The Endeavour

You have a bag of 27 coins. One of these coins is counterfeit and the rest are genuine. The genuine coins all weigh exactly the same, but the counterfeit coin is lighter. You have a simple balance. How can you find the counterfeit coin while using the scale the least number of times?

The surprising answer is that the false coin can be found while only using the scales only three times. Here’s how. Put nine coins on each side of the balance. If one side is lighter, the counterfeit is on that side; otherwise, it is one of the nine not on the scales. Now that you’ve narrowed it down to nine coins, apply the same idea recursively by putting three of the suspect coins on each side of the balance. The false coin is now either on the lighter side if the scales do not balance or one of the three remaining coins if the scales do balance. Now apply the same idea one last time to find which of the remaining three coins is the counterfeit. In general, you can find one counterfeit in 3ⁿ coins by using the scales n times.

The counterfeit coin problem came to mind when I was picking out homework problems for a probability class and ran into the following (problem 4.56 here):

A large number, N = mk, of people are subject to a blood test. This can be administered in two ways.

Each person can be tested separately. In this case N tests are required.

The blood samples of k people can be pooled and analyzed together. If the test is negative, this one test suffices for k people. If the test is positive, each of the k people must be tested separately, and, in all, k+1 test are required for the k people.

Suppose each person being tested has the disease with probability p. If the disease is rare, i.e. p is sufficiently small, the second approach will be more efficient. Consider the extremes. If p = 0, the first approach takes mk tests and the second approach takes only m tests. At the other extreme, if p = 1, the first approach still takes mk tests but the second approach now takes m(k+1) tests.

The homework problem asks for the expected number of tests used with each approach as a function of p for fixed k. Alternatively, you could assume that you always use the second method but need to find the optimal value of k. (This includes the possibility that k=1, which is equivalent to using the first method.)

I’d be curious to know whether these algorithms have names. I suspect computer scientists have given the coin testing algorithm a name. I also suspect the idea of pooling blood samples has several names, possibly one name when it is used in literally testing blood samples and other names when the same idea is applied to analogous testing problems.

Software Archeology

John — Wed, 11 Nov 2009 04:25:28 +0000

The most recent episode of Software Engineering Radio is Software Archeology with Dave Thomas. In his interview, Dave Thomas gives many practical tips for how to read code, especially when inheriting a project. This interview should be required listening for computer science students. They spend the majority of their time writing code while they’re in school and yet they will spend the majority of their time reading code once they get out — reading code in order to debug or extend it, and if they’re smart, reading code to learn from it.

Dave Thomas attributes one of his most unusual suggestions to Ward Cunningham. Thomas says Cunningham recommends pasting code into Microsoft Word and viewing it in a 2 point font. At this font size you cannot possibly read the code, but you can tell a great deal about the structure of the code. For example, you may spot duplicate code by recognizing a recurring shape.

I tested Ward Cunningham’s idea on a couple source files.

Example 1:

Example 2:

Example 1 has short functions. Near the bottom of the clip something is very repetitive. Skimming through the entire file you see several of these repetitive blocks. (This is test code. The blocks are computed values and expected values for comparison.)

Example 2 looks quite different from Example 1. The image comes from one long function. (This was taken from FORTRAN code that had been programmatically translated in to C++. The frequent short dashes on the left are labels for goto statements.)

Shaking a ladder: Monte Carlo in everyday life

John — Mon, 09 Nov 2009 15:54:00 +0000

In Flaw of Averages, Sam Savage uses the illustration of shaking a ladder to explain why someone would want to use Monte Carlo simulation. Before climbing a ladder, most people shake the ladder a little to make sure it’s sturdy.

When you position a ladder and climb it immediately, you’re saying that you’re satisfied that the ladder’s position is safe. You’re assuming it will stay in the position you placed it. But when you shake the ladder, you’re testing how it will behave at a variety of nearby positions. If the ladder remains sturdy, you have more confidence that accidental motions while you’re on the ladder are not likely to cause an accident. When you stick a single number into a model, you’re acting like someone climbing a ladder immediately. When you stick in a series of random inputs, it’s like you’re shaking the ladder.

The latest INFORMS podcast features an interview with Sam Savage (audio). He mentions the ladder analogy and adds an observation that I don’t recall seeing in his book. One criticism of Monte Carlo methods is that the validity of your results depends on the validity of your input distributions. It’s better to have realistic input distributions, but it’s better to perform a simulation with an incorrect distribution than to not try random input at all. The distribution of random forces likely to result from working while standing on a ladder is different from the distribution of forces from shaking the ladder with your hands. But that doesn’t mean it isn’t a good idea to shake the ladder anyway.

