# Are Mathematicians Qualified to Discuss Evolution? Part Two

In Part One of this essay I discussed my answer to the question of whether mathematicians were qualified to discuss evolution. The inspiration for these musings was this post, from Discovery Institute blogger Casey Luskin.

We now pick up the action in the second paragraph of Luskin's post:

The truth is that mathematics has a strong tradition of giving cogent critique of evolutionary biology. After all, Darwin's theory of evolution by natural selection is fundamentally based upon an algorithm which uses a mathematically describable trial and error process to attempt to produce complexity. Population genetics is rife with mathematics. In fact, one criticism of the alleged transitional fossil sequences for whales is that they represent evolutionary change on too rapid a timescale to be mathematically feasible. It seems that there is no good reason why those trained in mathematics cannot comment on the ability of the Neo-Darwinian mutation-selection process to generate the complexity of life.

No one who could write a paragraph like that should be passing judgment on who is, and is not, qualified to be discussing evolution.

Luskin's task here is to defend the DI's ridiculous list of vaguely defined scientists who dissent in some ill-defined way from modern evolutionary theory. In particular, he needs to justify the idea that mathematicians, as mathematicians, have some particular insight on this subject. So he searches deep within his sordid little brain and conjures up three talking points he's learned how to say but knows nothing about.

First we learn that natural selection is “based upon an algorithm which uses a mathematically describable trial and error process to attempt to produce complexity.” I won't go into all the ways that this is an awkward and incomprehensible sentence. The broader point is that it is entirely uncontroversial to say that the prolonged action of natural selection acting on random genetic variations can, in principle, craft complex structures. You don't need a degree in mathematics to get the idea. Whether it is a viable explanation in practice, however, depends entirely on the biological facts of the matter. Mathematicians as such have nothing to say about that question. Luskin would have you believe that dimwitted biologists work in bafflement over the complex logic by which natural selection operates, and need clear-thinking mathematicians to come in and set them straight.

Then we learn that population genetics is “rife with mathematics.” Indeed it is, but so what? The abstract models of population genetics show simply that under a variety of realistic assumptions, forces like natural selection and genetic drift can lead to great changes in the frequencies of alleles in a population. Mathematicians might have a leg-up in understanding the minutiae of some of these models, but that has nothing to do with their application in practice. In terms of defending the validity of evolutionary theory, the mathematics says simply that natural selection works effectively indeed.

Luskin's final point is the silliest of all. There's a reason he provides neither link nor reference to anyone arguing seriously that the impressive transitional forms linking bear-like mammals to modern whales represent a mathematically unfeasible change. Even in principle it would be impossible to make such an argument work.

So none of Luskin's three points provide any reason for thinking that mathematicians have some special insight into whether evolution is a viable theory. But we really must address that first sentence. As presented by Luskin, that strong tradition of mathematicians offering cogent critiques of evolution consists of two points. He mentions Granville Sewell's recent attempts to revive the thermodynamics argument. (I refuted Sewell's silly argument here.) Then he mentions the 1966 Wistar conference. That's it. A single conference forty years ago, and a recent attempt to revive one of the oldest and dumbest anti-evolution arguments ever offered.

He might have added the writings of David Berlinski or William Dembski to the list, but that would hardly help his case.

Luskin writes:

One of the best known mathematical forays into evolution was the 1966 Wistar Symposium, held in Philadelphia, where mathematicians and other scientists from related fields congregated to assess whether Neo-Darwinism is mathematically feasible. The conference was chaired by Nobel Laureate Sir Peter Medawar. The general consensus of many meeting participants was that Neo-Darwinism was simply not mathematically tenable.

This is a terribly misleading way of describing what happened at Wistar. In the preface to the conference proceedings, biologist Martin Kaplan describes the origin of the conference this way:

Perhaps a few words on the genesis of this Symposium would be of interest. Actually, the seed was sown in Geneva in the summer of 1965 during the course of two picnics held at Vicki Weisskopf's house and at my house, on two consecutive Sunday afternoons. Koprowski and I, the only biologists present, were confronted by a rather weird discussion between four mathematicians - Eden, Schutzenberger, Weisskopf and Ulam - on mathematical doubts concerning the Darwinian theory of evolution. At the end of several hours of heated debate, the biological contingent proposed that a symposium be arranged to consider the points of dispute more systematically, and with a more powerful array of biologists who could function adequately in the universe of discourse inhabited by mathematicians.

