Saturday, May 18, 2019

It's as easy as 1-2-3!

Counting, positioning, or measuring: what's in a number?

Remember pre-school or kindergarten: we all "learned our numbers".
Ah! but did we?

Want to count something? Just use the integers, starting at 0 and going in familiar step: 1, 2, 3 ....
The count takes on the dimension of what you are counting: dollars, inches, meters, liters, etc
You can do arithmetic on count, but because of the dimensioning, the results may or may not be viable: square inches are ok, but square dollars are not.

Want to rank or position something? Again, we fall back to the integers -- 1st or 2nd position is good; position 1.2 in a queue has no meaning or implementation. And, there is no dimension per se in a position.
Some arithmetic still applies, but it's tricky. Addition is not commutative:
• You can add 1 to the first position to get the second position,
• But you can't add first position to a 1. Stuff like that.

Want to measure something? You can use any rational number for measurement. (a number that can be fashioned by the ratio of two numbers). Really, anything on a measurement scale is rational and can be a measurement.

But there are irrational numbers which can not be formed by a ratio (like "pi"). Nonetheless, you can measure with irrational numbers. The area and circumference of a circle are measured with "pi"

For a number to be useful in measuring, every number in between has to be meaningful. That's why you don't do measurements with ranks and positions: the in-between numbers are not meaningful.

Calibration: And, to be meaningful, the scale has to be calibrated.  A ruler with irregular spacings or a warped or bent rule, or guesses without reference to benchmarks or other reference classes are uncalibrated. And, thus, every number in between is not meaningful.

Project management
And so, where does the rubber meet the road in project management?
• Budgets, schedules, resource estimates and utilization need calculation, measurement, and counting
• Anything else that's quantitative

We're done here!

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