Thursday, March 8, 2012

Optimal Frugality

Most people who don't know me who hear that I'm a frugal person assume I shop at sales or use coupons.  It's sort of hard to explain why doing that would actually cost me MORE money than what I currently spend.  Here's my funky attempt (with pictures!) to show why I think buying the cheapest thing in front of me at the moment is not the cheapest way to live.

There's a famous mathematical problem called the "Traveling Salesman Problem".  The idea is this:  there are a bunch of cities, and the salesman wants to visit each one.  How does he do it in a speedy way?  How can he visit each city but spend the least amount of time?

It's a famously hard problem to solve, especially when there are thousands of cities. (Why thousands?  This is a math problem, after all).   Naively, you'd think that he would just keep choosing to move from one city to the next nearest city.  But that can actually take him on a really long route -- and it turns out that sometimes going a bit out of his way early on can save him a lot of travel time later.

One of my colleagues, Bob Bosch, has some lovely pictures of this problem.  Here are a few dots from a much larger canvas of dots he started with.  How would you connect them with the shortest path?

Here is another small section of dots; in this image, Bosch has connected all the dots in the picture in the shortest possible path.  When you look at this small piece of the picture, it doesn't look like the best way to connect them, but Bosch is looking at the big picture.  So sometimes his lines run off the edge into other parts of the canvas.

What's the big picture?  It's a work of art!
The Da Vinci Curve by Bob Bosch
(used with permission of the artist)
That curvy thing is actually one single curve -- believe it or not, it's the shortest curve you could draw between all the dots in Mona Lisa's face.  If you will, it's the most frugal curve, using the smallest amount of ink.

But you can't draw this by standing at one point and wondering, "what's the closest point to me now?".  And for me, I can't bring my spending to a minimum by pulling out my wallet and asking, "what's the cheapest thing I could buy today?"  Sometimes I spend a bunch more, so that I can take smaller spending steps later. 

1 comment:

  1. Hello Miser Mom,

    We agree, Family comes first.
    That's why we started our own Blog as well entitled:
    We found an ingenious way to stop from having to cut coupons and search everywhere for them.
    So stop on by and say "hello"

    Chris & Mary Ann Bird