Archive for the ‘The Tech’ Category

Flat Priors and Other Improbable Tales

September 8, 2010

Some collected and invented stories about erroneous thinking in probability.

A Visit

It’s night. You are coming downstairs for a glass of water. You hear a creaking sound and look around a corner to see a man in a ski mask opening your front door. “What are the odds?” you think. “Normally that guy would have set off my burglar alarm and been scared off by the loud wailing, but he happened to stop by for a visit just one minute after the power went out.”


You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won’t believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!


About 100 billion people have ever lived, and there are about 7 billion people alive now. Therefore about 7% of people are extremely long-lived.


A man makes it through a long battery of physical and psychological tests and finally achieves his lifelong dream of joining the astronaut program. He immediately takes up heavy smoking. “What gives,” asks his friend. “I thought you were a health nut.”

“I am,” replies the man. “Anybody who smokes a lot will probably die of lung cancer.”

“Why would you want to die of lung cancer?” his friend asks.

“A shuttle explosion will kill you in two seconds,” he replies. “But now I’m gonna die of lung cancer, and that’ll take at least forty years.”

Hitchhiker’s Guide

It is known that there is an infinite number of worlds, simply because there is an infinite amount of space for them to be in. However, not every one of them is inhabited. Therefore, there must be a finite number of inhabited worlds. Any finite number divided by infinity is as near to nothing as makes no odds, so the average population of all the planets in the universe can be said to be zero. From this it follows that the population of the universe is also zero, and that any people you may meet from time to time are merely the product of a deranged imagination.
-Douglas Adams

Foreign Lands

In a certain country, people always name their first child a name that starts with “A”, their second child a name that starts with “B”, etc. Families in this country are anywhere from one to ten children; equal numbers of families have each. It is a tradition in this country for each father to randomly select one of his children each day to accompany him on a walk.

When visiting this country, you meet a man out walking with his daughter, who he introduces as Evelyn. You now know the man has at least five children. If he had exactly five, your chances of meeting the one whose names starts with “E” are 1/5. If he had more, say eight, your chances of meeting the one whose name starts with “E” are 1/8. Therefore, you conclude that it is most likely that Evelyn is the oldest child. You realize there was nothing special about Evelyn, and conclude that any time you meet a man walking with his child in this country, he is most likely to be walking with the oldest one.


Of all the gin joints, in all the towns, in all the world, she walks into mine.


While rummaging around in his parents’ attic, Sean comes across an old love letter to his mother. It’s from Rodrigo Valenzuela, a man he never knew, to his mother. It refers to “nights of fevered frenzy and mornings of muted passion”, is signed, “a mi amor”, and asks when her husband will be away again. The letter is dated eight months before Sean’s birth date. He looks in the mirror, wondering why he didn’t inherit his parent’s fiery orange hair and why salsa music has always stirred his soul.

Sean looks up information on paternity tests, and finds that if you send in one sample of DNA as the suspected father and one as the suspected child, the test will report a probability, which represents the probability that a man with the “father” DNA would sire a child at least as genetically different from him as the “child” DNA. Thus, a low percentage, like 0.001%, means that a true child would have only small chance of being as different from the father as the “child” sample is. This is the result we expect if the child is not from the father. A high percentage, like 60%, means the “child” and “father” DNA are very close, and is what we expect if the man is the true father.

Secretly, Sean collects a sample of the DNA of the man he’s always called “dad” and one of his own and sends them in for testing. As a control, Sean also collects a sample from his own son, and a second sample from himself and sends this sample in as well. Finally, Sean hunts down Rodrigo Valenzuela using Facebook, “friends” him, studies his “likes” and “interests”, uses them to befriend Roderigo in real life, asks to borrow his car, and steals a hair from the headrest. He sends in a third sample of Rodrigo and himself for testing.

Two weeks later the test results come back. Sean isn’t shocked. The probability for him and his “dad” is a scant 0.00004%. The probability from Roderigo and himself is 7%. Finally, the result from his son is 74%. Sean realizes that there’s some natural variation in the test, but the evidence is still clear: Roderigo is his true father.

The next day the clinic and says there’s been a mix up. They accidentally switched the samples from Sean and his son, so the 74% was actually the result of testing Sean’s son in the “father” role and Sean in the “child”. Sean is understandably upset. He goes to bed that night thinking that although Roderigo may be his father, it’s ten times as likely that his own son will, in the course of his life, discover time travel and go back to impregnate Sean’s mother.

