I am curious as to how Google's calculator worked. In particular, I am curious as to how they compute e^{n*pi*i}, as it is not immediately obvious how to compute it.

Clearly, e^{n*pi*i} = (e^{pi*i})^{n} = (-1)^{n} = +/-1. But what happens when we make n large?
For n=1 (and 2,3), Google returns -1
For n=4, we start seeing discrepencies on order of 10^-15
For larger n, the discrepencies grow

Notice that it is only the imaginary part of the result which is in error.
posted by Ben at 11:44 AM

Postcards from 1401 N. Shoreline Blvd, Mountain View, CA, 94043
posted by Ben at 11:13 AM

an impromptu Decemberfest

My friend Andy lives near Draegers, and so when I visited him this weekend we chose to stop in Draegers, as I have never been in it before.

It turns out that in addition to fancy glasswares, wines, truffles, and pates, Draegers has a fine selection of beers. I said "bring up the shopping cart" and dawdled for awhile, deciding what to not buy. Eventually I ended up buying eight beers.

Maresdous
Morimoto's Soba Ale, reviewed in this space recently
Delirium Nocturne
Allagash White
Bagel Beer Poppy
Unibroue Terrible, Trois Pistoles, and Blanche de Chambly

Of these eight, the Maresdous was gifted to Andy, and Morimotos was reviewed in this space recently. That evening, I was with my friends Jon, Glenn, and Chandra in The City, and we declared an impromptu Decemberfest.

We consumed three of those beers. We started with the Babel beer. It was thick and somewhat sweet. Good, but only in small doses. The obligatory joke about it being topologically equivalent to coffee cup beer was made.

We moved on to the Allagash. I had high hopes for this, as it was advertised as being brewed with orange peels and coriander. I was disappointed. It was too close to lager on the beer spectrum, and the carbonation overcame any flavor.

We finished with the Terrible. This was excellent, very rich and a very dark flavor. Despite being the last bottle opened, it was the first bottle finished.
posted by Ben at 10:20 AM

Morimoto's Roasted Soba Signature Ale

On my (details forthcoming) trip up to SF this weekend I bought some beer. One of the beers bore Morimoto's likeness and signature, and was advertised as made with roasted soba. Soba, for the purpose of background information, is a Japanese grain related to buckwheat, usually encountared in the form of noodles.

I just drank this beer. It had a crisp, bitter flavor which at this stage of my beer education I attributed to hops. So, let us say it has a strong hops flavor. The carbonation was fairly strong. I did not taste any soba in it, but I have not had soba noodles in some time.

Overall, a good beverage, though given my tastes in beer, I would spend my money on other beers and get this sheerly for the celebrity value.
posted by Ben at 10:20 PM