Computer Vision & Math contains: mathematics courses, covers: image analysis and data analysis, provides: image analysis software. Created and run by Peter Saveliev.

Bad math

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Not to be confused with wrong math...

Adding pounds to miles is the simplest example. But a more typical problem with how mathematics is used in applications is made-up and hidden parameters. Compare:

Note: You don't have to go far for examples of good math.

Especially in computational science, algorithms, software etc there is a lot of mathematics. It's tempting to make math stuff up just because you can. The consequences are dare.

The issues to be addressed:

  • Is it well defined? (existence and uniqueness)
  • Does it use made-up or hidden parameters?
  • Is there a physics analogy and is it valid?
  • Is it ugly?

Metaphor 1

There is nothing more practical than a good theory. Conversely, a bad theory makes things based on it very impractical.

This is you: "My car is great: a powerful engine, excellent mileage, leather interior, etc. I love it!"

image: square wheels 1.png

You don't mind the bumpy ride? "What bumpy ride? Aren't all cars supposed to run like this?"

image: square wheels 2.png

So, you haven't figured out the right shape (the math) for your wheels and you pay the price.

Metaphor 2

Pagerank is a starting point; it provides a rough sketch of page importance which is fine tuned by other more specific algorithms”.

Let’s consider this analogy: π = 3 is bad math, but it’s “a very good starting point” for solving many real life problems. For example, you can build a hut, no problem. But what if you want to do something more sophisticated like building an airplane? With π = 3 your plane will drop like a brick. And this will keep happening, no matter how much you fine tune your engineering. Suppose now that you replace π = 3 with π = 3.14159265358979. OK, you've replaced bad math with better math, or maybe even good enough math (you can build your plane now). But π = 3.14159265358979 is a time bomb! Sooner or later it will fail you when it’s not accurate enough anymore. Sooner or later you will need to understand what π is. Sooner or later you will need good math... (Is this what's happened to Google?)

Note: Bad math could be good something else...

Note: Sometimes good math is unavailable...