Mathematical Flimflam

[Audio version available at http://mathenchant.org/050.mp3.]

I’m a pure mathematician with no background in applied mathematics. But lately I’ve been striving to make a name for myself in the less-crowded field of mis-applied mathematics, and bogus science more broadly.

Now you may be asking yourself, is bogus science really less crowded a field than good science? After all, if Sturgeon’s law (“Ninety percent of everything is crap”) applies to science, then we can expect crappy science to predominate over the good kind. But bogosity transcends mere crappiness. For something to be bogus, I think there must be an attempt to deceive. Or at least, there must be the appearance of an attempt to deceive. Sometimes the appearance is itself a sham, and that’s the kind of second-order bogosity I enjoy practicing, when I try my hardest to act like someone who genuinely believes (and wants others to believe) a nonsensical theory.

My forum is the Festival of Bad Ad Hoc Hypotheses (BAHFest), held periodically in various locations around the world (San Francisco, Seattle, Cambridge, Sydney, and London). It’s a celebration of well-argued and thoroughly researched but completely incorrect scientific theories. BAHFest is dedicated to the proposition that no matter how absurd a premise is, you can find a way to abuse the tools of science to support your cause and make people laugh in the process. (Or make nerds laugh, anyway.)

BAHFest was the brainchild of Zach Weinersmith whose Infantapulting Hypothesis got the game going.

 

 

 

One of my favorite BAHFest talks (and, as it happens, another one that centers on babies) is Tomer Ullman’s “The Crying Game”.

 

 

If you have a favorite of your own, please submit it in the Comments!

Developing a BAHFest premise is a little bit like doing math, insofar as math is the game of formulating precise assumptions, based in reality or not, and seeing where they lead. The biggest difference is that in pure math, internal consistency is all that matters, whereas in science, Reality is the ultimate arbiter of value. When the science is bad, Reality says “That’s not true!” When the science is not merely bad but bogus, the scientist tells Reality “That’s what YOU say!” and shoves a bound and gagged Reality into a closet, keeping up a steady stream of patter to drown out Reality’s muffled protests. And when the bogosity is second-order bogosity, as in a BAHFest talk, the sonic overlay of the scientist’s patter and Reality’s protests is where the humor comes from. The more shameless the abuse of Reality, the funnier the talk.

EVOLUTION

A lot of BAHFest presentations parody evolutionary psychology, because the field lends itself so readily to parody: with a little creativity you can find evidence to support almost any Just-So Story (oops, I mean hypothesis) about how those funny creatures called modern humans got to be the way they are, and nobody can travel back in time to do experiments to test (and refute) your hypothesis. But if you want an example of true bogosity of the un-funny kind, I think it would be hard to top Scientific Creationism, recently rebranded as Intelligent Design theory. As a piece of mis-applied mathematics, the mathematical argument against Darwinism is hard to top (though if you know of some bogus math you find even more egregious, please post it to the Comments!).

Before addressing the mathematical “refutation” of Darwinism, let’s consider a popular debased version of it, promulgated by fiction writer Dean Koontz ¹ (in his novel “Breathless”) and by other writers with less flair and smaller readerships. Koontz puts the anti-evolution argument in the mouth of a character named Lamar Woolsey, a mathematician specializing in chaos theory. The argument goes that even if we assume a mutation rate of one mutation per microsecond, there isn’t time in the history of our planet to allow as complicated a creature as homo sapiens to reach its current level of complexity: the number of bits of information in the genome of even the simplest of creatures exceeds the number of microseconds available for its evolution. The problem with this argument is that in truth the inequality goes the other way: the number of bits of information in the genome of even the most complex of creatures is dwarfed by the number of microseconds available for its evolution. Koontz’s numerical claim is just a flat-out (and, I would like to believe, unintentional) falsehood.

More interesting is the “correct” version of this argument, which hinges on the fact that the number of microseconds in the history of our planet, or even the number of nanoseconds in the history of our universe, is minuscule in comparison with the number of possible genomes, which is an exponential function of the number of bits of data in our particular genome. (The human genome has only ten billion base pairs, more or less, but the number of ten-billion base-pair genomes is roughly four to the power of ten billion, which is much, much larger.) It’s argued that there’s no way that evolution could have hit upon the recipe for making humans any more than a bunch of monkeys banging away at typewriters could have hit upon the recipe for crème brûlée.²

It’s absolutely true that the number of possible genomes of the same order of complexity as the human genome is vastly greater than the number of nanoseconds that our universe has existed — absolutely true, and absolutely irrelevant. That’s because the accepted model of evolution isn’t brute-force exhaustive search or random exploration. It’s a guided search through a fitness landscape with a meaningful gradient that says “It’s probably good to go farther this way” or “It’s probably bad to go farther that way.” That is, evolution isn’t like sifting a haystack in search of a needle; it’s more like searching for an iron needle in a haystack using a metal detector. Plus, there are probably a lot more viable genomes for a human-type creature than the loosely-defined consensus we call the human genome; there could be plenty of equally good needles in the evolutionary haystack.

