A little simplicity goes a long way

Sometimes making a task just a little simpler can make a huge difference. Making something 5% easier might make you 20% more productive. Or 100% more productive.

To see how valuable a little simplification can be, turn it around and think about making things more complicated. A small increase in complexity might go unnoticed. But as complexity increases, your subjective perception of complexity increases even more. As you start to become stressed out, small increases in objective complexity produce big increases in perceived complexity. Eventually any further increase in complexity is fatal to creativity because it pushes you over your complexity limit.

graph of perceived complexity versus actual complexity

Clay Shirky discusses how this applies to information overload. He points out that we can feel like the amount of information coming in has greatly increased when it actually hasn’t. He did a little experiment to quantify this. When he thought that the amount of spam he was receiving had doubled, he would find that it had actually increased by about 25%. Turning this around, you may be able to feel like you’ve cut your amount of spam in half by just filtering out 20% of it.

A small decrease in complexity can be a big relief if you’re under stress. It may be enough to make the difference between being in a frazzled mental state to a calm mental state (moving out of F-state into C-state). If you’re up against your maximum complexity, a small simplification could make the difference between a problem being solvable or unsolvable.

Small simplifications are often dismissed as unimportant when they’re evaluated in the small. Maybe a new term makes it possible to refer to an idea in three syllables rather than six. No big deal if it’s a term you don’t use much. But if it’s a term you use all the time, it makes a difference. That’s why every group has its own jargon.

Suppose one application takes five mouse clicks to do what another can do in three. Maybe that’s no big deal. But if you’re under stress, those two mouse clicks might make the difference between deciding a finishing touch is worthwhile versus not worthwhile.

Suppose one programming language takes five lines of code to do what another language can do in four lines. So what? How long does it take to type one line of code? But multiply that by 10. Maybe you see 40 lines of code on your laptop at once but you can’t see 50. Or multiply by 10 again. Maybe you can hold 400 lines of code in your head but you can’t hold 500. Language features dismissed as “syntactic sugar” can make a real difference.

When you’re stressed and feel like only a radical change will do any good, think again. A small simplification might be enough to give you some breathing room by pulling you back down below your complexity limit.

Related post: What happens when you add another teller?

Three quotes on simplicity

It’s easy to decide what you’re going to do.  The hard thing is deciding what you’re not going to do.
Michael Dell

Clutter kills WOW.
Tom Peters

Any intelligent fool can make things bigger, more complex, and more violent. It takes a touch of genius — and a lot of courage — to move in the opposite direction.
Albert Einstein

Are Covey’s quadrants correlated?

I was reading a statistical article the other day that used the word “important” when I thought the author should have said “urgent.” Since I was in a statistical frame of mind, I wondered whether importance and urgency are positively or negatively correlated.

Stephen Covey is known for his four quadrant diagram and his advice that we should spend as much time as we can in quadrant 2, working on things that are important but not urgent.

The four-quadrant matrix for importance and urgency.

Are urgent tasks more likely, less likely, or equally likely to be important? In statistical jargon, are they positively correlated, negatively correlated, or uncorrelated?

I believe Covey’s assumption is that urgency is negatively correlated with importance, that is, urgent tasks are less likely to be important. That’s probably true of life in general, but there are contexts where the correlation is reversed. In the paper that prompted this musing, I believe urgency and importance were positively correlated.

In what areas of life are urgency and importance most positively correlated? Most negatively correlated?

Why Unicode is subtle

On its surface, Unicode is simple. It’s a replacement for ASCII to make room for more characters. Joel Spolsky assures us that it’s not that hard. But then how did Jukka Korpela have enough to say to fill his 678-page book Unicode Explained? Why is the Unicode standard 1472 printed pages?

It’s hard to say anything pithy about Unicode that is entirely correct. The best way to approach Unicode may be through a sequence of partially true statements.

The first approximation to a description of Unicode is that it is a 16 bit character set. Sixteen bits are enough to represent the union of all previous character set standards. It’s enough to contain nearly 30,000 CJK (Chinese-Japanese-Korean) characters with space left for mathematical symbols, braille, dingbats, etc.

Actually, Unicode is a 32-bit character set. It started out as a 16-bit character set. The first 16 bit range of the Unicode standard is called the Basic Multilingual Plane (BMP), and is complete for most purposes. The regions outside the BMP contain characters for archaic and fictional languages, rare CJK characters, and various symbols.

So essentially Unicode is just a catalog of characters with each character assigned a number and a standard name. What could be so complicated about that?

