Thread: Probability Theory

Hi All,

In my book , "The Fifth Revolution", (http://realityfound.org) I have written the sentence ...

"Given the right circumstances and raw material and enough “time”, anything that is possible has a probability of happening equal to “ONE.”"

Considering what "is possible" is "the spontaneous appearence of a single living cell", the "right circumstances" are the constant and random mixing and collisions of all possible natural elements, "raw material " is all the natural elements in the right proportions during the early Earth conditions and "eternity" as the amount of time, is this statement correct?

Thanks

Someone correct me if I'm wrong, but a probability of 1 indicates absolute certainty of an event, while the phrase "is possible" does not suggest absolute certainty, and hence will have a probability smaller than 1. Therefore the sentence is wrong, no?

X

Hi evilwill32,

That is exactly what I meant to say. The possibility of life on Earth is absolute because we exist. All I am saying is that if it (anything) is possible and the conditions are right (conducive to the probability happening.); and if the time frame is infinite, then the probability is “1”. No?
At least that is what Hawkins said about us being hit by a comet or meteorite. It is possible and therefore, in time we will be hit.

The time frame for life happening on Earth is not infinite; life on Earth only could (and did) happen between the formation of the Earth and its destruction (by the ageing Sun, or whatever the planet's ultimate fate will be).

Hi,

Earth is not the only planet where life might have formed. We just happened to win the biggest lottery ever.

Yes, I should not have used the term infinity, but we don't know yet what the final fate of the universe will be. Trillions of years, as the latest theories go, is a very long time.

Will someone please address the question "is the probabilty of "anything" that is possible, under "favorable conditions" and 100 trillions of years as a time frame, in fact equal to "1"."

No. The probability of a coin continuing to land on heads is 0, even though it's possible. There are evens that might be expected to happen once in the lifetime of the universe (though I couldn't provide an example) that would have a probability of roughly 1/2.

@ dickroose

Originally Posted by dickroose

The possibility of life on Earth is absolute because we exist.

If by "absolute" you mean "absolutely certain" -(mathematically speaking has probability equal to 1) then this statement contains flawed reasoning. Just because a certain outcome has been fulfilled does not mean that the probability of that outcome happening in the first place has probability 1.

Consider this: The probability of a fair coin landing on heads is 1/2. I flip the coin and it lands on heads. However, this does not imply that the probability of a heads occurring was "absolute" or had probability equal to 1.

Basically, the most we can deduce from the fact that "we exist" is that the probability of life is not equal to 0 i.e. is not an impossible event.

X

Hi evilwill32 and MagiMaster,

MagiMaster:
I believe the probability of a coin landing on heads at any time, even after an infinate number of tosses results in a head, is slightly less than 1/2. The coin could land on its edge.

evilwill32:
I really believe that your example is flawed. With the coin toss the probablity is indeed slightly less than 1/2. But that is only because you have three possible outcomes, (i.e.heads, tails or edge). In the context I am discussing there are only two possible outcomes (i.e. it happens or it doesn't happen. "binary 1/0").

I still believe that since it is possible (the number of possible combinations of all elements in the right portions and in all possible sequences is a numer that can be calculated, hugh as it might be); and given the circumstance and conditions on Earth 3.8 billion years ago; and given the trillions of years the universe will exist in its present form, the probibility of life spontainously being produced at some time, on some planet in the universe is "1". It only takes one cell of a living organism to start the chain of evolution.

It seems to me that this is exactly what Prof Hawkins said about a comet or meteorite hittinng Earth on a PBS Nova Program.

I would really like some Mathematician who is also an expert in Probably theory would jump in here and set us all straight. :-D

Given six events:
- A has a probability of 0 over a finite time
- B has a probability strictly between 0 and 1 over a finite time
- C has a probability of 1 over a finite time
- D has a probability of 0 over an infinite time
- E has a probability strictly between 0 and 1 over an infinite time
- F has a probability of 1 over an infinite time

What can we deduce when we change the time frame?
- A will probably still be 0 over infinite time, but consider an event that can't happen for the first second, but then will happen sometime afterwards. It's probability 0 for that 1 second interval, but not 0 over infinite time.
- B will probably be 1 over infinite time, but only if it might happen infinitely many times. Consider a coin that can only be flipped once. Even over infinite time, it's still only 50/50 that it'll be heads. (The chance of a coin landing on edge is a pointless sidetrack, and can be eliminated anyway. Assume we're talking about an idealized coin.)
- C will still be probability 1 over infinite time, but if we ask anything else, such as what's the probability it'll happen twice, we don't have enough information. It could be anything from 0 to 1.
- D will be 0 over a finite time, but if D was something like "X happens several times", X might still have any probabilty over the same interval.
- E and F could be anything over a finite time. There's not enough information to narrow either down at all.

