Infinite sequences

[paper stag]

Let there be two infinite sequences containing the numbers 0 and 1. They are grouped so that every possible distance from the nearest 1 to the next one exists by the number of zeros. For example, ...1, 0, 0, 1, 1, 0, 0, 0.... Each smaller sequence of 1s and 0s (e.g., ...1, 0, 0, 0, 1...) repeats an infinite number of times (i.e., each such arrangement will repeat infinitely many times), and every possible distance will occur. Suppose we have the following sets:

S1: (sequence x, 0, 1, sequence y).

S2: (sequence x, 0, 0, 1, sequence y).

Even though these different situations repeat an infinite number of times in both sets, do the sets have the same order of occurrence for the different series? Is it even possible to create two different sets if we assume that all configurations of consecutive numbers repeat many times?

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[hexed nimbus]

I don't think your initial conditions are possible? Like, you could have the sequence 1, 1, 0, 1, 0, 0, 1, ... such that, indexing from 0, the nth 1 is followed by n 0s, and that would satisfy your first condition, but you wouldn't get infinite repetition of every or even any finite subsequence. Apart from those consisting of isolated 1's surrounded by 0's. This question is either poorly posed or poorly paraphrased, seems like.

[paper stag]

well, I was trying to resolve philosophical problem with math, and I thought it will be a good representation. i will think how to fix the question then

[hexed nimbus]

What "philosophical problem"?

[paper stag]

a bit from Laplace's demon problem. let us suppose infinite universe in time, with infinite number of particles. sequence S represents all history of particle a. every sentence is "for moment Tn, a is touching b" (I know particles don't touch really, I'm trying this problem for more classical mechanics' model of particle). 0s would represent senteces where above mentioned sentence is false, and 1s sentences where it's true. my question is: if we will say particle a will touch all particles infinite number of times in infinite time, can we make two causal histories for it? like both sets of sentences would have to have different order.

i hope it's not too chaotic

[hexed nimbus]

See, the problem here is that the set of statements is uncountable.

Even supposing discrete time, you have infinitely many statements for each of the infinitely many times.

And it's not clear at all how the statements should be ordered.

Or even if an ordering exists (apart from the non-constructive ordering of the well-ordering theorem).

Like, if we suppose all the statements about time 1 should come before all the statements about time 2, then we'll actually just never reach a statement about time 2 because we have infinitely many statements about time 1 to get through first.

[paper stag]

what if we say: Tn lasts as long as it touches certain particle by very specific part (like, particle a would be a cube, and sentences would be true if it touched by its specific side)

[hexed nimbus]

What?

[paper stag]

you say problem is: in descrete time, there are uncoutbily many sentences before T2, so we would never reach T2. but if analyzed by us moments would last as long as very specific fact about particle a lasts, we could avoid it

[hexed nimbus]

No, that's not what I said. There are countably infinitely many statements before T2.

[paper stag]

oh, okay

[hexed nimbus]

Also, this doesn't fix anything at all because now we can have particles in different states at the same time.

[paper stag]

so your conclusion is: there couldn't be two sequences of particle a's history (having in mind assertion that it will touches infinitely many particles inginitely many times), or we can't know it?

[hexed nimbus]

Okay, wait. This is a different question. You were talking about, like, an infinite sequence of infinite sequences. Now you're only talking about the one infinite sequence of "something is touching particle a at time t".

[paper stag]

okay, my bad; i meant only infinite sequences made of finite sequences. so what would be answer for one infinite sequence? could there be two different, with assertion mentioned above?

[hexed nimbus]

Every infinite sequence is made of finite sequences! Your language lacks sufficient precision for math or philosophy.

[paper stag]

sorry, this day is bad for me

[hexed nimbus]

Well, maybe take a break or something.

[paper stag]

i just need answer. can there be two differnet infinite series with aforementioned assertion? it's really important for me to get answer as quickly as possible

[hexed nimbus]

I have no clue! You have not once managed to make a statement precise enough for me to actually understand what you're asking.

[paper stag]

okay, i will rethink it

[hexed nimbus]

And how could this random idle philosophy possibly have a deadline attached?

[paper stag]

well, i'm falling slowley into insanity because of philosophical problems. i just want to end it and start living without thinking about it, but i can't do this without resolving this

this is why it's mportant for me

[hexed nimbus]

You still have yet to coherently state a problem of either philosophy or mathematics.

The closest you came was your sideways reference to Laplace's demon.

[paper stag]

Is this reasoning clear for you:

There is particle a. It always touchs other particle. It will touch certain particle b infinitely many times, in different periods between those touches. Like it will touch b after 5 seconds of separation, then after million seconds of separation, then after 10 seconds etc. So there will occur every possible time of separation between touching of these two. Maybe this will not muddy the water as much.

Now: if a will touch b as mentioned above, can we have two different histories of a? This would mean that there was different order between sequences in at least one place, and everything was the same before and after it.

So, final question: can there be two different histories of a, if in each it will touch b infinitely many times, after different amounts of time?

If anything is unclear, i'm begging for patience

[paper stag]

@hexed nimbus