The Inevitability of Improbability

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

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

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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?

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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.

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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?

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.

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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.

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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.

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

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.

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!

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.

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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.

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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!).

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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).

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

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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.

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In peer-reviewed article in Theoretical Biology and Medical Modeling [The Universal Plausibility Metric (UPM) & Principle (UPP)] Dr. Abel notes

«Combinatorial imaginings and hypothetical scenarios can be endlessly argued simply on the grounds that they are theoretically possible. But there is a point beyond which arguing the plausibility of an absurdly low probability becomes operationally counterproductive»

When hypotheses require probabilistic resources that exceed Universal Plausibility Metrics, Dr. Abel argues that they ―should be considered not only operationally falsified hypotheses but bad metaphysics on a plane equivalent to blind faith and superstition. He then rigorously calculates the Universal Plausibility Metric (UPM), incorporating the maximum probabilistic resources available for the universe, galaxy, solar system, and the earth: and notes that

the Universal Plausibility Principle (UPP) states that «definitive operational falsification» of any chance hypothesis is provided by inequalities based on the probabilistic resources of the Earth (p < 1/10^-102), solar system (p < 1/10^-117), galaxy (p < 1/10^-127), Observable universe (p<1/10^-140)

@Edgar_Tamarian, you are finding out that the argument you are pointing to you, at least as you present it, relies on a fallacy. You’ve just seen a clear example of something that shows its reasoning is wrong:

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If the upper bound is 1 in 10^140 then dealing out playing cards should be impossible.

If you shuffle a deck and lay out the cards one by one, the odds of that specific outcome are 1 in 52!, or 1 in 8x10^67. The total probability of the order of 3 such hands is 1 in 5x10^203. According to Dr. Abel, I shouldn’t be able to shuffle a deck of cards and lay them out one by one more than 1 or 2 times. That seems a bit ridiculous.

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