Using Windows without a mouse

John — Mon, 09 Nov 2009 15:52:21 +0000

Why would you not want to use your mouse? Some tasks are most efficiently done with a mouse, but others can be done more efficiently with the keyboard.The problem isn’t so much using a mouse versus using a keyboard but rather the time it takes to switch between the two modes. Particularly when using a laptop with a touchpad, it’s faster to use the keyboard.

Why does it even matter? So what if you save a few seconds here and there? It’s a matter of keeping up with your thoughts. Suppose some series of tasks takes 20 seconds with a mouse but you can accomplish the same tasks in 12 seconds using the keyboard. The big deal isn’t that you’ve saved 8 seconds; the big deal is that you’re more likely to finish your tasks before you lose the thought that motivated them.

The same could be said for learning to type more quickly. Typing 20% faster doesn’t directly make you 20% more productive unless you’re a professional typist. The benefit is that your fingers can come closer to keeping up with your brain.

If you’d like to get in the habit of using your keyboard more and your mouse less, you may find this helpful. I’ve created a Twitter account for posting one tip per day on using Windows without a mouse. If you’d like to follow using Twitter, it’s @SansMouse. If you don’t use Twitter, you could subscribe via RSS. I’ve written a few dozen tips so far and they’re in a queue to be dribbled one per day. You could practice one simple tip per day until it is natural to use your mouse much less.

I use my mouse fairly often, though I’m trying to get into the habit of using it less. I’ve recently become persuaded that it’s worthwhile to use the keyboard more and that it doesn’t take that much effort.

Too much time on their hands?

John — Sat, 07 Nov 2009 14:20:21 +0000

Dan Wineman shared a profound insight on Twitter:

You say “looks like somebody has too much time on their hands” but all I hear is “I’m sad because I don’t know what creativity feels like.”

In place of “creativity” Wineman might have as easily said “persistence.” I found Wineman’s quote in a post by Dan Meyer responding to criticism of his research projects.

I’ve said that someone has too much time on their hands, but not since I read Meyer’s post. I see now that the phrase is often a sour grapes response to creativity. I don’t want to do that anymore.

When we see that someone has spent a thousand hours on a project that we think was a frivolous, it’s easy to say “what a waste of time.” We think how much good could have been done with that same amount of effort. But what was the realistic alternative? If that same person had spent a thousand hours in front of their television instead, no one would ever know and no one would ever criticize them. Instead, they created something.

Tree house photo from Succeed Blog. Full size photo.

Weekend miscellany

John — Sat, 07 Nov 2009 13:28:08 +0000

Movie plot diagrams

Geek teapot

Funny Unicode characters

Only lazy people work hard

Carnival of Mathematics #59

Python in the scientific world from the creator of Python

Take an extension chord and other practical presentation tips

Darth Vader balloon from Succeed Blog

How to delete pages from a PDF without Adobe Acrobat

John — Sat, 07 Nov 2009 01:54:59 +0000

How can you delete pages from a PDF file if you don’t have Adobe Acrobat?

Download PDFCreator from SourceForge. It installs as a printer. It lets you create PDFs from any application by selecting PDFCreator as your “printer.” To delete pages from an existing PDF, open the PDF in Adobe Reader and print to PDFCreator the pages you don’t want to delete.

I don’t have a lot of experience with PDFCreator; I just downloaded it today. But it looks good and it worked well for what I was trying to do.

Four patterns in Windows keyboard shortcuts

John — Thu, 05 Nov 2009 11:17:58 +0000

Here are four patterns for organizing the most common keyboard shortcuts for Windows. First I’ll list the patterns, then I’ll give some qualifications and elaborate on the patterns.

Keyboard shortcuts involving letters are all of the form Control- or Windows-.
The letters used in Control shortcuts and Windows shortcuts don’t overlap.
Control in combination with navigation keys moves the cursor. Shift in combination with navigation keys makes a selection.
The Tab key cycles through things. What the key cycles through depends on what it is paired with.

When I say Control- I refer to shortcuts such as Control-C, holding down the Control key and pressing C in order to copy something. When I say Windows- I refer to holding down the Windows logo key in and pressing some letter.

My goal here is to stick to the most common shortcuts, ones that work across several versions of Windows and with many applications. Also, I’m not including any accessibility sequences such as sticky keys etc.