Presumably these are the same dogmatic biologists who don't allow any dissent from their preferred view of things.

At any rate, what happened at Wistar was that Eden, Ulam and Schutzenberger were given a chance to present their objections and a cadre of biologists patiently explained why they were wrong. (Weisskopf did not present a paper at the conference). The conference proceedings do not record anyone beyond those three reporting any fundamental difficulties with Neo-Darwinian theory. General consensus indeed.

I'm afraid the mathematicians didn't shower themselves in glory at the conference. (This might be a good time to mention that Eden was an engineer and Weisskopf was a physicist). Eden and Ulam relied on standard probability arguments against Neo-Darwinism. As with all such arguments, their mathematical calculations left out so many relevant variables that they were effectively useless. Schutzenberger, meanwhile, relied on bad analogies of genes to computer programs, and seemed concerned that biologists had no clear explanation for how genes become organisms. The biologists were rightly unimpressed with this argument as well.

I should also point out that while as an attempt to provide mathematical challenges to Neo-Darwinism the conference fell flat, the critics did provide suggestions for how certain basic questions in evolution could be formulated mathematically. Some of their suggestions in this regard were quite sound.

One of these days I might do some posts examining in more detail the topics discussed at the Wistar conference. For now, however, let me close by noting that the claim that mathematicians as such have no authority for talking about evolution really should be no more controversial than claiming they have no authority to discuss eighteenth century Russian literature. And I suspect that no one would try to claim that biologists have especially keen insights to offer with regard to the work mathematicians do.

Yet a lot of otherwise sensible people find it perfectly reasonable to suggest that non-biologists should nonetheless have profound things to say about evolution. Why is that? I think there are two reasons. One reason is that since evolution is commonly thought to have profound social and religious implications, every two bit hack whose read a few pages of Gould or Dawkins and has an axe to grind fancies himself qualified to discuss the subject.

The second reason is that in certain scientific circles the idea lingers that biology is a second-class science, lacking the rigor of, say, physics. The physicists at the Wistar conference frequently expressed their lament that evolution seemed to be lacking in general principles and all-encompassing schemata. But the simple fact is that while there is a large mathematical component to modern evolutionary theory, many of the problems biologists study just don't lend themselves to mathematical treatments.

After all, applied mathematics proceedes by developing an abstract model representing some real-life situation of interest. Constructing such a model inevitably requires that you ignore large numbers of variables that affect the objects under study in real-life. This approach is practical when there are only a few variables with a major impact on what is being studied. Many things affect the flight of a thrown tennis ball, but most of them can be ignored when you are trying to predict its trajectory. That is sadly not the case in trying to model evolution over long time scales. There are too many important variables to develop a practical model.

It is a credit to biologists that they forge ahead nonetheless. It reflects badly on the scientific chauvinists that they insist so strongly on using inappropriate tools for the job.

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The thing I find most interesting about the focus of your post is how you focus on the mathematicians on the DI list. In reality, according to the NY Times article about the original list, of the 514 signers, there were 128 biologists, 76 chemists, 75 engineers, 63 physicists, 26 biochemists, and 24 professors of medicine.

I grant you that the NY Times (and Ed Brayton) considers 128 biologists to be "few"... but why the fuss about the mathematicians?

Why is Luskin so eager to argue that mathematicians have special qualifications to evaluate the issues of evolutionary science? Could it be because the Discovery Institute has so few actual scientists in its ranks that it's necessary to issue a brief on behalf of its two mathematical Fellows, Dembski and Berlinski? Yeah, that's probably all it is.

And Luskin is an earth scientist and an attorney, so what does he know about mathematicians anyway? Maybe he ought to clear that up first.

dlamming-

The reason for the focus was simply that Casey Luskin was discussing mathematicians and it was his post that I was responding to. But most of my remarks apply with no change to any other nonbiologist who wants to comment on evolution.

"Why is Luskin so eager to argue that mathematicians have special qualifications to evaluate the issues of evolutionary science?"

Because if you can't make the mathematics work, then all you are left with is assertion, which is no better a weapon than is used by the creationists.

In fact, one criticism of the alleged transitional fossil sequences for whales is that they represent evolutionary change on too rapid a timescale to be mathematically feasible.

