Science

My frustration with personal productivity systems like GTD is that they’re all about projects and tasks. They leave out a third category: programs. GTD thinks of a project as something that can be broken into a manageable number of tasks and scratched off a list. But programs go on indefinitely and cannot be divided into a small number of one-time tasks.

I’m using the word “program” as in an “exercise program” or a “research program.” (I could think of my exercise program as a project, but it’s one I hope not to complete for a few more decades.) Sometimes there is a neat hierarchy where programs spawn off projects that can be divided into tasks. But sometimes you just have programs and tasks.

One of my frustrations with managing software development in an academic environment was the large number of programs disguised as projects. (Sorry, I know it’s confusing to talk about “programs” in the context of software development and not mean computer instructions.) You can’t manage programs as if they were projects. For example, you can’t talk about “after” project is done if it’s not really a project but a never-ending program. You have to either acknowledge that a program is really a program, or you have to have some way to make it into a finite project.

Here are some of my favorite posts from the Reproducible Ideas blog.

Three reasons to distrust microarray results
Provenance in art and science
Forensic bioinformatics (continued)
Preserving (the memory of) documents
Programming is understanding
Musical chairs and reproducibility drills
Taking your code out for a walk

The most popular and most controversial was the first in the list, reasons to distrust microarray results.

The emphasis shifts from science to software development as you go down the list, though science and software are intertwined throughout the posts.

I’m in the process of folding ReproducibleResearch.org into the new ReproducibleResearch.net site. I will be giving the .org domain name to the folks now running the .net site. (See the announcement for a little more information.)

As part of this process, I’m winding down the blog that I started last July as part of the ReproducibleResearch.org site. I plan to keep the links to my old posts valid, but I do not know whether the new site will have a new blog. I wrote about reproducible research on this blog before starting the ReproducibleResearch.org site, and I will go back to writing about reproducible research here. (See reproducibility in the tag cloud.)

I wanted to point out an article by Steve Eddins posted this morning: Reproducible research in signal processing. His article comments on the article by Patrick Vandewalle, Jelena Kovačević, and Martin Vetterli announced recently on ReproducibleResearch.org.

Readers interested in reproducible research may also want to take a look at the Science in the open blog.

Related posts:

Irreproducible analysis
Using Photoshop on experimental results
Highlights from Reproducible Ideas

The latest episode of the Science and the Sea podcast explains how a protein that gives a certain species of jellyfish a faint glow is useful in research into cancer and other diseases.

Related posts:

Cartoon guide to cancer research
Naked mole rats and cancer
How to treat a stingray wound

Everybody thinks Dilbert is about their job. But this cartoon really is about my job. It does a remarkably good job of summarizing what it’s like to work in cancer research.

Related posts on cancer research

The latest .NET Rocks podcast interviews Pat Hynds on why projects fail. Toward the end of his interview he mentions a simple template for status reports.

1. What did you work on?
2. What did you get done?
3. What did you do that you didn’t anticipate having to do?
4. What did you plan to do that you didn’t get done?
5. What do you plan to do?
6. What do you need from others?

When I started managing a group of programmers, I’d focus on #1 and #2. But in some ways #3 is the most important question. That question can alert you to a major time sink that’s not include in your project estimates. That question can let you know of problems beyond an individual developer’s ability to resolve. That question that can tell you it’s time to buy something you were planning on building yourself.

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

Tony Rasa has written a Clippy-like program that will nag you every time you copy and paste code in Visual Studio.

See his post AntiPaste, because Pasting Code Is Harmful.

It’s a joke, but many a truth is told in jest.

The word “classical” has a standard meaning in the humanities, but not in science.

Ward Cheney and Will Light give a candid definition of “classical” in the scientific sense in the introduction to their book on approximation theory:

… the “classical” portion of approximation theory — understood to be the parts of the subject that were already in place when the authors were students.

There you have it: whatever was known when you were in school is classical. Yes, this definition is entirely relative. And it describes common usage pretty well.

When I hear of naked mole rats, I think of Rufus, the animated character from Kim Possible.

But it turns out the real rodents might be useful in cancer research. According to a recent 60-Second Science podcast, naked mole rats live in low-oxygen environments. The core of large tumors is also a low-oxygen environment, and so maybe studying naked mole rats can tell us something about cancer. So far researchers have found three genes in common between naked mole rats and cancer cells.

Harmonic mean has come up in a couple posts this week (with numbers and functions). This post will show how harmonic means come up in physical problems involving springs and resistors.

