Missing a point or two about models/law

by Thiyagarajan Maruthavanan (Rajan)

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