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Old August 27 2013, 04:18 PM   #39
Edit_XYZ
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Re: Whee are the aliens?

CorporalCaptain wrote: View Post
Edit_XYZ wrote: View Post
CorporalCaptain wrote: View Post

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
Annoyed much, CorporalCaptain?
BTW, a simplification is far from 'pulling out of one's 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.
Really?
You don't say?

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.
You are confusing the environments and the chemical steps to which they give birth.
I posited 100 environments that must occur in order, in order to create in the 'warm pond' or wherever the chemical steps for the appearance of life.
These environments are independent of each other, one can occur out of order* - in which case, of course, the fledgling molecule not being available, bye bye future self-replicating molecule.

*Unless you want to post a magical environment that creates the successive ones/a large number of the successive ones.

The overwhelming majority of the combinations you've counted are in fact impossible for this first reason alone. In fact, 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.
Cute. See above.

A second problem is that steps that are independent of each other can be interchanged. For example, if A and B aSo - here you're positing a magical initial condition that can create re independent of each other, but C depends on both A and B, then ABSo - here you're positing a magical initial condition that can create C 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.
The chemical steps necessary you achieve a self-replicating molecule cannot be interchanged (especially when talking about as few as 100*) - even if the 100 environments can appear independently of each other (although, if they have no fledgling molecule, they go nowhere).

If you interchange these chemical steps you will end up with a boring chemical soup - nothing self-replicating.

*When you want to talk about a more realistic ~1000 chemical steps - sure, you can probably interchange a few.
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