Thursday, January 22, 2009

The Tenth Decimal Place:
Least Yet Most Significant

A Computing Koan



In the city of the Sacred Serpent, Master Foo was holding court with his engineering students.

"The ways of the industry, my children, are very different from the way of the school", said the Master.

"But Master, we do computing in the classroom, and we will be doing computing in the Industry when we graduate in a few months' time. What is the real difference?", asked an acolyte.

"The differences are myriad, my children. But let me distill the essential differences into a single anecdote"

The Master continued,

Not far from here in space and time, a class of 50 novices like yours was given a computing exercise. The exercise was to compute the value of Pi to ten decimal places. Children worked hard, trying out different algorithms, and trying to produce the most elegant code ever written. At the end of the prescribed time, the Teacher, checking the output of the 50 programs, found the following:

Seven students could not solve the problem at all

Three students, getting confused between Pi and Phi, and had computed the Golden Mean instead of Pi.

20 students obtained the value of Pi correct up to eight decimal places, but incorrect thereafter.

18 students obtained the value of Pi correct up to nine decimal places, but not the tenth.

Two students obtained the value of Pi correct to all the ten decimal places.

To the first group, the Teacher gave zero marks. She gave the next group 50 marks for trying. The next two groups got 60 and 70 marks. The last two students obtained the full 100 marks.

And all was well.

Coincidentally, at a different place, a group of new recruits to the industry was given the same computing test at the end of their induction programme. The inductees were in high spirits, as they were approaching the end of their training, and would be professionals shortly.

Coincidentally again, the results of the Pi computing test was the same, with two engineers obtaining all decimal places right.

On the spot, the management fired the 48, and gave a bonus to the two who completed the task. For, the two represented revenues for the company, while the 48 were just cost.

"Therefore, remember this, my children: In the Industry, There Are No Marks for Trying.", concluded the Master.

"But sir," a student asked, "Of these two, which is the really, really the right way?"

"Moo", said Master Foo.

At this, the students were enlightened.