French press. It makes better coffee than a typical coffee machine. Also, a French press work without electricity. Next time a hurricane comes through Houston and knocks out our power, I can still make my coffee.

Reel mower. I had gasoline powered lawn mowers until last year. Sometimes they’d start, sometimes they wouldn’t. My reel mower always starts. And it’s quiet.

Rake. I had a leaf blower once. It was obnoxiously loud and a nuisance to my neighbors. I much prefer raking leaves even though it takes longer.

Pencil sharpener. With four children, we sharpen a fair number of pencils. We have owned a couple electric pencil sharpeners. They were noisy, hard to use, and soon wore out. Our mechanical pencil sharpener is cheaper and far more reliable.

I’m no Luddite, but I firmly believe that newer isn’t necessarily better.

Related posts:

Selective use of technology
Tim Bray’s high-tech monastic cell
Software bloat
What’s wrong with paper?

They say everyone’s Irish on St. Patrick’s Day. I’ve heard that I actually am part Irish (as well as Scottish, German, Cherokee, …) In any case, it’s nice of the Irish to share their holiday with the rest of the world.

St. Patrick’s Day 2007 in Seoul, Korea. Image credit: here via Wikipedia

Related posts:

Guinness beer
Why Mr. Scott is Scottish
Mathematical genealogy
Honey bee genealogy

GNU Emacs began in 1984 and has been in constant development ever since. The current version is 23.1. How many applications from 1984 are still in widespread use today? The only other one that comes to mind is TeX.

I used Emacs in graduate school and for a few years after that. I was fairly fluent with Emacs, though I never customized it much. I intended to learn Emacs Lisp and all that, but it never happened.

When I started developing Windows software I used Emacs at first, but the benefits of Visual Studio soon persuaded me give up my old editor. It was much easier to go with the flow.

I’ve revisited Emacs a couple times over the years. I still have some of the keystrokes burned into my memory. I use it on Linux now and then, but I mostly work on Windows, and my experience using Emacs on Windows has been frustrating to say the least. Tasks that are trivial in any Windows application, such as printing and spell checking, are surprisingly difficult to set up in Emacs. I’m sure it is possible to resolve these problems, though I never did.

The problems with printing and spell checking are part of the larger issue that Emacs is so idiosyncratic. It behaves nothing like a typical Windows program. Some people may say that’s a good thing. But it makes life more complicated if you switch between Emacs and more conventional Windows software.

Emacs is no more a typical Mac application than it is a typical Windows application. And yet my impression is that this is less of a problem for Mac users. I’d like to understand whether this is true and if so why.

One of the things I liked about Emacs was the way you could “live” there. An expert Emacs user might work inside Emacs all day, using it as an editor, debugger, shell, file system explorer, email program, etc. Steve Yegge is such an expert. When he blogged about his move from Windows to Mac,  he said the main reason for the switch was that he prefers the appearance of the fonts on a Mac. Changing operating systems was not a big deal for Yegge because he didn’t really live in Windows before, nor does he live in OS X now. He lives in Emacs. He concluded his essay by saying

So I’ll keep using my Macs. They’re all just plumbing for Emacs, anyway. And now my plumbing has nicer fonts.

Living inside Emacs comes at a price. Part of that price is writing lots of Emacs Lisp to glue things together. Another part of that price is the commitment to practicing using Emacs. As Yegge says elsewhere

… you need to make a serious, lifelong commitment to Emacs in order to master it. … So it’s not an editor for the faint of heart …

Yikes! I’m not ready to make a serious, lifelong commitment to a piece of software. To my wife? Yes. To my text editor? No.

One of the best features of Emacs is that it has custom “modes” for various kinds of files. Instead of using a separate program for editing every kind of file, Emacs users use one program with different modes. As soon as a new file type comes out, say for a new programming language, someone will post an Emacs mode for that new language.

I’d like to find an editor on Windows that is analogous to Emacs. By that I mostly have in mind a powerful, highly configurable editor with support for many file types. I’d want it to behave like a Windows application, not a foreign transplant, and integrate well with .NET.

There was a project to create such an editor, nicknamed Emacs.NET. It was announced in late 2007. It sounds like the project is still alive, but it doesn’t seem all that promising.

I’ve looked at a few Windows editors that claim to be highly configurable but are not well documented. So if such an editor is configurable, it’s configurable for the person who wrote it or possibly for anyone else willing to study the source code.

Any suggestions for a general purpose Windows editor? For starters, I’d be pleased to find something that’s good at editing LaTeX and HTML.

