Our beloved and dreaded Supreme Dark Lord (PBUH) put up a Darkstream (delayed slightly and intermittently interrupted by very irritating technical issues), in which he explained why the current Theory of Evolution by (Probably) Natural Selection, Biological Mutation, Genetic Drift, Sexual Selection, and Gene Flow (TE(p)NSBMGDSSaGF).

(That, it must be noted, is not one of his more elegant acronyms.)

It is a very interesting stream, particularly for those of you with a mathematical bent (like me). However, it is a bit esoteric and difficult to follow at times.

The basic argument that His Voxness presents is that the idea that the current Neo-Darwinian Synthesis of TE(p)NSBMGDSSaGF, cannot fully, or even remotely adequately, explain the way in which humans supposedly evolved from a separate branch of the tree of primates as chimpanzees did.

Here is the full Darkstream, so you can watch that at your leisure:

Now, I have an IQ which, last time I checked, is somewhere in the high 130s range – I think, I haven’t been tested in a long while and IQ does tend to decline slowly over time after you turn 20 or so – and Vox Day has an IQ of 150. Normally, I don’t have a hard time following his arguments, because I am well within the 2SD “communications gap” that he keeps talking about.

Most of my readers are 2+ SDs to the right of average. So it’s fair to say this is smarter than the average blog, and by quite some distance, actually. Indeed, yer ‘umble servant is very, very far from the smartest person here – several of my readers make me look stupid in terms of cognitive capacity with no effort whatsoever.

Yet, even I, and probably many of you, had a hard time following the Dark Lord’s arguments. And that is a natural result of both the Dark Lord’s style of communication, and the manner in which he presents his numbers.

But I figured it out eventually.

Being a mathematician by training – two really-for-real degrees in the subject, though if you start asking me to solve stochastic differential equations again, I’m going to have to beg to be excused – I think I can help provide a simple breakdown.

OK, so let’s start from, appropriately enough, the beginning.

We need three important facts to start looking at the Dark Lord’s approach.

First, we need to know how long it has been since – according to !SCIENCE!!! – humans and chimps separated into different species. The estimates range from like 4.5 to 25 million years, but the consensus [10,000-word rant about how “consensus != SCIENTIFIC METHOD” deleted for sake of brevity and sanity] sits at 9 million years since Chimp-Human Last Common Ancestor (CHLCA).

Second, we need to know the total number of genetic differences between humans and chimps. (Note: I have no idea why there is no “Bonobo-Human Last Common Ancestor”, because apparently bonobos are genetically about as similar to humans as chimps are. But, hey, it is what it is.)

That number comes to 40 million total mutations – 20 million human, and 20 million chimp, on average. This means that the average chimp, and the average human, have 40 million different genetic base pairs from each other. Put another way, chimps and humans have both “drifted” genetically from the CHLCA by 20 million base pairs of DNA, on average, each.

Third, we need to know what is the average time span between different generations for both chimps and humans. As it happens, that number is the same for both species, and it comes to 20 years.

OK, so let’s put what we have together for the moment.

1. Time since CHLCA: 9,000,000

2. Total human gene mutations since CHLCA: 20,000,000

3. Time between generations (both species): 20

All right, let’s now divide (1) by (3) to get the total number of generations since the CHLCA:

4. Generations since CHLCA: 450,000

Following me so far? It’s very simple maths at this point.

Right. Now, given (2), above, what is the average number of mutations per generation? That’s simple. Divide (2) by (4), to get:

5. Average mutations per generation: 44

Still with me?

All right, so far, so good. We’ve just been doing some very simple mathematics. We now need a few more basic facts.

We need to know what is the total number of base pairs exist in the human genome.

That comes to:

6. 3,088,286,401

And then we need to know the observed range of variations between different types of humans. That is to say, what is the observed range of mutations between ALL of humanity – whites, blacks, Chinese, Australian abos, Maoris, Pacific Islanders, Inuit, you name it.

That number is:

7. 324,000,000

Now, because chimpanzees are not human – we can all accept this, yes? – that means that chimps have 40,000,000 total DNA base pairs that ARE NOT, AND CANNOT BE, part of (7). Agreed?

Okay. So. If there are 44 mutations per generation for humans, then we should be able to look at the oldest set of human DNA ever sequenced, and figure out how many mutations have taken place since that point in time.

As it happens, the oldest set of human DNA we have available is:

8. Age of oldest human DNA to be sequenced in years: 430,000

Now, remember, from (3) above, there are 20 years between generations. So divide (8) by (3), and you get:

9. Total number of generations since oldest human DNA: 21,500

Therefore, the total number of mutations that took place over all of those generations in (9) is, very simply, (9) multiplied by (5). That number is:

10. Total mutations since oldest human DNA: 955,556

OK… so what the hell does all of that even mean????!!