I'll bet the "poof" "poof" "poof" of creationism isn't too rapid a timescale to be mathematically feasible though. That's because nothing is too unfeasible for creationism. Including evolution. So I don't see what Luskin's problem is.

There's a reason he provides neither link nor reference to anyone arguing seriously that the impressive transitional forms linking bear-like mammals to modern whales represent a mathematically unfeasible change.

Eh? Bearlike? The ancestors of whales were early artiodactyls -- hoofed animals. Not like cows, but something vaguely like carnivorous pigs.

Jason wrote:

At any rate, what happened at Wistar was that Eden, Ulam and Schutzenberger were given a chance to present their objections and a cadre of biologists patiently explained why they were wrong. (Weisskopf did not present a paper at the conference). The conference proceedings do not record anyone beyond those three reporting any fundamental difficulties with Neo-Darwinian theory.

By lumping Ulam together with Eden and SchÃ¼tzenberger, I believe you're conceding much too much to creationist slandermongers. On my reading of the proceedings, the gulf between the attitudes of Ulam (and Weisskopf) on the one hand, and Eden and SchÃ¼tzenberger on the other, seemed to be just as great as that between these latter two and the biologists. Whatever the differences of opinion between Ulam or Weisskopf and any of the biologists present, they didn't seem to me to be any more substantial than those between the biologists themselves.

I could find nothing at all in the proceedings of the symposium to indicate that any of its participants other than Eden and SchÃ¼tzenberger would have subscribed to the so-called "consensus" which Mr Luskin claims "many" of them came to---namely, "that Neo-Darwinism was simply not mathematically tenable". In the case of Ulam and Weisskopf, there are in fact numerous statements of theirs, recorded in the symposium's proceedings, which provide overwhelming evidence to the contrary---namely, that neither of them would have supported the position of Mr Luskin's so-called "consensus".

Jason wrote:

Eden and Ulam relied on standard probability arguments against Neo-Darwinism. ...

No, this is simply not true of Ulam's presentation. For some unknown reason creationist slandermongers have chosen to make up fibs about Ulam's presentation at this symposium. It's rather depressing to see them now being accepted at face value by the good guys.

While Luskin doesn't go so far as to make up fibs about the presentation, he does nevertheless try to insinuate that Ulam wpuld have supported his so-called "consensus" with a classic out-of-context quotation (bolding mine):

Stanislaw Ulam, quoted by Casey Luskin, wrote:

"[I]t seems to require many thousands, perhaps millions, of successive mutations to produce even the easiest complexity we see in life now. It appears, naively at least, that no matter how large the probability of a single mutation is, should it be even as great as one-half, you would get this probability raised to a millionth power, which is so very close to zero that the chances of such a chain seem to be practically non-existent."

To an experienced creationist watcher, the words I have bolded in the above quotation practically scream out "misleading quote mine!", in which the person being quoted outlines an apparent problem which they then go on to show is not really a problem at all. And in fact this is exactly what Ulam did. In his next two paragraphs, which Casey Luskin very conveniently fails to quote, Ulam went on to say:

But, I believe that the comments of Professor Eden, in the first five minutes of his talk at least, refer to a random construction of such molecules, and even those of us who are in the majority here, the non-mathematicians, realize that this is not the problem at all.

A mathematical treatment of evolution, if it is to be formulated at all, no matter how crudely, must include the mechanism of the advantages that single mutations bring about and the process of how these advantages, no matter how slight, serve to sieve out parts of the population, which then get additional advantages. It is the process of selection which might produce the more complicated organisms that exist today.

Ulam then went on to explain that his aim was to illustrate how one could go about setting up mathematical models for the process of selection. But before he proceeded to do this he openly warned his audience that the models he was about to come up with were so crude as to be completely unrealistic, and throughout his presentation he repeatedly emphasised that the values of the paremeters one would need to know to run his models were in fact subject to very large uncertainies, in many cases of several orders of magnitude.

In short, there was nothing at all in his presentation that could be reasonably construed as constituting a claim that any part of evolutionary theory was "mathematically untenable".

By David Wilson (not verified) on 16 Jul 2006 #permalink

I am not certain you are right about your reasoning that just because there are many variables influencing long-term evolution a mathematical model becomes less approriate. For me, a large number of variables, means that any description of the system will be very simplified but I think this applies equally to verbal and mathematical descriptions.