Related posts:

This post started out as an update to my earlier post One program to rule them all.

… I had been infatuated with Thoreau’s Walden and its story of living a basic life, close to nature. The heart of that undertaking, he had written, was to simplify your life. … In retrospect, I can see that although I thought that this was what I was doing, I was really just trying to add simplicity to my life. In addition to all the old things I had been doing … Of course, my life grew more and more complicated in the process.

A simplification has to remove or replace something else. You can’t just add on simplicity.

There may be an exception to this. Sometimes you can add a few missing pieces to make something more symmetric. In that case, the additions simplify the whole. (Mendeleev did something like this when he drew his periodic table.) Even then, I suppose you could say you’re removing the asymmetry. In any case, achieving simplicity usually requires more subtraction than addition.

Related posts:

Simplicity in old age
Simple legacy
A little simplicity goes a long way

You can install Quix by dragging it to your bookmark menu. However, if you want to use Quix to make it easier to use your browser without a mouse, you don’t want to have to click the Quix bookmark to get started. You can integrate Quix with your browser to be able to launch Quix from the keyboard.

For example, if you’re using Firefox on Windows, you can drag the Quix bookmarklet to your bookmarks toolbar. Next right-click on the bookmarklet, select “Properties”, and set “q” as the keyword. Then you can launch Quix by typing Ctrl-L q.

You can find directions here for integrating Quix with Chrome, IE, Firefox, Opera, and Safari.

Related posts:

Using Windows without a mouse
Four patterns in Windows shortcuts
@SansMouse — daily tips on using Windows without a mouse

Frozen baby woolly mammoth
Top 200 blogs for developers
Greece’s debt
Code is expendable; developers are not
Wanting it both ways
Code bubbles
Psychological disorder quiz

We are all familiar with the idea that we can estimate height in male adults from their weight. … But not one of us believes that adding 20 pounds by eating and minimizing exercise will add an inch to our height.

The problem is not simply that the direction of causality backward, it’s that we cannot use a static description to predict what will happen if we change something.

Although regression situations may give one the illusion of finding out what would happen if we changed something, in the absence of an experiment they offer merely offer guesses.

He summarizes his point by quoting George Box:

To find out what happens to a system when you interfere with it, you have to interfere with it (and not just passively observe it).

Remember this next time you hear claims such as every dollar spent on X saves so many dollars spent on Y. Or every minute spent exercising increases your life expectancy by so many minutes. Or every time you do some activity you increase or decrease your risk of cancer by so much. First of all, these kinds of statements are linear extrapolations on situations that are not linear. Second, they may be observations that do not describe what will happen when you change something. They may be no more true than the idea that gaining weight makes you taller.

Here’s an example of how observation and intervention differ. Lottery winners often go bankrupt within a couple years of receiving their prize. If you suddenly make someone a millionaire, they’re not a typical millionaire.

Related posts:

Numerator-only data
Randomized trials of parachute use

“Why do the white horses eat more than the black horses?”
“Don’t know. Why?”
“Because we have ten times as many white horses and black horses.”

Numerator-only data is data that leaves you asking “compared to what?” If I tell you the NASDAQ stock index closed at 2368 today, is that good or bad? The number by itself means nothing. Is that up or down compared to last week? Last year? If I tell you, for example, that the record high value was 5047, that gives you a denominator to compare it to.

Mark Biek pointed out the quality of the Google and Yahoo translations from Chinese back into English. The Google translation is awkward but understandable. The Yahoo translation, however, is a total failure. First of all, the translation is illegible in Firefox:

Using Internet Explorer 8, the text is legible, but it doesn’t make sense:

The two screen shots focus on different parts of the text. I chose a swatch near the top of the Firefox version where the text was most illegible. I chose the IE8 swatch to showcase the phrase “the smelly spicy jiao raccoon dog” that Mark had pointed out.

If hot things cool, and cool things warm up, could something hot cool down and warm back up?

The people I asked didn’t understand my question and just laughed. I have no idea how old I was, but I wasn’t old enough to articulate what I was thinking.

Here’s what I had in mind. I knew that hot things like a cup of coffee grew cold. And I knew that cold things, say a glass of milk, get warm. Well, could the coffee get so cold that it becomes a cold thing and start to warm back up?

Could the coffee become as cold as the glass of milk? Common sense suggests that can’t happen. When we say coffee grows cold, we mean that it becomes relatively colder, closer to room temperature. And when we say the milk is getting warm, we also mean it is getting closer to room temperature. We’ve never left a hot cup of coffee on a table and come back later to find that it has cooled off so much that it is colder than room temperature. But could there be small fluctuations?

