Can monkeys type

[maxg]

5*10^813 is quite a big number; so big, in fact, there is nothing physical that comes anywhere near it:

Attempt one - age of universe in seconds.

If the big bang theorist are right the earth is about 12,500,000,000 years old.

That is about 4 * 10^17 seconds. Minute in comparison.

OK - lets try something else:

Attempt two - weight of earth - in multiples of the electron

The Earth weighs about 6 * 10^24 Kilograms. An electron weighs about 9 * 10^-31 Kg.

The earth therefore weighs in at about 5.4 * 10^56 electron masses.

Still minute in comparison. Replace the earth with the whole universe - that is about 1 * 10^60 kilograms (very estimated).

In electrons then - 9 * 10^121 electron masses. Still not the tiniest fraction of the number we have in the example.

So here is a question for you

Let us forget the monkey idea - and teach electrons to type. Lets assume that the universe is about half way through its life - so we have another 12.5 billion years to go. We will call this number the rest of time (4 * 10^17 seconds).

Lets assume my mass number of the universe in electron units (9 * 10^121) is the actual total of electrons in the universe.

As discussed recently in a thread in 2 channel - electrons move really quickly down a wire - so lets assume they type in similar fashion. One go per seond.

Now - what is the probability that an electron will actually type the original sonnet before the end of time?

If you cant be bothered to calculate it yourself - trust me - it is still infinitesimally small.

Yup - 5*10^813 is a bigun' alrighty - it so big it dont really exist in this universe.

[fini]

Max,

I've heard scientists use the term, "type of charged particle" before, so maybe you're on to something...

[Ray Garrison]

5*10^813 is quite a big number; so big, in fact, there is nothing physical that comes anywhere near it:

Attempt one - age of universe in seconds.

If the big bang theorist are right the earth is about 12,500,000,000 years old.

That is about 4 * 10^17 seconds. Minute in comparison.

OK - lets try something else:

Attempt two - weight of earth - in multiples of the electron

The Earth weighs about 6 * 10^24 Kilograms. An electron weighs about 9 * 10^-31 Kg.

The earth therefore weighs in at about 5.4 * 10^56 electron masses.

Still minute in comparison. Replace the earth with the whole universe - that is about 1 * 10^60 kilograms (very estimated).

In electrons then - 9 * 10^121 electron masses. Still not the tiniest fraction of the number we have in the example.

So here is a question for you

Let us forget the monkey idea - and teach electrons to type. Lets assume that the universe is about half way through its life - so we have another 12.5 billion years to go. We will call this number the rest of time (4 * 10^17 seconds).

Lets assume my mass number of the universe in electron units (9 * 10^121) is the actual total of electrons in the universe.

As discussed recently in a thread in 2 channel - electrons move really quickly down a wire - so lets assume they type in similar fashion. One go per seond.

Now - what is the probability that an electron will actually type the original sonnet before the end of time?

If you cant be bothered to calculate it yourself - trust me - it is still infinitesimally small.

Yup - 5*10^813 is a bigun' alrighty - it so big it dont really exist in this universe.

Hi Max.

Really, really big numbers are one of the things that amuse and interest me, particularly after a couple of glasses of Merlot. I thought I'd get more raised eyebrows from the monkey typing example than I did - you're the first to point out just how big a number that really is.

If you want another interesting example, go back to the JPEG example (summed up as "How many different images can be encoded in an 8 bit color JPEG measuring 640 X 480?"). The answer, of course, is 2 to the 8th to the (640 times 480)th, or to put it another way, 256 to the 307200th. Which is, uh, rather a large number. How big? Well, here's an interesting thought experiment for you. Each pixel requires 8 bits. Hummm... Oxygen atoms have 8 electrons. Suppose we could use Oxygen atoms to store the state of each pixel. Electrons spinning one way are 0 bits, spinning the other way are 1 bits. We have a big cloud of monatomic Oxygen gas (and no open flame sources nearby.) How big a volume of gas would be required, at STP so each mole of gas takes up 22.4 liters, would be need to encode every possible variation of a little JPEG? That is, (256 to the 307200th) divided by (6.02 times 10 to the 23rd) times 22.4 equals number of liters. How does that compare to the size of the observable universe, figuring a spherical volume roughly 15 billion light years in radius - and don't get to wrapped up with curvature of space time, open vs closed space, etc.?

Even that's not a *REALLY* big number. I was reading a book about the inflationary theory of the Universe, and saw a conversation with Alan H. Guth in which he refered to one theory that indicated the true size of the universe might be Ten to the (Ten to the Twelth) - 10 ^ (10 ^ 12) - across. Someone asked him what units he was talking about - meters, centimeters, kilometers, angstroms, what? - and he responded it doesn't matter. When the number is *THAT* big, the units don't really mean very much.