Flat Prior

On whether or not the Large Hadron Collider would create a black hole that would consume Earth:

John Oliver: So, roughly speaking, what are the chances that the world is going to be destroyed? Is it one in a million, one in a billion?

Walter Wagner: Well, the best we can say right now is about a one in two chance.

JO: Hold on a second. Is the, if, 50 – 50?

WW: Yeah, 50-50.
WW: It’s a chance. It’s a 50-50 chance.

JO: You keep coming back to this 50-50 thing. It’s weird, Walter.

WW: Well, if you have something that can happen and something that won’t necessarily happen. It’s either gonna happen or it’s gonna not happen. And, so it’s, the best guess is one in two.

JO: I’m not sure that’s how probability works, Walter.

from The Daily Show

Ode To The Stinkiest Palindrome

July 16, 2010

Story 1

A rope hangs over a pulley. On one side is a monkey. On the other is a bunch of bananas. The monkey and the bananas weigh exactly the same, the rope is massless and unstretchable, and the pulley turns frictionlessly. Does the monkey get the bananas?

Yes. The monkey pulls up on the rope, then poops, becoming lighter. The bananas sink and the monkey climbs up on top the pulley and then hauls the bananas up.

Story 2

Answer: Just before you die, you see a light at the end of a long tunnel. Coming out of the light is the silhouette of a distinguished older gentleman in formal attire. He’s a man who appears to know everything. “It’s your final moment here on Earth,” he tells you. “This is the last thing you’ll do here.”

“What is poop?” you reply.

“That’s right for eight hundred dollars,” says Trebek. “So long kiddo. See you in Double Jeopardy.”

Story 3

You go to the zoo and are standing at the chimpanzee cage. A wizened old matriarch looks right at you and she seems almost human. Suddenly you get pegged from the side by an object coming out of nowhere. The damn chimps threw it at you! What is it? You look down. It’s a rotten banana.

Gross! You go to the bathroom to wash up. You wash and wash, mesmerized by the soap bubbles and flakes of skin twirling down the sink drain. Just as you’re leaving, you feel something squish under the heel of your brand new shoes. What is it? You look down. It’s souvenir baby seal some kid dropped.

You pick it up and take it outside. You look everywhere, but you don’t see a kid who looks like they need a seal. You do see a beautiful woman, so you smile and give her the seal. She thanks you and asks if you want to grab a giraffe coffee at the safari cafe, which is a normal cafe except that everything you buy has an animal name and costs three times as much. You order a safari dead cow burger. One of the toppings looks funny. It’s like a light brownish smear. What is it? You sniff it, then cautiously take a lick. It’s tahini.

The beautiful woman really like you. She takes you back to her place and puts on some Coltrane. She grabs you to dance and swirls and swirls until you topple together, falling eternally until everything is red silk and dizzying kisses. You reach down and feel something soft and warm. What is it? You look down to investigate. It’s her puppy, crawling under the sheets.

You impregnated then married the beautiful woman. You’re standing in the waiting room, pacing. A doctor in a white gown comes out and says your last name, preceded by “mister”. You’re not used to being called that.
“What happened?” you ask.
The doctor looks tired, but happy after the grueling 174-hour delivery. “Your wife is fine,” he says.
“And the baby?”
He gives you a wan smile. “Congratulations,” he says. “It’s a healthy little poop.”
“Sorry, Freudian slip. It’s a healthy little girl.”

A Wish

June 25, 2010

The next time I fly, the guy who sits next to me will have just gotten a tattoo. It’s a secret tattoo, though. He’s flying to run away from his old life, and the tattoo will be his only reminder.

But since he’s got this secret, he feels a dire need to tell someone. It’s been four days already, and he hasn’t told a soul. If he has to tell someone, it might as well be a stranger. He leans over to me and says, “Hey man, I just got a tattoo of some clouds.”

“Oh, uh, okay.” I look back at my book.

Twenty minutes later, his fidgeting starts to get more and more noticeable. Finally he leans over one more time. “It’s on my butt. The clouds are on my butt.” I pretend to be asleep.

After the flight, we go our separate ways. He begins his new life and never tells anyone about the secret tattoo.

Twenty years later, I see him walking on the street with his friends. He looks happy now. At first I’m not even sure it’s him, but there’s something about the eyes.

I walk up. “Hey man,” I say. “There’s a big red spot on Jupiter.”

“What? Do I know you?”

I don’t answer, but I have one more thing to say. “Oh, and there are clouds on Uranus.”


