**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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