[FOM] Knowledge - quantity/quality

Harvey Friedman friedman at math.ohio-state.edu
Sat Jan 24 05:14:58 EST 2004

I have been looking at

Charles Singer, A short history of scientific ideas to 1900, Oxford
University Press, 1959.

In particular I am looking at

IX. Culmination of the mechanical view of the world, 1850-1900.

I read there about how the physicists felt that there are purely mechanical
explanations of all sorts of phenomena, and they were desperately trying to
give such explanations, but coming up against brick walls.

I regard these efforts to explain the behavior of light, electricity,
magnetism, etc., as physics.

So the major figures were having great difficulties carrying out their
programs in physics.

This is still true today. I choose to emphasize this similarity. For some
reason, others choose to emphasizes differences.

Would Hilbert have written something like Problem #6 today?

I don't think that there is any question about it. Of course, he would
mention some additional physics that is even more mysterious.

Recall that I wrote in my posting of 1/21/04 5:50PM

>1) major clarifying foundations for even elementary quantum mechanics is
>probably hopeless until we get a far better grip on the foundations of less
>mysterious physics;

>2) in fact, we don't even have a good enough idea as to what foundations of
>physical science should or could look like, in the first place.

I submit that Hilbert would substantially agree with this.


I would like to comment briefly on two aspects of knowledge: quantity and

Of course quantity and quality are both vitally important.

However, it is clear that in science, quantity runs far ahead of quality.

I am not moved even by what is generally regarded as major scientific
events, if the underlying quality of knowledge surrounding it is poor. I am
deeply suspicious of knowledge without accompanying high quality.

At a more subtle level, I also take this view about mathematics. Of course,
in a sense, the quality of knowledge in mathematics is incomparably beyond
what it is outside mathematics. But... And this moves us into foundational
exposition - a matter for another posting.

Back to quality outside mathematics.

The quest for quality has nothing to do with "tidying up" or "bookkeeping",
despite what some who have no appreciation/understanding/familiarity with
quality say. 

I strongly believe that the systematic quest for quality will have enormous
consequences not only for its own sake, but also for its facilitation of the
quest for quantity.

The above statement is, of course, heavily controversial, because systematic
quest for quality (putting f.o.m. aside) has not really begun in earnest -
certainly not by a sufficient number of people.

But WELL BEFORE the systematic quest for quality takes hold sufficiently to
substantially impact the quest for quantity, it will have the following
profoundly important consequences:

1. There will be a huge increase in the number of people who seriously
understand substantial aspects of the subjects dealt with, than before the
relevant quest for quality got going.

2. Let X be a subject so affected. Researchers in subjects close to X will
gain such a better understanding of X that they will be able to connect some
of their ideas with ideas in X. There will be a major increase in the level
of productive interdisciplinary activity, leading, indirectly, to major help
in the quest for quantity.

Harvey Friedman


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