Real estate of names

A common convention for writing names (identifiers) in mathematical formulas makes poor use of the real estate on the page occupied by those names. Here is a design principle for using space more efficiently. The choice of a suitable notation is a vital part of designing clear and convincing presentations of scientific material. Good notation is precise, concise , and suggestive; poor notation may be ambiguous , clumsy, or misleading. Integral to the design of notation is choosing what names (iden-tifiers) to use to represent the entities involved. How to typeset formulas is also an important part of the design, for one would like formulas to use the available real estate effectively and efficiently. Let us examine how some of these design decisions are often made by focusing on a common usage of subscripts. Figure 0 shows two equations from physics [1] and one from computer science [0]. The first of these equations states that the potential difference between points a and b equals the difference between the potentials at these points. (The potential " at a point " is really the potential difference between that point and some implicit point, usually ground.) The second equation states that the angular magnification is minus the ratio of the focal lengths of the objective lens and eyepiece lens. The third equation specifies the lag time of a FIFO synchronizer circuit with N elements in terms of the cycle time a) V ab = V a − V b b) m θ = − f ob f ey c) t cy + t m < t lag < N t cy − t m Figure 0. Examples of a common usage of names in formulas. and a timing margin. The names in these formulas contain two parts: the type (like V for voltage), indicating which attribute is being measured, and the brand (like a), indicating where the measurement is obtained. In Figure 0, the types use a larger font than the brands. By encoding the types as part of the names themselves, it is easy to type-check the formulas. For example, by subtracting a voltage from a voltage in the right-hand side of equation (a), one gets a voltage, which is indeed the type indicated by the name in the left-hand side of the equation. But the brands are important, too. In fact, they are paramount in Figure 0—for one, they distinguish names …