RAZD writes:
The bigger point is quite simple: when you make (mistaken) assumptions about the possibilities your are limiting your answers to a (mistaken) subset of actual probabilities. Those assumptions should be part of the answer.
Understood. But you do not seem to realize that what amounts to the "assumptions" that you are complaining about. That info is already baked into the problem that Gelernter was talking about.
But first, lets go back to your dice examples. You populated charts up to 20 sided dice for commonly used dice, but you messed up your math according to your model.
If you'll notice, for any pair of dice where the # of sides on each die is 6 or greater, the number of 7s possible is 6. It doesn't matter if you roll two 6-sided dice, or two 100-sided dice, or any combination of 6to100-sided dice - rolling a pair of dice will always allow 6 possibilities of getting a 7. Now of course, your best odds are with two 6-sided dice. Any die used with sides greater than 6-sided will reduce your odds of getting a 7, cause there is still only 6 successes of all possibilities per one roll.
If you understand that, you may see where you made a mistake. Again, regardless of the die sizes, with
your model the question was "what is the probability that I will throw/roll a seven in
one try". You broke down the odds with various die combinations, but then you
ADDED those probabilities together to get a new probability that reflected
multiple tries, not just one as per your model. So the odds of getting a 7
in one try is not "26 out of 660", nor is it "78 out of 1580 possibilities, or about 1 in 20". The best odds you can get are 1 in 6. If you say, had a pair of 150-sided die, then getting a 7 would be less than 3 in 10000.
There are only 4 numbers discussed in the video (a remarkable paucity for a "Mathematical Challenges to Darwin's Theory of Evolution" don't you think?): the number of amino acids (20), the number of possible working proteins (1 in 10^77 will result in a functional fold), the possibility of getting a "right" 150 amino acid "string of beads" (20^150 = 1.4 x 10^195), and the number of atoms in the universe (number not given, just the comment that it is less than 20^150 = 1.4 x 10^195)
Well, there are more numbers than that discussed in the video, which you might know if you actually watched it, but if you are just referring to the issue of the proteins, those are sufficient. Though I must point out that your description is off. The 20^150 = 1.4 x 10^195 number refers to the possible number of combinations for a 150 AA protein, it is not a determination of what is "right". For the purpose of defining 'right', that would be the 1 in 10^77 number among all the possible combinations.
This should be a big red flag.
They are all (except for the number of amino acids used), WAG (wild ass guess) assumptions, bald assertions or outright falsehoods.
So you assert, but you still haven't given any support or specifics for that allegation.
As I've already shown in Message 51, the 20^150 = 1.4 x 10^195 calculation is wrong, badly, grossly wrong, because it only uses one of the worst possible ways to assemble 150 amino acids, one by one in order.
What is wrong is your understanding of what is being talked about. You simply are not getting it.
They are talking about a 150 AA protein. Not a 20 AA protein, not a 100 AA protein, nor a 149 AA protein. 150! Got it?
Now using their illustration. If you are making a necklace of 150 beads (not 149, nor 98, nor 32, nor any other # of beads....) and for each bead you can choose any one of 20 different types of beads, the total possible, number of different necklaces that can be made are 20^150 = 1.4 x 10^195. That's it, and that is indesputable. No other criteria are being applied.
We're not talking about whether one puts the necklace together one bead at a time, or a handful of 12 beads in a clump are added at a time (or any other combination of assembly), or if the bead-thread is sticky and long enough to dump in a bead bucket and come out with 150 attached - that all doesnt matter. There is no 'better' or "worse" way to assemble it. The assembly method is irrelevant.
Question for you: why was a 150 amino acid string protein chosen?
Consider that the first life would be the simplest, using the simplest molecules. As noted in Message 51 the smallest known protein is made with only 20 amino acids.
Why choose a much more complex protein than necessary if the argument is that it's formation has a low probability?
If you don't know whay a 150 AA protein was used, then go check the essay and or video again.
And the reason it was chosen has nothing to do with whether there are smaller proteins of less complexity, because the formation of the proteins is not at issue.
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