Month: February 2011

Programmers without computers

Posted on by John

When I started my first job as a programmer, I was surprised how much time my colleagues spent at their computers. Of course a computer programmer needs to spend a fair amount of time sitting at a computer, but why did people spend nearly 100% of their time in front of a monitor? This seemed strange to me since I hadn’t worked this way before. I had always alternated thinking away from a computer and sitting down at a computer.

I was even more puzzled when the network went down, which it often did. Half of us worked on Windows PCs and half worked on Unix workstations. When the network was down, the PC folks kept working because they had self-contained local work environments.

But the Unix folks would stand in the halls until the network came back up or go home if it looked like the network wasn’t going to come up soon.  They had computers on their desks, but these were primarily used as terminals to connect to servers. So without a network, the Unix folks essentially had no computers. Everyone agreed that meant they couldn’t get any work done. That seemed bizarre to me.

At that time, I knew how to program, but I knew almost nothing about professional software development. Many of my ideas were naive. But looking back, I think I was right about one thing: programmers need to stand up and think more. Too often, that’s the last thing we do.

Related links:

Absence of evidence

Posted on by John

Here’s a little saying that irritates me:

Absence of evidence is not evidence of absence.

It’s the kind of thing a Sherlock Holmes-like character might say in a detective novel. The idea is that we can’t be sure something doesn’t exist just because we haven’t seen it yet.

What bothers me is that the statement misuses the word “evidence.” The statement would be correct if we substituted “proof” for “evidence.” We can’t conclude with absolute certainty that something doesn’t exist just because we haven’t yet proved that it does. But evidence is not the same as proof.

Why do we believe that dodo birds are extinct? Because no one has seen one in three centuries. That is, there is an absence of evidence that they exist. That is tantamount to evidence that they do not exist. It’s logically possible that a dodo bird is alive and well somewhere, but there is overwhelming evidence to suggest this is not the case.

Evidence can lead to the wrong conclusion. Why did scientists believe that the coelacanth was extinct? Because no one had seen one except in fossils. The species was believed to have gone extinct 65 million years ago. But in 1938 a fisherman caught one. Absence of evidence is not proof of absence.

coelacanth, a fish once thought to be extinct

Though it is not proof, absence of evidence is unusually strong evidence due to subtle statistical result. Compare the following two scenarios.

Scenario 1: You’ve sequenced the DNA of a large number prostate tumors and found that not one had a particular genetic mutation. How confident can you be that prostate tumors never have this mutation?

Scenario 2: You’ve found that 40% of prostate tumors in your sample have a particular mutation. How confident can you be that 40% of all prostate tumors have this mutation?

It turns out you can have more confidence in the first scenario than the second. If you’ve tested N subjects and not found the mutation, the length of your confidence interval around zero is inversely proportional to N. But if you’ve tested N subjects and found the mutation in 40% of subjects, the length of your confidence interval around 0.40 is inversely proportional to √N. So, for example, if N = 10,000 then the former interval has length on the order of 1/10,000 while the latter interval has length on the order of 1/100. This is known as the rule of three. You can find both a frequentist and a Bayesian justification of the rule here.

Absence of evidence is unusually strong evidence that something is at least rare, though it’s not proof. Sometimes you catch a coelacanth.

Related posts

Like Laplace, only more so

Posted on by John

The Laplace distribution is pointy in the middle and fat in the tails relative to the normal distribution.This post is about a probability distribution that is more pointy in the middle and fatter in the tails.

Here are pictures of the normal and Laplace (a.k.a. double exponential) distributions.

Normal:

Laplace:

The normal density is proportional to exp(- x2/2) and the Laplace distribution is proportional to exp(-|x|). Near the origin, the normal density looks like 1 – x2/2 and the Laplace density looks like 1 – |x|. And as x gets large, the normal density goes to zero much faster than the Laplace.

Now let’s look at the distribution with density

f(x) = log(1 + 1/x²)

I don’t know a name for this. I asked on Cross Validated whether there was a name for this distribution and no knew of one. The density is related to the bounds on a density presented in this paper. Here’s a plot.

The density is unbounded near the origin, blowing up like -2 log( |x| ) as x approaches 0, and so is more pointed than the Laplace density. As x becomes large, log(1 + x-2) is asymptotically x-2 so the distribution has the same tail behavior as a Cauchy distribution, much heavier tailed than the Laplace density.

Here’s a plot of this new density and the Laplace density together to make the contrast more clear.

As William Huber pointed out in his answer on Cross Validated, this density has a closed-form CDF:

F(x) = 1/2 + (arctan(x) – x log( sin( arctan(x) ) ))/π

The paper mentioned above used a similar density as a Bayesian prior distribution in situations where many observations were expected to be small, though large values were expected as well.

Related posts:

How the term "scientist" came to be

Posted on by John

For most of history, scientists have been called natural philosophers. You might expect that scientist gradually and imperceptibly replaced natural philosopher over time. Surprisingly, it’s possible pinpoint exactly when and where the term scientist was born.

It was June 24, 1835 at a meeting of the British Association for the Advancement of Science. Romantic poet Samuel Taylor Coleridge was in attendance. (He had previously written about the scientific method.) Coleridge declared that although he was a true philosopher, the term philosopher should not be applied to the association’s members. William Whewell responded by coining the word scientist on the spot. He suggested

by analogy with artist, we may form scientist.

Since those who practice art are called artists, those who practice science should be called scientists.

This story is comes from the prologue of Laura Snyder’s new book The Philosophical Breakfast Club (ISBN 0767930487). The subtitle is “Four Remarkable Friends Who Transformed Science and Changed the World.” William Whewell was one of these four friends. The others were John Herschel, Richard Jones, and Charles Babbage.

Update 1: Will Fitzgerald created the following Google Books ngram that suggests that scientist was used occasionally before 1835 and would take another 30 years to start being widely used in books. Click on the image to visit the original ngram.

So it is with many innovations: the person credited with the innovation may not have been entirely original or immediately successful. Still, perhaps Whewell’s public confrontation with Coleridge gave scientist a push on the road to acceptance.

Update 2: Pat Ballew fills in more of the story on his blog including editorial opposition to the term scientist. Pat brings more famous people into the story, including H. L. Mencken, Michael Faraday, and William Cullen Bryant.

Update 3: Here’s an excerpt from The Philosophical Breakfast Club.

More 19th century science

The end of hard-edged science?

Posted on by John

Bradley Efron says that science is moving away from things like predicting sunrise times and toward predicting things like the weather. The trend is away from studying precisely predictable systems, what Efron calls “hard-edged science,” and toward studying systems “where predictability is tempered by a heavy dose of randomness.”

Hard-edged science still dominates public perceptions, but the attention of modern scientists has swung heavily toward rainfall-like subjects, the kind where random behavior plays a major role. … Deterministic Newtonian science is majestic, and the basis of modern science too, but a few hundred years of it pretty much exhausted nature’s storehouse of precisely predictable events. Subjects like biology, medicine, and economics require a more flexible scientific world view, the kind we statisticians are trained to understand.

Certainly there is increased interest in systems containing “a heavy dose of randomness” but can we really say that we have “pretty much exhausted nature’s storehouse of precisely predictable effects”?

Source: Modern Science and the Bayesian-Frequentist Controversy

More science posts

Final velocity

Posted on by John

My daughter and I were going over science homework this evening. A ball falls for 10 seconds. What is its final velocity?

JC: So how fast is the ball going when it hits the ground?

RC: Zero. It stops before it bounces back up.

JC: Well, how fast is it going just before it hits the ground?

RC: They didn’t ask the almost final velocity. They asked for the final velocity.