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I thought about calling this post “The Sum is Less than the Whole”. Changed my mind at the last second. This whole post is about how misusing simple arithmetic can really mess things up. I had this lesson drilled into me in junior high school wood shop class. We actually had a lecture about measuring and sawing and error. Try this: Take two boards of the same length and cut one of them into two parts. Is the length of the two cut boards lined up end to end the same as the length of the uncut board?

The sum of the lengths of the cut pieces are less than the length of the uncut board. The lost length is on the floor as sawdust. Hence the name “The Sawdust Principle. On the other hand, arithmetic gives precise answers.

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Let’s try another example: Let’s say I need 5 boards exactly 1 foot long. Sorry about not using metric units. I set up my table saw to cut sections that are exactly that length. The process of squaring up a table saw and setting the distance just right is not as simple as it sounds so I will run a test cut or three to make sure I am cutting exactly the length I want. Using good old arithmetic I grab a 5 foot board and start cutting it up.

After 4 cuts I have 4 boards that are the correct length and a piece of scrap that is just about a half inch too short. 2 inch of board has been turned into sawdust. You have to remember the sawdust. Here is the thing, arithmetic only works when you use it correctly. We humans make the mistake of ignoring small losses and discrepancies because we just really do not see them.

That mistake lets tiny bits of error build up until it becomes a real, sometimes dangerously large, mistake. Or, as I learned when studying numerical analysis: Error accumulates. Sawdust piles up on the floor. Do you worry about the milk that sticks to the side of a measuring cup when you are making biscuits?

Do you worry about the variation in the size of “large” eggs when you are scrambling them? For very good reasons we are used to ignoring small errors in measurement. But, if you are making biscuits and scrambled eggs by the ton the small errors start to add up to real money. The sawdust principle is a specific example of a general principle, the misapplication of knowledge. In the examples arithmetic is misapplied. 5 which is why I picked a 5 foot board to cut up. The problem is that I forgot about the kerf.