As the coffee and milk head toward room temperature, could they overshoot the target, just by a little bit? Say room temperature is 70 °F, the coffee starts out at 150 °F, and the milk starts out at 40 °F. We don’t expect the coffee to cool down to 40 °F or the milk to warm up to 150 °F. But could the coffee cool down to 69.5 °F and then go back up to 70 °F? Could the milk warm up to 70.5 °F and then cool back down to 70 °F?

I didn’t get a satisfactory answer to my childhood question until I was in college. Then I found out about Newton’s law of cooling. It says that the rate at which a warm body cools is proportional to the difference between its current temperature and the ambient temperature. This law can be written as a differential equation whose solution shows that the temperature of a warm body decreases exponentially to the ambient temperature. The temperature curve always slopes downward. It doesn’t wiggle even a little on its journey to room temperature. Cold bodies warm up the opposite way, exponentially approaching room temperature but never exceeding it.

In case it this seems obvious, think about thermostats. They don’t work this way. Say the temperature in a room is 85 °F and you’d like it to be 72 °F, so you turn on the air conditioning. Will the temperature steadily lower to 72 °F? Not exactly. If you were to plot the temperature in the room over time and look at the graph from far enough away, it would look like it is steadily going down to the desired temperature. But if you look at the graph more closely, you’ll see wiggles. The AC may cool the room to a little below 72 °F, maybe to 70 °F. The AC would cut off and the temperature would rise to 72 °F. Unlike the cup of hot coffee, the AC will often overshoot its target, though not by too much. The temperature may feel constant, but it is not. It oscillates around the desired temperature.

I post a little more than one article a day on average on a variety of topics. Here’s a list of some of the most popular posts by category.

This blog is also available as a podcast. The audio is automatically generated. The quality is good for ordinary prose but not as good for other content.

Here’s my contact info. If you submit a comment that never appears, please send me a note. I get thousands of spam comments, and so I filter spam aggressively. Sometimes a legitimate comment gets blocked. I enjoy hearing from you. I learn a lot from the comments.

I have several Twitter accounts, one personal account and six daily tip accounts. I keep the volume low on the daily tip accounts: one scheduled tip per day plus an occasional unscheduled tweet.

Two things stood out to me in the interview: a comparison of Lisp with C++, and a discussion of complexity.

You’ll often hear a programmer argue that language X is better than language Y.  To support their argument, they’ll say they wrote a program in Y, then wrote it in X in less time. For example, someone might argue that Ruby is better than Python because they were able to rewrite their web site using Ruby in half the time it took to write the original Python version. Such arguments are weak because you can write anything faster the second time. The first implementation required analysis and design that the second implementation can reuse entirely or at least learn from.

Rich Hickey argues that he can develop programs in Lisp faster than in C++. He offers as support that he first wrote something in Lisp and then took three times longer to rewrite it in C++. This is just a personal anecdote, not a scientific study, but it carries more weight than the usual anecdote because he’s claiming the first language was more efficient than the second.

In his discussion of incidental complexity, complexity coming from ones tools rather than from the intrinsic complexity of the problem being solved, Hickey says

I think programmers have become inured to incidental complexity, in particular by confusing familiar or concise with simple. And when they encounter complexity, they consider it a challenge to overcome, rather than an obstacle to remove. Overcoming complexity isn’t work, it’s waste.

The phrase “confusing familiar or concise with simple” is insightful. I never appreciated the arguments about the complexity of C++ until I got a little distance from the language; C++ was so familiar I didn’t appreciate how complex it is until I had a break from writing it. Also, simple solutions are usually concise, but concise solutions may not be simple. I chuckle whenever I hear someone say a problem was simple to solve because they were able to solve it in one line — one long stream of entirely mysterious commands.

Thanks to Omar Gomez for pointing out the interview article.

Related posts:

A little simplicity goes a long way
I disagree with Torvalds about C++
Baklava code

Tufte is a widely respected expert in data visualization. I attended one of his seminars years ago and thoroughly enjoyed it. I wish him well. I’m sure he will do a good job. However, there are limits on any statistician working for politicians.

I recommend listening to Ron Howard’s explanation for why he no longer consults for government. (Ron Howard the Stanford University professor, not Ron Howard the actor/director.) Howard  produced  a decision analysis of nuclear fuel reprocessing for the Carter administration, but his hands were tied for political reasons. He concludes

If this were the only case where I had this dispiriting result … perhaps I could treat it as an exception. But what I’ve found is every time I did a study like this … there was nobody home in terms of really wanting to know the result.

