Thread: Whee are the aliens? View Single Post
August 27 2013, 04:56 PM   #37
CorporalCaptain

Location: "Who are you?"
Re: Whee are the aliens?

Edit_XYZ wrote:
CorporalCaptain wrote:
 Edit_XYZ wrote: 1. Abiogenesis. What is the road from a bunch of chemicals to the "simplest" molecules that can replicate themselves halfway reliably? Let's - VERY optimistically - assume that a specific chain of 100 chemical reactions are enough to create this "simplest" molecule. Now - Darwinian selection has no part in creating this molecule; for Darwinian selection, you need self-replication, which you do not yet have. Which leaves probability in charge. For a very rough approximation, calculate factorial 100. It gives a number so close to 0 [sic] as the chance of this "simplest" molecule emerging, that the chances are life on Earth is alone in the observable universe (and a huge chunk of the unobservable one).
Care to explain just what 100! is a "very rough approximation" of in this context and how you know it even is an approximation?
I take it as a very rough approximation because it leaves out many factors:
-In the primordial earth, there were many environments, not just 100;
-As such, the problem of abiogenesis is more correctly stated as: 'these 100 steps should follow one after another without one or more destructive environments appearing between them, destroying the future self-replicating molecule';
-The number of steps necessary to create a molecule replicating half-way reliably is probably larger than 100;
Etc.

In essence, 100! is a simplification, only there to give a rough idea about the improbability of self-replicating molecules emerging.
So, in other words, it's just something you pulled out of your ass.

The issue isn't so much the 100 part, but the factorial. You seem to have settled on that, because you like the fact that 100! is astronomically huge.

Here are just two problems with your assumption that factorial is the correct function.

First, the steps that need to be performed in order are not all independent of each other. Certain later steps can occur only if their reactants are available. Therefore, not all of the combinations counted by your function are equally likely to occur, since some of them are in fact impossible, namely the ones describing sequences in which steps occur before their reactants are available. For example, if C depends on both A and B, then CAB, CBA, ACB, and BCA are four of the 6=3! sequences counted by your function, but they couldn't possibly occur, since C simply can't happen without the products of both A and B. This is one reason why your function grossly underestimates the odds of the final product occurring randomly. The impossible combinations, being ruled out, can't muck things up.

The overwhelming majority of the combinations you've counted are in fact impossible for this first reason alone. The number of impossible combinations is at least 99!. Just consider the combinations where the final step occurs first, and then count all ways of reordering the remaining 99 steps. Those are all impossible combinations, unless the molecule in question only needs one step to be produced. Similarly, the ones where the final step occurs second are also invalid. Assuming 100 steps are required to produce the molecule in question, then since the final step has to occur last, only at most 99! of the counted combinations are valid, which is at most 99!/100!=1% of the total counted. Further dependencies place further restrictions on the ordering.

A second problem is that steps that are independent of each other can be interchanged. For example, if A and B are independent of each other, but C depends on both A and B, then ABC and BAC are both valid sequences. Your function only admits one of them.

The factorial function counts the number of ways of reordering sequences. That's the wrong function to use in this case. There is no valid argument that it is even a rough approximation of the correct value.
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CorporalCaptain

Last edited by CorporalCaptain; August 27 2013 at 05:09 PM. Reason: clarification