Question from reader Richard Stevens:
A professional scientist, holding an MS in one of the hard sciences, addressed the argument that the probability of creating a protein or an enzyme by neo-Darwinian means is vanishingly small, e.g. 1E-150 or perhaps very much less. He did not question the mathematics. He argued simply that a chance of 1E-150 means it is “possible, not impossible,” and thus life “could have” arisen from non-life, or animal species could have arisen starting with a replicator molecule. Dr. Briggs, have you written to address the question of whether a sufficiently small probability is equivalent to zero probability?
Impossible is, it is thought, a probability of 0. Any probability greater than 0 would therefore seem to imply possible, just as 0 seems to imply impossible. But this is not so.
First and always remember that all probability is conditional. Every single one. Therefore, though as shorthand we can say “This has a probability of 1E-150”, we always mean “This has a probability of 1E-150 given these assumptions.”
Perhaps non-intuitively, the size of the probability has nothing to do with its possibility.
Start with an example of an impossibility with large probability. Here are the assumptions, or premises or evidence, of the probability. E = “In the room are a unicorn and Pegasus. Exactly one, and only one, will walk out.” Given E, what is the probability of Y = “Pegasus walks out”? Easy (via the statistical syllogism): 50%.
This example can be tweaked in the obvious way to make the probability higher. But 50% is surely much higher than 1E-150. Yet the event will never happen.
I conclude the event will “never happen”. By that I mean the probability of Y is 0. But since all probability is conditional, I must have had some conditioning evidence in mind. Call it E_2 (making the original E_1). My E_2 = “Pegasus and unicorns don’t exist, so no matter what E_1 says, neither can walk out of any room.”
My E_2 is directly related to the cause, or lack of cause, of Y. Y cannot be caused, no matter what, given E_2. Thus the event is impossible, even though E_1 gave it high probability. E_1 said nothing directly about cause. Though even if we put in an explicit cause, nothing would change. The event will still not happen.
I will leave as homework to find an example with small probability for an observable Y that is bound to happen.
It should be clear by now that what’s important are the premises of the probability, and not the probability itself per se. We judge the premises of the probability like we judge any other proposition. Some may be certain, some uncertain, some false. And all these judgments are with respect to other premises which are themselves more certain, and so on. Think of how mathematical theorems are built: chains of argument.
Since the premises are what is important, it does nothing for us, or should do nothing for us, to hear, for any Y, “The chance of Y is 1E-150” or even 1E-15,000,000, or however small you like but still greater than 0. This is because we hear nothing about the premises; therefore, we can say nothing about what the probability means.
It is worth pausing for a moment to emphasize this. Whenever you hear someday say “The chance of that is X%”, and you find yourself nodding along, it means that you have supplied the necessarily premises from which the probability is deduced. Whether your assumed premises match those of the speaker is an entirely different question. This allows the possibility of cheating. Always ask for details!
Thus is all we do is here some low probability and don’t know the defining premises, there is nothing we can say. We can’t even say the low probability is a “practical impossibility”. Impossibility is a causal word, not a probability word. Impossible speaks to the known utter lack of cause, in the given circumstance.
Thus it also does us no good to use the phrase “chances to occur”, which some use in connection with low probabilities. “Chance to occur” makes sense where the causal mechanism is known, or rather the outlines of it known, as in, say, dice throws. We don’t know the precise causes, for if we did, the probability would be extreme (0 or 1) for any throw outcome. But we understand what is means to make the throw, and that when the throw is made, we know what the possible outcomes are.
This is not the case with the 1E-150 probability. We do not know who is throwing the dice, so to speak. For example, suppose we can with reference to accurate biological causes, of the same limited sort as dice throws, deduce the 1E-150. We still do not know how and when the “throw” of amino acids occur. At a casino, dice throws are every, say, 30 seconds. An amino acid throw? Who knows? Every fraction of a second? Every year? What?
This is why I say most (I can’t say all, since I haven’t seen all) probability calculations with regard to Darwinian evolution are a bluff or a mask. We simply have no idea what’s happening. Pointing to small probabilities and then waving hands at very long times is how evolutionists “solve” these probability problems, but these “solutions” rarely hold up.
Here’s a better example, and then a puzzler, also for homework. E = “In a bad we have a slew of black balls and one white one. We reach in, with no peeking, and grab one out.” What is the probability Y = “Ball is white”?
Pr(Y|E) = small.
If you replace “slew” with a number, you replace “small” with one over that number. Any finite “slew” makes it easy for us to understand the causal mechanism, including the how and when. How often you reach into the bag (assuming replacement of the balls or not), makes the causal process clear. All probability calculations are easily deduced, and make physical (biological) sense.
Now let “slew” go to infinity, indeed the size of the infinity of the reals, for now our balls are real numbers, only one of which we’ll call “y”. We reach in and grab “y”. What is Pr(Y = y | E updated)?
Be explicit. What does cause mean here?
This is answered in Uncertainty.
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