Yep! Pi might be a "Normal" irrational number, which is a really poorly named classification that basically means that the "random" arrangement of numbers in pi isn't weighted and so you'll end up with 1 in 10 digits being 1, and that that will be true for all bases. We're kind of at a point where we think Pi is "normal", but we can't prove it.

If it is "normal" though, then that means that you could find any arbitrary sequence of numbers inside of pi, somewhere. Meaning that in base 128, pi would contain the ascii sequence for every book ever written, every book that ever will be written, every book that could be written, the accurate date of your death, and anything else you could ever imagine. Again, that's not proven, but we think it's the case

From a mathematical standpoint you're right, but from the standpoint of application pi has an infinitesimal accuracy without going to 45 digits. At 3.1415926535, we're more accurate than the distance between 3 atoms.

Yeah! It’s a really beautiful thing to think about. And exciting to imagine we may one day see a mathematician who works out the truth

There are a few possibilities:

1. All the universes existed from the start. Most just haven't diverged yet. At any given moment, there are an infinite number of completely identical universes.
2. The universes literally split, and some quirk of quantum mechanics makes this actually possible.
3. They aren't universes, they're timelines. All the universes are in quantum superposition with each other.
4. There aren't actually multiple universes. It's just acknowledgement of the infinite possibilities. (This is how I like to think of most quantum mechanics, tbh.)

Ah, but you see, this example takes place in the universe where CDs are susceptible as well

An infinite series of random letters would of course contain every book, that’s definitionally true.

But infinity itself does not empower the whims of the imagination (indeed this is the entire point). Yes, it is definitely impossible for the warehouse to contain a sentient race of CD people. Polycarbonate plastic simply cannot exhibit any of the qualities of being alive under any circumstances

I have disproven that an infinite set necessarily contains every arbitrary possibility. And quite simply, too. Notice how the set of natural numbers does not contain any grapes.

Thus, the burden of proof is now on those who claim they do know what is in the multiverse. Such as yourself. What evidence do you have for these “junk data” universes?

It's an analogy, the specific case doesn't matter. It demonstrates that infinite does not mean literally everything, it's possible for some item to be missing from any particular infinite set. In a box of infinite apples you won't have an orange; in a box of infinite fruit you won't have a chicken; in an infinite multiverse you by definition won't have a universe which isn't part of that multiverse.

I suppose then you’d have been more satisfied with the example of an infinite number of grains of sand, each polished smooth and strewn across an infinite beach.

Or simply an infinite expanse of empty space, each with unique coordinates, yet unable to be differentiated in the absence of any reference.

The point being, infinity itself is a concept we defined a certain way. And no part of that definition mandates variation. People who hear “infinity” and immediately conclude that, in one universe they are a singer, and in another they are an astronaut, and in another still they weren’t born at all, etc., are making an incorrect assumption about the nature of infinity itself.

Framed another way, we have exactly one example of a possible universe. Tell me, what creative force do you believe in which would intervene to ensure other universes play out differently?

Is there a similar strong will or intention in how a multiverse evolves?

Well, if we're talking about the many worlds theorem, then probably yeah, because both worlds came from a common starting point and evolve together. Like, imagine that I flip 100 quantum coins, creating 2^100 (1,267,650,600,228,229,401,496,703,205,376) universes in a multiverse. Every universe will be different, but the vast majority of them will have roughly 50 heads and roughly 50 tails. 7% of them will even have exactly 50 heads. There is one universe where every coin flip lands on heads, but it's only one universe among nonillions, you could spend your entire life searching universes and never find it. None of the universes are the same, but most of them are so boringly similar that you couldn't tell them apart. It's the central limit theorem, that lots of random events trend towards uniformity

nobody really knows, but if I had to guess I'd say that's probably the way our universe would be, our universe might technically be different from the one next to it, but it would only be different by a single electron on mars that decided to move an atom to the left. There might be a universe somewhere where all of the particles in a lotto wheel quantum tunnel to make the winning number be your number, but it would be outnumbered an infinity to one by universes where that didn't happen and it looks exactly the same as ours.