A Genetic Entropy Analogy

[MrAnderson (Mathew)]

@Dan_Eastwood

Suppose that fitness has a normal distribution N(\mu,\sigma^2), and we want to compare two members of the population (X_1, X_2) for relative fitness. The difference (Y) of the two also has a normal distribution,

Y = X_2 - X_1 \sim N(X_2 - X_1, 2\sigma^2)

The probability that X_2 is greater than X_1 can be calculated as

P[X_2 > X_1] = P\left[Z> {x_2 - x_1 \over \sqrt{2\sigma}} \right]

where x_1 and x_2 are the two values observed (and x_2 \geq x_1), and Z is a standard normal variable N(0, 1).

Example: let fitness X be distributed as N[100,1], and we observe fitness equal to 99 and 101 in two observations.

P[X_2 > X_1] = P\left[ Z >{101 - 99 \over \sqrt{2}} \right] = P\left[ Z> {2 \over1.414} \right] = P\left[Z> {1.414} \right] = 0.127

Calculating the probability that any two observations will differ by at least 2 is simply twice this amount (just like calculating a two-tail p-value). For the difference k=x_2-x_1,

P\left[ Z>|X_2 - X_1| \: \right ] = P\left[ Z >{|k| \over \sqrt{2}} \right] = 2\cdot P\left[ Z >1.414 \right)] = 2\cdot{0.1271} = 0.2543

My first thought when I saw this was “it’s cute that you think I would understand this.”

My second thought was… hang on… I think I do understand this… barely, but I do understand this…

My third thought was… hang on… he’s not just fixing my original example, he’s taking the larger theory that I have been trying to defend and develop in this thread and building out the math for it…

but that means A REAL SCIENTIST IS DOING SCIENCE WITH ME!!!

holysh!tholysh!tholysh!tholysh!tholysh!tholysh!tholysh!tholysh!tholysh!tholysh*t!!!

THIS IS AWESOME!!!

Ok! time to look up truncated normal distributions. Can’t be that complicat…

In all seriousness though, thank you Dan. This has made my day. I would love to continue to develop this if you are interested in helping me.

[Dan_Eastwood]

@MrAnderson

but that means A REAL SCIENTIST IS DOING SCIENCE WITH ME!!!

Well, probability calculations, at least.

@MrAnderson

Ok! time to look up truncated normal distributions. Can’t be that complicat…

Don’t panic. I can set up a spreadsheet to do the calculations for you. For now just understand that when you remove the failing students, that average of those who remain will be higher. This can estimate the increase in scores due to the purifying selection.

@MrAnderson

I want you to imagine that there is a class at a very prestigious school, and it has 10,000 students. The students have different abilities to get different test scores on a scale from 1 to 100, and lets assume the class average is 55%, and that everybody below 50% fails the class. That’s our purifying selection.

If the students are normally distributed with mean=55 and standard deviation = 10, then ~69% will pass, and the expected score among those passing will be 60.1. So long as the replacement students are not a lot worse than those who graduated (no more than 5 points worse on average), then we expect scores for the next year will be the same or better than 55.

This model can’t ever drop the average of passing students below 50, so Donny might not find it satisfactory. It does tell us something about the effects of purifying selection.

We want to be careful about continuing this calculation over multiple years, because in practice you replace individual students, not probability distributions (The second group won’t be normally distributed). This might be OK as an approximation, but a simulation modelling a large group of students over time would be needed for better results, or where a population crash is possible.

[Nesslig20]

@MrAnderson

So I guess that leads to my question: what do you think? Is this worth doing?

I get what you are coming from, but my advice hasn’t changed. I am very certain that Donny doesn’t do what he does out of good faith. As mentioned before, he even proudly declared this intentions to me in explicit terms. He desires attention on youtube. Even if he loses a debate, it will still earn him a veneer of respect in the eyes of his sycophants. That’s all that matters to him. A debate will only be bad for him if his performance is poor, but that’s largely outside of your control. You could demolish every single point he makes, yet he may still keep up his composure, crap all over the chess board, and fly back to his flock to declare victory. That’s why debates are a favorite anti-science cranks, and also why scientists don’t use live debates as a medium to discuss science. Winning a debate is not about the facts. It’s just a performance. A scientists or a science-minded individual who cares about every detail will always be at a disadvantage in a live debate against an uninhibited liar, or a total ignoramus, or both, who only knows how to gish gallop.

I would prefer you doing something like @dsterncardinale (aka ‘Creation Myths’ on youtube) does. Although, he also debated against creationists, but aside from that, he makes excellent videos that have several advantages over debates. They are short, focused on one point, and don’t provide (as much) clout to the opposition. Better yet, you may make your points without even mentioning Donny. Go straight to the source (Sanford in this case) and cover his arguments/claims instead.

Alternatively, you could do what I did and say you will only do a debate in a written format where you can take your time to respond to their claims. They will squirm at the very thought of it, because they know they will lose the aforementioned advantage. Under this setting, the Gish Gallop won’t be as effective and it puts them in a position where they have to read and comprehend the cited literature (both yours and their own). They normally won’t, or simply are unable to do. The moment I was writing this, I was reminded of an instance that proves my point even further. There was a debate from 4 years ago [link plus time stamp] where Donny presented a slide claiming, quote…

ENCODE project shows that at least 60% of the genome is functional

On that slide, he cited the 2007 pilot study of ENCODE, which actually said the following:

A total of 5% of the bases in the genome can be confidently identified as being under evolutionary constraint in mammals; for approximately 60% of these constrained bases, there is evidence of function based on the results of the experimental assays performed to date.

Not 60% of the genome. It refers to 60% of the 5% that is under evolutionary constraint; i.e. 3% of the genome. I found out about this error in a few minutes, but you cannot do this easily in a live debate. Indeed, Donny’s opponent did not correct him on this. But you have plenty of time to fact check under a written format.

Then again, it’s just my own opinion on the matter. If you still want to go for a live debate, that’s up to you.

[MrAnderson (Mathew)]

Ok, so I really like subverting SFT’s analogies, and if you guys don’t like the classroom one, how about this?

Donny also often uses the analogy of a car lot, where maybe we get rid of the worst (rustiest) car, but rust is just going to continue to build up on all of them until eventually they are all junk. That, he says, is genetic entropy.

But hang on, there isn’t any recombination or differential reproduction going on in Donny’s example. What happens if we add those?

So lets say that every week, they take all of the cars apart, and then randomly reassemble them all (lets just pretend the parts are interchangeable). Then you take your rustiest car, and you get rid of it, and you replace it with another car that has exactly the same amount of overall rustiness as your least rusty car.

How long until the whole lot rusts out? The answer is NEVER, because you are always mixing things around, and your new cars are always going to be some combination of your best parts, so relatively good parts are always being introduced to the lot and relatively bad parts are being removed.

It also helps them understand their “princess and the nucleotide paradox” because the rustier the part, the greater the chance it will increase the overall rustiness of the car such that it is the car that gets eliminated.

Is that better? It certainly eliminates the math. Maybe it’s more intuitive?