The Inevitability of Improbability



Some ID proponents claim that improbable events need a special explanation other than ordinary, run of the mill processes. This simply isn’t true, and is in part due to common biases in human intuition.

The reality is that extremely improbable events are inevitable. Improbable events must happen because time is moving forward. In many systems there are nearly an infinite number of possible outcomes that could occur, and one of those outcomes MUST occur as time moves forward. It is a bit like Schroedinger’s cat. The cat has to be alive or dead when the box is opened. A result must occur.

The same logic applies to genetics and evolution. There are nearly infinite possible evolutionary pathways that could occur, and due to the arrow of time some of those pathways must occur. Of the nearly infinite number of possible functional sequences that could evolve, it is inevitable that one of those extremely improbable functional sequences will evolve. For example, it has been estimated that there are 2.3 x 10^93 possible functional sequences for cytochrome c (reference), and that is just for the specific cytochrome c isoform we are familiar with. That calculation doesn’t take into account the possibility that there are other proteins with very different protein structures that could still have function equivalent to known cytochrome c. Of those numerous possible functional sequences we only see a tiny, tiny fraction in actual species.

We could also use the lottery to help illustrate the inevitability of improbability. In our example, the chances of winning the lottery is 1 in 100 million. There are exactly 100 million tickets sold in each drawing, and every drawing has a single winner. The last 5 winners are John, Susan, Sam, Leslie, and Stephanie. I think most people would say that you will inevitably have winners in a lottery when enough tickets are sold, but the results are still extremely improbable. The chances of those 5 specific people winning is 1 in 100 million to the 5th power, or 1 x 10^40. Do we need a separate mechanism to explain why some people lost and others won? No. So why would we think that a beneficial mutation needs a difference explanation than a neutral or detrimental mutation?

There is also a different lesson in all of this. We can learn a lot about how very natural human biases can affect our understanding of probabilities. We humans tend to put more importance on good occurrences than bad or inconsequential occurrences. Gambling addiction is often fed by this same tendcy where addicts will only remember the big jackpots and not all of the losses. Due to this asymmetry, we often think that good and bad things are somehow different from each other, but they are often the product of the same process. The simple fact is that the probability of an event that has already occurred is 1 in 1, because it happened.

(S. Joshua Swamidass) split this topic #2

A post was split to a new topic: Falter: Every Birth is a Statistical Impossibility


I am confused by this statement. I would think that if they are inevitable, then they are not improbable.


You would be wrong, as shown by the lottery example.

(Herculean Skeptic) #5

Are you saying that “extremely improbable events are inevitable” or “it is inevitable that even extremely improbable events will sometimes occur?”


It is related. The improbability of family trees is a perfect example of what I am talking about. In fact, the improbabilities ramp up even greater in that example if we include genetics. What are the chances that a specific sperm cell out of billions would win out? In that sperm cell, what are the chances that cross-over events happened at specific spots on the arms of paired chromosomes, and what are the chances the 100 or so mutations that are found in each gamete would happen at those precise locations?

(Timothy Horton) #7

Consider a lottery with possible winning numbers 000000 to 999999. It all one million tickets are sold (one for each possible number) it is inevitable one ticket will win. It is improbable any specific ticket will win.

(Bill Cole) #8

You are correct in saying that the probability of those specific 6 people winning the lottery is very small and the probability of any 6 people is much larger and on this we can agree.

What happens to your example if you change the lottery from drawing 6 balls to 20 balls?

(S. Joshua Swamidass) #9

It is much more than this. What he is explaining is that just about every event is astoundingly improbable in forward calculation of probabilities. Emphasizing the profound improbability of an event seems to be a good argument against it, but this is an absurd argument. It can be used to argue against any event, including events that we see happening all the time.

(Herculean Skeptic) #10

I do understand this. What I was asking (and I believe @Mung as well) has to do with the “someone will win the lottery” vs. “I will win the lottery” issue. That I will win the lottery is much more improbable than someone winning the lottery. So, in explaining away a bad argument, we just want to not create confusion.


The thing with the lottery is that we know how many losers there are. This isn’t the case with evolutionary pathways. We don’t know exactly how many pathways there are so we can’t know how many were not taken. However, every indication is that there are gobs and gobs of available pathways where the accumulation of mutations can produce functional change.


You were in the right track Bill, but then went off track. :slight_smile:

The number of balls is irrelevant. What is relevant is that you were talking about two different probabilities and two different events!

Do you agree @swamidass?


We obviously change our probability calculations. However, the same concepts apply. If we sell enough tickets we can ensure that someone wins, but any specific winner is still going to be immensely improbable. You are guaranteeing that something improbable will happen.

(Herculean Skeptic) #14

So, for this aspect, the lottery example is a bad one? I understand and agree with what you are saying. I’m just trying to close the loop on the analogy itself. Thanks for sticking with me! :slight_smile:


The purpose of the lottery analogy was to use something simple that people are already familiar with to help illustrate the basics of the argument. No analogy is perfect.

(Jon Garvey) #16

The lottery is a bad example because it deals with a situation where we don’t know the causal chain to Fred, as opposed to everyone else, winning, but we assume there were no unique circumstances. If we knew all the circumstances in advance, we would assign Fred;'s winning a probability of 1, and it would agree with our post hoc assessment that he had.

In practice,m though, after the event, we can still say that his “chance” was as good as everybody else’s) (because we still don’t know the exact causal chain.)

However, if we find that, in fact, the planet Venus won the lottery, it is no explanation to say, “Well, someone had to.” It was impossible before the event, and in the absence of some extraordinary explanation, is still impossible after it.

The first question is, then, “Are the causes known to be capable of producing the effect?” But that itself is an epistemological factor that affects the probabilities.


I think it brought clarity. We have two different events with two different probabilities. I just hope someone can explain it better than I.

Event 1: “a specific outcome given the probability distribution” e.g. Michael Callen will win the lottery.
Event 2: “someone will win”

“Improbable” and “Inevitable” are referring to two distinct events with different probabilities. It’s not the case that an improbable (event 1) becomes an inevitable (event 2 - a completely different event!).


In the case of mutations, we do know that the causes are capable of producing the effect. We know that substitutions, indels, recombination, and transposon activity (to name a few) are all naturally occurring, and the differences between species are substitutions, indels, recombination, and transposons (to name a few).


If you sell 100 million raffle tickets and pull out 1 winner it is inevitable that you will get an improbable result.

(Neil Rickert) #20

In mathematical probability, we have a probability space, which we can think of as the set of all possible outcomes. An event is a set of possible outcomes. A point event is a single possible outcome.

In cases where there is a continuous probability (rather than the discrete case), the probability of each possible outcome is zero. But there is going to be some outcome, no matter what. So it is certain that there will be events of probability zero.

We typically say that an event is “almost certain” if it has probability = 1, and we say that an event will “almost never” occur if it has probability = 0. The “almost” there reflects that events of probability 0 can and do occur.