hamming's law




Hamming's Law


R. W. (Dick) Hamming was, for 30 years, a senior scientist at Bell Telephone Laboratories, Inc. in Murray Hill, New Jersey.  His name is attached to an error-correcting code (the Hamming code) that won him the 1968 Turing Award.  He moved to the Naval Postgraduate School in Monterey, California in 1976.  Specializing in probability and combinatorics, he was a scientific generalist.  Among his general observations was his statement that "large quantitative changes produce qualitative changes".  This has been known as Hamming's Law.  I learned it in a bastardized, less intellectual, form which I believe has much more impact and is easier to apply.  What I learned as Hammings Law was:


Anything that changes by an order of magnitude is used differently.


As a concrete example, think of a horse.  We all know what horses are used for.  But now think of a horse one-tenth the size of a normal horse.  How would that be used?  Certainly entirely differently.  Or how about a horse ten times the size of a normal horse!  What would we do with such a magnificent animal?  Or, perhaps, what would it do with us?


In any case, the lesson here is: do not assume that when things change by large amounts that the surrounding characteristics will be unchanged.  I remember an event during the early days of nuclear power.  The people from GE's Hanford Works had evolved nuclear reactors with many tubes containing uranium which penetrated the graphite moderator stack.  Water flowed through these tubes to cool the uranium.  With thousands of such tubes in a single plant, the front and back faces of the reactors were plumber's nightmares.  A new design was proposed, called a "water wall" which basically provided a water plenum at each face, which would vastly simplify the plumbing problems.  All well and good for the relatively low temperatures and pressures for which the concept was developed.  But when civilian nuclear power was first explored, the Hanford group proposed using the perfected "water wall" design to make commercial electricity -- all you had to do was to raise the temperature and pressure of the water to the point where the effluent could be used to produce power in a turbine.  This large change in parameters, in fact, would cause enormous changes in the interaction between the materials used and the coolant water and the whole mechanical design of the "water wall" would become a high-pressure impossibility.  Good engineering design is a compromise between the various restraints.  You cannot simply keep such a design intact when large changes are made in the conditions and restraints of the system.


Even in the world of physics, the fundamental characteristics of nature change when the scale factors change by enough.  At very small (particle) dimensions or extremely low temperatures, quantum effects become important.  At very large (cosmic) dimensions general relativity becomes important.  Pity then the poor cosmologist who is stuck with extrapolating his or her theories across tens of orders of magnitude from our ability to measure.  Will the theories provide any modicum of reality after such enormous changes?  In cosmology we have no choice but to proceed anyway, finding direct or indirect experimental confirmation as best we can.  But we need to be nervous about the vast extrapolations being made and their potential consequences.


Be alert to when parameters in your projects change by large amounts.  Everything probably changes with that parameter, whether or not it is intended or desired.  Be careful to re-assess all your assumptions in the new conditions to be sure that something sensible is still being attempted.