Well, for starters there’s the issue of just what constitutes a character. For example, Greek writes the letter sigma as σ in the middle of a word but as ς at the end of a word. Are σ and ς two representations of one character or two characters? (Unicode says two characters.) Should the Greek letter π and the mathematical constant π be the same character? (Unicode says yes.) Should the Greek letter Ω and the symbol for electrical resistance in Ohms Ω be the same character? (Unicode says no.) The difficulties get more subtle (and politically charged) when considering Asian ideographs.

Once have agreement on how to catalog tens of thousands of characters, there’s still the question of how to map the Unicode characters to bytes. You could think of each byte representation as a compression or compatibility scheme. The most commonly used systems are UTF-8, and  UTF-16. The former is more compact (for Western languages) and compatible with ASCII. The latter is simpler to process. Once you agree on a byte representation, there’s the issue of how to order the bytes (endianness).

Once you’ve resolved character sets and encoding, there remain issues of software compatibility. For example, which web browsers and operating systems support which representations of Unicode? Which operating systems supply fonts for which characters? How do they behave when the desired font is unavailable? How do various programming languages support Unicode? What software can be used to produce Unicode? What happens when you copy a Unicode string from one program and paste it into another?

Things get even more complicated when you want to process Unicode text because this brings up internationalization and localization issues. These are extremely complex, though they’re not complexities with Unicode per se.

For more links, see my Unicode resources.

Learning is not the same as gaining information

Learning is not the same as just gaining information. Sometimes learning means letting go of previously held beliefs. While this is true in life in general, my point here is to show how this holds true when using the mathematical definition of information.

The information content of a probability density function p(x) is given by

integral of p(x) log p(x)

Suppose we have a Beta(2, 6) prior on the probability of success for a binary outcome.

plot of beta(2,6) density

The prior density has information content 0.597. Then suppose we observe a success. The posterior density is distributed as Beta(3, 6). The posterior density has information 0.516, less information than the prior density.

plot of beta(3,6) density

Observing a success pulled the posterior density toward the right. The posterior density is a little more diffuse than the prior and so has lower information content. In that sense, we know less than before we observed the data! Actually, we’re less certain than we were before observing the data. But if the true probability of response is larger than our prior would indicate, we’re closer to the truth by becoming less confident of our prior belief, and we’ve learned something.

Related: Use information theory to clarify and quantify goals

Contrasting Microsoft Word and LaTeX

Here’s an interesting graph from Marko Pinteric comparing Microsoft Word and Donald Knuth’s LaTeX.

comparing Word and Latex. Image by Marko Pinteric.

According to the graph, LaTeX becomes easier to use relative to Microsoft Word as the task becomes more complex. That matches my experience, though I’d add a few footnotes.

  1. Most people spend most of their time working with documents of complexity to the left of the cross over.
  2. Your first LaTeX document will take much longer to write than your first Word document.
  3. Word is much easier to use if you need to paste in figures.
  4. LaTeX documents look better, especially if they contain mathematics.

See Charles Petzold’s notes about the lengths he went to in order to produce is upcoming book in Word. I imagine someone of less talent and persistence than Petzold could not have pulled it off using Word, though they would have stood a better chance using LaTeX.

Before the 2007 version, Word documents were stored in an opaque binary format. This made it harder to compare two documents. A version control system, for example, could not diff two Word documents the same way it could diff two text files. It also made Word documents difficult to troubleshoot since you had no way to look beneath the WYSIWYG surface.

However, a Word 2007 document is a zip file containing a directory of XML files and embedded resources. You can change the extension of any Office 2007 file to .zip and unzip it, inspect and possibly change the contents, the re-zip it. This opens up many new possibilities.

I’ve written some notes that may be useful for people wanting to try out LaTeX on Windows.

New spin on the cathedral and the bazaar

Eric Raymond’s famous essay The Cathedral and the Bazaar compares commercial software projects to cathedrals and open source software projects to bazaars. Cathedrals are carefully planned. Bazaars are not. The organizational structure a bazaars emerges without deliberate coordination of its participants. The open source community has embraced the metaphor of the bazaar and the informality and spontaneity it implies.

Shmork wrote the following observation in the comments to a Coding Horror post yesterday that discussed the difficulties of using Linux software.

Almost nobody in the Western world shops at real-life bazaars either, because they are dodgy, unsafe, and unregulated. And in the Western world, we like things to be reliable, working, safe. So cathedral it is. Even our flea markets aren’t bazaars, really, they’re just knock-off cathedrals.

Being busy

From A Bias for Action:

The simple fact is that being busy is easier than not.  Most managers cannot admit that a fragmented day is actually the laziest day, the day that requires the least mental discipline and the most nervous energy.  Responding to each new request, chasing an answer to the latest question, and complaining about overwhelming demands are easier than setting priorities.