Close Enough

An engineer and a mathematician, both suitors for an attractive woman, are challenged by her.

"I will stand in one corner of a room.  You will stand in the other.  You may approach me any number of times however each time you approach you may only cover 1/2 the remaining distance between us.  Whoever reaches me will be the successful suitor"

The mathematician snorts and says that the problem is impossible, the approach asymptotic the women will never be reached, and stomps of in a huff.

The engineer declares that after a few turns they will be close enough for all practical intents and purposes.

I think this flippant story embodies some philosophy of engineering.  The Science of mathematics helps predict in a pure or ideal environment.  The practical engineer then has to adapt the various assumptions built into the ideal model to "fudge" the results.

The table below shows the engineer approaching the attractive women.  By move 21 the engineer is within 4 microns of the woman.  Since our bodies slosh around by 1000's of microns (a few millimeters) in the non-ideal real world situation they would actually be touching.  Good enough for all practical intents and purposes.

Move Proximity in mm
1 5000
2 2500
3 1250
4 625
5 312.5
6 156.25
7 78.125
8 39.0625
9 19.53125
10 9.765625
11 4.8828125
12 2.44140625
13 1.220703125
14 0.6103515625
15 0.30517578125
16 0.15258789062
17 0.07629394531
18 0.03814697266
19 0.01907348633
20 0.00953674316
21 0.00476837158