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Humanized > Weblog: Interface Math
Many people are unaware of the theoretical work that has been done in the HCI field. Work that transitions the field from mystic guruism to hard engineering.

12 May 2006

Interface Math

UI Design Fundamentals

Interface design isn’t about choosing a particularly pleasing color of blue. Nor is it something that can be slapped-on at the end of the product design cycle. For the user, the interface is the product. The technology behind a product is useless if no one can actually use it.

Google has really taken this to heart. Why do people use Google Maps? Because it’s just so nice to use. Microsoft’s Terraserver gave users access to high resolution satellite images many years before Google Maps did the same. (In fact, while attempting to be clever, I inadvertently terrified my to-be roommate: I used the service to view an aerial photograph of his home and asked him some leading questions about the stuff in his backyard. It took until the second quarter of college before he even talked to me, and then only warily.) But, it wasn’t until Google rethought online maps that the security and privacy issues of such a service came into the national conscience. Why? Because whereas Mircorsoft had given access to satellite imagery, Google made them accessible.

“Okay,” you say, “Sounds good. But, how do I convince my clients that there’s more to interface design than just aesthetics and fluffy feelings?” The answer: By using math.

Many people are unaware of the theoretical work that has been done in the field—work that transitions the field from mystic guruism to hard engineering. I’m only going to discuss three tools here, but there’s plenty more out there to explore.

Tool One: GOMS

The first tool that every designer should have in their tool kit is GOMS analysis, a model developed by Card, Moran, and Newell back in the early 80’s for predicting how long it will take a user to use an arbitrary interface. It’s predictions are fairly accurate and, more importantly, give an excellent means by which to compare the speed of two interfaces. There have been a number of developments in GOMS modeling in the last 25 years that take into account learning curves (NGOMSL) and parallelization (CPM-GOMS), but for the most part they are over kill: if you have a couple of interface ideas, and you want to know which one will be the quickest, break out GOMS. I wasn’t able to find a stellar introduction to GOMS online, so until we (or someone else) writes one, the best place to find a concise guide is still in Jef Raskin’s book, The Humane Interface.

Tool Two: Fitt’s Law

The second tool that every designer should have in their toolkit is Fitt’s Law, which was developed in the 50’s to predict how long it will take a user to target an object, based on the object’s size and the user’s distance from the object. The most common use is for predicting how long it will take the average user to move the cursor to an on-screen button or menu. There are lots of input device dependent constants in Fitt’s law that are needed for getting accurate results. However, if you just wish to know which of of a set of layouts is best, you can use Fitt’s law without worrying about the constants—they’ll all drop out in the comparison. Understanding Fitt’s law will give you an immediate benefit in all of your interface designs: just knowing it can explain why a Mac menu can be accessed over five times faster than a Windows menu.

These first two tools are remarkably powerful, and given that they were developed in the 80’s and the 50’s, no interface designer should have an excuse for being ignorant! But both tools suffer from the same problem: although they let you know which of two interfaces is better, they don’t give you a sense of whether you can create a third interface which is entirely better than the first two. It’s like trying to measure distance with a compass—you can only measure in relatives, never in absolutes.

Tool Three: Information Theory

The third, and most general, tool is a solid understanding of Information Theory, a full blown mathematical theory developed in the late 40’s by Shannon to describe the abstract notion of communication. The theory is general enough that it can be somewhat difficult to understand how to apply it to interface design. If you are feeling brave and have your wits about, then read through the fascinating The Magic Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information for a brain stimulating time. I know that my mind was reeling with interface thoughts after reading that paper. However, you can stick around here for a more guided tour. The end result being that you’ll be able to use information theory to give an absolute rating for how good your interface is (i.e., how good it is when compared with the theoretic-best interface).

Sound too good to be true? It isn’t. But you’ll have to wait until next time.

At Humanized, we don’t break these tools out for every interface problem: after using them for awhile, we developed an intuition for what the results were going to be. However, just knowing that the tools exist—and understanding how to effectively use them—really colors the way in which we think about interfaces. Plus, its great knowing that if I’m ever unsure, or get into a debate over some feature, I can rely on these tools for a definitive answer.

by Aza Raskin


6 Voices Add yours below.

Jim Sundfors
May 14th, 2006 5:06 pm

As the old saying goes,”the apple does not fall too far from the tree”. Thank you for offering the online help for those of us who were not born into the computer age and constantly struggle with something that your generation uses so easily

Sandy and I have very fond memories of your Dad and he was very instrumental in Sandy attaining so much of what she accomplished. For the “nerd” on the block he developed into some kind of genius that we perhaps did not recognize in the early days of our relationship.

I cannot say that I fully understand all that your present; however, I do recognize the fact that you have chosen a path that you will do exciting things

Good luck and keep on truckin’
We will be watching your progress with all the enthusiasm of a parent

Jim and Sandy Sundfors


This is interesting stuff and right now it’s an area I’m studying. I read The Humane Interface a few months ago but it’s not something that can be digested all at once. I will look forward to your future posts on this topic.


Jim, thank you very much for your kind words. I believe that it is my generation—born to the beginning of the person computer era—that has the duty to transform computers from ends to means: computers should be as transparent to the task at hand as our lungs are to breathing.

Some of our earlier posts, like A Pretty Neat Digital Watch and Preferences: Hiding Interface Complexity are much less technical. But I am also hoping to follow up on this article so that more people can enjoy the use of these amazing tools without having to delve into the warren of academic literature. I was truly surprised to find how little there is on the Internet that explains these concepts in everyday terms.

This tidy presentation of design fundamentals is a useful tool all by itself, a mini library of links. Thanks!


Is efficiency of use really the only metric that determines whether an interface is “good”?

- Jane

I like how you suggest that entropy should be considered when designing interfaces. Nice correlation between Information theory and interface design.


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