Cartoon by Ben Orlin, aka Math With Bad Drawings. Pre-order his new book “Change is the Only Constant”!

Dean Koontz is too canny a writer to have his mouthpiece Lamar Woolsey actually subscribe to Creationism. Instead, Lamar says that the science of evolution is not yet settled. This kind of assertion is a very popular trope in science denialism, and one of the best in its arsenal, going back to the very dawn of the Enlightenment and beyond; 17th century defenders of Church doctrine suggested that, instead of advocating heliocentrism, Galileo should teach the Ptolemy-Copernicus controversy.³  Perhaps the greatest milestone in the Pseudoscientific Revolution was the discovery that skepticism, in addition to serving as a tool in the pursuit of truth, could be enlisted as a source of deliberate misinformation.

Koontz’s Lamar Woolsey says: “Darwinian evolution offends me simply as a mathematician, as it does virtually every mathematician who has ever seriously thought about it” (and even asserts that “evolutionists hate mathematicians” because mathematicians point out the flaws in evolutionary theory). One thoughtful mathematician who’s taken the time to explain what’s wrong with probability-based criticisms of Darwinism is David Bailey, whose articles “Does probability refute evolution?” and “Misuse of probability by ‘creation scientists'” should be required reading for anyone who (rightly) marvels at the complexity of the living world and is inclined to conclude (wrongly) that natural processes cannot possibly account for it.

Do probabilistic arguments against Darwinism meet my somewhat stringent definition of flimflam, which requires an attempt to deceive? That depends on who’s making the argument. If it’s someone who hasn’t encountered the sort of counter-arguments David Bailey discusses so lucidly, then no — it’s just someone spreading misinformation. But if someone has seen those counterarguments and ignores them anyway, then yes, it’s flimflam.

There are critiques that can be made (and have been made) of Darwin’s original vision, but the ones I’ve seen don’t refute Darwin’s vision as much as complicate it, and they don’t point to the existence of huge explanatory gaps that can only be filled by invoking some radically different principle (such as meddling aliens, or a Flying Spaghetti Monster, or some other sort of intelligent Creator).

Of course, if you are 100% convinced that a belief in Darwinism leads to a loss of faith in God that in turn causes souls to be damned for all eternity, then it is your godly duty to continue to trot out arguments against Darwinism that you know to be bogus. But you shouldn’t pretend you’re engaged in rational debate. (Actually, you should, if that pretense will save souls. And if that mendacity costs you your own soul, you should still tell those lies, since the salvation of the many believers you’ll convert counts for more than the damnation of your own soul. Sacrificing yourself in this fashion would be a marvelously selfless action on your part. So selfless, in fact, that maybe it shouldn’t lead to your damnation after all! But I digress.)

If you want to prove the existence of God with probability, there’s a much more efficient way to do it, without the bother of invoking evolution. All you need is a coin. Toss the coin a hundred times and record the outcome as a length-100 sequence of H’s (Heads) and T’s (Tails). Now, according to the secular humanist theory of coin-tossing (which is only a theory, mind you!), each of the two-to-the-hundredth power different sequences of H’s and T’s is just as likely as every other⁴; so the probability of your having obtained this particular sequence of H’s and T’s is only one out of two-to-the-hundredth-power, or less than .000000000000000000000000000001. Now, by the very standards that these secular humanist probabilists claim to adhere to (dare I say, the very standards that these people worship), such a low probability is a rigorous disproof of the hypothesis under consideration! So using statisticians’ own methods, we’ve ruled out the Materialist theory of coin-toss outcomes, leaving its rival, the Providential theory, as the most plausible explanation. This means that your sequence of H’s and T’s is more than just a proof of God’s existence; it’s a message from God.  Get busy decoding it!

HOW TO LIE WITH STATISTICS

If probability theory lends itself to bogus forms of argument, statistics does even more so, especially if “statistics” is understood in the broadest sense and is taken to include the art of presenting data visually so as to create the visual impression that helps your case. As a teenager, I loved Darrell Huff’s book “How to Lie With Statistics”, and you can see traces of its influence in my BAHFest talk on eclipses, awe, and (of course) evolution. 

 

In the talk, I advocate spending a quadrillion dollars to build a wall all the way around the moon. How can I present the cost in a way that minimizes sticker-shock? Why, using a logarithmic scale, of course! (And also by introducing the notion of “logarithmic dollars”, which sounds meaningful but isn’t.)

