Thinking about Infinity

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Thinking about Infinity

Postby Insanity test on Mon Feb 15, 2010 11:59 pm

Have you ever though about infinity? I mean really thought about it?
It's actually quite a stupendous concept and makes everything seem rather small.

Take numbers, for example:
1000 is quite big. A thousand years is quite a long time.

But after a thousand is a million (I'm not counting ten thousand, that's just cheaty number naming) and a million really is alot bigger than a thousand. You can hold 1000 1cm cubes in your hand quite easily (if they're stuck together, that is) but a million is a thousand of them!

Then you have a billion. Now I prefer the british billion - makes logical sense 1000 x 1000 = 1,000,000 so billion = 1,000,000,000,000 or a million million.
But alas America has strong armed it's own measurement simply by using it a lot. So 1 billion is 1,000,000,000. but that's still stupidly big. There are only 31,556,926 seconds in a year! (thankyou Google, I'm sure I could have worked it out, but I'm lazy)

Now we have a trillion. I think you get the idea.

It goes on for a while with this naming system, getting to things like duodecillion and so on. at this point mathmaticians get bored of writing digits, so they use to the power of, written as superscript, but i can't do that here, so duodecillion is 10^39, the carat meaning to the power of.
But this is still small fry.

The number names keep going till they get to a number usually called a googol. No, not Google, a googol. (though that might not be entirely accidental)
This number is a 1 with 100 zeros after it. One Hundred.
This is a googol:


It's a number so big that you will see less milliseconds in your life than a googol. By quite a way.

But then things get a bit silly.
After a googol, there are a few names given along the -illion line (theres one for a googol too: duotrigintillion), but they run out quite soon.
So using the word googol, we get googolplex. A googol to the power of a googol.
Now this number is big.
No, bigger than that.
Really, really big.
If you imagine the googol i wrote above written downwards from the same one, then fill in the zeros to make a square, that's a goolol^2. Do the same toward you to make a cube of zeros and that's a googol^3.
A goololplex is googol^googol.
I'd write it down for you except that I can't. Not longhand.
The universe is quite big, isn't it? And atoms are very, very small.
Well, I can't write out this number because there aren't enough atoms in the universe on which to write it. Even if you put a single digit on every atom.
It's usually written out like this: 10^(10^100).

But there's more!
Above a googolplex there aren't alot of numbers that are commonly used.
The largest number ever used in a mathmatical proof is Graham's number.
I'm afraid I can't write this one out.
Not even in short hand, because I can't use brackets here.
Suffice to say it is to a googolplex what a googolplex is to 1. And then some.
Calculated in connection with a problem concerning n-dimentional hypercubes, no-one actually knows all the digits because it would take far to long to work all of them out, even for a computer - but we do know it ends in 7.

Anyway, I've driveled on about big numbers for a while now, but still - even at Graham's number - am No Closer to Infinity Than When I Started.

That's the ridiculous thing about infinity. Any number you can think of is no closer to infinity than 1.

If you add infinity to infinity, you get infinity!

If you raise infinity to the power of infinity, you get - infinity!

Strangely enough, however, if you take infinity from infinity, you get n. That's any number you want.

If you had an infinitely big hotel that was full, you could walk forever and not find an empty room. However! If you get everyone to shift along one room (which they can, because the hotel is infinite) you have a spare room. Then tell everyone else to leave. You've taken infinity from infinity, but you're still there. You were an occupant of the infinite hotel from which you took an infinite number of guests, but you are still there!

Anyway. I'm probably boring anyone who has the stamina to read all of this to tears. (well done, btw) Luckily I cannot write forever, so you won't get the complete works of Shakespeare from me.

I just thought I'd share my musings of vastness.

--/:Out of cheese Error:/--

Please shutdown Universe and reboot from Start.
Insanity test
Insane Hatter
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Re: Thinking about Infinity

Postby nil on Wed Feb 24, 2010 4:42 am

Thanks for your infinitely long post.

The fact is there is an end to infinity, so there is a biggest number... Of course nobody shall know it because if that number is ever uttered by a sentient being, the whole universe will collapse.

Well then you may ask, how did I know it? The fact is I am one of those nobodies, so of course I know it. It is a tremendously tremendously large number, that number, let's call it "Zeronity", even when expressed in short hand form, will take one's life time to speak, no matter in what sort of language.

You may ask how "Zeronity" came into place? Well, it's all because when the Universe was generated (as how it was generated or by whom, that will be another post for another time), the "computer" (consider it a metaphor of a computing device) has a maximum memory issue, so that's why it has a maximum number issue... So naturally, our universe will last only until Zeronity.

Unfortunately, we are very close to the limit of "Zeronity" now (as the age of the Universe is not counted in years but in Zeronity seconds), and our Universe will collapse very shortly. Please send all your money to the poster of this post so next time when we generate the universe we can afford a computer with a bigger memory....

Thank you for your attention
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Re: Thinking about Infinity

Postby Insanity test on Wed Mar 03, 2010 11:57 pm

An end to infinity? That sounds intriguing.

So if sentient knowledge of this number ends the universe and you know it, does that mean you aren't sentient?

Or is the universe in fact constantly being destroyed and re-made because of your ongoing knowledge of such??

I believe it was Hitchhikers which posited that as soon as someone understands the universe it will instantly be destroyed and something much more bewildering and complex will take it's place and that in fact many believed this had already happened. (Excepting of course the theory that this was all dreamt up to increase cosmic uncertainty and sell more copies of the Guide.) Perhaps the universe is therefore constantly being made more and more complex because of your knowledge of Zeronity (which incidentally sounds like it should be a film) which will always be the limit of understanding because of it's position at the end of Infinity meaning that we can never understand the universe because of it's constantly shifting boundaries despite the fact that you already do!! Arrgh my Brain Hurts!!

( :willy: )
--/:Out of cheese Error:/--

Please shutdown Universe and reboot from Start.
Insanity test
Insane Hatter
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