# Bill's math class

**URL:** <https://discourse.peacefulscience.org/t/bills-math-class/15672>\
**Category:** Conversation\
**Tags:** Design\
**Created:** [January 2, 2023, 11:48pm UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672 "2023-01-02T23:48:15Z")\
**Posts on this page:** 20\
**Page:** 1

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**Author:** ![CrisprCAS9](https://sea2.discourse-cdn.com/flex016/user_avatar/discourse.peacefulscience.org/crisprcas9/32/9145_2.png) [@CrisprCAS9](https://discourse.peacefulscience.org/u/CrisprCAS9)\
**Post date:** [January 2, 2023, 11:48pm UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/1 "2023-01-02T23:48:15Z")

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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…

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**Author:** ![Dan\_Eastwood](https://sea2.discourse-cdn.com/flex016/user_avatar/discourse.peacefulscience.org/dan_eastwood/32/2368_2.png) [@Dan\_Eastwood](https://discourse.peacefulscience.org/u/Dan_Eastwood)\
**Post date:** [January 2, 2023, 11:50pm UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/2 "2023-01-02T23:50:58Z")

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For reference:

> [@Multiplying Probabilities](https://discourse.peacefulscience.org/t/multiplying-probabilities/7630):
>
> Continuing the discussion from [Comments on Gpuccio: Functional Information Methodology](https://discourse.peacefulscience.org/t/comments-on-gpuccio-functional-information-methodology/7560/318): Pardon me, but my pet peeve has been perked! @AllenWitmerMiller, bring me my soapbox! slight_smile I am quoting @Gpuccio here, but only because this is the latest example of an error I see regularly, and darnit, I’m getting tired of correcting some basic probability calculations. The error is, probabilities do not multiply this way. If X is some event and the probability of X occurring in a single trial is 0.1, then the probability of X occurring in two trials generates the following probability distribution: The probability X does not occur in either of two trials: (1.0-0.1)\times(1.0 - 0.1) = 0.9 \times 0.9 = 0.81 The probability X occurs in the first trial but not the second: (0.1)\times(1.0 - 0.1) = 0.1 \times 0.9 = 0.09 The probability X does not occur in the first trial but does in the second: (1.0-0.1)\times(0.1) = 0.9 \times 0.1 = 0.09 The probability X occurs in both the first…

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**Author:** ![CrisprCAS9](https://sea2.discourse-cdn.com/flex016/user_avatar/discourse.peacefulscience.org/crisprcas9/32/9145_2.png) [@CrisprCAS9](https://discourse.peacefulscience.org/u/CrisprCAS9)\
**Post date:** [January 3, 2023, 12:54am UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/3 "2023-01-03T00:54:43Z")

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Continuing the discussion from [Personally attacking the opposite view](https://discourse.peacefulscience.org/t/personally-attacking-the-opposite-view/15614/605):

> [@On another topic](https://discourse.peacefulscience.org/t/15614/605):
>
> > The mean fixation times, obtained directly from the simulations, were uniformly between 3 × 10^4 and 10^6 generations (data not shown).
> 
> Small number is the one to use for small populations, you used the large one. That’s two orders of magnitude.
> 
> > [@On another topic](https://discourse.peacefulscience.org/t/15614/561):
> >
> > and 200 x bacterial time
> 
> Except you didn’t use 200x the bacterial time, you used a 200 year generation time for humans, because you multiplied generations by 200 and ended with years, and that’s how math works. Human generation time is 25 years, you used 200, that’s another order of magnitude.
> 
> So even assuming as you do that the numbers from Lynch you cite are relevant to the question and that it is appropriate to use human generation time for the entire mouse/human divergence, your math was wrong by 3 orders of magnitude.
> 
> Obviously, neither of those assumptions is even close to correct, but we’re not there yet.

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?

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**Author:** ![colewd](https://avatars.discourse-cdn.com/v4/letter/c/ecd19e/32.png) [@colewd](https://discourse.peacefulscience.org/u/colewd)\
**Post date:** [January 3, 2023, 4:14am UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/4 "2023-01-03T04:14:02Z")

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> [@CrisprCAS9](#):
>
> This thread exists for him to provide his mathematical support, and for the careful and respectful consideration of the same.

