The thinking is inspired by the Infinite Monkeys Theorem. Which does have an easy-to-understand mathematical proof (and the criticisms of said proof are more difficult to grasp).
Isn't it a property of infinity? If pi goes on infinitely without repeating itself, every possible combination of numbers appears somewhere in pi.
It's sort of like the idea that if the universe is infinitely big and mass and energy are randomly distributed throughout the universe, then an exact copy of you on an exact copy of Earth is out there somewhere.
This property of infinity has always fascinated me, so I'm very curious for where the logical fallacy might be.
Not necessarily. The number 1.01001000100001000001... never repeats itself, yet most other numbers can never be found in it.
A number that contains all other numbers infinitely many times (uniformly) would be called normal, but no one has managed to prove this for pi yet. In fact, no one even managed to prove that pi doesn't contain only 0s and 1s like the above after the X-th digit.
The fact you can't encode arbitrary data in a structured-but-irrational number doesn't mean you can't encode data in a 'random' irrational number.
The question is really 'Does every series of numbers of arbitrary finite length appear in pi?' I can't answer that because I'm not a mathematician, but I also can't dismiss it, because I'm not a mathematician. It sounds like a fair question to me.
>I can't answer that because I'm not a mathematician
So what? Mathematicians can't answer it either. It is an open question and because it is an open question claiming it is or isn't true makes no sense.
>The fact you can't encode arbitrary data in a structured-but-irrational number doesn't mean you can't encode data in a 'random' irrational number.
You can not encode data in a random number. If it is random you can not encode data in it, because it is random. I am not sure what you are saying here.
I demonstrated that numbers where the digits go on forever and never repeat exist, which don't contain every single possible substring of digits. Therefore we know that pi can either be such or a number or it is not, the answer to that is not known. Definitely it is not a property of pi being infinitely long and never repeating.
That's why I put random in quotes. Pi is not a random number. You can encode data in it eg find a place that matches your data and give people the offset. That's not very helpful for most things though.
just index on the number of ones. Ex 0.10110 there are two ones in a row, so reference those two ones to be the number two. For 00, flip it and refer to the same pair of ones.
That is totally missing the point. Of course for every number there is an encoding that contains all pieces of information.
That obviously applies to 0.00... = 0 as well, it contains 0, then 00, then 000 and so on. So every number and therefore every piece of information is contained in 0 as well, given the right encoding. Obviously if you can choose the encoding after choosing the number all number "contain" all information. That is very uninteresting though and totally misses the point.
Most physicists don't believe that infinity can actually exist in the universe.
Put another way, the program which searches those works of art in the digits of pi will never finish (for a sufficiently complex work of art). And if it never finishes, does it actually exist?
That's a completely different issue. Using math to solve physics problems deals with physical models. Models are imperfect and what kinds of math they use is completely separate from asking "does infinity exist in our actual universe".
To answer that question, you would have to dismiss with experimental evidence all models people can come up with that try to explain the universe without "infinities". It's neither completely clear what that would mean, nor whether it's even in principle possible to determine experimentally (it's also most likely completely irrelevant to any practical purpose).
It's not that shocking to me - you should try tutoring a class of mathematics undergrads! They make this class of error all the time. It's a "this sounds like it's obviously true, so the obvious reason must be right" kind of thing. Rigorous logic takes a lot of time to click for people.
feel free to prove me wrong. I never said it's efficient, the point is just that the information is out there. If pi has the following subnumbers 00, 01, 10, 11 in there, we can construct every perceivable data we can encode as binary. Even with 0 and 1. So we can construct a file by pointers to these four numbers. The bigger substrings we can match, the bigger the compression ratio. The set of pointers might even be way bigger than the file itself. It's nowhere near efficient or clever, but just entertaining
I don't think you can argue against IP because the way you arrange the pointers is IP itself, but still a funny thought experiment anyway
I'm not saying, that every piece of information is in there end to end, but that there are parts in there which can be used to construct it. I think I should've made the "encoded" part a bit more transparent haha. But I love the discussion that I kicked off!
It is somewhat shocking that again and again this logical fallacy comes up. Why do people think that this is true? It doesn't even sound true.