Michael Eriksson's Blog

A Swede in Germany

How an easy task can be harder to do right

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Recently, I have seen two old observation brought to my mind again:

  1. I often make more errors on an easy task than on a hard task.

  2. Doing a task well is far easier when I know the level of difficulty.

Explanations:

Both observations are easy to understand, even though they may seem counter-intuitive at a first glance. A good illustration is Sudoku (the solving of which has kept me entertained on my many recent train rides):

Firstly, with an easy puzzle, the numbers pop-up more or less by themselves and just have to be written down. The actual thinking needed is minor and each individual number is of little value to me. I have no incentives to do extra boring leg-work (notably checking that I put two numbers down in the right order, I am in a “work fast” mode, my brain tends to become inattentive, and I never gain a deeper “understanding” of the puzzle and its connections. With a harder puzzle, in contrast, the leg-work forms a smaller part of the overall work and is easier to justify (in particular, as an unnecessary error would ruin more of the time put in), I am in a “slow and thorough” mode, my brain pays close attention, and I see much more of the connections present (both through having to think on many different aspects to reach a solution and through the longer time spent on the puzzle).

Secondly, problems of different difficulty require different solutions. For instance, with easy puzzles, I find many number very fast by a strategy of looking at which numbers already present block which squares in other nine-blocks. With increasing difficulty, this strategy becomes less and less useful and slower methods, requiring more thinking must be used. For very hard puzzles, it often boils down to individual investigation on an ad hoc basis or “brute force” attacks (basically assuming different combinations of numbers and positions and trying to rule out all but one of these). Using the “advanced” methods on an easy puzzle would work—but it would be significantly slower than with the more basic methods. Conversely, the latter simply would not suffice to solve a harder puzzle at all. Knowing the difficulty of the puzzle is important when deciding on how it should be attacked.

Implications:

If other people are much the same (and in my observations so far, they are), this has interesting implications for e.g. judging competence levels, deciding who should be given what tasks, and how the education system should work. To take a specific example, consider dumbing-down and education: An increasing dumbing-down will lead to more of the bright students facing “too easy” tasks, while more of the dull students are faced with “just right” tasks—under-estimating the former and over-estimating the latter, possibly to the point that some students are ranked in a ridiculously wrong order. (To which must be added, obviously, off-topic issues like increasing boredom.) Similarly, it may seem a good idea to promote the entry-level employee who excels at the entry-level tasks—but on closer inspection the less successful entry-level colleague might be the better choice, because he fairs better with harder tasks post promotion. (Which is not in any way to say that lack of success on easy tasks would be a proof of excellence—incompetence is another common explanation… The point is that the judgement made must factor in that things may be different than they appear to be and that the relative success of two parties may change drastically as the difficulty of the tasks change.)

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Written by michaeleriksson

August 11, 2011 at 11:15 pm

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