A mathematical model does not have to aim at the very precise quantative predictions possible in physics. It can equally well be intended as a rough qualitative description.

I agree that there are disadvantages to using a mathematical approach. But there are advantages to, like clarity and it being obvious whether your proposed logic works.

By Johan Richter (not verified) on 16 Jul 2006 #permalink

Thanks David! I was looking for the context of that passage!

Where did you find it?

386sx said:

I'll bet the "poof" "poof" "poof" of creationism isn't too rapid a timescale to be mathematically feasible though.

This always makes me wonder...
Creationist claim bear like or hippopotamus like to whale is impossible because the time scale of 200 million years is to short for variations and selections to work. At the same time 3 seconds by the clock is not too short for creation of a whale to be believed.

FhnuZoag wrote:

Thanks David! I was looking for the context of that passage!

Where did you find it?

In a copy of the syposium's proceedings held in the Australian National University's library, which is about a mile or so from where I live.

By David Wilson (not verified) on 16 Jul 2006 #permalink

In addition, nearly all the so called biologists received their degrees from unaccredited bible colleges or diploma mills.

Why not use special pleading for mathematicians to argue about evolution? After all, (not to knock mathematicians, mathematics, or math ed.) the general population (especially of the US) doesn't care for math and their level of mathematical literacy is low. So, appologies for the conspiracy theory, this sounds like another one of those accept our ideas because we can do the math and other people can't. What's that old saying about bamboozling with BS.

By i like latin (not verified) on 16 Jul 2006 #permalink

Are biologists qualified to give an opinion on evolution? Natural selection is not important. It is an insignificant process working within a larger, poorly understood framework. Truth is, nobody really understands evolution all that well ... most "qualified individuals" and all the DI guys are just way off base.

Wow, that Wistar conference was forty years ago. I'm getting old.

And creationist arguments haven't aged a day... They're still the same as ever.

After all, Darwin's theory of evolution by natural selection is fundamentally based upon an algorithm which uses a mathematically describable trial and error process to attempt to produce complexity.

I think the bit where I added emphasis gives a clue to Luskin's problem. Complexity is merely a consequence of what results from the evolutionary processes that have, as a primary consequence, the greater reproduction rates of some genetic makeups.

David Wilson-

Thank you for providing the full context of the Ulam quote. I was going to do that myself, but then decided the blog entry was too long already. I would also point out that I said in my essay that some of the comments of the mathematicians were directed toward showing how evolutionary questions could be formulated mathematically. Ulam's essay was the one I had in mind.

But I also think it's clear from Ulam's remarks that he was skeptical of conventional Darwinian explanations for complex structures. That is implied in both his paper and the ensuing discussion, as recorded in the procedings. So I don't think my characterization of his argument is out of bounds. In several places he does, indeed, remark that his models are unrealistic. But in other places he suggests that he thinks they are unrealistic in ways that should make it easier for Darwinian explanations.

Nick-

Thanks for the correction. Note the remark from Part One about my level of expertise!

So, when you ask "Are Mathematicians Qualified to Discuss Evolution?", you think fellow Science Blogger Mark Chu-Carroll unqualified?

This is really just a form of ad hominem.

The real qualification ought to be a demonstrated ability to think and reason scientifically, to be able to objectively analyze information, and to continually ask, "If I'm wrong, how could I tell?"

Otherwise, it is just elitist credentialism.

As someone trained in mathematics (Ph.D.), I do not believe that mathematics in this context is a science and I do not believe therefore that there is anything special that a mathematician can bring to the table that cannot be brought by other educated people who happen also to be educated in a field that isn't actually science.

As someone whose undergraduate minor was physics, though, and as someone who has just finished supervising a doctoral thesis on a computational aspect of phylogenetics, I do think I have some credibility, not on the evolutionary biology itself, but on the nature of science itself. Further, I am an educator and to the extent that this is an issue about what to teach in schools I think I can make cogent arguments based on analogy with other disciplines about what one teaches to students at various points in their educational lives.

I use the word I here to mean myself. I think, though, that others with similar backgrounds should be able to make the same arguments.

