Life in the Universe and the Infinite Monkey Theorum

[The Doctor]

I used to argue every lesson with my RE teacher about there being life on other planets. (It was a good way of not having to do any actual work)

A good argument I came up with is the infinite monkey theorum:

Basically, if you have an infinite number of monkeys sitting at an infinite number of typewriters they will eventually type of the complete works of Shakespeare.

It'll probably take an infinite amount of time but it sould work.

It's fair to assume the size of the universe if infinite, therefore if you look for long enough you must find life.

Is this a good comparison?

[Bluevision]

Problem: The Universe isn't infinite. It may be very big, but it stops... somewhere.

But the good news is that I'd fathom to guess there's a higher probability of a planet giving birth to life than that a monkey's gonna write all of Shakespere's works! The concept of the theory works. Given enough chances, something's going to happen.

[Moose]

Well, all the infinite monkeys theorem really does is prove that the probability of it happening is non-zero, assuming truly random string generation. Given sufficient randomness, the probability is minuscule, but it's there all the same. Wikipedia has a pretty good article on it here.

The other problem with your idea is that the probability of finding life in the universe is 1. We've already found some. Us.

Think of it this way: James Randi is going to try and guess your card from a standard 52-card deck. What's the probability of him guessing your card? 1. This is because he's performing a trick. There's no randomness involved.

Before we can begin to make valid wild-guesses about probabilities, we need a better understanding of which variables are relevant, how relevant they are, and which ones (if any) are random.

[Otherworldly]

I used to argue every lesson with my RE teacher about there being life on other planets. (It was a good way of not having to do any actual work)

A good argument I came up with is the infinite monkey theorum:

Basically, if you have an infinite number of monkeys sitting at an infinite number of typewriters they will eventually type of the complete works of Shakespeare.

It'll probably take an infinite amount of time but it sould work.

It's fair to assume the size of the universe if infinite, therefore if you look for long enough you must find life.

Is this a good comparison?

I prefer to think of these things in terms of limits, which is more precise; an "infinite number" isn't really rigorous.

But, if the probability that one monkey will type the complete works of Shakespeare within a given amount of time is p, then the probability that at least one monkey out of N will do so is 1-(1-p)^N (provided the monkeys are working independently). As N approaches infinity, as long as p>0, the probability above goes to one. The value of p affects how fast the limit goes to one, but it does approach one for any p>0.

If the probability of life arising within a given volume of space is p, and the universe consists of N such units, then the probability of life existing somewhere is 1-(1-p)^N. The key assumption here is that occurrence of life in one region of space is independent of occurrence of life in another region of space. If that's the case, then as N goes to infinity, the probability of life goes to one.

So I would say you are OK with your idea, with a few implicit assumptions. But it says nothing about how frequent life would be; the average distance between life-bearing planets might be 10^{10100,000,000,000} light years, for example.

Well, all the infinite monkeys theorem really does is prove that the probability of it happening is non-zero, assuming truly random string generation.

The infinite monkeys theorem asserts that the probability goes to one. If all you want is non-zero probability, you only need one monkey.

The other problem with your idea is that the probability of finding life in the universe is 1. We've already found some. Us.

I suspect the OP means besides earth-bound life.

Before we can begin to make valid wild-guesses about probabilities, we need a better understanding of which variables are relevant, how relevant they are, and which ones (if any) are random.

You can always make guesses, they just might not be very accurate. But I think the basic idea of the OP is correct; if the universe is infinite, if the probability of life occurring within each volume of space is some positive number, and occurrence of life in different volumes of space is independent, then the probability of life occurring somewhere is one. That holds even if you exclude earth-bound life. If you want to move beyond that and say something about how densely life occurs, then you need to know some numbers. But if you just want to establish existence of life somewhere with probability one (again, excluding earth) and you have an infinite universe to work with, then you don't need to know the probability. Just that it's greater than zero.

[Gomar]

Think of it this way: James Randi is going to try and guess your card from a standard 52-card deck. What's the probability of him guessing your card? 1. This is because he's performing a trick. There's no randomness involved.

