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Quantitative Can Be Qualitative

What I want to discuss here is the idea that a quantitative change in one property can lead to qualitative changes in other properties that depend on it. Phase transitions come to mind—a small change in temperature might convert, say, water into ice—but it's not necessary for the change to be that abrupt. Consider window glass. I used to hear that window glass is just a very viscous liquid. I'm not sure that's exactly true, but let's suppose it is. If we imagine adjusting the viscosity of that liquid, there's no abrupt transition that occurs, but there's still a point where the liquid becomes suitable for use as a window.

Or consider consciousness. It's easy to imagine a whole continuum of awareness, from people through, say, dogs, insects, and plants, down to mud and rocks. The ends of the continuum are clearly qualitatively different, so we give the quality a name, consciousness, then end up debating whether the intermediate stages possess this indivisible quality.

The last two examples suggest a corollary to the basic idea, namely, that whenever a quantitative change leads to a non-abrupt qualitative one, there is necessarily a gray area in the definition of the quality. (Rearranged, the corollary can be stated as a topological fact: a continuous function from a connected space to a discrete space is constant.)

By the way, the existence of gray areas really used to bother me. I wanted there to be well-defined lines between, say, legal and illegal, or right and wrong (see Some Flaws in the Analogy). Now that I understand that words are not reality, though, it doesn't bother me so much—I figure the words are just useful but inexact classifications.

So, that's the general statement of the idea that quantitative can be qualitative. What I'd like to do now is point out how the idea applies to user interfaces.

In fact, it was in the context of user interfaces that I first came up with the idea. As I remember it, I'd been writing a hypertext editor that was designed to display lots of small pages in independent windows, and I was excited about being able to create links by dragging from one window to another. When I showed off the editor at work, though, everyone said “What's the point? I can already create links in, say, Word.”. I knew there was a point, but at the time I couldn't explain it properly. What I'd say now is that even a small quantitative change in the speed with which an operation (creating links) can be performed can produce a qualitative change in how often, and to what purpose, the operation is performed.

I ran into a similar thought on Joel on Software (November 22, 2000).

For example, usability theory holds that if you make a task 10% easier, you double the number of people that can accomplish it. I've always felt that if you can make it 10% easier to fill in a bug report, you'll get twice as many bug reports.

Interestingly, speed and ease of use aren't quite the same thing. A mouse-driven interface might be slow but easy to use, while a keyboard-driven interface might be fast but cryptic. Is it then necessary to optimize one parameter at the expense of the other? I don't think so. The way I see it, for each parameter there are thresholds at which qualitative changes occur, and as long as one can get the parameters over the relevant thresholds, the exact values don't really matter.


  See Also

  Bubbles and Barriers
  Experiment, An
  Long-Distance Driving
  Proverbs Are Ideas Too
  Restaurant Effect, The
  Reverse, The
  Rule of Correspondence, The
  Some Memes for Oni

o April (2000)
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