinity” enables to do some sort of mathematics. However, absent “infinity” another type of mathematics would have to be practiced.

Maybe “infinity” dependent mathematics is a specialized type, similar to making Euclidean geometry… infinitely: something that can be done, but something nobody does anymore.

To justify “Infinity” with the “one more” argument, assumes that there is an infinite amount of energy to keep on writing… “one more”. This is an axiom not found in nature. Nor in Euclid’s axiom (so his well-known “proof” is false! Just observing everybody says it, does not make it true!)

Axioms of mathematics were always written as an abstraction of nature.

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]]>Again, we argued this point previous with the finite tacos metaphor and I agreed with you then. But you are extending the metaphor to the point where it contradicts the basic laws of physics itself. And I say that because whatever number you are attempting to arrive at can only ever be conditional. In other words, you could measure the number of tacos I have eaten in my life and that number would be ‘finite’ but it wouldn’t ever be authoritative because it assumes certain conditions that don’t have to be true. I could have eaten a taco when you weren’t paying attention, and all it would take would be one unaccounted for taco to upset your number. But according to you, that could never happen because A] already has it covered. But it only has it covered because it remains undefined. Once it is defined, all it would take would be one extra ‘push’ to make it irrelevant. Even if you told me, on my deathbed, that I was about to eat my last taco, I’d do my best to shove another one in my mouth, but the very act of doing that, even if I did not succeed, would jeopardize your number for how could I even attempt a number beyond it? Even if I don’t eat another taco, I can still hold one in my cold dead hand. I have not ‘eaten’ the taco, so it doesn’t change that number, but what is that thing in my hand, a poodle? The property that defines the last particle had to be ‘true’ for the previous particle in order for it to lead to that last particle, and the ghost of the particle beyond the last is still sitting there in the dark because of what made the two previous particles true to begin with.

If I can start, I can stop. If I can stop, I can start. Infinite stopping would contradict the possibility of starting to begin with.

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]]>The conversation we are engaged in, is, in some ways, as old as Plato. It got really hot about 1,000 years ago around Paris. There are many concepts, entire theories, and all variants in between, attached to it: nominalism, realism, the problem of universals, conceptualism…

But I claim definitive progress has been made. Why? Because of elementary particle theory, Quantum physics, the theory of gravitation, plus the neuronanobiology around the corner. It was just a matter of putting it all together. Which only someone having seriously studied those fields could confidently do, let me immodestly add. I am not mentioning this for my personal glory, as I don’t exist as a person, but to explain that this obvious idea was not found before, simply because no one had such a deeply diverse background (and I had the good fortune to interact with many of the greatest). Not too many have studied *Model Theory* and the *Transplanckian Scale*. In depth.

I agree with your sentence: “You can exist without speaking, but you can’t speak without existing.” However what is speech, at the most basic level? A physical effect, a dynamic with an indentifiable pattern relating to previous pattern. The most fundamental notion here is “physical effect”.

I am just saying, first and fundamentally, that, just as speech is physics, so are ideas.

A speech is a pattern of elementary particles evolving in time. Could one make a long speech to a worm by just moving, say, ten elementary particles? Sure. The worm would play the role of the tape in the Turing machine, become the tape. Could we make a long speech with ten elementary particle, and no worm to register it? No. But one could make a long speech if one had trillion elementary particles at one’s disposal. Even without any worm. The speech would become the worm. And one needs many particles to make a worm.

Worms are made of zillions of elementary particles. But one trillion zillions is still a finite number. It is precisely because a worm is made of a finite, but very large number of elementary particles that it can store a very long discourse. But there is a limit to storage. A limit to speech.

We are the worms. However we have only a FINITE number of elementary particles at our disposal to geometrically arrange in ourselves. That FINITE number is given by considerations in gravitation and the transplanckian scale. (So, indeed, by studying the same field of knowledge I came to the conclusion that Special Relativity broke down at very high energies, causing Faster Than Light effects.)

To arrive to my conclusion about symbols, one needs just assume the ultimate realism: **ideas are physical objects, just like speeches are physical objects, or caravans in the desert are physical objects**.

PA

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