Howard’s interview is available from the here. The remarks above run from 5:00 to 8:15.

Brilliant bipolar minds
Internet law on .NET Rocks
Whatever happened to programming?
PowerShell survival guide

Business and economics

Drawing the line between free and paid
Federal worker compensation

Math

Nicomachus’s theorem
63rd Carnival of Mathematics

Miscellaneous

Why heroes use checklists
Free online OCR (haven’t tried it, but it looks interesting)

Parody

I want to focus on one line from the video. After showing simulated lightning strikes that hit a wooden rod five times and a copper rod five times, the narrator says

It’s five all, proof that metal does not attract lightning.

No, such an experiment would prove no such thing. I imagine the researchers conducted a much larger experiment and selected a representative sample. And I’m willing to accept their conclusion that metal does not attract lightning. But I would not accept such a conclusion from an experiment with 10 samples. What the experiment proves is that, under their experimental conditions, lightning will sometimes strike wood even a metal rod is nearby.

I have two complementary criticisms of this made-for-video science.

1. The results could easily happen if their conclusion were not true.
2. The results could easily not have happened if there conclusion were true.

Suppose in reality, lightning will not always strike the metal rod, but will prefer the metal. Suppose in the long run, lightning will strike the metal rod 60% of the time. It would not be unusual in that case to do an experiment with 10 strikes and find that half or more of the strikes hit wood.

Now suppose the researchers are exactly correct. In the long run, lightning has no preference for one rod or the other. What would viewers have thought if they showed a clip of 10 strikes, of which 6 hit metal and 4 hit wood? Many would have howled in protest. If lightning really had no preference for metal, the result should have been an even split, right? This is an example of the Law of Small Numbers. People underestimate the variability of small samples.

If the probability of lightning striking each rod is 50%, then in a sequence of experiments each containing 10 strikes, most will not have an exact 5-5 split. If you flip 10 fair coins, the most likely outcome is a 5-5 split, but this will happen only about 1/4 of the time. It’s more likely that you’ll get near a 5-5 split, sometimes with more heads and sometimes with more tails.

The exact 5-5 split in the video is good showmanship, but it’s misleading science.

Related posts:

Law of small numbers
Example of the law of small numbers
Law of medium numbers

In general, you learn things in school just in case you’ll need them later. Then once you get a job, you learn more things just in time when you need them.

When you learn just in time, you’re highly motivated. There’s no need to imagine whether you might apply what you’re learning since the application came first. But you can’t learn everything just in time. You have to learn some things before you can imagine using them. You need to have certain patterns in your head before you can recognize them in the wild.

Years ago someone told me that he never learned algebra and has never had a need for it. But I’ve learned algebra and use it constantly. It’s a lucky thing I was the one who learned algebra since I ended up needing it. But of course it’s not lucky. I would not have had any use for it either if I’d not learned it.

The difference between just-in-case and just-in-time is like the difference between training and trying. You can’t run a marathon by trying hard. The first person who tried that died. You have to train for it. You can’t just say that you’ll run 26 miles when you need to and do nothing until then.

Software developers prefer just in time learning. There’s so much out there that you aren’t going to need. You can’t learn every detail of every operating system, every programming language, every library etc. before you do any real work. You can only remember so much arbitrary information without a specific need for it. Even if you could learn it all in the abstract, you’d be decades into your career without having produced anything. On top of that, technological information has a short shelf life, so it’s not worthwhile to learn too much that you’re not sure you have a need for.

On the other hand, you need to know what’s available, even if you’re only going to learn the details just in time. You can’t say “I need to learn about version control system now” if you don’t even know what version control is. You need to have a survey knowledge of technology just in case. You can learn APIs just in time. But there’s a big gray area in between where it’s hard to know what is worthwhile to learn and when.

Related posts:

Software that gets used
Why programmers write unneeded code
Don’t standardize education, personalize it
Worthless technical books

I just ran across a paper of Mark Schervish¹ that contains a criticism of p-values I had not seen before. p-values are commonly used as measures of evidence despite the protests of many statisticians. It seems reasonable that a measure of evidence would have the following property. If a hypothesis H implies another hypothesis H’, then evidence in favor of H’ should be at least as great as evidence in favor of H.