Hold on. Probability of a magician of guessing your card, whether in a theater in Vegas or on the street in Times Square is 1/52. Why? Because you picked just 1 card out of 52.
Now we must consider how many guesses or tries the magician has. If he has 52 tries, then 100%; if he has only one guess then it's 1/52 (unless some trickery is involved).
Let's say a hacker is trying to guess my password. He knows my pw is 128bits, which is 16bytes(characters). Using numbers, alpha lower&upper case, and an infinite number of guesses, it should take the hacker 10,000 years to get it right.

[Otherworldly]

Hold on. Probability of a magician of guessing your card, whether in a theater in Vegas or on the street in Times Square is 1/52. Why? Because you picked just 1 card out of 52.
Now we must consider how many guesses or tries the magician has. If he has 52 tries, then 100%; if he has only one guess then it's 1/52 (unless some trickery is involved).

I think the assumption there was that there was trickery involved.

Let's say a hacker is trying to guess my password. He knows my pw is 128bits, which is 16bytes(characters). Using numbers, alpha lower&upper case, and an infinite number of guesses, it should take the hacker 10,000 years to get it right.

Unless I've miscalculated, that is one fast hacker.

[swampyankee]

Hold on. Probability of a magician of guessing your card, whether in a theater in Vegas or on the street in Times Square is 1/52. Why? Because you picked just 1 card out of 52.
Now we must consider how many guesses or tries the magician has. If he has 52 tries, then 100%; if he has only one guess then it's 1/52 (unless some trickery is involved).
Let's say a hacker is trying to guess my password. He knows my pw is 128bits, which is 16bytes(characters). Using numbers, alpha lower&upper case, and an infinite number of guesses, it should take the hacker 10,000 years to get it right.

One of the things crackers rely upon is that people usually pick words that are in a dictionary for their passwords.

[Moose]

Hold on. Probability of a magician of guessing your card, whether in a theater in Vegas or on the street in Times Square is 1/52. Why? Because you picked just 1 card out of 52.

Never, but never play 3-Card Monty, Gomar.

[Moose]

The infinite monkeys theorem asserts that the probability goes to one. If all you want is non-zero probability, you only need one monkey.

Yes, but this assumes infinite trials, infinite time, and in the OP's idea, an infinite universe. Outside of mathematics, each has to be proven individually before you can apply "infinite monkeys" to reality.

I suspect the OP means besides earth-bound life.

I know he does. That wasn't my point. To assign a probability, there has to be randomness. We simply don't have enough data to understand the randomness. Oh, there appears to be a significant random component in our own species' lineage (mutation), but it's not fully random (natural selection).

Non-randomness means the probability is weighted based on criteria we don't yet understand. We simply can't make reasonable assumptions under those conditions.

Gomar, for example, believes that there is randomness in a "pick my card" scenario being offered by a stage magician. I assert with considerable confidence that there is no randomness whatsoever to be found in that event.

You can always make guesses, they just might not be very accurate.

Key word being "valid". I distinguish between reasoned speculation and fantasy guessing.

[Gomar]

Unless I've miscalculated, that is one fast hacker.

Ye, I guess m5n3Gh4HdD8rHn1Y would take about 1million years to try out... even if you had an infinite amount of time.

[Otherworldly]

Yes, but this assumes infinite trials, infinite time, and in the OP's idea, an infinite universe. Outside of mathematics, each has to be proven individually before you can apply "infinite monkeys" to reality.

OK, let's have a look at what you wrote:

Well, all the infinite monkeys theorem really does is prove that the probability of it happening is non-zero, assuming truly random string generation.

The "assuming truly random string generation" makes it pretty clear that you are referring to the monkeys typing Shakespeare scenario, not the life-in-space scenario. And your characterization of the infinite monkeys theorem is not correct - it asserts that the probability is one, not only that it is non-zero.

Back to your more recent quote:

Yes, but this assumes infinite trials, infinite time, and in the OP's idea, an infinite universe. Outside of mathematics, each has to be proven individually before you can apply "infinite monkeys" to reality.

No, it most definitely does not assume infinite time. The OP did assume an infinite universe, and each region within that infinite universe is a trial, if occurrence of life in each region is independent of occurrence of life in each other region (this latter assumption is much stronger than necessary). Infinite time is not needed. If you think one or both of these conditions do not apply, that's fine, and for all I know, you may be right. But if the infinite monkey theorem does not apply, that does not mean that the infinite monkey theorem says something different than what it says. You even quoted the assumption in the post I commented on, immediately after the incorrect characterization of the conclusion of the theorem.

