Sharpening Your Axe

A man was walking in a forest one day, and he met a woodcutter. It was a hot day, and he sat down for a smoke and engaged in friendly banter with the woodcutter – things about the weather and such. 5 Marlboros later, he asked, “Mr. Woodcutter, you’ve been making little progress on chopping down the tree the last half hour. Perhaps your axe is too blunt, why don’t you sharpen it?”

“That’s the truth! The axe has not been sharpened for a long while now, I could make far better progress with a sharp axe!” said the woodcutter.

“Then why not you take some time to sharpen it now? You’d make good progress!” said the man.

“I don’t really have time for that, you know. I gotta chop down all these trees, I don’t have the luxury of sharpening my axe,” replied the woodcutter.
Everybody I know identifies with this story to some degree, and I see a good number people I know, including myself, in the shoes of the woodcutter at times. What is perfectly clear is this: the axe would eventually have to be sharpened or it will be blunted to such an extent that even minimal progress will be impossible. Questions abound: When do we need to sharpen the axe? How many times do we sharpen? Would a partial sharpening do, or do we need to sharpen it to full keeness?

The principle is clear to me – just sharpen the axe sufficiently, as an when would serve to accomplish your work in the minimum time, with minimal effort expended since effort per unit time is assumed a constant. Draw a crucial distinction between work and effort – work is what you’re tasked to do, effort is that which you expend to perform the work.

Abraham Lincoln suggested that 60% of the time budget for chopping down a tree should be spent sharpening it. Well, I did an Excel simulation using the solver tool, and the optimal sharpening/chopping schedule is in the chart below.

Assume that it takes 3 times faster to sharpen an axe than it takes to blunt it in normal chopping. That’s a reasonable assumption, I think, considering that a sharpening tool is way more abrasive than wood. Also assume that the chopping power of an axe is directly proportional to the sharpness of the axe, and that the axe gets blunted linearly with respect to time.