# Is the probability of an event that's happened meaningful?

I once got into an argument about the formation of life on Earth. My opponent calculated the odds of life evolving from chemical precursors given the estimated amount of time. (It was some fantastically small number). I replied that if I were to shuffle a deck of cards and lay them out one at a time, the odds of getting the order that I got would be 1:54!, which was considerably smaller than his number.
He accepted it, but upon reflection, I’m not sure if I do. So, do the odds of life evolving naturally in the given span of time mean less, more, or the same as the odds of laying out a deck of cards?

No matter how infinitessimal the odds could be, we wouldn’t be here to discuss it if they didn’t work out. Think of it this way: what are the odds that the exact sperm and egg cells from your parents are the ones that fused, and not some other pairing? What are the odds of your parents ever even meeting eachother in the first place, given all the chance circumstances involved in one’s life? You could calculate those odds to be amazingly slim, and yet here you are, and with that exact combination of DNA.

If small odds lead you to think there was some kind of predestination involved in creating life on Earth, would you not also believe that your own existence is also predestined, due to similarly small odds?
Someone else will come around explain this a lot better than I can, I’m sure…

It makes no sense to talk about the probability of an event that has already happened. Richard Feynman gave the classic rebuttal of this kind of reasoning. He mentioned that he had seen a car with the license plate ANZ912 on his way to the lecture, and asked what the odds of that were (obviously infinitesimal).

To expand on that, what he was really asking is, “What would someone have calculated the probability of seeing license plate ANZ912 to be before it actually happened?” This is a distinctly different question from asking what the probability would have been calculated to be once the license plate was seen, which is one. (To see why it’s one, consider what the right probability to assign to the license-plate viewing would be if you wanted to calculate the odds that Feynman not only saw ANZ912 on the way to the lecture, but also will see ANZ913 on the way home. Since the first event already happened, the odds of the compound event are the same as the odds of the viewing of ANZ913 alone, so the first part of the compound event must have a probability of one.)

Another way of saying it is that the odds of anything in particular happening are infinitesimal, whereas the odds of something happening are one, simply because there are so many alternative outcomes.

You mean 52!, right?

Probability can only be understand in the sense of repeating a process from the same starting point with the same relevant conditions many times and seeing what happens. In your deck example, you are claiming that if you repeated the same shuffling process an enormous amount of times, the probability of any of those resulting in that outcome is 1/52!. Now you can shuffle a deck many times. It makes sense there. You can’t redo history many times. Just once. So the notion of probability doesn’t apply.

…on the other hand, it doesn’t really apply to deck shuffling either, if you are in the real world. If we could really track your exact muscle movements, it would be easy to replicate what you did the first time. In fact, the physical deck of cards is really just a stand in for the mathematical idea of randomness, and our ignorance of what is happening at the fine muscular level.

So to say the probability of life appearing out of those chemicals is pointless, unless it’s further specified. What he probably means is, given such and such a batch of chemicals in such and such conditions with so much time and random interactions between the chemicals… if we were hypothetically able to replicate those circumstances many times, we would be able to see from the outcomes that life comes out of that very rarely. Thus, he claims the probability is low. The weakness in this claim is that it is very dependent on the model used. IMO, the interactions aren’t random, the time is usually understimated, and the anthropic prinicple is not appreciated.

I’ll stop there.

The probability of an event in the past that is known to have happened is 1. The probability of an event in the past that is not to have happened is 0. Whether or not this is sensible, it often helps with calculations.

Not if he leaves the jokers in the deck.

Slight nitpick: the probability is 1/54!. The odds are 1:(54! - 1). Remember, odds of 1:2 means a probability of 1/3.

The signficance or importance of an event is not part of the external world. The meaning isn’t in the event itself, but in the meaning our minds ascribe to it.

Also, unless we are talking about a game of chance or a lay of cards, and assume the activity which leads to result occurred, limits of human knowledge kick in.

If a particular event occurs, we don’t know all the events that had to take place prior to its occurance, and we don’t have much of an idea the probability of those prior causes were either.

Fucking smilies.

Maybe he left that “How to play poker” card in there too.

–Cliffy

Yes and no:

The best argument that the probability of this particular event (life begins on earth) isn’t meaningful is the anthropic principle (previously mentioned by muttrox).

On the other hand, even a sample of 1 (the number of earth-like planets we have studied so far) can tell us many things about our theories. Since we know that life began on earth at some point in the past, we can test hypotheses (regarding the composition of earth’s primordial seas) against this knowledge.

