Daniel Lemire's blog

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The fallacy of absolute numbers

I often come across the following type of arguments in research papers:

  • You could save 3 bits of storage for every value in your database. Surely that’s irrelevant. Nobody cares about saving 3 bits!
  • You can sort arrays in 10 ms. Surely, that cannot be improved upon? You are already down to 10 ms and nobody cares about such small delays.

I hope you can see what is wrong with these statements?

I call it the fallacy of absolute numbers: you express a measure or a gain in absolute value, and then conclude to optimality or near optimality because the number appears small (or large).

Remember: Saving 3 bits of storage out of 6 bits is a 2:1 compression ratio. Sorting in 5 ms instead of 10 ms doubles the speed.

Note: I am sure that someone else has documented this fallacy, but I could not find any reference to it.