Our universe is a square root of 2

Let us take a square root of, say, 2. It is an irrational number (see The Other Wiki, and thus, its digits never repeat itself. Now, let's if we present it in binary, we basically have an infinite sequence of ones and zeroes, in which every combination is possible. Now if we take the states of each and every particle in the universe for every moment the universe existed and encode them in binary, we get the (possibly infinite, but who cares?) sequence of bits which can be found in the binary representation of sqrt(2), because, hell, it is infinite! Thus, our universe can be represented by an irrational number and an offset in it (also, possibly infinite). Uhh, QED?

I disagree, it's obviously √π

Number matters not. The real kicker is any irrational number will suffice - it only changes the offset in it, because, hell, it is infinite!

Not really. I mean, you could have an irrational number that avoided a certain sequence. For instance, I can make up a string of 1s and 0s with no 11s as long as I want; obviously, I can't make up an infinite string, but there's no reason why an 11 will have to appear or it'll repeat itself.

.0100100010101000101001010001010101000001001001010000100100000101010001001...

Not really. Some other combination like '01' could be used as an escape-sequence, so that, for example, '01' means '01', but '0101' means '11'. I, personally, still think that ANY combination will eventually be found in an infinite number, because, hell... You got me. =] But you could prove yourself useful to the modern math by proving otherwise.

Well, numbers like π and sqrt(2) are believed to be normal in base 10, meaning that every decimal sequence of the same length occurs about the same amount. However, it would take about as many numbers to write out the first place a decimal sequence appears in pi as it would to just write out the sequence.

Uhh, that kinda defeats the purpose. I believe the plain infinite number format and number-offset format are equivalent, but mine is not so effective. Of course, it is infinity we are talking about here...

edited 4th Nov '10 9:16:51 AM by dryunya

Well yes. That's why the universe is in reality contained in a much denser storage medium, like a rotten sandwich.

Well it can be, considering that the state of every atom in the rotten sandwich can be represented with an infinite number. Agnosticism kicks in.

It's 42, you know it to be true.

IT's 42 and 108, silly.

The question whether the square root of 2 is a normal number is still an open problem AFAIK.

As for the number that our universe is, I suggest Chaitin's constant - that is, the probability that a randomly chosen Turing machine will halt.

Not only it is normal and trascendent, but it is also uncomputable - that is, you cannot write an algorithm that will return you the n-th digit of Chaitin's constant in a bounded amount of time -, uncompressible and, most of all, it encodes the halting problem: if you somehow knew Chaitin's constant, you could decide in finite time whether a given algorithm will eventually stop or not. Or, heck, prove or disprove every mathematical conjecture ever.

If the universe - as some argue - is computable, then knowing Chaitin's constant would allow you to answer any question about it.

It probably is the closest thing to the Answer to the Life, the Universe and Everything that exists in nature.

edited 5th Apr '11 12:45:18 PM by Carciofus