Visualizations

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Constraint Diagrams

October 10, 2004 in Systems Thinking, Visualizations | Comments

Decisions involve tradeoffs. Time at work subtracts from time with your family; money saved for the future subtracts from goods and services now; many food choices trade off among taste, convenience, price, and nutrition.

Some tradeoffs in computer science are the cost to update versus the cost to search, and execution time versus memory consumption. Tradeoffs in software development include implementation time versus execution time, and compilation time versus object code quality. Tradeoff in project management include resource pool size versus communications overhead, and cost versus time versus quality. These tradeoffs are some of the tradeoffs, respectively, in such tasks as choosing a data structure, algorithm, or cache size; choosing a programming language, a compiler and compiler settings; and choosing a project team size and personnel.

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Dot Numbers

August 14, 2003 in Illustrations, Math Education, Visualizations | Comments

Dot numbers are a new notation for numbers, that make integer addition look like rational multiplication. They may be useful in primary school math education. The idea is that once you understand integers and addition, you can learn another way to look at it that sets you up to understand fractions and multiplication.

I made up dot numbers a few years ago to try to explain negative numbers to my then-four-year-old son.

Basics

A dot number is a way of writing a number. A dot number is represented as a number of dots above a line. This is the number 3, as a dot number:

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Birthday Numerology

July 11, 2003 in Family, Visualizations

Double Trouble

In four months Miles will be twice Charlotte’s age. (He will be 10; she will still be 5.) A year ago, he was also twice Charlotte’s age. (He was 8; she was 4.) A year from now, he will have spent exactly one year at twice her age (if you truncate ages to the year), but that year will have been distributed into two intervals, at the beginning and end of a two-year period. See the gray portion of the illustration.

Back to the Future

Miles was recently twice Charlotte’s age (and will be again). But there was a time at which Charlotte’s age was twice Miles’s age. (But there wasn’t any time at which Charlotte wasn’t twice as old as Miles.)

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