## 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 |

Notes:

- The engineer and the mathematician might both be gay.
- The woman might actually be a nifty pocket calculator.
- Not all engineers are practical.