Math of PE Participation (Practical People Need Not Apply)

Calvin Waterbury · Post by **Calvin Waterbury** » Wed Apr 03, 2013 2:14 pm

Ok, this is just for fun amongst us "Think Tank" types or what some people call "Eggheads" or "Poindexters**."

I was watching the antics of the little red 707s on the Live Map and I began to wonder at the effect of adding more people on Pilotedge. I decided to start with "one" on the scope and added additional aircraft up to 30 for the sake of brevity and to see if there was any change to the seemingly linear increase. I am no mathematician, so you uber types

feel free to correct my feeble arithmetic. Don't get lost in the numbers. These are just some musings with rough figures assuming a somewhat static state possibility per each moment. I won't attempt to suggest probability at this juncture.

Feel free to skip to the bottom "30" step and following narrative. The details are only my worksheet and submitted for examination of my data.

Experiment

Starting with 1 we have 100% pilots with 0 interactionsand 0 additional interactions.
Adding 1 = 2 which is an increase of 100% and 2 interactions ("A" can interact with "B" and "B" can interact with "A.") 2 additional interactions.
Adding 1 = 3, increase of 50%, now we have 6 interactions (remember interactions go two ways between each pairing). 4 additional interactions.
... +1 = 4, increase of 33%, doubled to 12 interactions. 6 additional interactions.
... +1 = 5, increase 20%, 20 interactions. 8 additional.
... +1 = 6, ...17%, 30 interactions. 10 additional.
... +1 = 7, ...42 interactions. 12 additional.
... = 8, ...56. 14 additional.
... = 9, ...72. 16 additional.
... = 10, ...90. 18 additional.
... = 11, ...110. 20 additional.
... = 12, ...132. 22 additional.
... = 13, ...156. 24 additional.
... = 14, ...182. 26 additional.
... = 15, ...210. 28....
... = 16, ...240. 30....
... = 17, ...272. 32....
... = 18, ...306. 34....
... = 19, ...342. 36....
... = 20, ...380. 38....
... = 21, ....420. 40....
... = 22, ....462. 42....
... = 23, ....506. 44....
... = 24, ....552. 46....
... = 25, ....600. 48....
... = 26, ....650. 50....
... = 27, ....702. 52....
... = 28, ....756. 54....
... = 29, ....812. 56....
So, adding 1 to the last, 29th person we now equal 30. This brings us to a whopping 870 possible per moment interactions. In accordance with the linear addition of only 2 interactions we have witnessed gives us a final 58 additional interactions over the previous step. IMO, I think this is odd (see below).

Findings

Although the addition of each person affects the percentage increase of pilots in decreasing minute percents, the parabolic(?) increase in potential per moment interactions is substantial. The benefits for Pilotedge and PE pilots are clearly advantageous. The numbers show (and we already knew) if one adds the probable effect of a good "word of mouth" propagation of PE awareness outside of Pilotedge the ROI of getting more people/pilots on board is worth the investment.
I was surprised to find out there was a linear increase of only two interactions added to the Sigma of each person. I would have expected something more on an exponential curve (so many things in life are).
Given the above, I am inclined to think I did something wrong.
I am sure Pythagoras, Galileo, Newton or ??? would have produced a formula for what "X" number of entities does to the Delta as well as the Sigma, but I had no idea what to search for.
Lastly, I wouldn't tell anyone you actually read this thread, much less posted a comment. People will think you are weird.

At the end of the day... I had fun with this!

Ciao!

* "Egghead" comes from the obvious resemblance of a stereotyped, "bald" professor, usually in a lab coat. "Poindexter," on the other hand, has a less precise origin. See here and here.

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