[Scl] Comments on the style of the SCL document

[John F. Sowa]

After I responded to Pat's comment, I thought about
something John von Neumann once said, which applies
very well to the style of the JSL and the current
SCL document.

John
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As a mathematical discipline travels far from its empirical source, or 
still more, if it is a second and third generation only indirectly 
inspired from ideas coming from 'reality', it is beset with very grave 
dangers. It becomes more and more purely aestheticizing, more and more 
purely l'art pour l'art. This need not be bad, if the field is 
surrounded by correlated subjects, which still have closer empirical 
connections, or if the discipline is under the influence of men with an 
exceptionally well-developed taste.

But there is a grave danger that the subject will develop along the line 
of least resistance, that the stream, so far from its source, will 
separate into a multitude of insignificant branches, and that the 
discipline will become a disorganized mass of details and complexities.

In other words, at a great distance from its empirical source, or after 
much 'abstract' inbreeding, a mathematical subject is in danger of 
degeneration. At the inception the style is usually classical; when it 
shows signs of becoming baroque the danger signal is up. It would be 
easy to give examples, to trace specific evolutions into the baroque and 
the very high baroque, but this would be too technical.

In any event, whenever this stage is reached, the only remedy seems to 
me to be the rejuvenating return to the source: the reinjection of more 
or less directly empirical ideas. I am convinced that this is a 
necessary condition to conserve the freshness and the vitality of the 
subject, and that this will remain so in the future.

John von Neumann, from "The Mathematician"