Note that anything we ask about the real universe won't be over an infinite time, which tends to complicate things a lot.

If you do assume an infinite universe and you assume that each solar system is independent, then "Life evolved on Earth" implies that "Life evolved" is a non-zero probability, it would be safe to assume that life would evolve infinitely many times, but that's a lot of assumptions.

In general, an event with a non-zero probability that has infinitely many independant chances of happening will happen eventually, but again, the real visible universe isn't infinite in either time or space. There are events with a low enough chance that we wouldn't expect them to happen even once within the lifetime of the universe.

such as the probability of all of your subatomic particles dissappearing on earth and reappearing on mars. just thought i'd mention that as an example. even the propability of one of your cells doing that is expected only to happen in two or three times the lifetime of our current universe.

Hi MagiMaster,

If I understand you correctly your “C” reply correctly states the probably of the case I have posed.

In the finite case of life forming one cell by combining all the elements and/or proteins in the precise order and amount required to create one bit of matter with either DNA or RNA capability ...

1. The possibility of life is absolute because we exist.
2. The right circumstances and raw material existed on Earth 3.5 to 4 billion years ago. This mixing and combining of all elements in random sequence and proportions was happening all over the planet, quite possibly producing 100 billion unique combinations every day (I really have no way of knowing the number of unique combinations per day but I am confident it is at least 100 billion daily if you consider that each and every temperature change (i.e. Energy change) anywhere on Earth will probably cause some kind of combination or breakup of some combination.)
3. Now consider that this same process is going on on all the Planets in the universe. We have 100 billion galaxies, each with 100 billion solar systems (i.e. Stars). If we consider that only one planet in 1000,000 has the proper distance from the star, the size, a moon, water and an atmosphere we are still talking about 10^27 unique combinations per day. That is one BIG number!

However since we have no real numbers by which we can calculate the probably and no agreement on what Dr. Hawkins said about the probably of Earth being hit by a comet, meteoroid or asteroid, I shall consider changing my text to read "Given the right circumstances and raw material and enough “time”, anything that is possible has a probability of happening that very closely approaches “ONE.” And for all practical the probably has to be “1” because it happened here on this Earth, if no where else."

The chances of a whole cell suddenly popping into existence, even if all of the elemental components were nearby, is much, much lower than the inverse number of independent chances it has to happen.

Just to show some numbers (though they're made up), if you had 10^25 chances per hour, that'd be about 10^39 chances within the current lifetime of the universe. If the chances of it happening on once was 10^-100, we'd get the chance of it happening at least once so far as: 1 - (1 - 10^-100)^(10^39). That's hard to calculate directly, but we can change things around a bit to get: 1 - ((1 - 10^-100)^(10^100))^(10^-61). That simplifies to 1 - (1/e)^(10^-61).

Roughly speaking, there are about 61 zeros in front of that chance, so even a difference of a few orders of magnitude in those numbers makes a huge difference in the final chances. While you can argue that the first number is low, I doubt it's 60 orders of magnitude too low, and I suspect that the second number is probably way too high anyway (10^-1000 seems more reasonable).

Where did you get that number?

Originally Posted by MagiMaster

Just to show some numbers (though they're made up)

...

While you can argue that the first number is low, I doubt it's 60 orders of magnitude too low, and I suspect that the second number is probably way too high anyway (10^-1000 seems more reasonable).

10^-100 does mean "." followed by 100 numbers. An amazing small number if the numbers are leading "0's".

It may be an amazingly small number, but I don't think it's as amazingly small as the chance of a single-celled organism spontaneously coming together.

Hi,

I think I understand the problem we are having in communicating. But you would need to read my book in order to understand the problem too.

If you think you can explain the problem better on here, go ahead and try. I don't have enough time or interest to read your book.

Aside from that, I showed how even a few differences in the order of magnitude of those numbers would make a huge difference in final probability. Can you show that the order of magnitude of those two numbers aren't different?