Bill's math class

In several threads, @colewd has been asked to provide his math in support of some of his claims.

This thread exists for him to provide his mathematical support, and for the careful and respectful consideration of the same.

EDIT: And let me invite others to list their questions below, I know there are a few…


For reference:


Continuing the discussion from Personally attacking the opposite view:

So we went from 10^8 (random use of 200x), to 10^7 (human generation time) to 10^6 (mouse generation time). Then knock off another 100 because it’s the smaller number that matters (for reasons we haven’t gotten to yet). So… 10^4 give or take.

Now the challenge: What was the time since the most recent common ancestor between mouse and human, and what happens when you divide that time by the number above?


There is no point here IMO as the time to generate a new gene based on Lynch’s estimates will exceed available evolutionary time and will also exceed Behe’s estimate due to:

-The number of changes (Lynch 2 max Behe 6 max) in mammal gene families changes can exceed several hundred. (issue for both Behe and Lynch models)
-changes to mammal genes are often deleterious where Lynch assumes neutral (Issue for Lynch model)
-generations of mammals are much longer then bacteria (Issue for both Behe and Lynch model).
-bacterial populations can get much larger then mammal populations (issue for both Behe and Lynch)

Gene duplication and subsequent variation is not a viable evolutionary mechanism in mammals and other vertebrates. It also has not been experimentally demonstrated in bacteria.

How do you know? Have you done the math? Have you been able to show your work?

Of course not!

Show your work, Bill. That’s the point of the thread.


One of >4000 papers:


Again there is no point. The models show that the waiting time is excessive depending on generation times, gene duplication times, number of changes to find a functional adaption, and the amount of deleterious mutations.

We all know these conditions are substantially less favorable in bacteria then in mammals and vertebrates.

Why don’t we talk about mechanisms that may not have this type of challenge?

There is a very important point. If you can’t show your math, or even write down your starting assumptions, then there isn’t even a claim worth discussing.


Again there is every point, particularly since you’ve offered two objectively false claims about the relevant evidence to avoid showing your work.






One little point that’s been bothering me for a long time. You consistently misspell “than”. Could you fix that little thing, at least?

Does it? How do you know?! Have you… done the math?


Then you don’t know that the model says that! You’re just making stuff up!

And here’s the thing… I think you’ve realized that. I think you realize now that using your best numbers, you get a perfectly adequate number. So please, Bill…

Show your work!


Hi Dan
We are comparing 2 similar population genetic models with different working assumptions. This discussion is not about the math it is about the assumptions plugged into the mathematical models.

My point is very simple. When these models are applied to vertebrates (and associated generation times, gene duplication times, deleterious mutations, and sequence divergence between observed genes in the same family) it is clearly evident that what we observe in genetic variation between different mammals and vertebrates cannot be caused by gene duplication and associated variation.

Other mechanisms should be considered.

Are we? How can we know, when you can’t show your assumptions, or how those assumptions, ya know… impact the math!

How can the model be applied except with math, Bill?

For it to be ‘clearly evident’, you’d need to do math, Bill. Where’s your math, Bill? You just said you’d done it, where is it?


They may. They may not. That would depend on the formulation and parameters, wouldn’t it? Hence the need for the math.


You have put yourself in the situation of making a claim which you are incapable of verifying. I have no doubt that you believe you are correct, but the reason for that belief doesn’t seem to have anything to do with math. If it did, then you should be able to express those reasons clearly - and mathematically.

It’s a little bit unfair to put you on the spot and demand you produce supporting math. At the same time it is unfair to everyone else that you keep making this singular claim, over and over again, and expect people to accept it on your say-so. (Seriously, you must have brought this up in dozens of threads.)

I would be satisfied if you could make some effort to understand why this particular mathematical claim is flawed. No one can force this - you have to do the work yourself to really understand it. A little time spent with paper and pencil can do wonders for understanding.


Behe and Lynch already did the math.

The question is what assumptions are accurate given the make up of mammals, vertebrates and the magnitude of changes observed. This one is not hard if you are willing foo face reality and look at the models, the available empirical data and the assumptions objectively.

If you want to use the models to show how a vertebrate gene once copied can find new function through hundreds of random changes and fix in a population I would be interested but this looks like a waste of time at this point.

The comparative models above are for 2 changes.They are essentially informative toy models.

Because Lynch’s article has numbers bigger than a million.

A million is a very, very big number.

So numbers that are BIGGER than a million are REALLY, REALLY BIG.


It’s simple logic.


Hi Ron
Behe and Lynch already created a mathematical model. I am not interested in reinventing the wheel, a wheel that will simply tell us that gene duplication and random change are not a viable explanatory mechanism for the observed diversity of genes in mammals given the results of the bacterial toy models.

Part of the job is to make estimates and judge if there is reason to do the work. I have not seen any viable mammal models that shows how gene duplication and random change can consistently generate genes in new populations. There seems to be good reason that no one is taking this on.