By J. H. Saltzer
February 8, 1996; minor revisions, January 17, 1997 and January 30, 1998. Most of the material that was originally in this sidebar moved to chapter 1 in the revision of January 2001.

After reading the first chapter and hearing the first lecture, most students will have the term "incommensurate scaling" in their vocabulary, but some may have the wrong definition for it. It is worth asking the class to provide a definition. Usually someone will start by saying something like "when systems get bigger they get more complex." (This statement is correct, but it is the answer to a different question.) With some leading you should be able to get the class to produce a moderately fuzzy "when you increase the size of a system, not all parts grow at the same rate."

But the discussion can profitably be carried somewhat farther. One can ask what concept from 6.004 (and 6.001, though not many will remember it) is related. The answer is "orders of growth". Now one can ask for a more precise definition of incommensurate scaling in terms of the 6.004 concept: Different parts of a system exhibit different orders of growth.

You can scale a mouse up to the size of a rat; why does that work? (A factor of two or three may be small enough that adjustments in the coefficients can compensate for the different orders of growth.)

Now, starting with examples in Chapter 1, ask the class for other examples of incommensurate scaling in action.