Here’s one of the examples from Schervish’s paper. Suppose data come from a normal distribution with variance 1 and unknown mean μ. Let H be the hypothesis that μ is contained in the interval (-0.5, 0.5). Let H’ be the hypothesis that μ is contained in the interval (-0.82, 0.52). Then suppose you observe x = 2.18. The p-value for H is 0.0502 and the p-value for H’ is 0.0498. This says there is more evidence to support the hypothesis H that μ is in the smaller interval than there is to support the hypothesis H’ that μ is in the larger interval. If we adopt α = 0.05 as the cutoff for significance, we would reject the hypothesis that -0.82 < μ < 0.52 but accept the hypothesis that -0.5 < μ < 0.5. We’re willing to accept that we’ve found a bear, but doubtful that we’ve found a mammal.

¹ Mark J. Schervish. “P values: What They Are and What They Are Not.” The American Statistician, August 1996, Vol. 50, No. 3.

Update: I added the details of the p-value calculation here.

Related posts:

How loud is the evidence
The cult of significance testing
Most published research results are false

Bob Walsh: What’s next for Seth Godin?

Seth Godin: This. This is my life’s work. This is what I didn’t realize I was working on for the last ten years but I am. There’s no new book in the works. There’s just this mission to help people see how the world just changed really violently and to encourage them to do work that matters.

Seth Godin has always been passionate about his projects, but this one is different. His clarity and intensity are remarkable.

Related posts:

How to avoid being outsourced
Self-sufficiency is the road to poverty

International

Israeli web design
North Korean propaganda

Computing

What really happens when you navigate a URL
Seven deadly sins of JavaScript implementation
Gallery of processor cache effects
The R type system

Math

Math symbols in HTML
How to solve quadratic congruences
(Thanks to Nemo for filling in a gap.)

Productivity and expertise

The myth of efficiency
Don’t become an expert

Miscellaneous

Linguistic pet peeves
The dentist and the statistician
Punching a friend in the face

The law of large numbers is a mathematical theorem. It describes what happens as you average more and more random variables.

The law of small numbers is a semi-serious statement about about how people underestimate the variability of the average of a small number of random variables.

The law of medium numbers is a term coined by Gerald Weinberg in his book An Introduction to General Systems Thinking. He states the law as follows.

For medium number systems, we can expect that large fluctuations, irregularities, and discrepancy with any theory will occur more or less regularly.

The law of medium numbers applies to systems too large to study exactly and too small to study statistically. For example, it may be easier to understand the behavior of an individual or a nation than the dynamics of a small community. Atoms are simple, and so are stars, but medium-sized things like birds are complicated. Medium-sized systems are where you see chaos.

Weinberg warns that medium-sized systems challenge science because scientific disciplines define their boundaries by the set of problems they can handle. He says, for example, that

Mechanics, then, is the study of those systems for which the approximations of mechanics work successfully.

He warns that we should not be mislead by a discipline’s “success with systems of its own choosing.”

Weinberg’s book was written in 1975. Since that time there has been much more interest in the emergent properties of medium-sized systems that are not explained by more basic sciences. We may not understand these systems well, but we may appreciate the limits of our understanding better than we did a few decades ago.

Related posts:

Laws of large numbers and small numbers
Gerald Weinberg’s law of twins
Subnatural and supernatural

Let’s suppose that back in the 1980s I had said, “In a quarter century, when the digital revolution has made great progress and computer chips are millions of times faster than they are now, humanity will finally win the prize of being able to write a new encyclopedia and a new version of UNIX!” It would have sounded utterly pathetic.

The quote specifically alludes to Wikipedia and Linux, but Lanier is critical of web culture in general. I’m not sure what I think about his position, but at a minimum he provides a counterbalance to the people who speak about the web in messianic tones.

Random sequences clump more than most folks expect. For graphical applications, quasi-random sequence may be more appropriate.These sequences are “more random than random” in the sense that they behave more like what some folks expect from randomness. They jitter around like a random sequence, but they don’t clump as much.

Researchers conducting clinical trials are dismayed when a randomized trial puts several patients in a row on the same treatment. They want to assign patients one at a time to one of two treatments with equal probability, but they also want the allocation to work out evenly. This is like saying you want to flip a coin 100 times, and you also want to get exactly 50 heads and 50 tails. You can’t guarantee both, but there are effective compromises.

One approach is to randomize in blocks. For example, you could randomize in blocks of 10 patients by taking a sequence of 5 A’s and 5 B’s and randomly permuting the 10 letters. This guarantees that the allocations will be balanced, but some outcomes will be predictable. At a minimum, the last assignment in each block is always predictable: you assign whatever is left. Assignments could be even more predictable: if you give n A’s in a row in a block of 2n, you know the last n assignments will be all B’s.

