Analogies Not Considered Harmful

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According to Wikipedia, the phrase "Considered Harmful" was already a journalistic cliché used in headlines prior to the 1968 paper by Edsger Dijkstra entitled "Go To Statement Considered Harmful".

It's now something of a cliché/meme in IT and software circles, and the original careful, nuanced discussion is usually lost in people's eagerness to show off their knowledge of it.

While I was writing my post on Signal Reflection, I was given cause to reflect (pun intended ... sorry) on exactly the role and value of analogies in science, maths, and life in general. I've come to the conclusion that, like so many thing, analogies are neither good nor bad. They have their purpose, and each lies somewhere on a spectrum.

The first purpose of an analogy is to connect a new thing with something the listener (or reader) already knows. This then can serve to provide a framework, and a way of thinking about the new thing based on a familiar context. As such, a good analogy can be useful.

But for some analogies, they seem to me to be mostly useless. I've seen an analogy used to describe Diffie-Hellman-Merkle-Williamson key exchange algorithm in terms of mixing paints, an analogy that seemed particularly useless. Others, such as sending valuable items by using a double-locked strongbox might be better, but after the initial moments of going "OK, I can see how that might work", the listener/reader is then left with nothing to use.

On the other hand, the analogy of chemical molecules as "ball and stick", or perhaps even better, "ball and spring", actually lets you do something. It's possible to use it to calculate approximations of energy release. It's perhaps closer to being a model than an analogy, but there again, it's a continuum.

There's a saying:

The same is true of analogies. All are "wrong" in the sense that they can be pushed too far and either made to seem ridiculous, or to give wrong intuitions, or both. But some are useful.

When presented with an analogy, it's worth doing a quick assessment of where in the spectrum it lies.

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