Control key with letters

Here are the common Windows keyboard shortcuts of the form Control key followed by a letter.

A	Select all
B	Toggle bold
C	Copy
F	Find
G	Go to
H	Find and replace
I	Toggle italics
N	New
O	Open
P	Print
S	Save
U	Toggle underlining
V	Paste
W	Close document
X	Cut
Y	Redo
Z	Undo

Windows key with letters

Here are the common shortcuts using the Windows key with a letter.

D	Show desktop
E	Open file explorer
F	Find
L	Lock computer
M	Minimize all windows
R	Run command

Exceptions

There is one common shortcut that uses a letter and more than just the Control key or Windows key: the combination Windows-Shift-M maximizes all minimized windows. But there are no common shortcuts of the form Alt- or Control-Shift- etc.

F is the only letter used with both the Control key and the Windows key. In both cases the command finds something. Control-F finds text within a file and Windows-F searches across directories.

Navigation keys

All the navigation key shortcuts come in pairs.

Control-Home moves the cursor to the top of a document; Control-End moves the cursor to the end.

Control-Left Arrow moves the cursor to the left one word; Control-Right Arrow moves the cursor to the right one word.

Control-Up Arrow moves the cursor up a paragraph; Control-Down Arrow moves the cursor down a paragraph.

Control-Shift-Home selects from the top of the document to the cursor location; Control-Shift-End selects from the current location to the bottom of the document.

Control-Shift-Left Arrow selects one word to the left; Control-Shift-Right Arrow selects one word to the right.

Shift-Left-Arrow expands the selection one character to the left; Shift-Right-Arrow expands the selection one character to the right.

Shift-Up-Arrow selects one line up; Shift-Down-Arrow selects one line down.

Tabbing

The Tab key alone moves the focus in a window, cycling through the controls in the order specified by the application.

Control-Tab cycles through tabs or through windows in an application with multiple windows.

Alt-Tab cycles through running applications.

Windows-Tab cycles through the Task Bar.

Adding the Shift key to any of the above key reverses the cycle order. For example, Alt-Shift-Tab cycles through applications in the opposite order of Alt-Tab.

Miscellaneous shortcuts

Most common Windows keyboard shortcuts are listed above. However, there are several shortcuts that are commonly used but do not fall into a regular pattern. Some of these shortcuts are listed below.

Shift-F10 brings up a properties dialog, just like right-clicking.
Shift-Delete permanently deletes a file, bypassing the recycle bin.
Alt-F4 closes the active window or opens the shutdown dialog if there is no active window.
Alt-Down Arrow opens a drop down list box.
Alt-Print Screen grabs an image of the active window rather than the entire screen.
Alt-Space opens the current window’s system menu.
Windows-Pause brings up the System Properties dialog.

Most of the function keys are not used often. The most commonly used function keys are

F1 to bring up help,
F5 to refresh, and
F10 to activate an application’s menu bar.

A little coffee on the prairie

John — Wed, 04 Nov 2009 13:36:32 +0000

I was reading Little House on the Prairie with my youngest daughter the other day. Here’s a passage that surprised me.

Then Pa brought water from the creek, while Mary and Laura helped Ma get supper. Ma measured coffee beans into the coffee mill and Mary ground them.

I’d read this book with my other children and hadn’t given this part a thought. This time I thought about how odd it was that they had coffee. At this point the Ingalls family was moving from Wisconsin to Kansas some time in the 1870’s. The family of five and all their worldly goods were packed into a covered wagon. They shot wild game for food. They gathered water from creeks. And yet they had coffee.

Coffee doesn’t grow in the continental United States. It grows in the tropics at high altitudes. These settlers living off the land in the middle of nowhere had some coffee beans that had been imported from thousands of miles away. It’s interesting to think that despite all that they lacked, they had these tropical beans and apparently took them for granted. Said another way, of all the benefits of civilization, coffee made the short list of things settlers chose to take with them.

Manage your project portfolio

John — Tue, 03 Nov 2009 15:08:46 +0000

Most books on project management are written for someone managing one project at a time, working with a team of people who only work on that project. Some companies work that way, but certainly not all do. I’ve seldom worked that way. At one point I “managed” so many projects that I could not tell you the exact number without looking at my list.

Johanna Rothman’s new book Manage Your Project Portfolio addresses the challenges of managing not just one project but a portfolio of projects. The book does not tell you how to work multiple simultaneous projects but rather how to get away from working on multiple projects by prioritizing them and working on one at a time.