Have fun...

[maxg]

"Even that's not a *REALLY* big number. I was reading a book about the inflationary theory of the Universe, and saw a conversation with Alan H. Guth in which he refered to one theory that indicated the true size of the universe might be Ten to the (Ten to the Twelth) - 10 ^ (10 ^ 12) - across. "

You know - I don think that figure can be right if the big bang/crunch apply.

I happened to have provided an estimate of the age of the universe in seconds - 4 * 10^17

Now if we assume the universe started from a point source is has therefore been expanding at an astronomical pace to get to the size it is today. When I say astronomical we are talking about way faster than the speed of light.

In other words the universe should be something in the region of 12.5 billion light years across:

(12.5 * 10^9) * 365 * 24 * 60 * 60 * 300,000 = 3.6 * 10^30 kilometers.

It is a big place - but t'aint that big!

(I should add that within the theory of the expansion of space/time itself there is an allowance for an initial expansion outside of time and therefore unregulated by the speed of light limit - but no estimation as to the effect of this has produced a "time start point" sufficiently pre-expanded to get to the size he estimates - at least none that I have seen.)

Of course - I am not going to argue with Alan Guth on this - but how on earth does he get to that figure?

[Ray Garrison]

as the other 9,999 members of the forum roll their eyes and go back to listening to Radiohead...

I'll try to find the reference to the Guth quote. Simply trying to wrap my head around how big a number ten to the trillionth is proves, uh, frustrating.

Keep in mind the the limit of c as the fastest possible velocity only applies to things moving *within* space - time, not the expansion of space - time itself. Going back to the overworked analogy of the universe as expanding balloon with the stars and galaxies on the ballon's surface - saying that c is the maximum velocity with which anything can move through the latex forming the surface of the balloon has no bearing on how fast we can inflate the balloon. Or to look at it another way, if the maximum velocity with which an electromagnetic force can propogate through a wire is X, that doesn't mean that we can't draw the wire through a die at some multiple of X.

[maxg]

Agreed Ray (other 9,999 members in danger of approaching coma but anyway).

I refered to this as an initial expansion period after which space/time is established and the speed of light as a reference cuts in.

From all references I have seen space/time is presumed to be a closed system - so no pulling of wires through it.

We are therefore left with the question of initial expansion prior to the establishment of the universe's own physical rules governing its behaviour (i.e. space/time).

I have simply never seen a estimate sufficient to make up the difference between the perceived limit - (t * c) and the figure you quoted.

Of course - local expansions of space time are going to be possible within the fabric of the universe - but in theory these should be at the expense of contraction in other places - so no net gain.

On the subject of the big numbers that started this - I think that what we are basically proving is that there isnt anything that closes in on statistical probabilities of unlikely events for real biggies.

Anything over about 10^30 is gonna have real limited meaning in the real world - although I seem to recall the moves on a chessboard add up to about 10^64 - so lets call it 10^100 as a real practical limit.

Your number of 10^(800 and something) is just too out there to be even fathomable. It exists purely as a mathematical expression of probability and nothing more.

[DrWho]

To make a long story short, if you have only a finite number of outcomes and you take an infinite number of trials, you will end up getting the outcome you are looking for.

I don't think limiting the number of characters the monkeys type is valid - they should have to choose when they stop typing. And in that situation there are an infinite number of outcomes. []

That said, I don't think I could even type out all of Shakespeare's work...especially from memory. It should take a lot less time if the monkey's had the sonnett sitting in front of them.

[pauln]

The number of purmutations of human DNA is estimated to be about 10¹²⁵.

Now if large numbers like 100 to the 100th to the 100th to the 100th power seem to have an illusory existence (and likewise for real small numbers including zero (see below)), what about the middle range we are more confortable with like 4, -3 and 9? You know that for all the great mathematics done in the last five years, negative numbers where only accepted in the 1930's... some still don't accept them.

By the way, is anyone disturbed by the stangeness of zero?:

0^x = 0 for any positive x, so as x gets very close to zero it seems to indicate that 0⁰ should be zero. But x⁰ = 1 for any x that is not zero so as x gets close to zero it seems reasonable to say 0⁰ is one. 0⁰ is undefined.

0!=1 , 1!=1 both one factorial and zero factorial equal one...

n n!<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

0 1

1 1

2 2

3 6

4 24

5 120

6 720

7 5040

8 40320

9 362880

10 3628800

15 1307674368000

20 2432902008176640000

70 1.19785717... × 10¹⁰⁰

[r.cherry]

really, i swear you folks crack me up in here...