Midtrip: Saratoga Springs & some geometry

It is, or it was, mid-trip (my record tend to lag a week behind the flow of the moment). I came back to Saratoga Springs last Saturday night. Came back – because Saratoga is one of the 5 places on Earth that I think of as home. Of all the small towns in America that I have seen – well it’s simply the best. Precisely the right size, lots of nice shops, bars & restaurants & places downtown on Broadway & the small back streets. You can actually spend a few days exploring it. No surrounding suburban sprawl to speak of. Instead the residential areas with very beautiful houses is close to downtown. The town seemed even livelier now than in 2004, but it is not touristy at all (except in August – I’m told – with the horse-races). The shopping mall outside town is also friendly with a Barnes & Nobles you can go to and read magazines over a coffee.

Regrettably the Borders bookshop on Broadway has closed down (as all Borders I think) but a new bookshop is going to open on the other side of the street. This I find strange. If Borders had to close because of competition with net-shopping, why would a new bookshop fare better? And why not move into the empty Borders house?

Speaking about book-shops, there is an incredible antiquarian bookshop in town – it’s called “The Lyrical Ballad”. You move deeper and deeper into the house into room after room all filled with books in no particular order that I can discern.

Driving up from Philadelphia the immensity of the Appalachian mountains struck me. This is a part of the country I’ve never been to before. You don’t need much imagination to see that this mountainous wilderness was a barrier to west-ward settlement. It must also have been a barrier for the east-moving native colonizers of America too. I read somewhere that the eastern seaboard may not have been inhabited for that long when the ships from good old England arrived. What would have happened if history in Europe had been delayed by 500 years? Perhaps I wouldn’t be writing these words just now. Counterfactual history. Anyway, at the Lyrical Ballad I found a book about the Wilderness Road – the road through the mountains taken by the first west-ward immigrants.

I met friends from 2004: Sarah Goodwin, Steve Goodwin, Bob DeSieno, Mark Huibregtse and people I did not knew that well then and also made a few new acquaintances.

As you may suspect, I spent most of the time in Saratoga hollydaying (apart from two days in Bennington) but I did give a seminar on Thursday and on Friday I went to Mark’s First Year Seminar. What a F.Y.S (or first year experience) is, is well-known in America, but for Swedish readers here’s a short description: Most Liberal Arts colleges have what they call First Year Experience (or Seminar, or …) for the new students. Apart from a general introduction to college life and studies and a socialization experience, it is also aimed at introducing the students to the particular characteristics of a liberal education. Various seminars are offered centered on various subjects, among them mathematics.

The seminar run by Mark is focused on Geometry. The students read Euclid (at the moment the first book). There is an on-line edition with interactive pictures that is used in the seminar.

To Swedish ears this must sound incredible. Too many it may also sound as a complete waste of time. I mean, Euclid, isn’t that 2500 years old stuff? And I admit, I sat down a little prejudiced because I’ve never really liked geometry myself – in particular that type of “synthetic” geometry.

But amazingly it worked! Even I understood the proofs and the general drift of the argument: From working with parallelograms and proving theorems on areas – over the 5:th (parallel) postulate – to an elegant proof of the Pythagorean theorem. And the humanistic aspects of mathematics are there too, as Mark pointed out. It’s there in the comment that the Greeks did not have the real numbers and so no quantitative measure of areas, it’s there in the comment that some areas (lengths really) could not be sized up by the only numbers the Greek knew about (the natural numbers), it’s there in one aspect of mathematics that is often so hard to communicate: the logical character of the subject.

From this class I went away with the happy realization that studying Euclid is not at all useless. Here the strength of the liberal arts context shone through.

… and many thoughts about what we should choose for contents in our courses …

Later in the day, as I walked down Nelson Avenue I ran into Bob again (he lives on that street) so we had occasion to chat a little more and I met his wife. Then I strolled downtown to photograph houses and do some shopping. It was Friday night and I got 2 beers for the prize of 1, but my watch had stopped at 4 pm and I had to rush home to be in time for the nights dinner party.

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