As a math major and physics minor, I remember having Newton's equations of motion derived several times in my undergraduate years, and I remember using examples from physics as I taught calculus. I also remember my astonishment when I found that one of my grad school officemates had never seen the equations of motion derived. He had majored in math and minored in philosophy. With a background like that, or perhaps a minor in psychology (such as Dembski's), it is I believe reasonable to question a mathematician's credentials as a scientist.

Two relevant points about the nature of science are burned in my brain from my physics classes. The first is that science, at least physics, is not about why things happen. It is merely a description of what happens, done in such a way as to quantify the what so that predictions about future experiments can be made. This is similar to what Lisa Randall of Harvard has written in John Brockman's Intelligent Thought (page 203): But scientists don't ask questions about purpose; they ask questions about consequences. Newton's laws don't tell us why a ball should follow a certain trajectory; it just tells us that it does and how to calculate it.

The second is that one is not doing science if one is merely whining about the problematic parts of current science. I whined to a physics prof about the many particles being seemingly invented just to correct for problems in the data. Surely, I argued, this was all too Ptolemaic. He said that yes, it was, and if I really believed this strongly enough then I should change majors to physics so I could come up with a better theory that covered the known data but did so in a less ad hoc manner. That, after all, would be science. The current theory is fleshed out with more and better data. As data comes in, problems in the theory occur because science is never completely done. And every so often, a brilliant person comes up with a new theory that is consistent with the data but in a more elegant, simplified, and compelling way, and that does better at predicting the data in future experiments.

It is on this last point that ID falls completely flat. It is not science. It is an argument from hubris: I am a smart person. When I apply the scientific method, I find that I don't understand this. Therefore this is unknowable by the scientific method and must have occurred by a 'technology' that is indistinguishable from magic. ID falls flat as science because as a purportedly more comprehensive theory there is nothing that it could not explain. All of Dembski's mathematics is nothing more than whining about the fact that he does not understand how it is that evolution could have beaten his self-imposed and seemingly-impossible odds. It isn't biology, and as mathematics it fails because it proves only that *Dembski* can't figure out the problem.

Finally, as an educator, I will argue that I do have something to say on the issue of when we expose schoolchildren to the fact that what they learned in grade N may have to be re-learned with adjustments in grade N+1. In elementary school we start by telling students not to think about 1/0, or worse yet, 0/0. These are undefined. By high school some students will have seen that there are ways in which these can be dealt with. By the time they (or some of them) get to calculus, they will learn how to deal with 0/0 in a mature way. The same can be done in biology, and it is here that I think we (more carefully put, they who are the biologists) can in fact argue from authority. The experts in a discipline spend part of their time figuring out how best to teach their discipline, and we should listen to the experts.

I think that mathematicians are in fact better situated to understand the evidence for evolution than others. The following argument will be very convincing for mathematicians because they will quickly understand how to construct tree-like structures from strings of letters.

The data from ERV's, pseudogenes, regular genes, etc, can be ordered in a tree like structure. The fact that the trees coming from different parts of the genome match each other (as well as the fossil based tree) is simply inexplicable without common descent.

Creationism is not uncommon among professional mathematicians, I estimate that at least 5% of them hold this position. However, I think that most of them can in fact change their position upon learning about the topic. The argument about the matching tree structures is particularly effective on mathematicians because they know they can reconstruct those trees themselves when given DNA data.

Yet a lot of otherwise sensible people find it perfectly reasonable to suggest that non-biologists should nonetheless have profound things to say about evolution. Why is that? I think there are two reasons.

A third problem was identified by Jacques Monod (1974): "[A] curious aspect of the theory of evolution is that everybody thinks he understands it."

A Scientific Dissent From Darwinism
"We are skeptical of claims for the ability of random mutation and natural selection to account for the complexity of life. Careful examination of the evidence for Darwinian theory should be encouraged."
"We are skeptical of claims for the ability of random mutation and natural selection to account for the complexity of life. Careful examination of the evidence for Darwinian theory should be encouraged."

Shouldn't any biologist worth his/her salt have little problem in signing this petition? I'm afraid that it is all too common for up and coming workers just to accept the current thinking without anything in the way of serious questioning of the "accepted wisdom".

Natural Selection by random mutation simply does not explain the reality that we see. Have you guys lost the ability to be "scientists"? The inconsistencies, "holes" and general lack of explanatory power are quite glaring. The DI guys are right on this. Taken literally and in islolation the above quote is not so crazy.