Another approach is to “encourage” balance rather than enforce it. When you’ve given more A’s than B’s you could increase the probability of assigning a B. The greater the imbalance, the more heavily you bias the randomization probability in favor of the treatment that has been assigned less. This is a sort of compromise between equal randomization and block randomization. All assignments are random, though some assignments may be more predictable than others. Large imbalances are less likely than with equal randomization, but more likely than with block randomization. You can tune how aggressively the method responds to imbalances in order to make the method more like equal randomization or more like block randomization.

No approach to randomization will satisfy everyone because there are conflicting requirements. Randomization is a dilemma to be managed rather than a problem to be solved.

Related posts:

Quasi-random sequences in art and integration
Three ways of tuning an adaptively randomized trial
Population drift
Galen and clinical trials

This weekend I was an appraiser at a DI competition for an improvisation challenge. Teams could prepare for the overall format of the challenge, but some elements of the challenge were randomly selected on the day of the competition. This year the improvisations centered around endangered things. Teams were given a list of 10 endangered things ahead of time, but they wouldn’t know which thing would be theirs until just before they had to perform. Some of the things on the list were endangered animals, such as the giant panda. There were also other things in danger of disappearing, such as the VHS tape. The students also had to use a randomly chosen stock character and had to include a character with a randomly chosen “unimpressive superpower.”

There were 13 teams in the elementary division. What would you expect from 13 teams randomly selecting 10 endangered things? Obviously some endangered thing has to be chosen at least twice. Would you expect every item on the list to be chosen at least once? How often do you expect the most common item would be chosen?

In our case, three teams were assigned “glaciers” and five were assigned “the landline telephone.” The other items were assigned once or not at all. (No one was assigned “the Yiddish language”. Too bad. I really wanted to see what the students would do with that one.)

Is there reason to suspect that the assignments were not random? How likely is it that in a competition of 13 teams that five or more teams would be given the same subject? How likely is it that every subject would be used at least once? See an explanation here. Make a guess before looking at my answer.

Here’s some Python code you could use to simulate the selection of endangered things.

from random import random

num_reps     = 100000 # number of simulation repetitions
num_subjects = 10     # number of endangered things
num_teams    = 13     # number of teams competing

def maxperday():
    tally = [0] * num_subjects
    for i in range(num_teams):
        subject = int(random()*num_subjects)
        tally[subject] += 1
    return max(tally)

total = 0
for rep in range(num_reps):
    if maxperday() >= 5:
        total += 1
print float(total)/num_reps

The night I met Einstein

Copyright

Copyright reform act

Computing

Code Myopia
Probability distributions in Excel
Top 25 most dangerous programming errors
When open source is no longer the underdog
What does functional programming mean?

Math

Why sin(11) is approximately -1
Math teachers at play carnival#23
Calculator trick

Psychology

Suckers for irrelevancy
What happens when you get drunk?

John Ioannidis suggested popular areas of research publish a greater proportion of false results in his paper Why most published research findings are false. Of course popular areas produce more results, and so they will naturally produce more false results. But Ioannidis is saying that they also produce a greater proportion of false results.

Now Thomas Pfeiffer and Robert Hoffmann have produced empirical support for Ioannidis’s theory in the paper Large-Scale Assessment of the Effect of Popularity on the Reliability of Research. Pfeiffer and Hoffmann review two reasons why popular areas have more false results.

First, in highly competitive fields there might be stronger incentives to ‘‘manufacture’’ positive results by, for example, modifying data or statistical tests until formal statistical significance is obtained. This leads to inflated error rates for individual findings: actual error probabilities are larger than those given in the publications. … The second effect results from multiple independent testing of the same hypotheses by competing research groups. The more often a hypothesis is tested, the more likely a positive result is obtained and published even if the hypothesis is false.

In other words,

1. In a popular area there’s more temptation to fiddle with the data or analysis until you get what you expect.
2. The more people who test an idea, the more likely someone is going to find data in support of it by chance.

The authors produce evidence of the two effects above in the context of papers written about protein interactions in yeast. They conclude that “The second effect is about 10 times larger than the first one.”