June 12, 2010

I took a short break from reading Steven Strogatz’s Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life earlier today and checked Facebook. Usually, the status updates of my Facebook friends are a seemingly-random menagerie of links to news stories, jokes, anecdotes, and these things: ^_^. Today, though, I found that in just the last twenty minutes, ten or so of my friends had posted nearly identical messages. They had somehow synced.

In this case, it’s not surprising. They were restating the result of the recently-concluded World Cup soccer game, but with more exclamation points than I’d get from Reuters. (Actually, Facebook status updates are the primary way I keep in touch with mainstream sports.) My Facebook synced today because of a strong, external signal influencing all the individual updates. That’s the way we normally think about synchrony. If you want it, you need some sort of a central clock for everyone to follow. A computer chip’s parts sync this way. Coworkers on a project are synced by a manager. Orchestras have conductors. Tug-of-war teams count to three.

By contrast, Strogatz is interested in spontaneous synchrony – synchrony where you won’t expect it and no one’s in charge. A great visual and audio introduction is Strogatz’s own TED talk.

Sync is a broad survey of nonlinear systems from spirals in oscillatory chemical reactions to synchronized menstruation induced by armpit sweat. What’s captivating about it is the story. Like James Gleik’s Chaos or Kip Thorne’s Black Holes and Time Warps, it carries you along from a few researchers diddling around with a curious idea to the creation of a large scientific field. We explore different branches where the original research lead, all the time seeing the different ways scientists and mathematicians approach their problems. From Strogatz, you also get a sense of the way these different approaches contribute to a complete understanding. At different times, Strogatz describes analytical work (solving equations), computer simulations, visualization (including building models from string and clay), laboratory experiments, and field research. Each endeavor feeds back into the others in this story about the science of synchrony.

I was curious, as I read the book, what it would be like if it had been technical as well. What if Strogatz had included didactic discussions of the solvable systems he’d worked on, or outlined the topological proofs he mentioned, or showed the results of the research as he would in a technical scientific talk, all integrated into the same story? A skeptical answer would be that lay readers wouldn’t touch the book and that technical readers would not be interested in the fluff. Strogatz already wrote an introductory textbook on nonlinear dynamics (which I haven’t read, but I’m told it’s good). I’ve seen textbooks that have little biographies inserted here and there, and I’ve seen popular books that use some equations or put technical appendices at the end. I am curious about a book intended to teach an undergraduate course that’s a truly integrated historical story and didactic text. There is an extensive bibliography allowing me to pursue the technical aspect of whatever ideas interest me the most, but that is something quite different from an organized presentation.

I picked up Sync while browsing, and read it because I remembered both the TED talk I linked above and Strogatz’s amusing math columns in the New York Times.

The Crank Continuum

June 11, 2010

I’ve had one true crank on this blog. He jumped into the comments on this post with mathematical gibberish he claimed disproved relativity. Another time I saw a crank letter written to a researcher at JPL who worked on dark matter. This crank even provided a little mechanical apparatus intended to demonstrate the existence of dark matter. It consisted of a rubber or nylon sheet that was stretched over a wire frame, and then you were supposed to roll a marble around on it.

It’s kind of surprising that these cranks fit so well with the descriptions of many others in Martin Gardner’s Fads and Fallacies in the Name of Science. Half a century after Gardner wrote his books, cranks, and belief in what they have to say, hasn’t changed much.

I picked up this book after Douglas Hofstadter mentioned it in an article reprinted in Scientific American after Gardner’s recent death. It’s essentially descriptive, spending surprisingly (and refreshingly) little time refuting crank theories of physics and medicine, and instead mostly detailing them. Gardner does, of course, refute each crank theory, but his most important contribution is to collect enough of them that cranks begin to look similar. (You can read Gardner’s generalizations about cranks in the Hofstadter article, or in chapter 1 of the book.)

Another surprising fact was that cranks are not just weirdos shouting loudly on obscure corners of the internet (ahem). Many cranks were fairly normal, and even learned and respected people outside of their crankery. A surprising array of famous, respected people bought into and campaigned for crank theories. Upton Sinclair recurs throughout the book, advocating a number of useless medical and dietary systems. Some other delusional supporters or even creators of crank ideas include Aldous Huxley, Clifton Fadiman, Oliver Heaviside, Walt Whitman, Arthur Conan Doyle, William James, H. G. Wells, and Jesus (last one added by me; the others are from Gardner. However, many of Gardner’s cranks theories are motivated by proving or justifying religious claims).