Here are a couple quotes from the beginning of the book.

Quite often I have the chance to visit a team to help management figure out why they’re not making much progress. When I get there, I find a small team working on more projects than they have people.

Multitasking occurs when managers don’t make decisions about which projects to do first, second, third, last, and even more important, never.

I wish I could have read Johanna Rothman’s book a decade ago. On the other hand, I would not have appreciated the book as much a decade ago. Still, it might have helped me prevent some of the errors I made. I hope that many people will read the book before they become overwhelmed and appreciate its wisdom.

Yet another view of the negative binomial

John — Tue, 03 Nov 2009 15:03:48 +0000

A while back I wrote a post on three views of the negative binomial distribution. This post adds a fourth view.

One of the shortcomings of the Poisson distribution is that its variance exactly equals its mean. It is common in practice for the variance of count data to be larger than the mean, so it’s natural to look for a distribution like the Poisson but with larger variance. We start with a Poisson random variable X with mean λ, but then we make λ itself random and suppose that λ comes from a gamma(α, β) distribution. Then the marginal distribution on X is a negative binomial distribution with parameters r = α and p = 1/(β + 1).

The previous post said that the negative binomial is useful because it has more variance than the Poisson. The derivation above explains why the negative binomial should have more variance than the Poisson.

For details, see updated notes on the negative binomial distribution.

Zero-knowledge password management in JavaScript

John — Mon, 02 Nov 2009 15:30:24 +0000

The most recent guest on Jon Udell’s Interviews with Innovators podcast was Marco Barulli. Barulli discusses Clipperz, a zero-knowledge password management application. The software encrypts passwords (or arbitrary text) using client-side JavaScript. Your data is encrypted on your computer and the encrypted version is uploaded to the Clipperz server. When you want to retrieve your data, the encrypted data is downloaded to your computer and decrypted there. Your unencrypted data never leaves your computer.

For more information, see the article on Jon Udell’s blog or listen to the podcast. Even if you’re not interested in using the Clipperz product, you may find the discussion of JavaScript and cryptography techniques interesting.

PowerShell 2.0 for Windows XP etc.

John — Mon, 02 Nov 2009 14:56:28 +0000

PowerShell version 2.0 shipped with Windows 7 and with Windows Server 2008 R2, but it only recently became available for other versions of Windows.

The release of PowerShell 2.0 has been more like a leak than a product launch. The announcement page hardly reads like an announcement. The title reads “Description of the Windows Management Framework on Windows XP, Windows Server 2003, Windows Vista, and Windows Server 2008.” What’s this “Windows Management Framework”? I’ve never heard of that. I just want the new PowerShell. The first time I saw this page was when someone sent me a link saying PowerShell 2.0 was available for XP. I thought they’d sent me the wrong link by mistake because I didn’t see anything about PowerShell at first. Only if you scroll down to the middle of a long page can you see links to download PowerShell.

I expected something more like the following.

PowerShell 2.0 Released

Download for your platform:

XP
Vista (32 bit, 64 bit)
Server 2003 (32 bit, 64 bit)
Server 2008 (32 bit, 64 bit)

Weekend miscellany

John — Sat, 31 Oct 2009 03:49:38 +0000

Two links on naked mole rats and cancer

Three links on software development, academia, and industry

Four kinds of periodic tables

Five miscellaneous links

Minimalism in computing
10 recently discovered photographs
Awkward Facebook recommendations
Five things science cannot prove
AlternativeTo.net (enter a program name and find competing products)

Student-t as a mixture of normals

John — Sat, 31 Oct 2009 03:48:30 +0000

You can express a Student-t distribution as a continuous mixture of normal distributions. Some properties of the t distribution are easier to prove in this form. Here are notes with details.

I ran across this tidbit reading Bayesian Data Analysis by Gelman et al.

Related post: Beer, Wine, and Statistics (origin of the Student-t distribution)

Listening to music with your whole body

John — Fri, 30 Oct 2009 12:22:32 +0000

Amazing presentation from Evelyn Glennie, a deaf percussionist.

Simple backup software

John — Thu, 29 Oct 2009 14:54:44 +0000

I was asking about backup software for Windows the other day and a couple people recommended Cobian Backup. It’s simple to use, but also very configurable. And it’s free.

You can have the software simply copy files or you can have it zip the output (.zip or .7z format). In either case, you don’t need the backup software in order to restore your files.

