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.

Daniel Lemire, "The fallacy of absolute numbers," in Daniel Lemire's blog, June 18, 2010.

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Daniel Lemire

A computer science professor at the University of Quebec (TELUQ).

5 thoughts on “The fallacy of absolute numbers”

  1. Hi Daniel, love your blog.
    I see your point, but…
    I just did a Google search for ‘fish’, the results… “About 359,000,000 results (0.17 seconds) ”

    Suppose Google told me that they could make it 100 times faster, just 0.0017 seconds!

    I really would not care, for me, in this context there is no difference between 0.17 seconds and even 0.00000000000017 seconds.

    Of course, you might argue that if I build a crawler can call google a million times, then I would care. This is true, but there really are papers that make similar claims in domains for which we just don’t need speedup.

    One example is a paper on a faster way to do a calculations on human ancestor remains. They had a speed-up of a factor of two. However, every prehistoric human ancestor remain we have could comfortably be placed in a small suitcase. Making the algorithm faster was polishing the wrong apple, we just don’t need to speedup that problems.

  2. When people talk about the improving or comparing any algorithm the only meaningful way to present it is the Pareto front. I learned about it too late, possibly should put blog post about it.

  3. On the other hand, beware of the fallacy of relative numbers: if my web site has the fastest growth in access, that is may be because it went up from 1 access (myself) to, say, 100. This is usually clear with the rate of adoption of, say, new browsers.

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