Science

Bigger animals have more cells than smaller animals. More cells means more cellular metabolism and so more heat produced. How does the amount of heat an animal produces vary with its size? We clearly expect it to go up with size, but does it increase in proportion to volume? Surface area? Something in between?

A first guess would be that metabolism (equivalently, heat produced) goes up in proportion to volume. If cells are all roughly the same size, then number of cells increases proportionately with volume. But heat is dissipated through the surface. Surface area increases in proportion to the square of length but volume increases in proportion to the cube of length. That means the ratio of surface area to volume decreases as overall size increases. The surface area to volume ratio for an elephant is much smaller than it is for a mouse. If an elephant’s metabolism per unit volume were the same as that of a mouse, the elephant’s skin would burn up.

So metabolism cannot be proportional to volume. What about surface area? Here we get into variety and controversy. Many people assume metabolism is proportional to surface area based on the argument above. This idea was first proposed by Max Rubner in 1883. Others emphasize data that supports the theory that suggests metabolism is proportional to surface area.

In the 1930’s, Max Kleiber proposed that metabolism increases according to body mass raised to the power ³/₄. (I’ve been a little sloppy here using body mass and volume interchangeably. Body mass is more accurate, though to first approximation animals have uniform density.) If metabolism were proportional to volume, the exponent would be 1. If it were proportional to surface area, the exponent would be ²/₃. But Kleiber’s law says it’s somewhere in between, namely ³/₄. The image below comes from a paper by Kleiber from 1947.

The graph shows that on a log-log plot, the metabolism rate versus body mass for a large variety of animals has slope approximately ³/₄.

So why the exponent ³/₄? There is a theoretical explanation called the metabolic scaling theory proposed by Geoffrey West, Brian Enquist, and James Brown. Metabolic scaling theory says that circulatory systems and other networks are fractal-like because this is the most efficient way to serve an animal’s physiological needs. To quote Enquist:

Although living things occupy a three-dimensional space, their internal physiology and anatomy operate as if they were four-dimensional. … Fractal geometry has literally given life an added dimension.

The fractal theory would explain the power law exponent exponent ³/₄ simply: it’s the ratio of the volume dimension to the fractal dimension. However, as I suggested earlier, this theory is controversial. Some biologists dispute Kleiber’s law. Others accept Kleiber’s law as an empirical observation but dispute the theoretical explanation of West, Enquist, and Brown.

To read more about metabolism and power laws, see chapter 17 of Complexity: A Guided Tour.

Related posts:

Networks and power laws
Rate of regularizing English verbs

To first approximation, out planet is a sphere. But how accurate is that approximation? What’s a better approximation? How good is that? This post will answer these questions and some related questions.

How well does a sphere describe the Earth’s shape? The Earth’s polar diameter is about 43 kilometers shorter than its equatorial diameter, a difference of about 0.3%.This is due to the equatorial bulge caused by the Earth’s rotation.

What’s a more accurate description of the Earth’s shape? An oblate spheroid.

What is an oblate spheroid? It’s the shape you get by spinning an ellipse around it’s minor axis. That says if you were to take a cross-section of the Earth containing the polar axis, the shape you get would be an ellipse. The polar axis would be the minor axis and the equatorial axis would be the major axis. But if you were to take a cross-section through the equator, or any plane parallel to the equator, you’d get a circle.

What is a prolate spheroid? A prolate spheroid is what you get by spinning an ellipse around its major axis.

What is an ellipsoid? An ellipsoid satisfies the following equation.

A sphere is an ellipsoid with a = b = c. An oblate spheroid is an ellipsoid with a = b > c. A prolate spheroid is an ellipsoid with a = b < c. A scalene ellipsoid is an ellipsoid for which a, b, and c are all distinct.

How good is the oblate spheroid model? The error in approximating the Earth’s shape as an oblate spheroid is less than 100 meters, two orders of magnitude better than the spherical model.

How are other planets shaped? The other planets in our solar system are also oblate spheroids with Saturn being the most oblate: the polar diameter of Saturn is about 10% shorter than its equatorial diameter.

Related post: Finding distances using longitude and latitude

One of my daughters had the following assignment for science. First you boil a couple leaves of red cabbage and pour off the water. In our case the water was inky blue, but the results may vary according to your water chemistry and possibly by your cabbage. Next add a little diluted ammonia to the water and the color will change. Add the right amount of vinegar and it will change back to the original color. Add more vinegar and it will turn a new color. The liquid can turn a wide spectrum of colors. (Which colors? You’ll need to do the experiment to find out!)