Well, it’s simple, actually. Let’s assume that the Neo-Darwinian Synthesis is correct, for the sake of argument. Then, once the oldest human DNA we have available is sequenced, we should expect to find just shy of a million genetic base pair differences between modern humans and those ancient humans.

And that’s the important part. We expect to see this.

Will we?

I haven’t the foggiest notion. Neither, I imagine, does anyone else, and nobody will until such time as the actual data on the subject are released.

What we do know, however, is that everything here depends on two simple variables.

The first is the time since the CHLCA. Estimates put this as recently as 4 million years ago, to as far back as 25 million years.

The second is the total number of mutations that we would expect to see in that oldest human DNA therefore varies entirely on the time since the CHLCA.

Here’s why. Take a look at the following screenshots from a very simple spreadsheet model that I mocked up in Gnumeric, using three different inputs for the time since the CHLCA:

So we should expect to see somewhere between 344,000 and 2.15 million mutations between us today, and the oldest available human DNA. And, remember, those mutations have to be genetically distinct from the available spectrum of 324 million mutations in modern humans from the base genome.

This number, whatever it turns out to be, is a falsification criterion for the Neo-Darwinian Synthesis.

Seriously. All anyone has to do is to look at the observed genetic differences between humans today, and the oldest human DNA that we have available, and ask: are the differences in line with my model?

If yes, then great, the Neo-Darwinian synthesis is likely true.

If not, then the synthesis has a serious problem.

The formulation here is really simple:

Total mutations since oldest human DNA = Human mutations since CHLCA * Age of oldest human DNA / Time since CHLCA

If you work through the algebra yourself, you will see that it is so. This is a simple enough formula and can likely be generalised across species with (supposed) common ancestors.

Now, it must be noted that this is not a linear formula, at all. The reason why that is important is because linear equations are very easy to test against. If you have a linear relationship between various data points, you can setup and run linear regressions.

That equation, again, is not a linear relationship. But, it’s very easy to turn it into one.

All you have to do is take natural logarithms on both sides:

It should be immediately obvious that this translates very easily into a linear equation of the form:

That equation, right there, is a classic multiple linear regression formula.

Any decent mathematician worth his salt would be quite annoyed at how slipshod the notation is, but this is for demonstration purposes only.

However, if you have the data, running that regression is really easy – PROVIDED certain very important assumptions about non-correlation between factors and a few other things are met. In this case, they might not be.

Even so, if you have the data, you can run the necessary regression analysis in a spreadsheet. Seriously. It’s not that hard.

It should then be a relatively simple matter to run some regressions to test whether it’s even remotely true. All we have to do is go into the field, find some really old DNA from various species, calculate a few parameters as noted above, such as the length of time since the last common ancestor and the time between generations and the total size of the animal genome, and plug in some numbers into those variables.

The regression should prove, or disprove, in very short order, whether or not the current Neo-Darwinian Synthesis has any sort of predictive power whatsoever.

To be even halfway empirically reliable, a linear regression of this sort should have an R-squared (basically, a correlation coefficient) of upwards of 70% (assuming again that all of the various fairly stringent criteria for proper OLS regression are met).

If it does not, then it needs to be scratched and we need to start over again – because the entire point of a scientific theory, such as the Theory of Evolution by whatever means, has to be testable. It has to be falsifiable. It must be possible both to make predictions using the theory, and back-test successfully using available historical data.

If neither the back-tests nor the predictions hold up, the theory is bunk. It’s just that simple.

Now, I will say for the record that there is one glaring problem with His Voxness’s formulation, at least as I understand it, and it has to do with this business of 324 million or so variations across the human genome.

As Vox himself points out, we should be able to go back 20 years and look at DNA from the previous generation, and compare the number of mutations observed in that generation against current DNA, and we should therefore see 44 mutations, on average, against the current population.

That means that there should be 44 base pairs completely distinct from the existing 324-odd million variations present across the entire spectrum of humanity.

Can we be sure that this is the case, though? I am not entirely convinced of this, which is where this line of mathematical argument could potentially run into some problems. I am happy to be corrected about this, we shall see what happens.

In the meantime – the fact is that the evolutionists now have a testable, measurable heuristic against which their entire theory can be judged. If they refuse to use it, then the rest of us certainly should. And if empirical evidence fails to support their theory, then we need to start looking post haste at alternatives that better fit the facts.