Visualizing numbers

Many of our students go blank when viewing numbers, tables and formulas. Some they have necessary skills to understand the math, but cannot make it vivid enough. Here I address this and additional reasons.

Short numbers. The simplest sort of a problem with numbers is a lack of interest. For me it is hard to remember my car number or bank account or a password unless I have a clear visualization to go with it and spaced repetition of using it. To generate this visualization I try autobiographical memory. For example my car number is 84-514-79. I had hard time remembering it, until I decided that enough is enough. Immediately I got a strategy: I was born in 1974, and in 1984 I was 10, in 1979 I was 5. 1514 was 500 years ago. Remembering 10-500-5 is very easy. I have several other methods, but autobiographical method is easy to explain.

Graphs. If you need to analyse complex graphs, you should use technical analysis (like support and resistance). However most of the graphs are monotonous and very simple. Probably 90% of the graphs are either straight lines, or powers of x or exponents. If you remember what X and Y. direction of the graph and direction of the curvature you are in a good shape. Occasionally, the unfortunate of us (those holding PhD in math) need to tesseract multidimensional manifolds. If you need something as complex, contact me [email protected]. For bars we choose our reference and see how other bars relate to it. Nothing is as deceptive as statistics. See for example linear vs logarithmic plots. navigate your graph with care and try various methods of visualization to get through.

Tables. Tables may be simple and they may be complex. To make simple tables we use colours: red for bad, green for good, red for do not care. If you do not have colors in the table, visualize the colours. Occasionally we need to compare numbers. If so, try to visualize bar graph. With financial data or energy we have a sort of flow, and a good way to visualize it is like reservoirs of various size with pipes. The water may be coloured.

Formulas. Never try to remember formulas as a song. It is best if you understand where the formula comes from. Most of the connections in the formulas are either powers (including inverse powers) or exponent. If something declines or explodes with time it is usually an exponent. If the effect happens in space it is usually a square. If several dimensions help each other they usually multiply, if they interfere they divide. Try to use your common sense to make sense out of formulas and remember this sense. Try to separate the formula into elements and plot a graph per element – usually it will be monotonic with some belly.

Combinations. Often we have many types of data interconnecting with each other. They represent the issue we study from various angles. Do not try to think about it as a puzzle, but more of a shadow. When we have the issue of interest and analyse it under some angle we get its shadow in front of us in a table or in a graph. We should always ask ourselves why the author decided to visualize the data the way is is visualized, and how it would look under a different angle. By analysing additional projections that are not referred to by the author, we get better understanding of the underlying laws.

Numbers are a language. They say something to people who know how to listen to them. Try to hear the music of the numbers. You may find it hypnotizing and beautiful.