Related posts:

Why microarray conclusions are so often wrong
Using Photoshop on experimental results
Irreproducible analysis
Make up your own rules of probability

What exactly is noncommercial use? If I include a photo in software that I’m give away, is that noncommercial use? What if someone includes the photo in  iTunes? That’s software that is freely given away, although it’s clearly a distribution channel for Apple music sales. What about Internet Explorer? Microsoft gives away IE, and it’s not an obvious distribution channel for Microsoft, but most people would call IE commercial software. Is it the nature of the organization rather than the nature of the product that determines whether something is non-commercial?

Sometimes “noncommercial” is used as an opposite of “professional.” But what about employees of charitable organizations such as the American Red Cross? Is a Red Cross relief worker in Haiti doing noncommercial work? What about a lawyer working at Red Cross headquarters? Would it change anything if the lawyer were a volunteer?

Sometimes “educational” is used as a synonym for noncommercial. But if your profession is education, is your work professional or educational? Does it matter whether a school is public or private? Most people would agree that a student doing a homework assignment is engaged in noncommercial activity. What if the student is a teaching assistant receiving a small salary? In that case is it noncommercial use when the student is doing his own homework but commercial use when he’s preparing to teach a class? Isn’t education almost always a commercial activity? After all, why are students in school? They’re preparing to make a living at something. They may have blatant commercial motives for doing their homework.

Not only can you argue that educational use is commercial, you can argue that commercial use is educational. If an accountant looks up a tax regulation, they’re trying to learn something. Isn’t that educational? Is it educational use when a student looks up a tax regulation but commercial use when an accountant looks up the same regulation?

Individuals and organizations are free to define “commercial” or “noncommercial” use however they please. Personally, I’d rather either sell something or give it away without regard for how it’s going to be used.

The easiest, most obvious way to obtain a polynomial approximation is to use a truncated Taylor series. But such a polynomial may not be the most efficient approximation. Forman Acton gives the example of approximating cos(π x) on the interval [-1, 1] in his classic book Numerical Methods that Work. The point of this example is not the usefulness of the final result; a footnote below explains that this isn’t how cosines are computed in practice. The point is that you can sometimes improve a convenient but suboptimal approximation with a small change.

The goal in Acton’s example is to approximate cos(π x) with a maximum error of less than 10^-6 across the interval. The Taylor polynomial

is accurate to within about 10^-7 and so is certainly good enough. However the last term of the series, the x¹⁶ term, contributes less than the other terms to the accuracy of the approximation. On the other hand, this term cannot simply be discarded because without it the error rises to 10^-5. The clever idea is to replace the x¹⁶ term with a linear combination of the other terms. After all, x¹⁶ doesn’t look that different from x¹⁴ or x¹². Acton uses the 16th Chebyshev polynomial to approximate x¹⁶ by a combination of smaller even powers of x. This new approximation is almost as accurate as the original Taylor polynomial with an error that remains below the desire threshold. Acton calls this process economizing an approximation.

This process could be repeated to see whether the x¹⁴ term could be eliminated. Or you could directly find a Chebyshev series approximation to cos(π x) from the beginning. Acton did not have a symbolic computation package like Mathematica when he wrote his book in 1970 and so he was computing his approximations by hand. Directly computing a Chebyshev approximation would have been a lot of work. By just replacing the highest order term, he achieved nearly the same effect but with less effort.

Computing power has improved several orders of magnitude since Acton wrote his book, and some of his examples now seem quaint. However, I don’t know of a better book for teaching how to think about numerical analysis than Numerical Methods that Work. Acton has another good book that is harder to find, Real Computing Made Real: Preventing Errors in Scientific and Engineering Calculations.

Footnote 1: evaluating polynomials

Suppose you want to write code to evaluate the polynomial

P(x) = a₀ + a₂x² + a₄x⁴ + … + a₁₄x¹⁴.

The first step would be to reduce this to a 7th degree polynomial in y = x².

Q(y) = a₀ + a₁y + a₂y² + … + a₇y⁷.

Directly evaluating Q(y) would take 1 + 2 + 3 + … + 7 = 28 multiplications, computing every power of y directly. For example, computing y⁵ as y*y*y*y*y. Factoring the polynomial is much more efficient:

((((((a₇y + a₆)y + a₅)y + a₄)y + a₃)y + a₂)y + a₁)y + a₀

Footnote 2: computing sine and cosine

The point of Acton’s example was to improve on a Taylor polynomial evaluated a moderate distance from the point where the Taylor series is centered. It does not illustrate how cosines are actually computed. See this answer on StackOverflow for an outline of how trig functions are computed in practice.

