Archive for February, 2007

Crackpots, teaching, and open access to knowledge

February 26, 2007

As a future math teacher there are quite a few issues I am thinking about these days. One of them is “crackpots”. Academic outcasts if you prefer. The point I’m going to develop is that a person may evolve into a crackpot not because of lack of intelligence or self-criticism, but more because of lack of knowledge — or more precisely of guidance to acquire knowledge.

Let’s start from the beginning. We’ve all read papers which contained serious errors. This can happen even to the best minds (think Poincaré and the discovery of chaos). So as long as there is later recognition that the idea was wrong, and if it happens only a few times in a career, there’s no problem.

Less often, but still often enough, one encounters what can be called ‘a bold claim’. Again nothing wrong with this if it is acknowledged as such and thrown out only in an attempt to stimulate the reader’s imagination or to justify an otherwise perfectly rigorous definition.

Then there’s the issue of expository style. That’s usually when one starts viewing a paper as crackpotish. But there are many aspects here, and one needs to be careful. John Baez has a semi-serious crackpot index which does a good job at pointing out the kinds of behaviour that usually occur. Most of them are well-taken. My point is that some perfectly sane people could yet have a fairly high such index due to a succession of misunderstandings.

When I was in high school, I naively thought that papers published in La Recherche (roughly similar to American Scientist) were very technical. I then heard about Nature as being a “professional publication”, but could not find it at the local newsagent and felt puzzled. Now suppose I had left high school and instead of going on at the university I had opted for some two-year professional course and found a job. At that point my view of science as it is actually done was completely flawed: papers written in discursive style with very few equations, bigger fonts to emphasize the main arguments, and so on. I’m not sure I might not have turned into a crackpot myself in that case, for example plotting some graph related to prime numbers like those seen in La Recherche and starting to believe that I had done work on-par with these researchers!

Of course these days there’s the internet. But what may still be lacking is a less flawed presentation of actual research results in the media, and in the classroom. That’s something I’d like to test next year with a class.

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Archeological news

February 25, 2007

In case you don’t know already, great places to learn about recent discoveries are this page over at archeology.org, and this one from archaelogica.org.

I’ve been dreaming for a while that one day perhaps copies of some of the texts that have disappeared at Alexandria will be found, say hidden in a jar or as still-decypherable burried burnt scrolls

A small LaTeX try

February 24, 2007

Let’s use a little \LaTeX. First a few sentences with inline code: suppose I’d like to talk about a manifold \mathcal C and its cotangent bundle T^*\mathcal C. But in fact its a very simple case, namely \mathbb{R}^ {2n}. And now consider the Schrödinger equation for a wavefunction \psi defined on \mathcal C, that is E \psi=-\frac{\hbar^2}{2m}\Delta \psi + V\cdot \psi. At this point all the \LaTeX should have been embedded in the text. And now here’s a displayed equation: $A \otimes B \cong C$. Ok that last bit must be centered manually it seems, but so far so good!

Once upon a time…

February 24, 2007

I’m beginning a blog here at WordPress.com in part because of its apparently nice LaTeX support; we’ll see how it goes.

Topics to be discussed here: sightseing across the globe, sciences (maths, archeology, neurosciences, etc.) and arts (composers, museums, etc.).

Don’t expect too much at this point. Also, frequency of postings is undefined for now.