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In "A History of Vector Analysis" by Michael J. Crowe
(Dover Books, ISBN 0-486-67910-1) we find an
interesting chronology worthy of note.
The struggle by William Rowan Hamilton and James Clerk
Maxwell to have their 4-dimensional algebraic representation
of EM theory accepted is singular indeed.
The opposition:
Lord Kelvin
Oliver Heaviside
Josiah Willard Gibbs
The fight:
1840 - 1900
Brutal professional spats, the loggerheads arguing that
if you can't boil it down to 3vectors - you need a shrink.
Hamilton had concluded that no system of closed algebra
for 3-space existed. His discovery ii = jj = kk = ijk is
one of the most remarkable in history, and perhaps never
has so much mathematical literature simply been scuttled
by those afraid to associate with heretics like Hamilton
and Maxwell. (The topic was dead and off-limits by 1900)
The immediate result:
Quaternion product broken into 'dot' and 'cross' products
Quaternion field flux broken into 'divergence' and 'curl'
(Note the sign reversal, Hamilton/Maxwell argued for 'convergence')
Hamilton frustrated, hazed, isolated. Maxwell disgusted.
Indeed it may have been Oliver Heaviside who 'para-phrased' Maxwell's
deeper theory into four equations with greatly complicated algebra
(in the name simplifying it)
The long term result:
Not until the 1990's was it discovered that the Pauli Exclusion
Matrices of Quantum Mechanics were one and the same as Hamilton's
quaternions.
Also in the 1990's a seminal work, "Clifford Algebra and Spinors"
by Perti Lounesto (London Mathematical Society, Lecture Note Series 239,
Cambridge University Press) revealed the connection between Clifford
Algebra, the bivector, and the Quaternion Group. This forms the basis
for a more complete theory of Classical EM.
100 years of obfuscation. Also, the key work: Hamilton's "Elements of
Quaternions" (both editions) proves nearly impossible to acquire.
100 years with matrix "rack-o-math" hegemony.
Interesting side notes:
Much of this occurred under auspices of Yale at a time when the roving
eye of mass media was poorly understood.
The contributions of Kelvin to Thermodynamics reveals he had very deep
understanding, his two water jet experiment (static generator) notable.
But he missed a crucial connection (heat is cathodic).
"Gibbs Free Energy" bears a name which will live him down in infamy if
he is ever determined to have been involved in work that hid truths.
The point of this post:
All of these honorable men in our history are presented as heroes and
angels and pauper survivors as we idealize them. But if EM theory was
indeed corrupted to keep us in the pen as "The Wave" certainly implies,
then this corruption and its form certainly are on exhibit here for all
to see. How many of these three were S&B? Can the moods and attitudes
of this struggle provide us today with an archetype of a smear campaign?
Maybe ...
Any thoughts?
(Dover Books, ISBN 0-486-67910-1) we find an
interesting chronology worthy of note.
The struggle by William Rowan Hamilton and James Clerk
Maxwell to have their 4-dimensional algebraic representation
of EM theory accepted is singular indeed.
The opposition:
Lord Kelvin
Oliver Heaviside
Josiah Willard Gibbs
The fight:
1840 - 1900
Brutal professional spats, the loggerheads arguing that
if you can't boil it down to 3vectors - you need a shrink.
Hamilton had concluded that no system of closed algebra
for 3-space existed. His discovery ii = jj = kk = ijk is
one of the most remarkable in history, and perhaps never
has so much mathematical literature simply been scuttled
by those afraid to associate with heretics like Hamilton
and Maxwell. (The topic was dead and off-limits by 1900)
The immediate result:
Quaternion product broken into 'dot' and 'cross' products
Quaternion field flux broken into 'divergence' and 'curl'
(Note the sign reversal, Hamilton/Maxwell argued for 'convergence')
Hamilton frustrated, hazed, isolated. Maxwell disgusted.
Indeed it may have been Oliver Heaviside who 'para-phrased' Maxwell's
deeper theory into four equations with greatly complicated algebra
(in the name simplifying it)
The long term result:
Not until the 1990's was it discovered that the Pauli Exclusion
Matrices of Quantum Mechanics were one and the same as Hamilton's
quaternions.
Also in the 1990's a seminal work, "Clifford Algebra and Spinors"
by Perti Lounesto (London Mathematical Society, Lecture Note Series 239,
Cambridge University Press) revealed the connection between Clifford
Algebra, the bivector, and the Quaternion Group. This forms the basis
for a more complete theory of Classical EM.
100 years of obfuscation. Also, the key work: Hamilton's "Elements of
Quaternions" (both editions) proves nearly impossible to acquire.
100 years with matrix "rack-o-math" hegemony.
Interesting side notes:
Much of this occurred under auspices of Yale at a time when the roving
eye of mass media was poorly understood.
The contributions of Kelvin to Thermodynamics reveals he had very deep
understanding, his two water jet experiment (static generator) notable.
But he missed a crucial connection (heat is cathodic).
"Gibbs Free Energy" bears a name which will live him down in infamy if
he is ever determined to have been involved in work that hid truths.
The point of this post:
All of these honorable men in our history are presented as heroes and
angels and pauper survivors as we idealize them. But if EM theory was
indeed corrupted to keep us in the pen as "The Wave" certainly implies,
then this corruption and its form certainly are on exhibit here for all
to see. How many of these three were S&B? Can the moods and attitudes
of this struggle provide us today with an archetype of a smear campaign?
Maybe ...
Any thoughts?
