# At Mind Matters News: Why just anything can’t happen given an infinite sum of universes

Baylor engineering prof Robert J. Marks says, we can figure out why, using simple mathematical reasoning in this universe:

Can anything happen if there are an infinite number of universes each with an infinite number of possibilities in each? Can you be bald in one universe and fully haired in another? Can you have two eyeballs in this universe and three in another? The answer is no. In a nutshell, the reason is that some infinities are bigger than other infinities. (And this is not a claim like infinity plus one is bigger than infinity. Infinity plus one is still infinity.)

The number of points on a line segment from, say zero to one, is a bigger infinity than the number of counting numbers {1,2,3,…}. We can label the infinite number of universes in the multiverse as universe #1, #2, #3, etc. Because they can be counted, this infinity is said to be countably infinite. This looks to be the smallest infinity. (“Smallest infinity” sounds like an oxymoron but isn’t.) And, no, true infinity is not the same as the symbol ∞. In mathematics, ∞ typically means “increasing without bound.” And no matter how high you count, you still have infinity to go.

Robert J. Marks, “Why just anything can’t happen given an infinite sum of universes” at Mind Matters News

By now, you can guess where this is heading, re claims about a multiverse: to Hilbert’s infamous Hotel:

Infinity is conceptually weird. Assuming that it is a reality leads to absurdities as illustrated by Hilbert’s hotel. Hilbert’s hotel has an infinite number of rooms labeled 1,2,3, etc. There is no vacancy in the hotel. All the rooms are occupied. Nevertheless, a room can be made available by moving the lodger in room 1 to room 2, the lodger in room 2 to room 3, 3 to 4, etc. Doing so leaves room 1 unoccupied for a new guest. In Hilbert’s hotel, there is literally always room for one more.

In fact, a hundred rooms can be vacated in Hilbert’s fully occupied hotel. Move the occupant of room 1 to room 101, the occupant of room 2 to 102, 3 to 103, etc. Doing so vacates the first 100 rooms.

But here’s the real surprise. A countably infinite number of rooms can be vacated in Hilbert’s fully occupied hotel. Every occupant looks at their room number, doubles it, and moves to that room. So room 1’s occupant is moved to room 2, room 2’s occupant is moved to room 4, room 3 to room 6, 4 to 8, etc. This leaves all of the odd numbered rooms, (1,3,5,…), empty so Hilbert’s hotel, despite being totally full, can still accept a countably infinite number of new guests! More.

Takehome: It can be shown mathematically that the infinite does not exist in reality, only in our minds. Thus an infinite number of universes cannot exist.

You may also wish to read:
Yes, you CAN manipulate infinity — in math. The hyperreals are bigger (and smaller) than your average number — and better! Hyperreal numbers are a new type of number that was developed to simplify and rethink the way that we deal with very large and very small numbers. It reduces the complexity of the task and allows us to use our well-honed high-school algebra skills to solve complex problems easily. (Jonathan Bartlett)
and
The jump of Chaitin’s Omega number Gregory Chaitin explains, “For any infinity, there’s a bigger infinity, which is the infinity of all subsets of the previous step.” Chaitin tells us, “In the mathematics that I would say is discovered not invented, you feel you’re touching a reality beyond normal reality.”

## 2 Replies to “At Mind Matters News: Why just anything can’t happen given an infinite sum of universes”

1. 1
Fasteddious says:

A simpler reason that you cannot, “be bald in one universe and fully haired in another”, is that you are unique; the “you” in the other universe is not you yourself. Even in the “many worlds” interpretation of quantum physics, your equivalent in any of the other worlds is not you, even if his universe split from yours only a nanosecond ago.

2. 2
Origenes says:

Fasteddious @1 — I was thinking along the same lines.

Another question though. If anything goes in our Multiverse, what can we be certain of? Are there any events that cannot happen? Are there states of affair that cannot be true?

Can it be that Biden is an alien from Osiris? Given an infinite amount of universes where this is the case, why not?
Can my monitor suddenly turn into a horse? If not, why not?
And so on …