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What's with the school algebra?

\(f(x) = y\) is a simplification, but it's a useful simplification. Pragmatic analysis strives the mask the tedious, complicated stuff with succinct distillations.

In this case, working backwards

The principle involved in dealing with all the little pieces is the divide-and-conquer idea of analysis. And a simple question keeps the process from going off the rails:

How does this step bring us closer to a usable result?

Black box warnings: hide it in plain sight

The purpose of prominent warnings is to deter the reader.

My sources

We've just remembered why we always have done it this way

In the late 1990s I worked as a public utilities regulator in California. Every week I would receive a dozen copies of documents ranging from a single sheet to thick stacks. After setting aside a few copies for various purposes eight were sent to recycling.

Finally, I asked:

Why 12 copies?

No one seemed to know until someone thought to ask the most senior clerk. She said

That’s the most copies that you can type with a carbon-set

The carbon-set was a stack of alternating typing paper and carbon paper used to produce copies on typewriters. It predated office copiers. Like the two-space after a period rule, the technology’s influence lasted far longer than the technology itself.

More business processes than we might care to admit to ourselves have similar rationales. Recognizing and rationalizing them can lead to quicker, simpler solutions to more important problems that are ensnared by forgotten history.