## Sunday, July 16, 2023

### Building the Appian Way

As a project, the Appian Way was monumental for its time: Phase I, built in only one year .... 312 BCE ... the paved road (originally, a military road) cuts through the Alban hills and the coastal Pontine marshes to connect Rome to far southeast Brindisi.

But think about this: the Project Executive Officer, PEO, one Appius Claudius Caecus, did not have a couple of tools at his disposal that we so routinely use that they are not even noticeable:
• There was no "0" in the Roman system of math. "Nothing" was not a number. Roman numerals are/were for counting and positioning (ranking, or ordering), but not for measuring. Today, we say that Roman numerals are "cardinal" numbers, meaning numbers that are for counting.

How did Caecus calculate his project variances? Was zero-variance not a possibility, given no '0" in the system?

However, to build a road, you've got to be able to measure things. So, when it came to measuring and dealing with quantities, the Romans relied on a separate system known as the Roman system of measurement. This system was based on various units and standards, such as the foot (pes), the inch (uncia), the palm (palmus), and the cubit (cubitus), among others. These units were used for measuring length, weight, capacity, and other quantities.

• There were no fractions in their system of mathematics, even though a pseudo-system of fractions existed in ancient Egypt. Maybe if Marc Antony has been around three centuries earlier, he could have brought fractions home.

• And, there were no negative numbers. This concept is almost middle-ages in its origin. Not until the 16th century did negative numbers really come into general mathematics.

Does this mean that Planned Value - Earned Value (*) was always positive? That if circumstances were such that at some point EV were greater than PV, a negative number to be sure, that Caecus could only describe that he was ahead of plan, but couldn't calculate it?

• And, of course, there was no concept of random effects and probability.
Those effects were left to the Gods. (See my review of the book on risk management entitled "Against the Gods")
They did it
So, somehow, the Romans built a magnificent road, parts of which survive today, without a "0", without fractions (formally at least. One can imagine half a cubit, even if they can't formally express the idea), and without negative numbers.

I wonder if I could run a PMO without these tools? Doubtful! And, my PMO would also have random numbers and systems of probability which also did not come along until about the 18th century.

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(*) PV - EV is a variance, calculated at a specific point in time, that indicates positive or negative schedule variance. You've either earned what you've planned at the right time, or you've not. Some caution, however: this formula is only valid for only the duration of the baseline timeline of the project; it's not valid thereafter. Example: It's invalid to be a year late beyond the baseline delivering all the EV, and then declare that PV - EV is 0, thus no schedule variance!

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