(04 August 1805 - 02 September 1865)
One of the most significant Irish scientists, William Rowan Hamilton
made noteworthy contributions in the field of classical mechanics,
algebra and optics. What is interesting to note is that Hamilton, from
the tender age of five, showed signs of making it big in the world. His
immense talent was appropriately nutured right from the very beginning,
which further enhanced his capabilities. While Hamilton is known to have
contributed in various fields, it is his work in the reformulation of
Newtonian mechanics, now called Hamiltonian mechanics, that tops the
list. This work proves to be the foundation of the modern study of
classical field theories such as electromagnetism, and to the
development of quantum mechanics. To know more about this inventor of
quaternions, read through these following lines
Early Life
Fourth of the nine children of Sarah Hutton and
Archibald Hamilton, young William Hamilton was born in Dublin, Ireland.
His father, a solicitor by profession, was mostly touring England
practising legal business. As such, he had little or no time to teach
young Hamilton. It was due to this reason that William Hamilton, at the
age of three, was sent to live with his uncle James Hamilton. A graduate
from the Trinity College, his uncle ran a school in Talbots Castle.
Young Hamilton displayed signs of being a fast learner right from the
very childhood. By the age of five, he had learned three languages
including, Latin, Greek and Hebrew and before 12, he broadened his
knowledge in various other languages, such as Arabic, Sanskrit, Persian,
Syriac, French, and Italian. While until then, languages seemed to be
the only love of Hamilton, it was a meeting with Zerah Colburn that
altered the passion. Colburn, who was a master at mental arithmetic,
competed with Hamilton and emerged as the winner. Not used to being
beaten in any contest of intellect, this defeat sparked in Hamilton an
interest in mathematics and rest as they is history.
Introduction To Mathematics
Hamilton’s formal introduction to mathematics
came the following year, in 1818, when he studied Clairaut’s Algebra.
His mastery over French made it somewhat easier for him to understand
the concept. By the age of fifteen, he started studying the works of
Newton and Laplace. During this time, Hamilton was also involved in
preparations for entrance at the Trinity College, Dublin. At the age of
18, Hamilton found himself a seat at the Trinity College and in his very
first year, acquired ‘optime’ in Classics, a distinction awarded only
once in twenty years. Hamilton submitted his first paper to the Royal
Irish Academy in the year 1824, entitled, On Caustics. His progress
somewhat declined the following year, with him earning grade ‘bene’
instead of the usual ‘value bene’. However, Hamilton soon bucked up and
in 1826, again amazed everyone by bagging an 'optime' in both science
and Classics, a feat unheard of. In the final year as an undergraduate,
Hamilton presented a memoir, Theory of Systems of Rays, to the Royal
Irish Academy. It was in this paper that Hamilton introduced the
characteristic function for optics.
His Trysts
During this time, the post of Andrews
Professorship of Astronomy was vacant in the University of Dublin. Under
the persuasion of Boyton, Hamilton’s finals examiner, the latter
applied for the position, in spite of knowing that already six
applicants had applied for the vacancy. In 1827, a little prior to his
graduation, Hamilton was offered the position of Professor of Astronomy.
This appointment not only meant Hamilton having the honorary title,
Royal Astronomer of Ireland, but also allowing him the benefit of
staying at the Dunsink Observatory. However, this selection invited a
great deal of criticism and controversy, since Hamilton did not have
much experience in the field.
Hamilton’s predecessor, Dr. Brinkley, pointed
out the fact that Hamilton’s decision was incorrect and that he should
have waited for a fellowship. Hamilton’s newest acquisition of the chair
of professorship, however, did not upgrade his level of intellect much.
This was due to the fact that although Hamilton had insightful
knowledge of theoretical astronomy, he had little or no knowledge of the
regular work of the practical astronomers. Also, Hamilton had a belief
that he could do wonders in the field of research than being engaged in
observation. The authorities of the university, however, thought
otherwise. If Hamilton dedicated himself thoroughly to practical
astronomy, they assured to provide him with the best and the most
advanced of instruments and adequate staff members.
His Contributions in Optics & Mechanics
The same year, i.e. in 1827, Hamilton presented a
theory of a single function, now known as Hamilton's principal
function. The theory brought together mechanics, optics and mathematics,
thus helping establish the wave theory of light. The Royal Irish
Academy paper was entitled Theory of Systems of Rays, with the first
part being printed in 1828 in the Transactions of the Royal Irish
Academy. The second and the third part were printed in three voluminous
supplements, which were published in Transactions as well as in the two
papers On a General Method in Dynamics, which appeared in the
Philosophical Transactions in 1834 and 1835. it was in these editions
that Hamilton’s formulation of the concept of “Varying Action” was
mentioned. According to this theory, a single ray of light entering a
biaxial crystal at a certain angle emerged as a hollow cone of rays.
