Archive for the ‘science’ Category

Mike Brown, Planet Killer: “Mercury is Pissing Me Off”

December 19, 2010

Mike Brown is famous for discovering Eris, a dwarf planet larger than Pluto orbiting out on the far edge of the solar system. Ultimately, Eris’ discovery led to the redefinition of the word “planet” and the eradication of Pluto from children’s lunchboxes.

Brown’s new book, How I Killed Pluto and Why It Had It Coming tells the story of his team’s discovery of a complete menagerie out past Neptune – a place most astronomers thought held little but hydrogen, comets, and a few bits of rock that occasionally get flung out there by gas giants.

In an interview from last Wednesday, December 15, Brown told me that his most scientifically-important discovery was not Eris, but Sedna, a large object lying so far away from the gravitational perturbations of Jupiter and friends that its orbit can be traced back to the beginning of the solar system, and whose existence has challenged astronomers’ conception of how the planets formed.

Brown also showed me the sonograms of his embryonic daughter (now 5 years old) to compare side-by-side with photographs of Venus taken by the Venera Lander, and commented on the gravitational influence of my mother.

Part 1 (17 minutes: Hate mail, the process of writing, science of the early solar system)

Part 2 (31 minutes: More science, more writing, international intrigue, Pluto’s appeal and wimpiness)

Sync

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.

Bounce, Part 6

January 11, 2010

Last time, we looked at what Galileo had to say about free fall. This time, we’ll take one more example from his dialog and try to squeeze a little moral out of it.

Galileo presents his ideas through the character Salviati, who explains them to his companions Sagredo and Simplicio. Salviati’s interlocutors raise all manner of objection to his theories, but Salviati answers them and convinces everyone of his point all the more surely in the process. One such objection is given by Sagredo, who doesn’t believe that the velocity of a falling object increases evenly with each second of falling:

So far as I see at present, the definition might have been put a little more clearly perhaps without changing the fundamental idea, namely, uniformly accelerated motion is such that its speed increases in proportion to the space traversed; so that, for example, the speed acquired by a body in falling four cubits would be double that acquired in falling two cubits and this latter speed would be double that acquired in the first cubit.

Sagredo is suggesting that rather than Galileo’s law

v \propto t,

that the velocity of a falling body increases the same amount each second, we should instead have

v \propto x,

the the velocity increases the same amount each meter the body falls. These are different hypotheses, and so we need to distinguish between them. Given that Salviati states he is not interested in examining the fundamental cause of gravity, and only in characterizing its behavior, there is only one way to do this – experiment.

Instead, Salviati offers the following retort:

…that motion should be completed instantaneously; and here is a very clear demonstration of it. If the velocities are in proportion to the spaces traversed, or to be traversed, then these spaces are traversed in equal intervals of time; if, therefore, the velocity with which the falling body traverses a space of eight feet were double that with which it covered the first four feet (just as the one distance is double the other) then the time-intervals required for these passages would be equal. But for one and the same body to fall eight feet and four feet in the same time is possible only in the case of instantaneous [discontinuous] motion;

What a strange counterargument! It makes absolutely no sense. Gaining an even increment of speed for each unit of time is a perfectly consistent mathematical law, and does not at all imply instantaneous motion. We can write this law as

\frac{dx}{dt} = c(x - x_0),

which implies that the distance fallen increases exponentially with time. This is completely contrary to observation, and it would be hard to build a unified mechanics like Newton’s that respects this law, but it isn’t logically impossible for the reasons Salviati cites.

And how do Salviati’s friends respond to this argument? Do they rip it apart, or restate their objection more clearly, or request further detail?

Sagredo replies,

You present these recondite matters with too much evidence and ease; this great facility makes them less appreciated than they would be had they been presented in a more abstruse manner. For, in my opinion, people esteem more lightly that knowledge which they acquire with so little labor than that acquired through long and obscure discussion.

I guess it’s easier to convince the people you’re arguing with when they’re fictional characters you invented yourself!

Everyone makes mistakes, and they hadn’t gotten around to inventing peer review in the sixteenth century, so let’s forgive Galileo, and take a further look at this hypothesis.

Suppose we have a projectile with constant horizontal velocity and vertical velocity that changes according to the distance traveled in the vertical direction.

What happens if we shoot it up out of a cannon? We know from experience that the cannonball slows down, so it must be losing a constant amount of velocity for each unit height it gains.

The cannonball slows down its vertical velocity, but as it does so, its vertical position changes less. Since its vertical position changes less, the change in its vertical velocity slows down more. In fact, the cannonball asymptotically reaches a certain height above ground, and then stays there!

If the vertical height isn’t changing, then according to this law the vertical distance traveled is zero, and because vertical velocity only changes when vertical height changes, the vertical velocity stays zero. This cannonball would never come down.

On the other hand, if it were pushed down just a little bit, it would gain speed very rapidly, falling exponentially back toward Earth. The motion under Sagredo’s law is absurd, but I wonder why Galileo brought it up at all, only to miss the point.

