Reading a friends blog, I find reference to Conservapedia (there should really be a
"context" attribute of the html anchor tag; that way one could link to examples of stupidity without floating the page rank), a
reaction to wikipedia's liberal bent. What liberal bent?. Anybody can add points and topics to wikipedia via a community driven
process. It's open and inclusive. As such, the point of conservapedia must be more about exclusion: a place where conservatives
can find opinions and information without any pesky conflicting points being raised. Enabling ignorance seems like an odd mission
statement to me but, if that's how they want to use their time, let them. Reading more of my friends posting and of the web site
itself, I find that one of their issues with wikipedia seems to involve mathematics:
Wikipedia has many entries on mathematical concepts, but lacked any entry on the basic concept of an elementary proof
until this omission was pointed out here. Elementary proofs require a rigor lacking in many mathematical claims promoted on
Wikipedia.
A mathematical response is available at Good Math, Bad Math.
Initially I thought "Good grief! Does all rational thought annoy the social conservatives?". Ok, I knew that they are angry
at biology because they don't like evolution. Initially, the anger was over natural selection and the idea that the inherent
randomness was an affront to a God's plan (perhaps if they had known of the Law of large numbers it would have been ok); Lamarckian was ok. Later, the diversification of species and
initial formation of life became the sticky points. Most recently I hear people refuting evolution itself which I find amusing as
it is both directly observable and fairly obvious once it's pointed out... oh well. I knew that some conservatives were angry at
physics for such areas as cosmology and quantum mechanics. I even knew that they were angry at the field of statistics for poking
enormous holes in many of their theories. But pure math... how could anybody object?
Thinking about it a bit more, however, it occurs to me that there is a bit of a history of such uncomfortable interactions
between mathematics and social thought. Georg Cantor's work on the
transinfinite caused a great social and theological stir; indeed Cantor was greatly concerned with these issues himself. Gauss,
it seems, had thought about non-Euclidean geometries but was concerned about the theological implications so did not publish the
work. Goedel's work on incompleteness and Turing's on the halting problem both caused significant philosophical turmoil
both inside the mathematical community and outside of it. The idea that some numbers are irrational greatly bothered the greeks.
Mathematical problems in the Bible (pi equals three) or the Koran
(inconsistent inheritance rules) lead some to argue that they cannot be divine
documents.
In each of these cases, mathematical thinking challenged beliefs people held about the universe. Is this somehow the case with
the conservatives and complex numbers? I suppose that the very ideas of abstraction and subtlety are anathemas to fundamentalism
but I am not sure that this is the issue here. In any case, I am reasonably confident that complex numbers are not part of a
liberal conspiracy. Then again google tells me that there are 45,600 pages mentioning both the quaternions and communism (soon 45,601?). Who would have guessed?
I recently read an interesting series of discussions, pointed to from
metafilter, about whether .9 repeating equals 1 (it does). At times, the threads took on almost religious aspects. I would
have liked to ask many of the participants "What do you think the real numbers are? How do you define them? Do they somehow
correspond to the space that we live in?" For the last question, at least, I personally would be happy to have a better answer
than I currently do (where does Plank's constant fit in).
We commonly have a sense of familiarity with the real numbers that isn't quite justified. The notion of incomputable number is kind of upsetting, that
most real numbers are incomputable is yet more upsetting, and that it has physical implications is enough to drive one batty. There is
also the belief that the passage from integers to rationals to reals is the only way one can do things.... whoops!. Finally, and despite the terminology, the real numbers are not
comparatively more simple nor the complex numbers comparatively less real.
In some distant way, it reminds me a bit of a group of French (ha!) mathematicians, Association des collaborateurs de Nicolas Bourbaki, who wanted to reduce
all of mathematics to set theory. Thus the two groups have in common that they wish mathematics to be reduced down to
primitives. The main difference between the two groups is that the members of Bourbaki were great mathematicians who had a
profound understanding what they were talking about; far from wishing to limit the roles of abstraction, they wished to make it
stronger, unassailable. Regarding conservapedia, I am bewildered.
What's the point in all of this? I just wanted to offer some historical instances of interactions between social and
mathematical thought. History has shown that when one finds instances where the two are incompatible, it is time for social
thought to evolve. All things said and done, I suspect that wikipedia will continue to be the more useful source of
information.
