Quaternions
On 16th of October 1843, a bright October day, Sir William Rowan Hamilton discovered the numbers later
called Quaternions.
He had been trying to find a satisfactory way to multiply three dimensional points
for several years, in such a way as to allow division.
The gordian knot was battered when the idea of using four
dimensions instead of three came into his mind, as he walked
with his wife by the Royal Canal. Because this incident is precisely located in
time and place, the event now is
very well-known in the international mathematical community, and people from all
over the world know about "Hamilton's Bridge". When he made the discovery,
Hamilton was resting under the Brougham (or Broom) Bridge, so he took out his penknife, and
scratched the fundamental formula:
i2 = j2 = k2 = ijk = -1
into the stone right there. No trace of this can be
found today, but in 1958 a commemorative plaque was erected reminding the
discovery and showing the formula.
In the theory which Sir William Hamilton present to the Academy a few weeks later in November,
1843, the term quaternion was used to name a certain quadrinomial
expression, of which one part was called (by analogy to ordinary
algebra) the real part, while the three other parts made up together a
trinomial, which (by the same analogy) was called the imaginary part of the
quaternion. The square of the former part being always a positive, but
the square of the latter part (or trinomial) being always a negative quantity.
This incident might be as outstanding as Archimedes' discovery
while bathing, or Poincare's while stepping off a bus. The Royal Canal
and the Bridge are still existing and tangible, this makes the
scene so well imaginable, and let mathematicians of all times pilgrim to
Broom Bridge.