Suppose we have two springs in series with stiffness k₁ and k₂:

Then the combined stiffness k of the two springs satisfies 1/k = 1/k₁ + 1/k₂. Think about what this says in the extremes. If one of the springs were infinitely stiff, say k₂ = ∞. Then k = k₁. It would be as if the second spring were not there. Being infinitely stiff, we could think of it as an extension of the block it is attached to. Now think of one of the springs having no stiffness at all, say k₁ = 0. Then k = 0. One mushy spring makes the combination mushy.

Next think of two springs in parallel:

Now the combined stiffness of the two springs is k = k₁ + k₂. Again think of the two extremes. If one spring is infinitely stiff, say k₁ = ∞, then k = ∞ and the combination is infinitely stiff. And if one spring has no stiffness, say k₂ = 0, then k = k₁. We could imagine the spring with no stiffness isn’t there.

The stiffness of springs in series adds harmonically. The stiffness of the combination is half the harmonic mean of the two individual stiffnesses.

Electrical resistors combine in a way that is the opposite of mechanical springs. Resistors in parallel combine like springs in series, and vice versa.

If two resistors have resistance r₁ and r₂, the combined resistance r of the two resistors in parallel satisfies 1/r = 1/r₁ + 1/r₂. If one of the resistors has infinite resistance, say r₂ = ∞, then r = r₁. It would be as if the second resistor were not there. All electrons would flow through the first resistor.

If the two resistors were in series, then r = r₁ + r₂. If one resistor has infinite resistance, so does the combination. Electrons cannot flow through the combination if they cannot flow through one of the resistors. And if one resistor has zero resistance, say r₂ = 0, then r = r₁. Since the second resistor offers no resistance to the flow of electrons, it may as well not be there.

These physical problems illustrate why zeros as handled specially in the definition of means.

Image credit: Wikipedia

Keith Hill has a fun blog post on using Unicode characters in PowerShell function names. Here’s an example from his article using the square root symbol for the square root function.

PS> function √($num) { [Math]::Sqrt($num) }
PS> √ 81
9

As Keith points out, these symbols are not practical since they’re difficult to enter, but they’re fun to play around with.

Here’s another example using the symbol for pounds sterling

for the function to convert British pounds to US dollars.

PS> function £($num) { 1.44*$num }
PS> £ 300.00
432

(As I write this, a British pound is worth $1.44 USD. If you wanted to get fancy, you could call a web service in your function to get the current exchange rate.)

I read once that someone (Larry Wall?) had semi-seriously suggested using the Japanese Yen currency symbol

for the “zip” function in Perl 6 since the symbol looks like a zipper.

Mathematica lets you use Greek letters as variable and function names, and it provides convenient ways to enter these characters, either graphically or via their TeX representations. I think this is a great idea. It could make mathematical source code much more readable. But I don’t use it because I’ve never got into the habit of doing so.

There are some dangers to allowing Unicode characters in programming languages. Because Unicode characters are semantic rather than visual, two characters may have the same graphical representation. Here are a couple examples. The Roman letter A (U+0041) and the capital Greek letter Α (U+0391) look the same but correspond to different characters. Also, the the Greek letter Ω (U+03A9) and the symbol Ω (U+2126) for Ohms (unit of electrical resistance) have the same visual representation but are different characters. (Or at least they may have the same visual representation. A font designer may choose, for example, to distinguish Omega and Ohm, but that’s not a concern to the Unicode Consortium.)

The programmer is the last link in the chain of a software project. Everyone higher up the organization chart can leave out details, but the programmer cannot. Anything left unspecified will be decided by the programmer. He cannot pass the buck because he has to make something work. Programmers make good decisions, bad decisions, and many arbitrary but neutral decisions.

When you see software with a silly interface, odds are the interface details were not specified and the programmer chose the path of least effort. Why should I press # after entering my five-digit zip code on a phone? It’s logically possible to determine what my zip code is as soon as I enter the fifth digit, but it makes life easier for some phone system programmer if the pound sign is a universal end-of-input signal. Or why should I select an account at the ATM if I only have one account? Again, I’m sure this made life easier for some programmer.

Some programmers are lazy. But some are unsung heroes. They understand gritty details of their company that no one else knows about. They have to: they have to specify these details to dumb machines. Most people don’t want to solve problems down to the final detail and programmers — for better and for worse — are the ones who fill in the gaps.

Some of the details that programmers fill in regard what to do when things go wrong. A client says a program is supposed to collect the user’s Social Security number (SSN). Fine. But what if the user doesn’t have an SSN? What if they enter an invalid SSN? (Is there a way to know whether an SSN is valid?)  After a few questions like that, the client will throw up his hands and leave it up to the developer. But the developer cannot throw up his hands. He has to decide something, even if he passively decides to let the software crash in case of unexpected input.

Update: Changed “analyst” to “client” above. See discussion below. “Client” more accurately reflects what I meant.

Related posts:
Paper doesn’t abort
Where does the programming effort go?

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