If, for example, we hypothesize that earth’s primordial seas had a very low pH, we could reject it on the basis that this composition would strongly inhibit the formation of amino acids necessary for the existance of life as we know it.

Alternately, we may find another hypothesis more appealing if it is consistent with other known facts and it suggests a mechanism that encouraged amino acids and other compounds to form (by the chemical composition, temperature, and other parameters it suggests). We may also prefer a hypothesis which suggests a higher probability of life forming and pursue it more vigorously.

When your friend calculated his probability, what method did he use? What, exactly did he calculate? Surely he does not posess complete knowledge of earth’s primordial chemistry, or of the earth’s first pseudo lifeforms, so I would consider the possibility that he had calculated the probability incorrectly.

a little nitpick-

Hyperelastic wrote:

Actually, since he saw the plate just a few hours before in the same general area the odds are much better that he will see it on the way home then that he would have seen it at all, originally.

How one would figure the odds on this, I haven’t a clue.

Well, that is useful for arguing about which theory is correct. “Life got started somehow” is indisputable. However, “Life got started because a random group of molecules floating in the ocean happened to arrange themselves in such a way to spontaneously form a bacterium-like organism” is not quite so indisputable. A probability based arguement would be most useful if it were possible to calculate the probability of a competing theory, but it can point out potential weaknesses if the odds are very low.

Good question. The answer is no. Probablity is only useful when talking about events that haven’t happened yet.

Think about rolling a die. The probability of getting a 6 is 1/6. But when you actually roll it, its location is determined by the angle and strength that you throw it, and the properties of the die and surface it lands on. If at the point its in the air you said the chances were still 1/6, you’d be wrong.

My answer would be, as always, it depends what you mean

Suppose I’ve just tossed a coin, and ask what is the probability it’s heads. That could mean “1/2” for a theoretical coin, nearly 1/2, for a real coin, or either 0 or 1 but you don’t know which, given what actually happened. These are all valid questions to ask, but the which the phrase “the probability it’s heads” means depends on context.

The same for life on earth. IMHO it’s a semantic point - you’re using the phrase in slightly different ways and answered your own questions accurately.

Apologies for the offtopic, but…

I’d never even thought that other countries would have different playing cards. Makes sense, I guess. In the UK, the extra card is one that tells you the rules to Bridge. (I think; I don’t play the game). That’ll make a good quiz question, asking what the US have instead…(I assume you are from the USA?)

I’m not sure it’s quite that clear-cut. I’m sure I’ve seen non-bridge inserts (and definately no rules insert) in packs in UK, though I don’t have a pack handy to make sure, though the bridge one does seem common. Is the poker card universal or just common in the US?

I’m reminded of a joke ending “…and I had a rules of draw and stud poker high!”

To which should probably be added “but which are believed to be similar to events that have occurred.”

In Science & Creationism it is argued that this probability is vanishingly close to one, and it is also pointed out that there are life forms in Yellowstone, IIRC, that sprung into existence independent of other life on Earth. My copy is buried, so I can’t give you a specific reference–just the book to go to.

Another problem your opponent has is question begging. He’s saying that out of all the possible outcomes, the fact that this one obtained implies that there is a god who wanted it so. How do we know that this conclusion is good? Because we’re special. Poorly stated indeed, but I hope the idea comes across; he needs the a priori assumption that we are special to draw the conclusion that god must have wanted us, because the mere fact that some particular outcome obtained does not, in and of itself, imply that there is anything special about it.

Consider the cards you’ve dealt. Does that particular order of the deal imply that god intervened and made it so? Why would it? Why would we think that god would intervene in the shuffling of a deck? We wouldn’t. But if god wouldn’t intervene in the shuffling of a deck, why would she intervene in the bubbling stew of pre-life Earth? Because we’re special! Much more special than the dealing of a deck of cards! Why are we more special than a deck of cards? Until your opponent explains that, he’s just making a huge leap that is totally unjustified.

Now, if you’re feeling mean, you can point out that given the poor design of humans, e.g. bipedal locomotion on a quadrapedal frame and all the problems that causes, and given that the most massive order in the animal kingdom is the beetle, a wonderfully diverse collection of highly adapted little miracles, the safest conclusion is that god really loves beetles and only made us on a lark. Seriously, can we conclude anything than god’s inordinate fondness for beetles.