# Are any authors experimenting with including (formally meaningless) aids to human understanding in their mathematical writing?

Are any authors experimenting with including (formally meaningless) aids to human understanding in their mathematical writing?

For instance, there's at least five ways to understand a function, listed below. Maybe it would be useful to write $f : X \overset{\mathrm{graph}}{\longrightarrow} Y$ to indicate that it is helpful for the problem at hand to visualize $f$ as a graph, for example.

As promised, here's a list of five ways of understanding a function $f : X \rightarrow Y.$

1. (Two circles, with criss-crossing lines) Imagine two circles; visualize the elements of $X$ in the left circle and the elements of $Y$ in the right. Then draw (possibly criss-crossing) line segments from each element on the left to a unique element on the right.

2. (Two circles, without criss-crossing lines) Again draw two circles, and visualize the elements of $X$ in the left circle. This time, draw a horizontal arrow across to the right circle for each element of $X,$ and label the head of each such arrow with an element of $Y$.

3. (Labeling/Painting) Imagine $Y$ as a set of labels. A labeling of $X$ = a function. Equivalently, imagine that $X$ is a canvas and that $Y$ is your color palette. A painting = a function.

4. (Graphical) Imagine a 2 or 3 dimensional graph.

5. (Transformational). A function is something you can do to an element of $X$ to transform it into an element of $Y$. The result of this transformation is consistent, in the sense that the same element of $X$ always yields the same element of $Y$.

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Does "formally meaningless" mean that the text could be understood if such aids are removed? –  RghtHndSd Aug 28 '13 at 13:54
@user18921 Just to be sure, are you really wanting to know if there are any authors who practice what you wrote above? And if there are, you want to know who they are? Is this really the intent of your question? –  Git Gud Aug 28 '13 at 13:55
@rghthndsd, yes, it means if we computerized the writing, the aids would be discarded. –  goblin Aug 28 '13 at 14:00
@GitGud, yes, precisely. Reading another author's attempt at implementing this general idea (it doesn't have to be regarding functions) would allow me to gauge whether its actually useful. –  goblin Aug 28 '13 at 14:01
How is this any different from "Are authors attempting to write clearly, with examples and motivation?" –  Isaac Solomon Aug 28 '13 at 14:03