I know he does. That wasn't my point. To assign a probability, there has to be randomness. We simply don't have enough data to understand the randomness. Oh, there appears to be a significant random component in our own species' lineage (mutation), but it's not fully random (natural selection).

Non-randomness means the probability is weighted based on criteria we don't yet understand. We simply can't make reasonable assumptions under those conditions.

The usual definition of non-random would mean deterministic. There are some philosophical differences out there about what probabilities really mean, but I can't say I've ever before heard someone define non-random to mean that you don't know the probability distribution of a random event.

The notion of conditional probabilities is extremely well developed in probability theory. The unconditional probability distribution of something is <some set of numbers>; if you learn more, then the new probability distribution (conditional on what you now know) is <some different set of numbers>. This idea is used all the time in, for example, stochastic processes; the probability of the different outcomes are continually revised as the process evolves. That doesn't mean the process is "non-random".

Key word being "valid". I distinguish between reasoned speculation and fantasy guessing.

I think you need to distinguish between arguments that invalidate the OP's point, and arguments that do not invalidate it.

The OP made one assumption explicitly, and another implicitly. The explicit assumption was that the universe was infinite. I can state various versions of the implicit assumption that get the conclusion, but one of them would be, the probability of life occurring within a given volume of space is greater than zero, and independent of the probability of life occurring within a different volume of space. (Much stronger than necessary.) Under these two assumptions, the infinite monkey theorem applies. It does not matter what the probability is (only that it is non-zero), and it does not matter whether you know the probability or not. If, based on very best knowledge of the distribution of matter in the universe and the processes which generate life, the probability of life occurring within each volume of X cubic light years of space is 10^-25, then the infinite monkey theorem applies (again, the infinite universe assumption is needed). If tomorrow, we learn more about the universe and the way life develops, and revise our probability to either 0.999999999999999999999999999999999999999999999999 999 or to 10^{-1,000,000,000,000,000,000,000,000,000}, the infinite monkey theorem still applies (once again, the infinite universe assumption is needed).

If you want to invalidate the OP's argument, you need to invalidate one of the assumptions on which it rests. If the universe is finite, that does it. Saying, "but we don't know what the probability of life is!" doesn't do it, because the argument does not rest on a specific value of the probability of life, only on it being positive. And your characterization of what the infinite monkey theorem says is simply wrong - it produces a probability of one, not a non-zero probability.

[astromark]

I would look at what 'Moose' has said... hes right,. I would add that you also know that no amount of monkeys in any amount of time is ever ( thats infinity ) going to write the entire works of anyone... I will get slaughtered because my infinite time is in fact finite. Just 13.7 billion years. You are not going to get a single line... Yes we all assume the obvious fact. Life is here a case study of 1. Is it any place else ? Yes I would think rife...
Will we ever find it... Just after the monkey writes The Bard...

[manxman]

http://www.bbc.co.uk/iplayer/episode...ty_and_Beyond/


this program from a few hours ago answers alot of questions about very large numbers.

to count to a billion would take 30 years to count from 1 to 1 trillion would take longer than humans have been in existance.

the odds of the monkey typing the complete works of the bard are the same as winning the national lottery every week for 29,000 years in a row.

infinity is an area that would/will drive you mental.

[cosmocrazy]

Problem: The Universe isn't infinite. It may be very big, but it stops... somewhere..

This isn't necessarily true, we don't know whether its finite or not.

But the good news is that I'd fathom to guess there's a higher probability of a planet giving birth to life than that a monkey's gonna write all of Shakespeare's works! The concept of the theory works. Given enough chances, something's going to happen.

agreed

[manxman]

it cannot be anything else but infinite.

whats the alternative..?? what else is there after space otherwise.

[Moose]

Infinite time is not needed.

No, it isn't. In fact, only one of infinite monkeys, infinite time, or infinite trials is required to mathematically produce a probability of 1.

Infinity, however, is a mathematical construct. There are no infinite monkeys, nor infinite time in the real world. If you wish to argue there are infinite monkeys or infinite time in the real world, I await your evidence.

If you want to invalidate the OP's argument, you need to invalidate one of the assumptions on which it rests.

No. The OP would "need" to establish, if he were of a mind to make the assertions you've just made, that his assumptions are true. I don't "need" to do a thing.