The software has all the features you’d expect. You can perform full, incremental, or differential backups. You can run backups manually or as scheduled tasks. Etc.

How to test a random number generator

John — Wed, 28 Oct 2009 00:28:00 +0000

Random number generators are challenging to test.

The output is supposed to be unpredictable, so how do you know when the generator working correctly?
Your tests will fail occasionally, but how do you decide whether they’re failing too often?
What kinds of errors are most common when writing random number generation software?

These are some of the questions I address in Chapter 10 of Beautiful Testing.

The book is now in stock at Amazon. It is supposed to be in book stores by Friday. All profits from Beautiful Testing go to Nothing But Nets, a project to distribute anti-malarial bed nets.

Bayesian clinical trials in one zip code

John — Tue, 27 Oct 2009 11:06:05 +0000

I recently ran across this quote from Mithat Gönen of Memorial Sloan-Kettering Cancer Center:

While there are certainly some at other centers, the bulk of applied Bayesian clinical trial design in this country is largely confined to a single zip code.

from “Bayesian clinical trials: no more excuses,” Clinical Trials 2009; 6; 203.

The zip code Gönen alludes to is 77030, the zip code of M. D. Anderson Cancer Center. I can’t say how much activity there is elsewhere, but certainly we design and conduct a lot of Bayesian clinical trials at MDACC.

Shallow bugs versus reported bugs

John — Mon, 26 Oct 2009 04:05:50 +0000

The open source community has a saying: With enough eyes, all bugs are shallow. When enough people look at a piece of code, someone is going find and fix the bugs.

A related principle is that with enough users, all bugs will be reported. With enough people use the software, someone else is going to run into the problem. Someone will report it. Someone will talk about it in an online forum. Someone will blog about it and post a work-around until the bug is fixed. This principle deserves more attention; it’s not cited as often as the shallow bugs principle.

Ideally, you want to use software with lots of eyes and lots of users. Firefox is an open source product with lots eyes and lots of users. But more often you have to pick eyes or users. You have to choose between open but obscure software and closed but popular software. Open source projects may have more people looking at the source code, and so they have the “many eyes make shallow bugs” maxim working for them. But the user base for many open source projects is tiny compared to their commercial counterparts. The number of users to find and report bugs is small, and the number who document fixes and work-arounds is even smaller.

I’m not ideologically attached to open source or commercial software. I use both. I just want my software to work. And when it doesn’t work, I want to find a solution quickly.

How to differentiate a non-differentiable function

John — Mon, 26 Oct 2009 04:03:13 +0000

How can we extend the idea of derivative so that more functions are differentiable? Why would we want to do so? How can we make sense of a delta “function” that isn’t really a function? We’ll answer these questions in this post.

Suppose f(x) is a differentiable function of one variable. Suppose φ(x) is an infinitely differentiable function that is zero outside of some finite interval. Functions like φ are called test functions. Integration by parts says that

where the integrals are over the entire real line. (The fact that φ is zero outside a finite interval mean the “uv” term from integration by parts is zero.) Now suppose f(x) is not differentiable. Then the left side of the equation above does not make sense, but the right side does. We use the right hand side to develop the definition of the generalized derivative.

We think of the function f not as a function of real numbers, but as a distribution that operates on tests functions. That is, we associate with f the linear functional on the space of tests functions that maps φ to ∫ f(x) φ(x) dx. Then the distributional derivative of this functional is another linear functional, the distribution that maps test functions φ to -∫ f(x) φ’(x) dx. In summary,

We can use this procedure to define as many derivatives of f as we’d like, as long as f is integrable. So f could be some horribly ill-behaved function, differentiable nowhere in the classical sense, and we could define its 37th derivative by repeatedly applying this idea. (Distributions are also called “generalized functions.” Distributional derivatives are also called “generalized derivatives” or “weak derivatives.”)

By the way, this same procedure is used to make sense of the delta function. The delta function isn’t a function at all. It is the distribution δ that evaluates test functions at zero, i.e. δ maps φ to φ(0). (The delta function often nonsensically defined to be a function that is infinite at zero and zero everywhere else.)

Why would we want to be able to differentiate more functions? When we can differentiate more functions, we can look in a bigger space for solutions to differential equations. Sometimes this allows us to find solutions to equations that do not have classical solutions. Other times this allows us to find classical solutions more easily. We may first prove that a generalized solution exists, and then prove that the generalized solution is in fact a classical solution.