Too much philosophizing can be dangerous, but this sort of philosophy – extracting results from speculative physical laws – is exactly what theoretical physicists do. The name of the game for a theoretical cosmologist, for example, is to come up with some crazy ideas about how the universe might work, the way Sagredo came up with an idea about falling bodies. Then, the cosmologist tries to work out the consequences of the theory, for example that cannonballs ought to hang in midair until a slight breeze comes along and gives them a downward tap, and they come plummeting back to Earth extremely quickly. If the theory doesn’t agree with observation, it’s wrong.

One difference between the Renaissance and Internet Age versions is that Sagredo’s and Salviati’s theories about falling are easy to test. The experiment doesn’t require any equipment. You just drop something. If you don’t have a thing, you can try jumping instead. But with advanced theoretical ideas, it can be very difficult to make the required observations. That’s why we need giant particle accelerators and kilometer-long interferometers and thirty-meter telescopes and ridiculously-good gyroscopes.

But another problem is that working out the consequences of modern theories is hard. We saw an example of Galileo failing to work out the consequences of a theory, but that was a simple mistake, and if someone had brought his attention to it, he’d have been able to fix it. Some of today’s new ideas about physics are so complicated that even if we can state the law (the equivalent of Sagredo’s idea about velocity being proportional to distance fallen), we may not know how to get to the conclusion (cannonballs hanging over our heads).

We’ve come long way since Galileo, figuring out lots of ways to check ourselves and test our ideas. But there’s a much longer way left to go.

Origins

October 3, 2008

“Ah, the origin of the universe,” sighs physicist Leonard Susskind from the stage of Beckman Auditorium. “Boy, does that ever take me back.”

An hour later, Paul Davies intoned for the third time, “as Lenny already mentioned…” before explaining again that the universe is in fact quite old, and did or did not, perhaps, depending on your point of view and interpretation of various fine intricacies some small subset of specialists may or may not understand, come from somewhere.

The third physicist to speak, Caltech’s own Sean Carroll, probably couldn’t even tell who to credit before making a point. Was it “as Paul already mentioned,” or “as Lenny alluded,” or “as Paul said that Lenny previously indicated that I might say when it was my turn, about the point Paul made clarifying Lenny’s tangent on my thesis…”

Perhaps you see the difficulty, at something like the Origins conference, in keeping your physicists apart. When it comes to speculating on genesis, they appear to be bosons. (Note to non-physics people: that’s not as mean as you think. “Boson” is the name of a famous circus clown. He invented gravity. To help him juggle.)

Michael Shermer, director of the Skeptic Society, brought a host of eminent scientists to Caltech last Saturday to speak before a lay audience (like me). Ostensibly, their goal was to collectively meditate on whether “science makes belief in God obsolete.”

The scientists involved were as nonplussed by the imponderability of this question as any other reasonable person would be, and proceeded to talk about their research, instead.

Cristof Koch, Caltech’s (literally) colorful neuroscience professor, shocked his audience by explaining that, as a scientist, he thinks consciousness comes from somewhere. He tries to find out where by looking very closely.

For example, in occasional unfortunate instances, it’s medically necessary to stick all sorts of wires in epileptic people’s brains. As long as you’re doing that, you might as well mess around with some science.

It turns out that each concept you can consciously identify, such as “redness”, “pain”, and “Halle Berry-ness”) (a special property shared by her image, text of her name, and a sound recording of her name, but not images of other actresses or anything else researchers can think of), corresponds somewhere in your brain to the binary activity of a neuron. If you are seeing Halle Berry, the neuron fires. If you aren’t it doesn’t.

Sounds simple, right? That’s because it’s from a talk for designed for simple people. Consciousness is complicated, comes in varying degrees, and is notoriously slippy to analyze. But does Koch think the study of consciousness involves theology? No.

Do Susskind, Davies, and Carroll think that God can help explain the origin of the universe? No. If you stretch, it’s a slightly-fuzzy no. But still no.

Does David Prothero, Caltech/Occidental-affiliated expert on the fossil evidence of evolution, think religious considerations aid our understanding of the origin of life, or the Cambrian proliferation of life? Emphatic no.

But frankly, they just don’t seem that worried about it. They were brought in to talk about God. But except for Prothero, whose science is the target of a vigorous attack from certain flavors of Christianity, the speakers at the Origins conference confined their theological ruminations to a couple of bullet points on their final “in conclusion…” slide.

Sean Carroll excitedly delved into Boltzmann’s hypothesis that the universe’s low-entropy past is a statistical blip in an infinite history, then excoriated the idea and presented a new model of baby universes pinching off and “never writing home to their parents.”

Susskind compared the finely-tuned nature of physical constants to the finely-tuned sequence of a human genome to illustrate his idea of how string theory might explain the state of the universe.

Prothero described lab experiments in creating the chemistry of life. Davies speculated on the meta-laws constraining choices among logically-consistent universes. Koch told me I would forget the color of his orange shirt (I think), and that this was based on science.

So imagine that. You work so hard to bring a bunch of great scientists together to have a discussion about some sort of general silliness mankind spends its time fretting over, but they ignore the bait and discuss their scientific passions instead. Well, newly-minted frosh, welcome to Caltech.