From Intelligent Perception
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:
- Machine learning vs statistics,
- Pattern recognition vs data analysis,
- PageRank (and its variations mentioned here) vs acyclic ranking,
- Image segmentation vs graph representation of the topology of images (and Pixcavator in particular),
- Graph representation of images vs cubical complexes,
- Math in economics (and Wall Street too!) vs math in physics.
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?
1 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!"
You don't mind the bumpy ride? "What bumpy ride? Aren't all cars supposed to run like this?"
So, you haven't figured out the right shape (the math) for your wheels and you pay the price.
2 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...