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Basic math for designers

Most people function best with business as usual. Regular salary, vacation in a familiar place, television series with a predictable plot, church on Sundays, and a reserved spot in the restaurant. Change implies danger. With that attitude we’ve been able to survive for millions of years.

This is the lifestyle of people who don’t want to think and act as designers. Or entrepreneurs. The Dutch saying, “Doing normal is crazy enough,” comes from these people. Unfortunately for designers, this group is also their main target.

The mathematical representation of a predictable life is a straight line, at most marked with some peaks: for marriage (“the most beautiful day of a life”; after that it will never get better), a handful of births, and a dip at divorce. Preferably the line will make an angle of 3%, to correct for inflation and the annual raise in salary. What makes such a life line still seem interesting is the championship of your favorite club, the joint, and the 10 seconds of ecstasy finding out if your lottery ticket won a price.

Thinking in straight lines is predictable and safe. You know where you are, where it is all going, and what to expect.

For people who intentionally don’t want to know what is mainstream, life is a bit more complicated. They are aware that linear thinking is not really linear at all. More like logarithmic. It is the reason why we feel that the range [close by, further away, far away, and extremely far away] is a growing range with logical increments. But in reality such a range has to be logarithmic. If “close by” equals 10 meters, and further away is 100 meters, then far away is 100 kilometers (by bike) and 100 lightyears is extremely far away. While our intuition tells us that the steps are comparable each time, in reality they grow exponentially by a factor of 10. Calculating in logarithms is a mathematical trick to show exponential growth on a linear scale. Otherwise it is very difficult for us to grasp. Details are only important within the close range.

Logarithmic thinking is what designers do as well. They make models (like sketches, maquettes, quotes, planning, and animations) from what is not yet there, by removing non-relevant details. Guessing the relevance is – besides creativity – one of the most important skills of designers. Although few are aware that they think logarithmically, mathematical principles play an important role in design processes. The design of a plan requires logic, where humor and surprise thrive from the lack of logic. Selecting the relevant options while composing music, or designing a layout or building, is so complex that it would be better to leave those decisions to our subconscious. The lines in a design process are hardly ever straight (otherwise it would be called a production process) and are likely to be discontinuous, leading into a different direction than the one the customer originally indicated. Designers understand how that works, even if they pretend not to.

Every designer who draws a curve on a computer screen is working with geometry. It may be helpful to understand how the formula of Béziers works, but it is not essential in order to draw a nice curve. A well-developed skill in judging shapes works just as well.

Soccer, baseball, and basketball players know very well what a parabola looks like, including the distortions from wind and rotation of the ball. Yet none of them would know the exact formula.

Likewise, type designers are capable of seeing the flow of curves with extreme accuracy. The point where a curve and straight line meet, they experience almost as a corner, a discontinued “second derivative.” A road with such a shape is deadly dangerous.

Type designers “feel” how to correct such a path, without knowing the mathematics behind it.

On the other hand, understanding the inside mathematics may help to find the right design solution in a more efficient way than just trial and error. In this series of articles, we’ll look into more details of the mathematics behind design processes and type design in particular.