Isn't about time we looked seriously into this? A new biology is needed. One that will sweep the Creationist nonsense away once and for all. More biologists should be sigining this petition and let dear old Darwin go to bed.

I feel one of those pesky paradigm shifts coming on ...

Pepper, I have two questions for you.

1) Does anyone actually believe that random mutation and natural selection alone account for the complexity of life? If not, why bother to write and sign a petition to be skeptical of it?

2) Has anything in evolutionary theory progressed since Darwin's initial proposal of a mechanism for evolution? If so, why the need to put him to bed as though he was the end of all thought and not the beginning?

And one thought: just because you haven't "looked seriously into this", that doesn't mean that nobody else has.

Pepper writes:

Shouldn't any biologist worth his/her salt have little problem in signing this petition?

You're right, the statement itself could be signed in complete honesty by any biologist, even the most rabid atheistic demonic ones ... if taken literally and in isolation as a scientific claim and not for what it is, a PR propoganda stunt. If that's all it takes to be a 'Darwin Doubter', then I guess I'm one too! Woo-HOO!!

What I'm wondering is who are these people making "claims for the ability of random mutation and natural selection to account for the complexity of life", and what exactly are they saying?

We should emphasize that the statement does not contain any arguments, it only contains the statement itself and a list of names and educational pedigree. It is by definition an argument to authority. Is it too much to ask that the people signing the statement actually be authorities in the field of which they are dissenting? Maybe then the statement itself wouldn't have been so nonsensical.

Pough ...

1) Must people take things so literally all the time? The petition is patently nonsensical (as Dave S point out) and I was not seriously suggesting that it should be signed. I was merely pointing out that the statement itself is not as whacky as those who wrote it. Maybe I need to work some more on my facetiousness skills?

2) Yes. Again, such a literal reading of my post. Being a Darwin-doubter does hardly make him the end of all thought.

one thought: Again, must you take things so literally?

Anyway, off-topic now so ...

Must people take things so literally all the time?

If you know a sure way to discern insincerity from sincere stupidity without tone of voice or facial expression, be sure to share it.

Maybe I need to work some more on my facetiousness skills?

Probably. It just gets so hard to tell, even when people take things WAY over the top. No matter how obviously dumb you make a post, there is someone saying something dumber and being honest in another thread.

pough -

Did you know the word "facetious" is one of only 2 words in the English language where the vowels a, e, i, o and u appear in that order? Can you name the other?

O.K., ... now I'm being facetious. :)

Pough, there's no need to descend to that level. Maybe I am stupid - and I'm sincerely sorry for not being as educated as yourself. Maybe I should just quit getting involved in discussions of evolution until I am sufficently "credentialified"?

All I'm saying, in my clumsy and uneducated ramblings, is that one of the central tenets (the statement) of the DI's view on evolution is quite possibly true. The sort of Creationsists that the DI represents will always win the argument over whether traditional Darwinian processes can account for what we see around us - because they don't in fact describe them all that well.

Dave S was able to discern from my dumb post what I was saying: the statement that the skeptics are signatories to is maybe accurate.

@Dave S:

abstemious, acheilous, anemious, annelidous, arsenious and caesious.
(I had to search for them obviuosly for I have no brain.)

- yours,
a "mere armchair biologist" who speaks with absolutely no authority at all.

What level? I was calling you insincere, based on your admission of being fecesish. ;-) I was thrown off by your faux-creationist style (you did a very good job of sounding like some of the sincere dopes). I hope we don't need credentials or education; I have none.

Pepper says:

abstemious, acheilous, anemious, annelidous, arsenious and caesious.
(I had to search for them obviuosly for I have no brain.)

Yikes, look like more than one after all! Good catch. I only knew of the first.

Just a personal note with apologies for a topic change. I'm a lawyer and law is so much easier (I won't guess how many degrees of magnitude easier)than any science. So when I think of how painful it is to hear amateurs or beginners(even well meaning ones) discuss a legal topic with which I am familiar, I can only imagine what biologists feel in the current climate. All complexities smoothed over, liberal use of white-out to avoid contrary positions...One of my brothers is a mathematician: if he's talking about topology or analysis, all is well. If he starts in on biology however, I get my geneticist brother on speaker phone, the proper source for the job at hand.