It seems that as you cross over into the realm of crankery, you begin to believe your discovery has more and more power and wider and wider applicability. Medical cranks, for example, rarely believe they have a cure for cervical cancer. They think they have a cure for everything. Sometimes they even branch out and extend their theory of physiology to explain physics.

Crankery is dangerous, because in some ways it’s difficult for a layman to see the difference between crank science and real science. In crank science, the observations frequently go against the crank’s theory. The crank then comes up with excuses for why this is so (read Gardner’s chapter on Dr. Joseph Banks Rhine’s work on ESP for an especially clear example). But you can find scientists doing the same thing! A chemist’s reaction doesn’t come out right, so he assumes it was contaminated. A particle physicist doesn’t see the effect he was looking for, so he assumes it occurs at just slightly higher energy. How can we tell the difference between honest excuses – those that are truly identifying mistakes in the experimental conditions – and dishonest ones – those that are the result of a researcher who would find an excuse under any circumstances? In recent years I’ve heard from time to time about new attempts to publish scientists’ negative results and to make their complete lab processes and all data openly available. These are two efforts that should help distinguish them from cranks.

But another problem with the crank mindset is that there’s no sharp dividing line. Aside from science, I’ve read a bit about training distance runners, so I’ll use that here. One clear crank is Percy Cerutty, a coach who demanded his runners carry spears and “run like the primitive man”, advocated strange diets, and in general believed, as cranks do, that he had stumbled onto secrets that no one else knew. Eventually, his runners left him. A more marginal case is Arthur Lydiard. Lydiard is a coach who created a fairly rigid, systematized training system and then advocated it as being the best possible. His system was based on trial and error in his early days of coaching. He tried a few different things and then stuck with what seemed to work best. But he began to believe that all his advice was better, stronger, and more iron-clad than it was. He also began to think his general ideas applied not just to running, but to all athletic endeavors (specifically shot put, rugby, and rowing come to mind). He’s an in-between crank, because he did hold himself accountable to the results of his methods, and he did coach Olympic champions, but he also lost touch with reality (Lydiard still has a large following of distance runners today, many of whom would be incensed if they read this summary.)

Modern coaches, too, tend to believe in their methods beyond the level their results support, and babble on endlessly about aspects of human physiology that are not as well-understood as they indicate. But the point is that they do this to varying degrees, with coaches ranging widely from true cranks to rational, down-to-earth people with a healthy dose of skepticism towards even their own practices and a realistic viewpoint on the success and failure of their athletes.

I have frequently found myself buying into crank athletic ideas, believing, for example, that all my injuries are due exclusively to running on hard roads (as opposed to trails or grass), although I had no data to support the belief. After reading scores of books and hundreds of articles, I now believe mostly that I’m not very sure about anything regarding training distance runners.

Surely, there is a crank continuum in science as well. On the one hand, there is an ideal scientist who (perhaps) evaluates all new evidence they receive with a perfectly-rational Bayesian approach, drawing conclusions only to the extent warranted by the evidence (and their prior beliefs). But scientists, even good ones, don’t do all do that. Once in a while they begin to believe in their own theories even when the evidence starts to pile against them. The outcomes they want to see happen affect the results of their experiments, or they choose not to publish results they don’t like. Their error bars grow just large enough that the data is consistent.

Usually it’s not hard to tell a crank. Also, as Gardner points out in his book, just because there are some intermediate cases, doesn’t mean that most cases aren’t clear-cut. But I’m glad I read about what cranks do, how they justify their delusions, because I don’t have to look too long and hard to see hints of the same behavior in myself.

Scientia Pro Publica #31 is Up

May 24, 2010

This blog teaches you science. For example, if your pet canary read this blog, it would learn that it is descended from dinosaurs, and it would think it is hot shit. Then it would learn that it is going to die one day. That’s science.

My post The Evolution of Sexy is one of those featured on the latest edition of Scientia Pro Publica at 360 Degree Skeptic. Not because I did such a good job, but because I filled out a submission form recommending myself.

You should go read the blog carnival because all the posts are awesome, except for one, which sucks really hard. Which one? I’m not telling you. You will have to read them all and find it for yourself. It will be like finding a specific needle in a stack of ten needles, except instead of needles you have a blog posts.

We Need a Power Pyramid

May 22, 2010

You know this thing, right?

USDA food pyramid

Thanks to the food pyramid, which almost all Americans recognize, we basically know what healthy eating is. You can find a lot of bickering about the details. You will even find some nutritionists who claim everything about it is wrong, but they are sensationalists.