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.

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**Author:** ![CrisprCAS9](https://sea2.discourse-cdn.com/flex016/user_avatar/discourse.peacefulscience.org/crisprcas9/32/9145_2.png) [@CrisprCAS9](https://discourse.peacefulscience.org/u/CrisprCAS9)\
**Post date:** [January 3, 2023, 4:27pm UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/5 "2023-01-03T16:27:06Z")

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> [@colewd](#):
>
> There is no point here IMO as the time to generate a new gene based on Lynch’s estimates will exceed available evolutionary time

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.

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**Author:** ![Mercer](https://avatars.discourse-cdn.com/v4/letter/m/e274bd/32.png) [@Mercer](https://discourse.peacefulscience.org/u/Mercer)\
**Post date:** [January 3, 2023, 4:27pm UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/6 "2023-01-03T16:27:18Z")

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> [@colewd](#):
>
> It also has not been experimentally demonstrated in bacteria.

One of \>4000 papers:

[https://www.sciencedirect.com/science/article/abs/pii/S0006291X22015923?via%3Dihub](https://www.sciencedirect.com/science/article/abs/pii/S0006291X22015923?via%3Dihub)

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**Author:** ![colewd](https://avatars.discourse-cdn.com/v4/letter/c/ecd19e/32.png) [@colewd](https://discourse.peacefulscience.org/u/colewd)\
**Post date:** [January 3, 2023, 5:27pm UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/7 "2023-01-03T17:27:13Z")

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> [@CrisprCAS9](#):
>
> Show your work, Bill. That’s the point of the thread

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?

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**Author:** ![Dan\_Eastwood](https://sea2.discourse-cdn.com/flex016/user_avatar/discourse.peacefulscience.org/dan_eastwood/32/2368_2.png) [@Dan\_Eastwood](https://discourse.peacefulscience.org/u/Dan_Eastwood)\
**Post date:** [January 3, 2023, 5:37pm UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/8 "2023-01-03T17:37:29Z")

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> [@colewd](#):
>
> Again there is no point.

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.

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**Author:** ![Mercer](https://avatars.discourse-cdn.com/v4/letter/m/e274bd/32.png) [@Mercer](https://discourse.peacefulscience.org/u/Mercer)\
**Post date:** [January 3, 2023, 5:38pm UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/9 "2023-01-03T17:38:39Z")

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> [@colewd](#):
>
> > [@CrisprCAS9](#):
> >
> > Show your work, Bill. That’s the point of the thread
> 
> Again there is no point.

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

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**Author:** ![Rumraket](https://sea2.discourse-cdn.com/flex016/user_avatar/discourse.peacefulscience.org/rumraket/32/9328_2.png) [@Rumraket](https://discourse.peacefulscience.org/u/Rumraket)\
**Post date:** [January 3, 2023, 5:38pm UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/10 "2023-01-03T17:38:41Z")

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> [@colewd](#):
>
> The models show that the waiting time is excessive

SHOW

YOUR

WORK.

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**Author:** ![John\_Harshman](https://sea2.discourse-cdn.com/flex016/user_avatar/discourse.peacefulscience.org/john_harshman/32/1121_2.png) [@John\_Harshman](https://discourse.peacefulscience.org/u/John_Harshman)\
**Post date:** [January 3, 2023, 9:31pm UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/11 "2023-01-03T21:31:00Z")

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> [@colewd](#):
>
> We all know these conditions are substantially less favorable in bacteria then in mammals and vertebrates.

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

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**Author:** ![CrisprCAS9](https://sea2.discourse-cdn.com/flex016/user_avatar/discourse.peacefulscience.org/crisprcas9/32/9145_2.png) [@CrisprCAS9](https://discourse.peacefulscience.org/u/CrisprCAS9)\
**Post date:** [January 3, 2023, 9:31pm UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/12 "2023-01-03T21:31:26Z")

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> [@colewd](#):
>
> The models show that the waiting time is excessive

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

No?!