The big mathematical scam in my talk comes a little bit earlier, when I try to support my claim that there’s a causal link between human brain volume and “eclipse dosage” (defined as the fraction of the time that a spot on Earth witnesses total eclipses of the sun; it’s decreasing everywhere, albeit slowly, as the Moon gets farther and farther away from the Earth). I start with a disabling punch to people’s math anxiety by showing a slide that introduces inappropriate mathematical technology (Lagrange’s formula for polynomial interpolation) using needlessly intimidating notation.⁵ The reason I say that Lagrange interpolation is inappropriate is that I apply it in the case of just two data-points, so that “fitting with a polynomial” is just a pretentious way of saying “drawing a straight line through the points”. Of course, using just two data-points is statistically suspect from the get-go, but I make use of this ludicrously underpowered analysis in an even more bogus way, by tacitly arguing that IF the two data-simplifications (both straight lines: one for eclipses and one for brains) match up, THEN it implies a correlation between the original data. As it happens, the straight lines don’t match up, but I make them match up by using another trick I learned from “How to Lie With Statistics”, namely, adjusting the vertical axis to make the graph tell the story I want it to tell. (As Huff writes, “If you torture the data long enough, it will confess to anything.”)

And none of this even mentions my bogus conflation of correlation with causation. If I did my job as a BAHFest speaker, this didn’t occur to you while I was giving my talk, because part of the art of flimflam is distraction, and I did my best to distract.

QUESTIONS NOBODY ASKED

In preparation for presenting my hypothesis and having to answer questions afterwards, I tried to anticipate the questions I might be asked. My feeling is that, just as good fantasy and science-fiction writers often create more convincing worlds by coming up with extra details that never actually find their way onto the page, a BAHFest speaker can give a better talk if they really psych themselves into buying their own pitch.

As it happens, nobody asked the questions I came up with, but in case you’ve seen the video and want to know a little bit more about the “world-building” I did in advance, here are the questions nobody asked and the answers I would have given if someone had.

Q. You gave a Lamarckian hypothesis about the evolution of human intelligence, and then invoked a general “Equivalence Principle” that you said guaranteed that there’d be a more complicated Darwinian hypothesis that was essentially equivalent. But you never presented that Darwinian hypothesis. Could you present it now?

A. I was hoping nobody would ask. The answer is a bit, um, unpleasant. But since you asked: There’s natural genetic variation in skull size. When early humans with large skulls saw a total eclipse, their heads could accommodate the extra brain matter; when early humans with smaller skulls saw a total solar eclipse, their heads exploded. This severely compromised their reproductive fitness, especially if the explosion was forceful and the individual’s existing offspring were nearby at the time of the explosion. As evidence, I mention the fact that at many archeological sites we find not just intact skulls but skull fragments. Do we really have to dwell on this?

Q. Isn’t part of awe a feeling of humility? If so, and if humans know that human technology is behind making eclipses great again, wouldn’t that knowledge undermine feelings of awe and cancel out the brain trauma and all its benefits?

A. You’re 100% right. That’s why, if my plan moves forward, it’ll have to be done in secrecy. Plus, I’ll have to ask Zach to remove this video from the web, so that we can blame the sudden appearance of the lunar wall on space aliens.

Q. Have you talked to anyone in the Trump administration about this project?

A. Funny you should ask. They really liked my idea of a wall, but they didn’t like the solar energy part; they’d prefer to see first if there are fossil fuels on the moon that can be exploited. Which makes more sense than you might think, since the catastrophe that caused the KT extinction could have flung some dinosaur carcasses into outer space, and some of them could have landed on the moon. So there could be petrochemicals there.

Q. You talked about the wall having a positive effect on the lunar economy. But what about its effects on lunar society?

A. I think the wall will divide lunar society into two classes. All the rich people will live on the near side of the wall that faces the lights of Earth, the “Fun Side”, and all the poor people will live on the far side that faces interplanetary space, the “Dull Side”. And people being what they are, some of the dregs of lunar society will try to enjoy the good life by sneaking over to the Fun Side, instead of earning those perks the honest way, by choosing rich ancestors. So the wall will also serve as a barrier to illegal migration.

Q. When I was a professional football player⁶, I was worried about brain damage; I even retired early because of concerns about football making my brain unable to do mathematics after my retirement. But now you’re telling me that brain-trauma may actually have been making me smarter? Please clarify.

A. I’m so glad you’re here tonight, John, so that I can apologize to you in person on behalf of the entire scientific community, for squandering the opportunity you presented to us during your career at the NFL. We could’ve done FMRIs, biopsies, you name it, to help us better understand the difference between the good kind of brain damage that occurs when you metaphorically bang your head against a math problem, and the bad kind that occurs when you literally bang your head against other people. You could’ve been the Phineas Gage of the 21st century, immortalized in Neurology 101 textbooks! Instead, you’re just another mathematician. So: sorr-yyy…

Q. You cited a study that showed that inflammation can promote synaptic plasticity in some situations. But isn’t there far more evidence that inflammation is bad for the brain?