It’s not complicated, it’s important information, and basically right. Eat lots of plants, fewer animal products (Don’t hate, vegetarians. “None” is a special case of “fewer”.), and only a little junk food. Most Americans pretty much know what healthy eating is. (Knowing what it is is quite different from doing it!)

I think we need one of these for energy consumption. We seem, as a nation, to be out of touch with the basics on this, and like the food pyramid, it’s important and it’s simple. Everyone should know the basics about energy the same way they do about healthy food.

I recently heard earnest praise of the iPad because by reading books on it, or using it as a scratchpad, it saves paper. That’s true; the iPad saves paper. But remember, homicide cuts down on traffic congestion. So I started trying to calculate which is better on environmental terms – books or iPad. I estimated that reading books sustainably winds up taking a lot more ground space than generating the energy to manufacture and use an iPad. Then I googled and found an article from the New York Times with a similar goal, but its conclusion was that once you read more than a few hundred books, the overall impact of the iPad is significantly less than buying new books. Now what do I do?

I want to use less energy, but it’s irrational to go to all ends figuring out every last thing about doing it. It doesn’t matter which choice I make because the energy involved in using an iPad or reading the books is very low when compared to more significant types of consumption.

When thinking about conserving energy, we are pretty dumb. We spend far too much attention on things that are visible, immediate, and easy to understand, rather than things that are significant. Unplugging your cell phone charger when not in use to reduce power consumption is like going to New Orleans after Hurricane Katrina and helping re-sort someone’s sock drawer.

Magazine articles that calculate the gallons of water saved if you run the faucet for 15 fewer seconds while brushing your teeth are missing the point. Why bother brushing your teeth in tiny little spurts of water from the faucet if you are about to take a hot bath? And a hot bath pales in comparison to watering your lawn. Don’t stop brushing your teeth. Stop watering your lawn.

My calculation about the iPad and similar calculations are dangerous. Even if they’re correct, they encourage us to focus in the wrong direction. There are hundreds of similar minutiae I could worry about. Metal forks or recyclable bio-forks at the cafeteria? Paper or plastic at the supermarket? How much energy do I use when downloading a porno?

To be realistic, you are only going to worry about energy consumption a certain amount. After that, you’ll have to get on with your life. Spend the worrying where it counts. In order to do this, we need to know what counts and what doesn’t.

For this, I highly recommend David J. MacKay’s Sustainable Energy – without the hot air, which you can download for free at the link. He gives a clear, straightforward account of how we use energy and how we can potentially generate it.

Take a look at this graphic, for example:

From David J. MacKay's 'Sustainable Energy without the hot air' pp. 204

Current consumption per person in cartoon Britain 2008 (left two columns), and a future consumption plan, along with a possible breakdown of fuels (right two columns). This plan requires that electricity supply be increased from 18 to 48 kWh/d per person of electricity. (MacKay's caption)

This is really good – clear and informative. MacKay’s book contains many fantastic charts, plots, and graphics visualizing energy consumption and generation.

This graphic, though, is for people who are reading an entire book about energy. That makes it for a minority. We need something simpler and more iconic, like a food pyramid for energy consumption.

It may also be useful for the graphic to show not total consumption, but how much energy can be saved by cutting back in certain areas. Cutting back in transportation energy is easy and huge potential benefit. That goes on bottom. Turning off the lights is a very small thing by comparison. That goes in a tiny little triangle on top.

One difficulty is that the power pyramid is dependent on the people it’s targeting. Here in the San Francisco Bay area, I use almost no power for heating because the weather is nice. Also, living in Berkeley, a bicycle-friendly city with good public transit, I choose to forgo a car and use very little energy for transportation. Someone living in rural Wisconsin will naturally have a very different pyramid than I will.

We’ve gotten to where most people know that we’re using too much energy, but we have a lot of work to do in consolidating the message. We need a simple, effective, clear image, like the food pyramid, that can be put where people will see it hundreds of times, and burn in the basic idea. As MacKay points out, the slogan “Every little bit helps,” is not this message, and is in fact its antithesis.

The Evolution of Sexy

May 22, 2010

Evolution is all about survival of the fittest. Wild animals are locked in an arms race, driven to be the fast enough to chase down a gazelle or strong enough to fight a python, or else so stealthy they escape the hawk’s eye or so poisonous they kill any attacker. But then why does a bird of paradise do things like this:

Or look like this?:

Red Bird of Paradise, from Flickr

I just read Jerry Coyne’s Why Evolution Is True, which devotes a good chunk of one chapter to the mating behaviors of birds. What sort of natural selection could lead to such diverse and unusual features in animals? These mating dances don’t seem to help obtaining food or avoiding predators.

