Infinite odd numbers

It is really interesting to read this and compare with my earlier speculation about infinity.

In that infinite universe, Paddy Murphy Night not only occurs once, or several times, but an infinite number of times. (However, non-Paddy Murphy Night also occurs an infinite number of times. This illustrates Cantor’s principle that if you remove an infinite set from an infinite set, another infinite set remains…)1

1 For example, the set of whole numbers continues to infinity, but so does the set of even numbers. If you subtract the even numbers from the whole numbers, you still have an infinite set of odd numbers.

The notion that odd numbers can continue infinitely and still never repeat or never become even numbers, seems however to challenge the idea that infinite time and space will inevitably create recurring patterns.

The quote is from Robert Anton Wilson’s Quantum psychology (p. 67).

Arguing about Infinity

― Just imagine what it means when you say the Universe is infinite! If time and space are really infinite, then eventually somewhere, at some point it will create recurring patterns and it will start repeating itself. One part of the Universe will be truly identical to an other part. Any detail of it, up to the number of protons in any single atom…

A universe like this will ultimately create a person that is completely identical to me or to you. Just think of it: somewhere, someone has exactly same thoughts that go through your head right now. And it wont stop there, because the infinite universe will create an infinite number of exactly the same person ― those who slightly differ not counted.

So, while we are sitting here and arguing with me, there are an infinite number of us, the same two guys having the same conversation. And later, when you sit and write this in your blog, there are an infinite number of you who are writing exactly the same post. Having said that: there will be also an infinite number of people reading it! Crazy isn’t it, Imandes?

― No. I think you are wrong. You are not talking about an Infinite Universe, you are talking about a finite universe in fact. Because if one part of the universe doesn’t differ from an other one, then these two are identical. If you travel through the universe and find someone who is totally like myself, who has the same body, the same parents, the same future, who’s living on the same planet, in the same solar system, then there should be no doubt that it’s myself and nobody else!

If the universe is repeating itself, then it’s not infinite, it’s a closed circle. An infinite universe will never repeat itself. It will evolve and evolve and evolve and every-time and always and everywhere it will be unique, not a single atom will be the same as another one. Just like numbers.