Infinity : really endless?

Though infinitesimals are BAD MATHS you are of course correct (and Zeno's paradox doesn't work in the real world - ask any tortoise). However travelling on a finite closed loop for an infine journey only works if there is an infinite amount of time in which to travel. The impossibility of doing such a thing therefore diminishes the thought experiment in my book. You get phrases like "imagine travelling the same path once, twice, forever - forgetting that forever itself may not exists.

In a finite universe, with a finite amount of energy there are a finite number of things.

Hey Mr Nutty! What say you and I have an infinity of drinks?? I will drink to that!

https://www.youtube.com/watch?v=eGguwYPC32I

if this is true

and a dimension is really within another dimension within another dimension within another dimension

then im implying that theres an infinite amount of dimensions

im not sure if it ever stops or

if infinity is really even possible

I've always viewed infinity as kind of inherently conceptual. It's not something we can ever fully grasp, by definition (even if we can use it in math -- not dissimilar to aspects of quantum physics actually). I also view it (and the idea of an infinite cosmos) like a house of mirrors -- it's possible there actually is a limit out there, but we're bound to never see it because of the way time/space is constructed, and our limited points of view.

does π contain all sequences of numbers within it or does infinity only mean that it never concludes but not that it inevitably expresses even permutation of digits?

every* permutation

There are mathematicians and philosophers of math who still explore the possibilities of a non-infinitarian worldview, which rejects things like mathematical induction (you can just keep counting up naturals forever without a problem) and the law of the excluded middle (proof by contradition), they're not mainstream (most people are mathematical Platonists) but they aren't absolute kooks either (what does it even mean to provide non-constructive proofs that certain very large numbers must exist? Numbers so large we could never compute them or write them down?)

does π contain all sequences of numbers within it

Presumably yes, since we know of no reason for it not to, but to actually prove this might be immensely hard; at any rate, no one's done so yet.

Maybe infinity is exists but math is just insufficient to grapple with it.

if infinity does exist does that suggest god does too

it could just be an infinity of zero information

https://en.wikipedia.org/wiki/Apophatic_theology

math is just insufficient to grapple with it

chill, math has got this

just popping in to say I misread John Scotus Erigena in that wikipedia entry as John Scrotus Erogena.

Infinity is for ppl that dont like maths but like, man, the, like, ideas, man, behind maths

hmmm tell me more

Full disclosure im, like, one of them, man

darragh trying to bring up the old mathematicians vs physicists beef

https://www.youtube.com/watch?v=obCjODeoLVw

Everyone vs physicists imo

everyone vs feynman

The possibilities are endless

am i wrong in thinking that if there were infinite dimensions, than any object that exists here also exists in infinite other dimensions? since it exists here, it's a non-zero probability that it occurs in any given dimension. so wouldn't a non-zero probability applied to infinite simulations lead to endless copies of every conceivable thing or thought? just asking in advance so i can be ready for infinity

fuck if I know

i worry about this.

i am not a mathematician but i find this hastily googled answer satisfying:

But there’s a subtle distinction when it comes to probabilities in the context of infinite things: although the probability is zero of getting an infinite string of “tails,” it is nontheless possible to get such a string. This is in contrast with experiments having finite numbers of outcomes.

In the finite case, “probability zero” means impossible. That’s no longer true in the infinite case. (A very simple illustration: if I asked you to pick a number — any number — the probability of picking any specific number is also 0. However, if I asked you to pick a number, you could certainly do it. The number you pick, therefore, has been picked even though the probability of picking it was 0.)

wouldn't a non-zero probability applied to infinite simulations lead to endless copies of every conceivable thing or thought?

This is where removing infinity from pure number and trying to apply it to physical reality demonstrably leads to chronic puddling of thoughts in the brain pan.

See also the exciting companion thread: Eternity: Classic or Dud?

If there are infinite dimensions (by which I assume you mean, universes), then of course there is one where an identical copy of you exists that chose 3 coffees this morning rather than 2, and as a result, was motivated to actually make a difference in the world.

Personally, I don't buy it. There's enough excess in the sheer number of baryons, stars, and galaxies. The quandaries of 20th century physics were about the difficulty of humans to understand the fields that underlie reality, but don't change the essential fact that we're conscious beings trapped in a deterministic universe, and that determinism extends to our own thought.

Infinity : really endless or endlessly real?

infinity is not limited to an immeasurable number of universes but also an infinite number of non-universes as well. true infinity occludes any particularism/distinction and since we can only think through distinction we can never understand infinity.

If there are infinite dimensions (by which I assume you mean, universes), then of course there is one where an identical copy of you exists that chose 3 coffees this morning rather than 2, and as a result, was motivated to actually make a difference in the world.

and if there is an identical copy that exists, that means there's also another identical copy, etc ---> infinity, right?

not saying i believe in infinite dimensions, of course. i hardly believe in the dimension i'm apparently currently residing in! but it is fun to think about.

i feel like i should listen to some iasos while pondering this possibility

trying to conceptualize infinity is like trying not to think about anything

just a reminder

answer is

                                  
8b       d8  ,adPPYba, ,adPPYba,  
`8b     d8' a8P_____88 I8[    ""  
 `8b   d8'  8PP"""""""  `"Y8ba,   
  `8b,d8'   "8b,   ,aa aa    ]8I  
    Y88'     `"Ybbd8"' `"YbbdP"'  
    d8'                           
   d8'                            

In the finite case, “probability zero” means impossible. That’s no longer true in the infinite case. (A very simple illustration: if I asked you to pick a number — any number — the probability of picking any specific number is also 0. However, if I asked you to pick a number, you could certainly do it. The number you pick, therefore, has been picked even though the probability of picking it was 0.)

this is misleading. say you draw a number uniformly randomly from the continuum of numbers between 0 and 1. the number is an infinitely long string of digits and you can approximate it to any arbitrary accuracy by expanding decimal places and rounding. how can you tell if the number you drew is 0.5? you can't. even if the number you drew rounds to 0.50000000000000000000000000000, no finite expansion can ever tell you that it is 0.5. so it is meaningful to say that the probability of picking any given number is 0: when you draw a number from the continuum, you can't know which precise number you drew. furthermore, the collection of all numbers that can be described with a finite amount of information has 'measure zero', so you can almost never even ask the question 'are these numbers equal'

imo pondering infinity is not 'like trying not to think about anything' (although they are both things i love to do when hi), or particularly, like, man, the ideas, math, man, or even something that will drive you insane (the myth that Cantor commit suicide due to a madness he got from pondering infinity is just that; he just had bpd), but rather something that is fun and fruitful to think about. i don't know anything about physics, but imo the continuum and related concepts like infinity are conceptual tools used to de-clutter otherwise unmanageably large discreet spaces, rather than having some intrinsic meaning (they just happen to sit very weirdly with our intuition, for some reason) and should be de-mystified

sounds otm

hi flopson