A. Well, yes. But the science isn’t settled yet, and I think it’s fair to say that the truth is somewhere in between the extremes. In the meantime, I say we should teach the controversy.

Q. Do you really think you can build a wall around the moon for just a quadrillion dollars? I mean, a quadrillion dollars doesn’t go as far as it used to.

A. Well, remember that the raw materials are already on the moon, and the energy can come from the sun. So the main expense is getting equipment and personnel to the moon, and yes, I think a quadrillion would do it, if you’re satisfied with building a mile-high wall that would roll the eclipse clock back 28,000 years. But if we’re willing to spend a quintillion dollars, we could do so much more. We could build a hundred-mile-high wall with rotatable solar panels that could selectively block or admit the sun’s light. Then we could have eclipses where the lunar disk appears to wobble around, and the solar corona does The Wave on the periphery. Wouldn’t that be awesome? I can feel my brain swelling already just imagining it.

WHAT NEXT?

Why do I do BAHFest? Because it’s fun. And because, as I said at the end of my first BAHFest appearance, “In a time when real science is mistaken for fake science and bad science masquerades as good science, it is so important to make a place in this world for bad science that says that it’s bad science.”

But (hardball question) why is it so important? Well, maybe it does some good. Showing people examples of how science can go wrong can help reinforce the principles that keep science right. For instance, I’d like to think that if stats professors tell jokes about how football causes winter, etc., it’ll help their students avoid the mistake of confusing correlation with causation. But has anyone actually studied this?

One of Randall Munroe’s most famous xkcd cartoons. Check out https://xkcd.com/ for lots more!

I’m reminded of musical satirist Tom Lehrer‘s assessment of his own impact on American society; he liked to quote Peter Cook who, on the opening of his Establishment Club in London, said it was modeled on “those wonderful Berlin cabarets which did so much to stop the rise of Hitler”.

I and my BAHFest co-presenters try to make our talks funny, but underlying all these funny presentations is the somewhat depressing fact that it’s scarily easy to come up with rationales for crazy theories (witness the recent resurgence of Flat Earth-ism). People believe what they want to believe, and can be quite inventive when it comes to dismissing evidence that, taken at face value, would force them to abandon cherished beliefs. By doing this dismissing in as shameless a way as possible, I tried to amuse an audience for ten minutes, and the video is out there on the internet. And I’d like to believe that BAHFest talks help make people more skeptical. But somehow, for all my ability to entertain outlandish ideas, I can’t quite make myself believe that.

And yet, giving a BAHFest talk is fun, so I’m gonna do it again. I’ll submit another deliberately bogus hypothesis next year. And no, I won’t tell you ahead of time what it is.

Next month (July 17): My Favorite Theorem.

Thanks to Sandi Gubin, Tom Knight, Christian Lawson-Perfect, Henry Picciotto, Ben Orlin, Evan Romer, Kelly Weinersmith, and Zach Weinersmith.

ENDNOTES

#1. I actually enjoy Koontz enormously and have a lot of admiration for his storytelling chops. His early work tends toward purplitude and overuse of certain words and tropes, but over the years he’s shed the distracting tics of his early work and emerged as a writer of surprisingly broad interests. Unfortunately sometimes the depth of his understanding doesn’t match the breadth of his interests. One webpage I’ve seen suggests that Koontz got his ideas about evolution from one Robert Webster Kehr, who not only claims that mathematics disproves evolution but also denies the existence of photons.

#2. In addition to loving the taste of crème brûlée, I love the spelling, with one accent mark per syllable. “Brûlée” is one of my favorite menu-participles, right up there with “drizzled”.

#3. For more on Galileo and other figures in the Scientific Revolution, the different forms of push-back they had to contend with, and the strategies they came up with, see Robert Crease’s book, listed in the References.

#4. If you haven’t taken a course in probability, you might be inclined to think that the different possible sequences aren’t equally likely; for instance, you might think that if you toss a coin four times, the outcome HHHH is less likely than the outcome HTHT. In that case, give it a try! If you perform the experiment often enough, you’ll find that both of these outcomes tend to occur about one-sixteenth of the time.

#5. Here’s the formula:

Sure, the polynomial that fits the data points depends on the data points being fitted, but is it really necessary to include the data points as subscripts in the notation? (Yes, if one’s goal is to intimidate!)

#6. John Urschel was in fact one of the judges at BAHFest East 2019 (and I knew ahead of time that he would be), so the specificity of that imaginary Q-and-A exchange wasn’t an accident. He and his wife have written a book about his dual career.

REFERENCES

David Bailey, “Does probability refute evolution?” (last revised 2019).

David Bailey, “Misuse of probability by ‘creation scientists'” (2009).

Robert Crease, “The Workshop and the World”, 2019.