Best practice is to construct a mathematical model first. And then you carry out experiment (or theorize about the thought experiment). In an actual experiment, all of the events have occurred by the time you analyze the data. But you continue to use the probabilities from the model which was built before the events have occurred.
If somebody already won the lottery, you can talk about the probability of that. But you need to be clear that you are modeling a hypothetical situation before the winning ticket was drawn. And you need to be clear what the model is.
And then there’s the question of conditional probability. That’s where a lot of probability arguments from ID proponents go wrong.
If I bought a ticket, and the draw was last night but I do not know the results, is it reasonable for me to wonder about the probability I won before I do find out the results
We do assign probabilities to retrodictions in science, I believe.
I think the issue is not when an event occurred, but the state of knowledge about the event.
Seems to me we have been through these issues in another thread, possibly the random mutations thread. I’d assign high probability to that myself…
You would need a carefully specified mathematical model. And it should be an open model so that others can see whether any inappropriate information was smuggled in.
The easy example would be the probability of life originating.
We can look at the probability that life originated somewhere (but we don’t know where). Then to make use of that, you need to know a lot more about how many planets there are in the entire cosmos where life could have originated.
If you want to be specific about life on earth, then you need to look at the conditional probability:
Probability(life originated on earth given the condition that it life is known to exist on earh). It’s not easy to estimate that probability either, but that conditional probability might be close to 1.
Many of the bad arguments coming from critics of evolution are based on estimating absolute probabilities, where conditional probabilities should be used.
Could you explain in more detail, what you mean ‘‘life originated on earth given the condition…life is known to exist on earh…but that conditional probability might be close to 1’’
I wrote a post on the time element that commented on in the OP but decided to not post it. From the OP:
Improbable events must happen because time is moving forward.
I’d like to highlight the following from the linked wikipedia article.
All the events in {\displaystyle {\mathcal {F}}} that contain the selected outcome {\displaystyle \omega } (recall that each event is a subset of {\displaystyle \Omega }) are said to “have occurred”.
They “have occurred,” but their probability is not 1.0.
If you think that the absolute probability of life originating on earth is miniscule, then the absolute probability that life exists on earth should also be miniscule. But that latter miniscule number appears in the denominator when you calculate conditional probability.
Or, looked at the other way, if life on earth did not originate here then it came from elsewhere. And, at present, there is no evidence to support this possibility.
I think there is some imprecision in the language here You are talking about something that has happened as if it will happen. Did you mean to say that if you pull out one winner that you did get an improbable result?
I think this is the point I’ve been attempting to make. If you pull out one winner you got a highly probable result. p=1.0. This is assuming of course that pulling out a winner is inevitable.
Could we discuss the case where the lottery may or may not have a winner? Simply declaring that there will always be a winner could be seen as begging the question.
If the lottery has 100 million tickets and only one is sold and that ticket happens to win, does that require a special explanation?
FWIW, I agree with you and Neil that for science we should be careful to specify the nature of the probability model and how it applies to the events whose probabilities we are are estimating.
Then there is the separate issue of how one interprets probability: eg as limitations in human knowledge versus as independent of people’s knowledge. That too can vary by context (eg QM versus just about anything else). That issue was the one I was referring to in the lottery example.
Please consider the following passage by Richard Dawkins:
Let us hear the conclusion of the whole matter. The essence of life is statistical improbability on a colossal scale. Whatever is the explanation for life, therefore, it cannot be chance. The true explanation for the existence of life must embody the very antithesis of chance. The antithesis of chance is nonrandom survival, properly understood. Nonrandom survival, improperly understood, is not the antithesis of chance, it is chance itself. There is a continuum connecting these two extremes, and it is the continuum from single-step selection to cumulative selection. Single-step selection is just another way of saying pure chance. This is what I mean by nonrandom survival improperly understood. Cumulative selection, by slow and gradual degrees, is the explanation, the only workable explanation that has ever been proposed, for the existence of life’s complex design.
Dawkins, Richard. The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe without Design (p. 450). W. W. Norton & Company. Kindle Edition.
Is he not arguing that the statistical improbability of life does require a special kind of explanation?
Of couse it isn’t. Whatever you think about how unlikely it is for life to originate, surely we can agree that life originating inside the core of the Sun, is less probable, than life originating somewhere on Earth where conditions are milder and less hostile?
In either case, the probability might be very low, but one is clearly much less probable than the other. The probability thus depends on some prior conditions, hence it is a conditional probability.
I don’t know the context for your quote so I cannot say what Dawkins motives are.
But there is nothing special about the scientific explanation of life, when we have one. We will have a causal model and that model will involve a probability distribution for its predictions. We then can apply that distribution within the context (eg background conditions for exogenous variables). . We make and justify assumptions for unknowns that enter into the context needed to calculate the probability. Whether we choose to call the result improbable is a matter of how we choose to define that adjective. Is .05 improbable?
Note that I am using probability distribution to include the degenerate case which assigns one event 1 and others zero (that assumes a discrete random variable in the model).
We considering ‘‘perfect’’ condition like Earth, I never talked about the probability of life originating on Pluto, but only on Earth. in that case, since I all conditions are met. then I do not need to take into account any condition. My point is even if all conditions are met you still need to calculate the probability of forming proteins and all stuff for a cell. If conditions are met it does not automatically mean life is inevitable.
My point is even if all conditions are met you still need to calculate the probability of forming proteins and all stuff for a cell.
How do you know what the simplest, or the first, or the most probable form of life is? What do you know about the conditions that are most favorable to it’s origin?
If conditions are met it does not automatically mean life is inevitable.
Sure, but you still have to know what the conditions are, and what exactly you’re attempting to calculate the probability of.
that contain the selected outcome {\displaystyle \omega }
(recall that each event is a subset of {\displaystyle \Omega }
) are said to “have occurred”.