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!**

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**Author:** ![colewd](https://avatars.discourse-cdn.com/v4/letter/c/ecd19e/32.png) [@colewd](https://discourse.peacefulscience.org/u/colewd)\
**Post date:** [January 3, 2023, 9:39pm UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/13 "2023-01-03T21:39:55Z")

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> [@Dan\_Eastwood](#):
>
> 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.

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.

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**Author:** ![CrisprCAS9](https://sea2.discourse-cdn.com/flex016/user_avatar/discourse.peacefulscience.org/crisprcas9/32/9145_2.png) [@CrisprCAS9](https://discourse.peacefulscience.org/u/CrisprCAS9)\
**Post date:** [January 3, 2023, 9:44pm UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/14 "2023-01-03T21:44:14Z")

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> [@colewd](#):
>
> We are comparing 2 similar population genetic models with different working assumptions.

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

> [@colewd](#):
>
> This discussion is not about the math it is about the assumptions

> [@colewd](#):
>
> When these models are applied to vertebrates

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

> [@colewd](#):
>
> 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.

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?

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**Author:** ![RonSewell](https://sea2.discourse-cdn.com/flex016/user_avatar/discourse.peacefulscience.org/ronsewell/32/6194_2.png) [@RonSewell](https://discourse.peacefulscience.org/u/RonSewell)\
**Post date:** [January 3, 2023, 9:47pm UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/15 "2023-01-03T21:47:02Z")

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> [@colewd](#):
>
> 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.

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

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**Author:** ![Dan\_Eastwood](https://sea2.discourse-cdn.com/flex016/user_avatar/discourse.peacefulscience.org/dan_eastwood/32/2368_2.png) [@Dan\_Eastwood](https://discourse.peacefulscience.org/u/Dan_Eastwood)\
**Post date:** [January 3, 2023, 10:20pm UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/16 "2023-01-03T22:20:40Z")

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Bill,  
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.

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**Author:** ![colewd](https://avatars.discourse-cdn.com/v4/letter/c/ecd19e/32.png) [@colewd](https://discourse.peacefulscience.org/u/colewd)\
**Post date:** [January 3, 2023, 10:22pm UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/17 "2023-01-03T22:22:14Z")

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> [@CrisprCAS9](#):
>
> 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?

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.

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**Author:** ![Faizal\_Ali](https://sea2.discourse-cdn.com/flex016/user_avatar/discourse.peacefulscience.org/faizal_ali/32/12416_2.png) [@Faizal\_Ali](https://discourse.peacefulscience.org/u/Faizal_Ali)\
**Post date:** [January 3, 2023, 10:22pm UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/18 "2023-01-03T22:22:35Z")

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> [@CrisprCAS9](#):
>
> Does it? How do you know?! Have you… done the math?

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._

And, as everyone knows, \ ***_REALLY REALLY BIG NUMBERS MEAN GODDIDIT_.**

It’s simple logic.

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<div class="post-metadata">

**Author:** ![colewd](https://avatars.discourse-cdn.com/v4/letter/c/ecd19e/32.png) [@colewd](https://discourse.peacefulscience.org/u/colewd)\
**Post date:** [January 3, 2023, 10:23pm UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/19 "2023-01-03T22:23:01Z")

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> [@RonSewell](#):
>
> They may. They may not. That would depend on the formulation and parameters, wouldn’t it? Hence the need for the math.

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.

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**Author:** ![Dan\_Eastwood](https://sea2.discourse-cdn.com/flex016/user_avatar/discourse.peacefulscience.org/dan_eastwood/32/2368_2.png) [@Dan\_Eastwood](https://discourse.peacefulscience.org/u/Dan_Eastwood)\
**Post date:** [January 3, 2023, 10:23pm UTC](https://discourse.peacefulscience.org/t/bills-math-class/15672/20 "2023-01-03T22:23:36Z")

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Closed on January 3, 2023, 10:23pm UTC



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