The idea is that a peacock, for example, has a whacked-out tail because peahens think that’s hot. (A “peacock” is specifically male and a “peahen” female. Together they’re “peafowl”, and if you eat asparagus you will peafowl.) Therefore, the peacocks with the most-whacked-out tails will get laid and have sons with whacked-out tails, too.

Coyne cites a few experiments that agree with this “sexual selection” hypothesis. Peacocks with more eye spots get more sex, and when some of their eye spots are removed, they get less. Red-winged blackbirds get run out of their territory (and lose their harem of fine blackbird honeys) if they can’t sing. Other decorated birds do poorly at attracting a mate if their colors are painted over.

The surprising upshot is that ornamental tails may be detrimental to survival. They’re heavy and awkward. Peacocks suck at flying, at least in part due to their absurd tails. Nonetheless, the ornamentation can be advantageous over all if having a great tail leads to getting great tail. You might have better chances of escaping predators without the giant colorful feathers, but if you live to be 100 and never get it on, you still lose (by genetic standards). In this way, evolution can create adaptations that hurt individuals’ survival odds and presumably harm the species as a whole.

Come get some, baby.

This reasoning is predicated on females liking ornamented tails, and it’s unclear why they should do that. If crazy tails are detrimental to male health, then shouldn’t females like plain males, because they’re fittest? Females who prefer plain tails will have kids with plain tails, and hence their kids will be more likely to survive. So it would appear that females are willfully injuring themselves by deciding that blue eye spots make for a hunky peacock tail.

Coyne presents three hypotheses that may solve this conundrum of sexual selection:

  1. Females choose males that will be good dads. The ornamentation may be a signal for this.
  2. Females choose males that have good genes and will sire strong, healthy children. Only strong, healthy peacocks can afford to grow fancy tails, so the tails are a signal.
  3. Males are exploiting a trait that exists in female psychology for some other reason. For example, the male ornamentation looks like a fruit the female likes, or females like anything novel or decorative. Males caught on to this and females got duped.

In the case of peacocks, there’s some evidence for number 2 – that only males with good genes grow big tails. Coyne cites a study that found that the children of fancy peacocks are in fact healthier.

The other hypotheses are also interesting and have some experimental evidence to support them in other species, but here I want to head in a fourth direction.

Even if ornamented plumage is a signal for a healthy peacock, why should that be? Wouldn’t everyone be better off with a less-ostentatious signal? What’s the real reason that tails grew into giant fans?

Maybe there isn’t one. The tails don’t necessarily have to signal anything, or trick the females. The tails of peacocks and similar adornments in other animals may be there, despite their negative survival effects, because evolving such traits is the expected outcome of a simple iterated game with thousands of players.

Suppose that long ago, before the peacock got so ridiculous-looking, peahens started to develop a slight preference for longer tails in peacocks for an arbitrary reason, perhaps because malnourished peacocks had smaller tails, or even due to genetic drift (i.e. randomly).

Think about two peahens who are pretty much the same, but one prefers longer tails, as is the fashion, and the other prefers short tails. The one who prefers long tails is at a reproductive advantage, but not because long tails are innately better. Her advantage is that if she chooses a long-tail mate, she’ll have long-tail sons, and all the other peahens, who in general have started to prefer long-tail peacocks, will want to get down with her sons. Her sons will have daughters who have long-tail-selecting tendencies.

The selective pressure on an individual peahen’s preferences now comes not from survival fitness considerations, but from the preferences of all the other peahens. It’s a game theory situation where the payoff for one player depends both on that player’s actions, and on the actions of everyone else.

Because each peahen now feels a pressure to prefer long tails, once we get a few generations down the line, more peahens prefer long tails. When that happens, the selective pressure on any one individual peahen to prefer long tails becomes even greater. It’s a runaway, positive-feedback effect.

Eventually peacock tails are three meters wide and have hundreds of brighly-colored eye spots. Although it didn’t make it into Coyne’s book, I found that this idea has been around since the 1979, and is called the sexy son hypothesis.

If the sexy son hypothesis plays a large role in sexual selection, it says that a peacock’s tail is essentially arbitrary – it just happened to be the feature peafowl fixated on. We might then expect that as we look at different species, their sexual selection should exaggerate different features.

That’s true. In other birds, we see sexual selection acting to create long feathers growing out of the head, or strange crests, or bright chest plumage, or even to create strange behaviors like elaborate mating dances or songs.

