measure theory and cog. psych.

Measure theory defines three attributes for some variable to be considered a measure*.

  1. Non-negativity:
    It’s the idea that a value should not go to negative when measured (by whatever means/equipment in the real world.
  2. Null empty set:
    It’s the idea that the measure becomes zero for a null set.
  3. Countable additivity:
    This one basically means if there are ‘n’ sets with measures ‘X1, X2, …, Xn’ then the measure of the Union of all the ‘n’ sets is less than or equal to sum of ‘X1, X2, … , Xn’
  • — I think it can be extrapolated/extended to measure of any geometric properties, but not beyond that. Very tellingly, it is used widely in a field called real analysis. After all, in electrical engineering we have all sorts complex, negative, fractional numbers. I picked up these definitons from Fractal Geometry book rather than the wikipedia links provided.

ps: There’s a more generalized definition of measure, that might fit these too here.

** — If you think about these are all just a set of rules for determining if a given set belongs/satisfies the properties of a set of numbers, but that’s beside the point here.

As much as i have been a fan of cognitive psychology, so far, i am now beginnning to wonder, which and how many of these concepts like executive control,,etc.. have been shown to obey these laws. I haven’t done a thorough survey or research, but deeply suspect there hasn’t been any published attempts in these directions. I would like to see some, but i think it may not be easy to pick a property that’s easy enough to deal with.

Also, i begin to wonder how many of these apply or scale to organizational psychology? or committee-centered decision-making policies. Again i suspect there’s been very little attempts to scale/correlate cog,psych concepts into organizational/behavioural psychology, never mind cross-checking with relevant math area’s base assumptions.

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