The usual definition of non-random would mean deterministic.

And your interpretation would be a straw man of what I've said. It's not entirely deterministic. It's not entirely random either. Which means you cannot treat the real world like an exercise where it is entirely deterministic nor entirely random.

[Moose]

it cannot be anything else but infinite.

Why not? Humans have had failures of imagination in the past. Why not simply reserve judgment until we're in a position to know?

[manxman]

because i havent got several trillion years in me moose.

altho my atoms have i think or am i wrong on that.

i must admit i am finding alot of the material here extremely thought provoking as it subject matter that i never really gave full consideration too.

im a janes defence man from way back in my 20s and early 30s had a stack 5 ft high.

[Moose]

because i havent got several trillion years in me moose.

True enough, we may never know for sure.

But we can't assume an infinite supply of environments (and/or an infinite amount of time) to justify using a mathematical theorem (that only works as advertised if you assume at least one prerequisite component is infinite) in order to conclude that there is definitely non-us life out there.

One is allowed to make assumptions in math, but sooner or later, one has to come back and justify them. This hasn't been done.

[manxman]

i revert back to my thinking about infinity will drive you mental quote moose.

but to be fair i am trying to mentally file it all in some kind of order for future reference.

[Certassar]

Basically, if you have an infinite number of monkeys sitting at an infinite number of typewriters they will eventually type of the complete works of Shakespeare.

I'd say that the Internet pretty much disproves that theorem.

[cosmocrazy]

I'd say that the Internet pretty much disproves that theorem.

good call!

[cosmocrazy]

i revert back to my thinking about infinity will drive you mental quote moose.

but to be fair i am trying to mentally file it all in some kind of order for future reference.

The problem is we are not mentally capable of imagining infinity in a physical form.

[Moose]

I'd say that the Internet pretty much disproves that theorem.

[Cougar]

i havent got several trillion years in me moose... altho my atoms have i think or am i wrong on that.

Most attempts at a Grand Unified Theory strongly suggest that even protons decay, albeit with a very, very long half-life. However, decades of careful experimentation on billions of trillions of protons have yet to detect one decaying.

[Jens]

it cannot be anything else but infinite.

One poster has stated it is finite. You have stated it is infinite.

I would take a position in between: we really don't know. The big bang seems to indicate it is finite.

You ask how it could be finite? Just as an example, imagine that if you keep going far enough in one direction, you come back to where you are. . . In that case, there is nothing outside of it, and yet it is not infinite. Strange? Yes. But we cannot a priori dismiss that possibility.

[Murphy]

One poster has stated it is finite. You have stated it is infinite.

I would take a position in between...

What exactly is in between Infinite and Finite? I don't think that makes sense mathematically, like asking what is half of infinity...

[Jens]

What exactly is in between Infinite and Finite? I don't think that makes sense mathematically, like asking what is half of infinity...

Sorry, I meant "an agnostic position." In the sense of not being willing to make a categorical statement one way or the other.

[tnjrp]

I would take a position in between: we really don't know

This is correct, of course, but...

The big bang seems to indicate it is finite

...this isn't. AFAIK.

The evidence for the so-called Big Bang model indicates that the current state of the observable universe had a begining within a finite span of time, but it doesn't really conclusively and certainly tell us if there was or was not something before that nor yet does it proscribe a spatially finite universe.

While it might be a very long shot to assume information has passed through the Big Bang event or will survive indefinitely into the future -- so no infinite time, really -- it isn't overruled that we exist in a Tegmark level 1 multiverse -- which will give us infinite monkeys.

It's another thing of course that most of those "monkeys" probably will never be able to send us any of their "versions of Shakespeare's works" since they won't be able to causally interact with us.

[Jens]

The evidence for the so-called Big Bang model indicates that the current state of the observable universe had a begining within a finite span of time, but it doesn't really conclusively and certainly tell us if there was or was not something before that nor yet does it proscribe a spatially finite universe.

This is always a bit of a puzzle for me. I may be relying on old information, but I used to have a book written by a sort of non-mainstream cosmologist named Eric Lerner, that was called "the big bang never happened". And he was basically arguing, IIRC, that the big bang was sort of a "local event." And my interpretation of The History of Time is that Hawkins was arguing that space itself was created with the big bang, and didn't exist before it.