Dublin is one of the nicer places I've been to. I found its occupants
to be warm, friendly, helpful, and extremely proud of their city, as well
as knowledgeable of its history and attractions. The friendly people
at the hotel where I was staying (no fewer than three were at the front
desk chatting amongst themselves at any given time) told us that if there's
anything we wanted to see, just let them know and they'd explain how to
get there. And indeed, they had an encyclopedic knowledge of the place.

Now, Dublin is one of the few cities I know (besides Königsberg*)
to have a genuine *math tourist attraction*, or at least one that
isn't on the campus of a university in the town (e.g. both Cambridges,
Princeton, etc). Now be warned that if you're not a mathematician
of some ilk, this is probably frightfully boring stuff, and even many of
you who know the math are going to be amazed that anyone could be interested in seeing such a thing. But hear me
out.

Dublin was the home of Sir William Rowan Hamilton, 1805-1865, a professor
at Trinity College and one of the most famous Irish mathematicians.
He had a fascinating, somewhat tragic life, but is most remembered for
thinking up quaternions, which are a noncommutative algebra of triples
(and the first noncommutative algebra discovered). Hamilton was the first
person to consider complex numbers as an algebra of ordered pairs, and
he was stymied that no such algebra seemed to exist for triples. Since physicists
need to do physics in 3-space (and later 4-space!) it would be incredibly
useful.

One October morning in 1843 he was walking along the Royal Canal (not
the best area of Dublin then, or now) with his wife when he had a eureka
moment, and everything came together. He realized that everything would
work if he admitted a *fourth* dimension in the multiplication of triples.
He was so excited that he carved the result into Brougham Bridge, which
they had just passed:

**i**^{2} = j^{2} = k^{2} = i j k = -1

This is the multiplication equation for quaternions the way i^{2} = -1
is the the equation for complex numbers; a quaternion is in the form ai
+ bj + ck +d, where a,b,c and d are reals. They actually have lots of different
formulations, which really belong in their own node.

Once he had presented this to the academy they were so impressed that
the mayor of Dublin had a stone plaque erected on the bridge which reads:
"Here as he walked by on the 16th of October 1843 Sir William Rowan
Hamilton in a flash of genius discovered the fundamental formula for quaternion
multiplication **i**^{2} = j^{2} = k^{2} = i j k = -1 he cut (?) on a stone
of this bridge" (The (?) part is worn and hard to make out.)

I had to go see it. It happened *right there*, and how many other
things can you say that about? But I remembered it was there only after
we arrived, and I didn't know the bridge name. I tried asking at the hotel,
but only one of them had even vaguely heard of Hamilton, much less the plaque.
Fortunately, two pints of Guinness and one trip to an internet cafe
later I had the answer. (Note: if you try this yourself, remember that "Brougham"
is pronounced "broom". Welcome to Ireland.) Both my jovial hotel
managers and the taxi driver that took me there were absolutely floored
by this. They did not know which was hardest to believe: that there was
a famous mathematician from Dublin that they had never heard of, that there
was a tourist attraction they didn't know about, or that an American vacationing
in Dublin would actually want to see it. The taxi driver was extremely enthusiastic
and insisted on seeing the plaque himself (it's a small stone bridge,
and you have to climb down under the bridge next to the canal to see it).
Afterwords he couldn't stop talking about it.

So if you're ever in Ireland, you too can see the least-visited tourist
attraction in Dublin. You'll also make a taxi driver's day.

*Euler developed parts of graph theory out of wondering why it seemed
impossible to tour the city crossing all seven bridges of Königsberg exactly once.