In the derivation you first begin with the same Pf, then find an equation with R, and then get the new equation (which you drop reference to Pf in, instead just using the form with R, which could change values), which is exactly what the author did. Only when you tried to go back and see how he/she derived the equation did you say “Hey, when R a certain value then I_ex and I_nat are the same!” But that is the point…they are the same for the initial case we use to derive the general equation, but if we find empircally that R_actual is actually different from R_initial, then we get an inequality.

It isn’t something worth belaboring, you should just accept that the notation was confusing, but not incorrect for what the author was doing.

Anyway, for the rest of your criticism, what is it? It seemed tied up to your notation confusion, so I thought it was the same.

The rest of the paper flows from that derivation. If the number of attempts that are possible (R_actual) are much less than the attempts needed (R_needed, the value at which I_nat = I_ex, or even better, I_nat > I_ex), then it is likely that chance is not capable of producing the necessary functional information.

Atom

They may be different, they may be the same.

If they may be different, then they are not representing the same number, so they should be different. It is an error, but an error of notation.

I notice nobody has tried to answer the rest of my criticism. I’ve got more, too.

Bob

I think that even if you get your R’s and Pf‘s straightened around to Bob’s satisfaction, it won’t change his mind. He doesn’t want to believe.

We need some indication that the P_f’s are different, or the argument should have been developed in terms of the inequality from the start.

I think the reason is because the Pf‘s are not yet different, as long as we haven’t stated what R is. They may be different, they may be the same.

So the author was starting with the assumption that they are the same and then coming up with an equation that makes R the free variable. As you change R, you change Pf. If you don’t change R, you don’t change Pf.

So yeah, I guess the author could have made that clearer, but I don’t think the author was in error.

What do you think?

Bob, go easy on ‘em.

…so Pf will only equal the original Pf for one R value.

Right. And at that point I(E_x) = I_nat, so the inequality can never hold. We need some indication that the P_f’s are different, or the argument should have been developed in terms of the inequality from the start.

I think it’s time to break the Polya out.

Bob

Pf = 1-(1-0.5)^1/R

Then when Pf = M(E_x)/N (in other words, when we have equality with our intrinsic problem probability), we get:

M(E_x)/N = 1-(1-0.5)^1/R

Since we know what is on the left and can calculate, we can solve for R, which tells us how many attempts we need to have at least a 0.5 chance of solving the problem. If we want to change it to a .10 chance, we get a different value for R.

So the author is using Pf from the original equation to derive a new equation (once he/she plugs in the value for 0.5 chance of solving the problem), and so Pf will only equal the original Pf for one R value.

If we find R << R_needed, then the author’s inequality will hold.
{DH corrected per Atom #39}

You wrote:

The only way I can make sense of this is if they are different Pf’s, in which case the author should be made to stand in a corner and recite How to Solve It as punishment for poor notation.

From my single reading of the paper, the author seemed to make it clear that Inat needs to take into account R, the number of tries nature has to solve the problem, whereas the intrinsic difficulty of the problem has no reference to number of attempts. In this way, if the nature, given a number of tries can only generate M bits of functional information, and N is the amount of functional information needed to have a reasonable change of solving the problem, and N >> M, then we say nature will probably not be able to solve the problem in that many attempts.

So the Pf’s would need to be different, since one would take into account R, where as the other would not.

So, is this paper admitting that irreducible complexity may not so much be found at the biological structure level but in the abstract physical regime that constrains biological realities? Although I myself am not adverse to this notion, it would no doubt be hotly a contended between theists and atheists – a battle fought in a much more logically highfalutin and abstract realm than contentions over the probability of the molecular engineering of particular structures; for like the laws of physics, the conceivable structures of morphospace have a platonic/conceptual status rather than flesh and blood existence! However, down at the earthy particulars of biological realities, this rendition of ID is not so different from conventional first order evolution.

Talking about earthy realities: Denyse this might be your lucky day: Prof Larry Moran might give you a kiss for all this; but judging from what he gets up to with Parisian statues you might get something else as well, so watch your back.