A bowerbird that collects old bottlecaps off the streets of cities is sexy.  A human who does that is...?

Australian bowerbirds are sexually selected not for a physical feature, but for the behavior of building huge, colorful, extravagant "bowers" that they don't even use as nests.

The sexy son hypothesis also suggests that the sexually-selected feature should be as extreme as possible, limited either by the physiology of the animal so that it would be impossible to make it any more extreme, or by the point where the fitness disadvantage to males becomes so great that even the extra mating advantage isn’t worth it any more.

What we have, then, is a hypothesis – the germ of a scientific idea. Once we’ve formulated the sexy son hypothesis, we need to expand on two frontiers in order to test it. One one hand, we should try to develop models of how the sexy son hypothesis works and make quantitative predictions. For example, we might predict a positive correlation between the mating effectiveness of a male and that of his male descendents – the heritability of sexiness. If we went further, we might even be able to predict how strong that correlation should be, based on how detrimental ornamentation is to survival odds and how much variability there is in male reproductive success. On the other hand, we should begin experimental studies to test these predictions.

In a 2008 forum article in Behavioral Ecology, Testing the sexy son hypothesis—a research framework for empirical approaches, Huk and Wenkel summarize the research on the sexy son hypothesis:

To sum up, it can be concluded that empirical studies dealing with critical predictions to date only partially support SSH; that is, only studies with rather small direct fitness consequences are compatible with critical SSH predictions. Contrary, the demonstration of compensation of considerable lower direct reproductive success via a heritable genetic effect of male attractiveness, and hence male mating status in sons, is not demonstrated until now. Thus, facultative polygyny in biparental species seems to be best explained by sexual conflict. Approaches derived from quantitative genetic models of mate choice came to similar results (Kirkpatrick and Barton 1997; Charmantier and Sheldon 2006; Hadfield et al. 2006; Qvarnström et al. 2006). Recent studies therefore support the position that inferior direct reproductive success cannot be overcompensated by a “sexy son” effect (e.g., Kirkpatrick 1985). Thus, attractiveness of sexy sons and its resulting fitness advantages seem to be of minor biological effect.

Certainly not a strong avowal, but not damning, either. The jury is still out, so until next time, stay sexy.

Coral Reefs are 85% Shark?

May 18, 2010

In a recent TED Talk, Enric Sala says that before being sullied by people, a healthy coral reef stores 85% of its biomass in the form of sharks.

He shows this image of the “inverted pyramid” of reef biology:

When reading through these calculations, don't forget that I neglected that sharks eat their own young, and they also eat your own young.

I found this pretty surprising, as did the guy who organizes the talks, Chris Anderson. Anderson asked Sala after the talk:

Your inverted pyramid showing 85% of the biomass is in predators – that seems impossible. How could 85% survive on 15%?

To which Sala replied:

Imagine that you have two gears of a watch – a big one and a small one. The big one is moving very slowly and the small one is moving fast. That’s basically – the animals in the lower parts of the food chain, they reproduce really fast. They grow really fast they produce millions of eggs. And there you have sharks, and large fish that live 25 years. They live very slowly they have very slow metabolism, and basically they just maintain their biomass so basically the producion surplus of these guys down there is enough to maintain this biomass that is not moving…

Everything I know about sharks I learned from old Batman movies, but we don’t need much biological knowledge to see if this makes sense. We’ll simplify things to just two trophic levels – sharks and fish. If there are really 3, that doesn’t matter, because if fish are the entire bottom of the pyramid they’re 15% of the biomass, and if they’re the middle of the pyramid they’re maybe 12%, which is close enough.

The striking fact was the high ratio (about 6) between the sharks’ mass and the fishes’ mass, so let’s try to derive a formula for this ratio based on Sala’s idea that sharks have slow metabolism and don’t eat much compared to fish.

Suppose the biomass fraction of the sharks is B_s (0.85 in the video) and of the fish B_f. The basal metabolic rate of the sharks is M_s and of the fish M_f. “Basal metabolic rate” here means the number of calories per kilogram per day needed to maintain the same mass. The eating rates are E_s and E_f. “Eating rate” means calories eaten per kilogram per day.

According to Sala, the sharks are just chillin’ at the same body mass, so

M_s = E_s .

The fish, on the other hand, need to grow, so that they’ll be more there for the sharks to eat. We can write this as

B_s E_s = C(E_f - M_f)B_f .

