How Math Explains the World.pdf

are some problems that are so intrinsically difficult that it may not be pos-
sible to get them right; at least not in a reasonable amount of time.

Another Visit to the Garage

Every so often, we are confronted by an uncomfortably lengthy “to-do” list.
Early in life, I adopted the strategy of getting the more onerous chores
done first. There were a couple of reasons for this. The first was that at the
outset I always had more energy, and the distasteful jobs always require
more energy, either physical or emotional. The second was that once the
onerous chores are out of the way, I could see the finish line, and this
seemed to give me renewed energy for completing the remaining jobs.
I had stumbled on a strategy for scheduling tasks that goes by the name
of “decreasing-times processing.” If one takes a close look at the schedules
that exhibited the unusual anomalies in our earlier trip to the garage,
some of the problems were the result of lengthy tasks being scheduled too
late. In an attempt to prevent this, the decreasing-times processing algo-
rithm was devised. It consists of constructing the priority list by arranging
the tasks in decreasing order of required time (ties are resolved by choos-
ing the task with the smallest number first, so if T3 and T5 require the
same time, T3 is scheduled first).

T1-3

T9-9

T2-2 T3-2 T4 -2

T5-4 T6-4 T7-4 T8-4

The priority list is T9, T5, T6, T7, T8, T1, T2, T3, T4. With four mechan-
ics, the schedule looks like this.

Mechanic Task Start and Finish Times

0 2 3 6 10 12

Al T 1 T9 Done

Bob T 2 T5 T8 Idle Done

Chuck T3 T6 Idle Done

Don T 4 T7 Idle Done

156 How Math Explains the World