Julia- Thanks (sort of) for bringing this dispute to our attention. I just did a first skim of the paper whose URL you provided and of the paper it was critiquing. I haven't yet noticed the point where we get quoted. My first general impression is that the arguments on both sides are far too long and complicated. We take a sort of common-sense practical intermediate position.
So let me try to make our view clear for all your colleagues. It is sloppy to use dimensional quantities in the argument of a log function. In real life, we all get sloppy sometimes yet still survive. So long as there's a point at which the difference
of two such sloppy logs will be taken, as in a time derivative, no harm is done. We get away with precisely such slop in elementary statistical physics. (See Boltzmann's tomb.) Sometimes even an implicit understanding of what the natural units are might make it sort of ok. Other times one is left with useless pseudo-equations.
BTW, it was interesting to see it mentioned that there are papers going back to at least 1960 in which people noted that Marx's comparisons of rates of income and amounts of capital are dimensional nonsense. I'd wondered if anybody else had noticed. That would be an example in which repairing the equations to the point where the argument could even be evaluated would require adding some whole new line of argument, e.g. setting some characteristic time scale such as a human lifetime.
So again, there are points where dimensional errors make arguments worthless and other points where they are really only temporary lapses in notation on the way to a sound argument. Your colleagues don't seem to be "seriously deluded" but rather seem to be slightly over-reacting to some of the real errors that have been made.
(published on 02/16/12)