This breakthrough is still known by its original name, "conical
refraction".
One thing that was common in all Hamilton’s
research was that they were, somehow or the other, based on the
principle of “Varying Action”. While the principle is based on the
calculus of variation, it, however, revealed a detailed mathematical
structure than that had been previously understood. Though Hamilton’s
take on classical mechanics is based on the same physical principles of
Newton and Lagrange, it provides a powerful new technique for working
with the equations of motion. Both Lagrangian and Hamiltonian approaches
were initially developed to describe the motion of discrete systems and
have proven to be critical in the study of continuous classical systems
in physics, and even quantum mechanical systems. As such, the
techniques are still in use in electromagnetism, quantum mechanics,
quantum relativity theory, and quantum field theory.
His Contributions in Quaternions
Hamilton’s another greatest contribution in the
field of mathematical science was his discovery of quaternions in 1843.
In this, Hamilton was looking for ways to extend complex numbers to
higher spatial dimensions. While he failed to successfully find a
three-dimensional system, he effectively created the four-dimensional
system, wherein which he created quaternions. Interestingly, Hamilton’s
formulation of the equation came when he was walking with his wife along
the Royal canal. Fearing that he might forget the equation by the time
he got back home, he carved the same into the side of the nearby Broom
Bridge, using his penknife. This marked the discovery of the quaternion
group.
Hamilton described a quaternion as an ordered
four-element multiple of real numbers, and described the first element
as the 'scalar' part, and the remaining three as the 'vector' part. As a
method of analysis, Hamilton introduced both quaternions and
biquaternions, as the extension to eight dimensions by establishment of
complex number coefficients. Hamilton had declared that the quaternions
would play a pivotal role as an instrument of research. During his end
days, Hamilton was working on a definitive statement of quaternion
science. Posthumously, his son published Elements of Quaternions, a
hefty volume of 762 pages, in 1866. Today, the quaternions are used in
computer graphics, control theory, signal processing, and orbital
mechanics, mainly for representing rotations/orientations.
Personal Life
The journey to Summerhill in 1824 along with
uncle James was an important one in the personal life of Hamilton, for
it was there that Hamilton first met Catherine, daughter of the Disney
family, which the two were visiting. Hamilton was instantly struck with
the cupid’s arrow and fell head over heels in love with the lady.
However, since he was too young to propose marriage, he returned without
saying anything. Year 1825’s month of February wasn’t a very favorable
one for Hamilton as it was then that Catherine’s mother broke the news
of Catherine’s marriage to a clergyman. Hamilton was deeply hurt. The
turmoil in his personal life affected his career as well. What’s more,
Hamilton even had suicidal thoughts occurring to him. It was during this
period that Hamilton turned to poetry as a means of letting out his
anguish. Hamilton was so much in love with Catherine that for him, it
did not later matter whom he married. As a result, he tied the nuptial
knot with Helen Maria Bayly who lived just across the fields from the
observatory. The couple had a son named, William Edward Hamilton.
Death & Legacy
A severe attack of gouttook the life of Sir
William Rowan Hamilton on September 2, 1865. This attack was the result
of his excessive drinking and overeating. Hamilton was interred at the
Mount Jerome Cemetery in Dublin. Recognized one amongst Ireland’s
leading scientists, Hamilton is being increasingly celebrated year after
year for his groundbreaking discoveries. For the same, he has been
honored in a number of ways. An applied mathematics research institute,
in the name Hamilton Institute, was formulated at NUI Maynooth in the
year 2001. Ireland’s Royal Irish Academy also holds an annual public
lecture by the name Hamilton lecture at which celebrated scientists from
around the world take part in. The RCSI Hamilton Society was founded in
the year 2004.
Year 2005 marked the 200th anniversary of Sir William
Rowan Hamilton. As such, it was celebrated with great pomp and show.
While the Irish government designated the year as Hamilton Year,
celebrating Irish science, Trinity College Dublin commemorated the
contribution made by this prolific scientist by launching the Hamilton
Mathematics Institute TCD. In the same year, the Central Bank of Ireland
issued a commemorative coin. Numerous concepts and objects in mechanics
have been given the name of Hamilton. The term Hamiltonian stands for
both, a function and an operator in physics. The algebra of quaternions
is mostly denoted by the letter H, to honor the contributions made by
Hamilton.
