Missing a point or two about models/law

There is too much chatter once again about laws governing networks after the recent IEEE article critiquing Metcalfe’s law with even Metcalfe himself pitching in to defend his position/law. In all this chatter I find all these smart folks missing out two basic ( really basic) points.

  1. All these laws posit a boundary value calculation (maximum) and not the actual value for a specific instance of a network. Any CS grad would be easily point out that the above arguments are Big Oh evaluation (worst case) and not Theta evaluation (average case).
    • Telephone kind of networks (with direct externalities) can attain a maximum of n^2 (= n*(n-1)/2 )  and no more. (Metcalfe’s)
    • A network with nodes who are ‘humans’ and have value realized in the overall if sub-grouped can attain a maximum of 2^n ( = Summation[ nC1 + nC2 …. nCn] ) and no more. ( Reed’s)
  2. The other far more important & subtle point being that “ALL models are wrong but some models are useful

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