16 November 2015

Some concepts are very complex and need a long explanation. But we might decide to take a shortcut and simplify the concept when describing it.

That short explanation is misleading.

Lets see why… For example, we might be trying to explain electro-magnetism. A full explanation will include Maxwell’s equations, definitions of electric and magnetic fields a discussion of ferromagnets, and more. A shortcut explanation might be that magnets attract like rubber bands.

The shortcut might suffice for a while. It gets the rough idea of “attraction” across, but cannot be trusted as a base for further inference. Rubber bands break if they are stretched too much, but magnets still work over very far distances - albeit weakly. Coldness increases the power of magnets, but decreases the flexibility of a rubber band.

To refine our understanding of magnets, we need to start imagining rubber bands that behave differently with temperature, knowing that they get weaker with heath. This is an exception to our common sense, and it requires a bunch of effort to remember it and apply it properly.

Pretty soon we start keeping all these exceptions to the rule in our heads. This is wasteful, and defeats the point of the short explanation. We could have redirected that extra effort to towards learning Maxwell’s equations properly. A person which blindly follows the rubber band model might save effort for a little bit, but over time they will spend more mental energy to keep their mental model in sync with reality. They will have larger error and disappointment when the model fails…

The cautious thing would be to realize when the model works and when it doesn’t work and to only use it, when it works, for a while, and not depend too much on it. Misleading models are a shaky foundation for reasoning.

But which models are not misleading? Even the laws of physics get disputed by other physicists.

The answer is that there are no perfect models. Every model is an abstraction over reality, and all abstractions are leaky. That’s the law of leaky abstractions, defined by Joel Spolsky. All models that we use in the daily life are imprecise in some way.

But lets not despair. Some models are more precise and trustworthy than others. They can go a very, very long way towards practicality.

Physics models, for example, a.k.a. the laws of physics, are usually so precise that the scientists in CERN can use them to take single particles and hit them with really high speed, and measure very tiny deviations from their expectations.

Other models, usually the non-scientific ones, are much less reliable. Many economic models are only approximate, and they have been derived in situations, that are no longer applicable as the markets and regulations evolve. Lets just remember this every time there is a market crash.

To be fair, even leak-free abstractions might not be able to fully predict everything. For example, many deterministic mathematical models of dynamic systems can exhibit chaotic behavior - which means that even the slightest error in measurement of the truth can lead to enormous deviations over time. This is why you can’t predict the weather. The world changes deterministically according to the law of physics, but similar starting conditions can lead to very different outcomes over time. This is what people refer to as the butterfly effect. A change as small as the flap of the wings of a butterfly might cause a hurricane in to future to happen, or not. If the butterfly is at the right place at the right time.

Getting back to the situation in which we need to provide a short explanation for something too complex, we have several options.

One option is to provide a metaphorical explanation, a shortcut, but make it clear that it isn’t what actually happens. This way they at least are aware that we aren’t giving them the full story. This can be the quickest approach, as long as our audience doesn’t keep on asking “Why?”

Another option is to ask our audience to bear with us while we develop the idea. This works well in college classes and other situations, but is not always available. Neither our audience, nor us have time for it, for everything. A benefit of this approach is that we’ll get to actually understand the concept better if we have to fully teach it.

Yet another option is is to find some middle ground in which we gradually build up the concept, and progressively close each leak in understanding. We can make the practical parts rock solid, and hand-wave around the non-important parts. It may be really hard to know which parts are important though.

There is no single right approach that works all the time. Read the situation.

You'll receive emails containing the text and images of the essay, once or twice per week. Usually less often.

I write these posts to clarify my thoughts and improve my communication. They are mainly written for myself, and my future self, but I'd love to hear any comments you might have, especially if you disagree with what I've written, or if you've found it valuable in any way. Message me on Twitter @themitak or email me at comments@dimitarsimeonov.com.