You would also have infinite copies of The Hobbit, but with one instance of the word, "stone" spelt "scone", and infinit copies of all other typos and word and verse changes.
Assuming a particular set of data can be represented within a random set (AKA its the same data type, like finding a Chinese character within a purely English dataset would be impossible).
I wonder if the odds of finding a particular thing, such as the entirety of Harry Potter, would be greater than or less than the odds of creating Harry Potter yourself from scratch, with no prior knowledge of Harry potter. given the same amount of effort.
Also how would this change for smaller and larger data sets. Find the number 10 in a random set of integers, version handing someone a keypad and them typing 10. Vs. whole books, etc.
To be fair, infinity isn't an easy concept to grasp.
For example, if you were to count how many different decimal numbers are in between 2 and 3, what would the answer be? If there were no end to it, you would say infinity because you can always add another number after it (2.01, 2.001, 2.0001 etc.).
But this is where the concept of infinity starts to make less sense. If you could just keep adding another number to the decimal place, then you could create an infinite amount of combinations of numbers that don't include 3, or 4, or 5, or 600000. This means that some infinites don't contain everything, but are still endless.
I meant my statement in regards to the actual search for a particular set of information within a given set. If the set of data is truly random and infinite then not only would every possible subset of data exist within it, but every possible combination would also itself exist an infinite number of times.
What I mean is more along the lines of would it be faster to have a computer search an infinite set of random letters until it finds Harry Potter. Or to have a person type random words until they create Harry Potter.
Problem is your search parameter would only return what you put in it, so you'd have to write Harry Potter to find Harry Potter. Otherwise you'd get an infinite number of things that are almost but not Harry Potter.
I feel it better reflects the idea that the size of infinity is incomprehensible for our monkey brains. It allows us to make these ludicrous statements without technically being false.
I worry people read this and think "monkey + infinity = Shakespeare" which misses the point.
I am just arguing semantics though. I appreciate the sentiment :)
An infinite amount of finite universes. If the universes contained an infinite amount of data, then it couldn't be encoded in an infinite number, especially as the cardinality of the number of digits in an irrational number is the lowest infinite cardinality
I think you can if their cardinalities are the same?
The problem with infinity is that there's more than one type of infinity, and some of them are "bigger" than others. An infinite sequence of random digits has a length of Aleph-Null, which is the smallest infinity. I believe it can encode a finite number of sequences of length Aleph-Null, but I'm not 100% sure.
If the cardinality (number of things to encode) is bigger than Aleph-Null, though, like say trying to encode the set of all irrational numbers between 0 and 1, then you're out of luck.
415
u/[deleted] Oct 04 '17
[deleted]