The left hand side represents the amount the sharks eat. The right hand side is the extra amount the fish eat, multiplied by some conversion factor C that turns surplus calories eaten by the fish into calories for the sharks. These two equations give the ratio of biomass of sharks to fish.

\frac{B_s}{B_f} = \frac{(E_f - M_f)C_f}{M_s}

To get a high ratio of shark mass to fish mass, we need low shark metabolism (to reduce their appetite and not eat the scant fish away completely), low fish metabolism (which is wasted energy), high fish eating rates (to be converted to shark food), and a high conversion rate (to make shark food efficiently).

I think it would be helpful here to introduce the voraciousness of the fish, V, defined by

V = \frac{E_f - M_f}{M_f} .

This is a number like 2 or 6. A voraciousness of 0 would mean the fish eat just enough to survive if there were no sharks around. A voraciousness of 1 means they eat twice as much as they need, and a voraciousness of 4 means they eat 5 times their minimum diet. We’ll also introduce R, the ratio of shark to fish mass by

R = \frac{B_s}{B_f} .

With these new variables, the equation describing the aquatic eating habits is

R = V C \frac{M_f}{M_s}

We might expect 1 kilogram of fishy-fishy to use more energy than 1 kilogram of death shark because sharks are bigger and they keep their cool, except unless they smell blood in the water. (This is just the first search result for a shark feeding frenzy:)

I remember hearing somewhere that in general, biological organisms that are fairly similar (e.g. all mammals) will follow simple power laws when you scale them. Sharks are basically just big fish, so they should be on the same scaling law. We could try to create a heuristic argument for what this should be for the metabolic rate, but I’m not sure how to do that, and it would likely be wrong. Instead, I turned to wikipedia and found Kleiber’s Law, that total metabolism of the animal scales with the 3/4 power of the mass, or that metabolic rate per kilogram (which we are using) scales with the -1/4 power of the mass of the animal.

So let’s introduce a new variable, S, for the ratio of the sizes of the shark to the fish. Then Kleiber’s law states

\frac{M_f}{M_s} = S^{1/4}

This finally gives us a simple equation for the ratio R of shark mass to fish mass.

R = C V S^{1/4}

Sala gave roughly R = 6, and a reasonable guess is C = 0.1 because the surplus food is getting eaten by fish, turned into new fish, and then eaten by sharks, and that takes a lot of energy.

How big is a shark compared to a fish? I googled this and found that a Caribbean reef shark is a big shark for a reef, and weighs up to 70kg. I’d think a mid-level predator fish would be at least 1kg, but let’s be nice and say just 100g. Then S = 700 so S^{1/4} = 5. That fills in enough to solve for V, the voraciousness of the fish.

V = \frac{6}{0.1*5} = 10

So the fish in Sala’s reef must be eating ten times as much daily as they need just to maintain body weight. I suppose this is a conceivable rate to get the food down the gut, but is it a reasonable rate to have the fishes’ bodies effectively processing all that food? A human base metabolism might be half a pound of dry mass, and a newborn baby is maybe 2.5 pounds of dry mass, so the rate that fish in the coral reefs are eating and growing is roughly equivalent to a woman who eats enough to grow a set of twins every day. You can find animals doing some pretty wild things if you look hard (or just turn on the Discovery Channel), so it might be possible. Nonetheless I find it dubious that coral reefs are 85% shark.


March 9, 2010

A good way to market your product is to give it a name that’s two words, but the last letter of the first word is the same as the first letter of the last word. Then you mash them together to form one long superword that’s the name of your product.

For example, suppose you invented a new toy for sad women, and it’s basically a fancy vibrator. Congratulations, that’s the Vaginantidepressant! Or let’s say it’s a great new way to serve your dog eggs – the Fidomellette. The exception is when you start breeding miniature pack animals. There, you don’t drop any letters – they stay as Smallllamas.

  • Want to grow cruciferae in the cold harsh winter? Build a Broccoligloo.
  • the redundant Backnapsack
  • the slimy, bouncy Kangarooze
  • the Talkingorilla
  • a cute little knife for when you can’t stand the sight of one more carnation – the Floristabber
  • too many cetacean pests in your ocean? get the Whaleliminator.
  • want to make bad choices while tripping? get some AlcohoLSD. where? grow it in the Drugarden.
  • miss the League Of Nations, much? Good old Woodrowilson
  • and when the current President wants fish? Obamackerel.
  • No more! Thistupid topican notake uprecious timeven ifriends wanto keepestering yountil yourectum explodestunningly.