Now we’ve got a jug of ammonia left over. What can you do with a jug of ammonia? Any practical uses? Fun uses? Any more science demonstrations?

According to the Science Podcast, a study shows elephants in captivity have about half the median life expectancy of elephants in the wild.

audio, transcript

Suppose a new study comes out saying a drug or a food or a habit lowers your risk of some disease. What is the probability that the study’s result is correct? Obviously this is a very important question, but one that is not raised often enough.

[click to continue...]

Michael Lugo pointed out this article explaining why the shape of the moon’s orbit around the sun is not what you might expect.

60-Second Science has a story about a bizarre form of animal defense. There are caterpillars that vomit on attackers. And they don’t spew corrosive chemicals as animals sometimes do. They spew surfactants (think soap). Audio

The duck-billed platypus is the most recent species to have its genome sequenced. These odd animals are even more strange at the DNA level. Some features of their DNA are avian, some are reptilian, and of course some are mammalian. See the Science Daily article for more details.

Yesterday’s Science at NASA podcast had an entertaining story about duct tape and Apollo 17. (Transcript, audio)

The lunar rover lost a fender and they taped it back on with duct tape. That worked for a while, then they had to make a new fender with laminated maps and duct tape.

Why is a fender such a big deal? Without a fender, the astronauts would get dirty. So why is that a big deal?

1. Dirt is dark, and dark absorbs sun light. A dirty astronaut may become a fried astronaut.
2. Dirt scratches visors, making it hard to see.
3. Dirt gets in parts like hinges and breaks them.

According to a Science Magazine story, it looks like humans have been in North America one thousand years longer than previously believed. New DNA evidence suggests people were in North America by 12,000 B.C. The study also suggests that the first Native Americans may have arrived via the Pacific Coast rather than migrating across the land bridge that once connected Asia and North America.

Read the article or listed to the podcast.

According to the latest Scientific American podcast, there is no scientific evidence to back up the common belief that everyone should drink eight glasses of water per day. Nor is there scientific evidence to back up many of the claimed benefits of increased water consumption: improved skin, better regulated appetite, etc.

However, the podcast equates “no scientific evidence” with “not true.” The title of the podcast is The Mythical Daily Water Requirement. “Mythical” means “false.” (There are more nuanced uses of the word “myth,” but I don’t think they are relevant here.)

It has been known for some time that the eight-glass-a-day recommendation is not well substantiated by experiments. That’s not to say increased water consumption isn’t beneficial. After all, there have not been any randomized trials to prove that parachutes improve your chances of survival when jumping from an airplane either.

Randomized trials are not the only way to learn about the world, and are not as effective as commonly believed. Most published research findings are false. Randomized trials are a tool for exploring reality, sometimes the best tool for a particular task, but not the only tool.

It’s plausible that drinking eight glasses of water per day is beneficial, or at least harmless, based on anecdotal evidence. Certainly drinking too little water is fatal (though there have been no randomized trials to confirm this!) and so it is reasonable to presume there is some curve showing increased benefit with increased water intake, up to a point. The curve would go back down at some point, as it is possible to drink too much water. It would be interesting to see randomized studies to explore where the curve flattens out, exploring consumption levels safely between the harmful extremes.

It is widely assumed that parachute use improves your chances of surviving a leap from an airplane. However, a meta analysis suggests this practice is not adequately supported by controlled experiments. See the article Parachute use to prevent death and major trauma related to gravitational challenge: systematic review of randomized controlled trials by Gordon C S Smith and Jill P Pell. The authors summarize their conclusions in the abstract.

As with many interventions intended to prevent ill health, the effectiveness of parachutes has not been subjected to rigorous evaluation by using randomised controlled trials. Advocates of evidence based medicine have criticised the adoption of interventions evaluated by using only observational data. We think that everyone might benefit if the most radical protagonists of evidence based medicine organised and participated in a double blind, randomised, placebo controlled, crossover trial of the parachute.

In 1601, an English sea captain did a controlled experiment to test whether lemon juice could prevent scurvy.  He had four ships, three control and one experimental.  The experimental group got three teaspoons of lemon juice a day while the control group received none. No one in the experimental group developed scurvy while 110 out of 278 in the control group died of scurvy. Nevertheless, citrus juice was not fully adopted to prevent scurvy until 1865.

Overwhelming evidence of superiority is not sufficient to drive innovation.

Source: Diffusion of Innovations

The March 6 Nature podcast has a story about the Large Hadron Collider. The LHC is expected to gather 15 petabytes (15,000,000 gigabytes) of data. One of the people interviewed said that 15 petabytes of data would require a stack of DVDs the height of Mount Blanc.