Related posts:

Old math books
Chebyshev polynomials
Orthogonal polynomials
Interpolation errors

Suppose you decide to grow your own food. Are you going to buy your gardening tools from Ace Hardware? If you really want to be self-reliant, you should make your own tools. Are you going to take your chances with what water happens to fall on your property, or are you going to rely on municipal water? Are you going to forgo fertilizer or rely on someone else to sell it to you? Carried to extremes, self-reliance ends in a Robinson Crusoe-like existence.

People in poor countries are often poor because they are self-reliant in the sense that they must do many things for themselves. They do not have the opportunities for specialization and trade that are available to those who live in more prosperous countries.

Some degree of self-reliance makes economic sense. Transaction costs, for example, make it impractical to outsource small tasks. It also makes sense to do some things that are not economically feasible. For example, an orthodontist may choose to make some of her own clothing or keep a garden for the pleasure of doing so, not because these activities are worth her time. In general, however, specialization and large trading communities are the road to prosperity. Without a large economic community, no one can become an orthodontist (or an accountant, barrista, electrician, …)

Why do we so often value self-sufficiency more than specialization and trade? Here are a three reasons that come to mind.

1. In America, self-sufficiency is deeply rooted in our culture. We admire the pioneer spirit, and this leads to seeing as virtues actions that were once a necessity.
2. Self-sufficient people are generally well liked, especially if they’re not too prosperous.  Conversely, those who create wealth by leveraging the labor of others are often treated with suspicion and jealously.
3. Our school system encourages “well roundedness” rather than excellence. The way to succeed is to be moderately good at everything, even if you’re not outstanding at anything. (More on this idea here.)

Update: After writing this post, I read Russ Robert’s book The Choice: A Fable of Free Trade and Protectionism. I discovered one of the later chapters is entitled “Self-Sufficiency Is the Road to Poverty.” Excellent book.

Related posts:

Evaluate people at their best or at their worst?
Make something and sell it
Do something dull
Transaction costs

I was looking into the functions in Excel 2007 while preparing for a class I taught yesterday. I wanted to emphasize that certain functions are everywhere, not only in mathematical packages like Mathematica and R, but also in Python and even Excel.

Excel’s set of functions is inconsistent, both in the functionality provided and in the names it uses. Having an asymmetric API makes it harder to remember what is available and how to use it. On the other hand, the most commonly needed functions are available. The functions are individually reasonable even though they do not fit together into a simple pattern.

For details, see my notes Probability distributions in Excel 2007.

I discovered along the way that Excel has a GAMMALN function to compute the logarithm of the Gamma function Γ(x). This is a very useful function to have, even more useful than the Gamma function itself for reasons explained here.

Related links:

Comparison of data analysis packages from Brendan O’Connor

R, Excel, and the Windows clipboard (good tips in the comments)

1) Quotes

Quotation marks in LaTeX files begin with two back ticks, ``, and end with two single quotes, ''.

The first “Yes” was written as

``Yes.''

in LaTeX while the one with the backward opening quote was written as

"Yes."

2) Differentials

Differentials, most commonly the dx at the end of an integer, should have a little space separating them from other elements. The “dx” is a unit and so it needs a little space to keep from looking like the product of “d” and “x.” You can do this in LaTeX by inserting \, before and between differentials.

The first integral was written as

 \int_0^1 f(x) \, dx

while the second forgot the \, and was written as

 \int_0^1 f(x)  dx

The need for a little extra space around differentials becomes more obvious in multiple integrals.

The first was written as

dx \, dy = r \, dr \, d\theta

while the second was written as

dx  dy = r  dr  d\theta

3) Multi-letter function names

The LaTeX commands for typesetting functions like sin, cos, log, max, etc. begin with a backslash. The command \log keeps “log,” for example, from looking like the product of variables “l”, “o”, and “g.”

The first example above was written as

\log e^x = x

and the second as

log e^x = x

The double angle identity for sine is readable when properly typeset and a jumbled mess when the necessary backslashes are left out.

The first example was written

\sin 2u = 2 \sin u \cos u

and the second as

sin 2u = 2 sin u cos u

4) Failure to use math mode

LaTeX uses math mode to distinguish variables from ordinary letters. Variables are typeset in math italic, a special style that is not the same as ordinary italic prose.

The first sentence was written as

Given a matrix $A$ and vector $b$, solve $Ax = b$.

and the second as

Given a matrix A and vector b, solve Ax = b.

Related posts:

Microsoft equation editor
Converting Excel tables to LaTeX
Typesetting music in LaTeX
Contrasting Word and LaTeX
Things that work best when you don’t notice them