# Approximate problems and approximate solutions

I ran across this quote from John Tukey a couple days ago:

An approximate answer to the right problem is worth a good deal more than an exact answer to an approximate problem.

Too often approximate problems take on a life of their own and we forget that they were approximations. We worry about numerical results to many significant figures when the original model might be doing well to get within 20% of reality. Better to produce a crude solution to a more realistic problem. As G. K. Chesterton said, anything worth doing is worth doing poorly.

On the other hand, you’ll probably face less criticism if you produce exact solutions to unrealistic problems than if you produce approximate solutions to realistic problems. At least that’s what I’ve seen. I suppose this is because it takes less understanding to find fault with your solution than to evaluate your choice of problem to solve.

## 4 thoughts on “Approximate problems and approximate solutions”

1. Andrew Gelman

I don’t like Tukey’s saying. It’s too crudely lexicographical. Which is better has got to depend on how good each of the two approximations are.

2. John Venier

My favorite story along those lines is the old chestnut about the fellow looking for his wallet at night under a streetlamp, when he lost it a block away, because the light was better.

Regarding improving the saying, what about:

An approximate answer to the right problem is worth a good deal more than an exact answer to the wrong problem.

3. One more thing in favour of approximate solutions: they are generally more quickly obtained, so they are usable sooner. If you can discover today that roughly half your customers cannot use your online payment system, that’s worth far more than knowing that 46.2% of them were having problems in a week’s time.

Put another way, Google could sit and calculate exactly the most relevant page it ever found for your search on “first aid cut finger”, but you’d rather have the answer *now*.

4. Eduardo Durigan

i love this Tukey’s quote but the word BEST gives a clever and different approach and something may be BEST and could be either exact or approximate (according to the issue and the moment); so, best answers to best problems.