Here’s an analogy that explains how generalized solutions might lead to classical solutions. Suppose you want to find the minimum value of a function for integer arguments. You might first look for a real number that minimizes the function. This lets you, for example, use derivatives in your search for the minimum. If the real minimum you find happens to also be an integer, then you’ve solved your original problem. Distributions and generalized derivatives work much the same way. You might find a classical solution by first looking in a larger space of possible solutions, a space that allows you to use more powerful techniques in your search for a solution.

Weekend miscellany

John — Sat, 24 Oct 2009 04:15:16 +0000

Reviewing catch blocks

John — Fri, 23 Oct 2009 01:40:10 +0000

Here’s an interesting exercise. If you’re writing code in a language like C# or C++ that has catch statements, write a script to report all catch blocks. You might be surprised at what you find. Some questions to ask:

Do catch blocks swallow exceptions and thus mask problems?
Is information lost by catching an exception and throwing a new one?
Are exceptions logged appropriately?
Are notification messages grammatically correct and helpful?

Here’s a PowerShell script that will report all catch statements plus the five lines following the catch statement.

Normal tail probability bounds

John — Thu, 22 Oct 2009 14:27:31 +0000

Here are some notes on upper and lower bounds on the probability P(Z > t) for a standard normal random random variable Z. I wrote up these notes to settle a issue that came up in a probability class I’m teaching. It’s surprising that there are simple functions that provide efficient bounds on the normal distribution function.

Worthless technical books

John — Wed, 21 Oct 2009 04:06:02 +0000

I sold six technical books to a used book store on the way home today. The store paid me $5 total for four of the books. Two books they didn’t want at all. The books were not that old, but they were practically worthless.

It’s sobering to think how little a technical book is worth a few years after it is printed. It’s a good reminder to focus on things that will last.

Book review: Trade-Off

John — Tue, 20 Oct 2009 13:22:24 +0000

I enjoyed listening to Moira Gunn’s interview with Kevin Maney, author of the new book Trade-Off: Why Some Things Catch On and Others Don’t.

The book was a little disappointing after listening to the interview. I felt I had heard most of what Maney had to say before I read the book.

In a nutshell, the message of the book is that you should either strive for fidelity (exclusivity, quality) or convenience (accessibility, affordability). You can succeed by excelling at fidelity or at convenience. But if you strive for both, you’ll lose to companies that are better at one criteria or the other. Maney gives several interesting examples of companies that have succeeded along the edges of the fidelity/convenience graph but then failed when they started pursuing the diagonal.

Related post:

I am not an operating system (how Microsoft and Apple are forced into their respective marketing positions)

A sort of opposite to Parkinson’s Law

John — Mon, 19 Oct 2009 14:57:52 +0000

Parkinson’s Law says that work expands to the time allowed. I’ve seen that law play out over and over. However, I’ve also seen a sort of contraction to Parkinson’s Law. Sometimes work gets done faster when you have more time for it.

Sometimes when I’ve planned a large block of uninterrupted, say going into the office when hardly anyone else is there, I get through my to do list in the first hour of the day. Knowing that I have plenty of time, I think more clearly and end up not needing the extra time. When that happens, I sometimes think “If I’d known this would just take 30 minutes to solve, I would have done it sooner.” But it’s not that simple. Just because it took 30 minutes on a good day doesn’t mean that it could have been done during just any 30-minute time slot earlier.

In his book Symmetry and the Monster, Mark Ronan shares a story along these lines. Ronan tells how John Conway worked on a famous mathematical problem. Conway and his wife agreed that he would carve out Saturdays from noon to midnight and Wednesdays from 6 PM to midnight for working on this challenge. He started one Saturday and cracked the problem that evening. Perhaps Conway would have been able to solve his problem by working on it and hour at a time here and there. But it seems reasonable that having a large block of time, and knowing that other large blocks were scheduled, helped Conway think more clearly.

My guess is that Parkinson’s law applies best to projects involving several people and to one-person projects that are not well defined. But for well-defined projects, especially projects requiring creative problem solving, having more time might lead to not needing so much time.

Weekend miscellany

John — Sat, 17 Oct 2009 00:26:59 +0000

The Fourth Paradigm: Data-Intensive Scientific Discovery free book

Beautiful Testing has gone to press. Should be in bookstores by October 30.

Placebos have side effects too

10/GUI prototype for human-computer interaction

Math Teachers at Play #17. This is a much larger edition than usual.

How schools invented letter grades

Assembly of the International Space Station time-lapse animation

When noise is your friend: smoothed analysis

Fame Frenzy music video