A bizarre title, but nothing to do with the fact that I am constitutionally lazy. Rather, it is related to the war I and a colleague are attempting to wage against the way physics is (in the UK at least) treated as a form of applied mathematics.
It also has direct application to astrophysics – I know one student who went to study physics at university in 2002, in large part attracted by astronomy, but after a second year including astrophysics was saying "I hate stars." He was quite reasonable at maths, but it is the way that the subject was presented that put him off.
What’s wrong with work, though? Owen Barfield said that a thing can be a symbol of something of which it is itself a part, and I'm picking out the thermodynamic concept of work as that symbol. Even at high school in the early 1960s, I found things slipping below the radar because work, momentum, etc., all were treated as applied maths concepts. Therefore the mathematical treatment of viscosity of gases according to the kinetic theory rolled over my brain like water off the proverbial duck’s back.
Now, I am not averse to maths, in fact I have recently started to teach a course in its history (mostly up to 1900), but what was the connection with the laboratory method for determining the viscosity of a liquid?
Turning again after nearly 40 years to the "Kinetic Theory of Gases" by Sir James Jeans, I find he brings in PdV straight in without explanation, rather like a deus ex machina from 19th century Classical Thermodynamics. "Machina" is the right word, because as Craig Bohren [1] says, the subject has still not completely lost its smell of engines.
I find that even in Ralph Baierlein's generally excellent book on thermal physics, he brings it in to a quantum treatment of loss of energy in adiabatic expansion.
Here's where a few years ago I convinced myself that "work" really "works", and is not some mystic thingamajig like Newton's contemporaries feared gravitation was:
In the classical model, I worked out on an old envelope that the particles bouncing back from the walls of a slowly expanding box were losing momentum and hence kinetic energy in the right amount.
On the quantum model, if one keeps the number of nodes in the particle wavefunction constant, the same numerical result occurs. Now I can really believe in the work concept, and model the core and "mantle" of a star as being separated by the skin of a virtual balloon.
The spread of this skeletal mathematical approach, in the USA at least, is traced in an article by David Kaiser (MIT) in the May 2007 Physics World entitled "Turning physicists into quantum mechanics". In the UK, school physics is a threatened species in the wild as the system tries to turn budding physicists into formula monkeys.
If, in the course of learning physics, you have encountered any bugbears of your own, please let me know.
[1] author of two excellent books without equations:
Bohren, C.F Clouds in a Glass of Beer: Simple Experiments in Atmospheric Physics (Dover, 2001 ISBN: 0486417387)
Bohren, C.F., What Light Through Yonder Window Breaks?: More Experiments in Atmospheric Physics (Dover, 2006 ISBN: 0486453367)
"I Hate Work!" (and I Don't Do Applied Mathematics)
Comments
—
Robert H. Olley
Quondam Physics Department
University of Reading
England
Robert H Olley | 07/25/08 | 12:44 PM
I suppose I am only an ignorant engineer, but I cannot believe what I am seeing printed here.
Physics is NOT best taught as PURE MATH. The math came about as a result of seeking a quantitative answer...it does not lead to the answer or a complete explanation of a phenomenon.
Its true that quantum mechanics cannot be taught according to intuition, but is erroneous to believe that quantum mechanics is merely an outcome or expression of linear algebra.
Pure math also precludes the use of creative thought, because it is so highly axiomatic. While I am sure many physicists prefer the beauty of their PDE's and Jacobian matrices, there are few physicists who ever discovered anything uselful by surrounding themselves in adventures in pure mathematics.
In nearly all cases, advancements in math went alongside an observation or problem posed in the phsyical sciences. Math was used as a tool to explain behavior; it is NOT the complete language of that behavior. Try to remember Kurt Godel here...
I also object to your stereotypical distaste for "the smell of engines". Those smelly engines are why you have electric power available for your Beowulf cluster or whatever arrangement you use to ponder the implosions of stars. I don't think Lord Kelvin, Carnot, or Clausius would object to a legacy built upon the foundations of very real and necessary thermodynamic cycles that make modern life possible today.
Go back to your backscatter collecting SEM and remind yourself that you too are victim of the scattering properties of an accelerated lepton in your quest to deduce structure :)
Physics is NOT best taught as PURE MATH. The math came about as a result of seeking a quantitative answer...it does not lead to the answer or a complete explanation of a phenomenon.
Its true that quantum mechanics cannot be taught according to intuition, but is erroneous to believe that quantum mechanics is merely an outcome or expression of linear algebra.
Pure math also precludes the use of creative thought, because it is so highly axiomatic. While I am sure many physicists prefer the beauty of their PDE's and Jacobian matrices, there are few physicists who ever discovered anything uselful by surrounding themselves in adventures in pure mathematics.
In nearly all cases, advancements in math went alongside an observation or problem posed in the phsyical sciences. Math was used as a tool to explain behavior; it is NOT the complete language of that behavior. Try to remember Kurt Godel here...
I also object to your stereotypical distaste for "the smell of engines". Those smelly engines are why you have electric power available for your Beowulf cluster or whatever arrangement you use to ponder the implosions of stars. I don't think Lord Kelvin, Carnot, or Clausius would object to a legacy built upon the foundations of very real and necessary thermodynamic cycles that make modern life possible today.
Go back to your backscatter collecting SEM and remind yourself that you too are victim of the scattering properties of an accelerated lepton in your quest to deduce structure :)
Erik Snyder (not verified) | 07/25/08 | 13:31 PM
Dear Robert,
I am a mathematician. I only found physics clear when it was presented as pure math with mathematical clarity. When,appeal was made ( by hand-waving) to experimental or heuristic, it always got confusing.
The physical intuition must be there--and it is properly placed in the axioms--which are suggested by experiment. This was Galileo's, Newton's, Maxwell's approach. What math does best is get the maximum clarity from physical axioms.
Dear Erik,
What distaste for engines? I distaste hand-waving arguments or
unsupported formulae. I LOVE engines--grew up doing experiments, build a betatron when I was 14--from the wonderful column in Scientific American by Strong. I was a radio ham as a teenager--with an interest in homebrew high
frequency circuits.
Just because I like mathematical clarity, doesn't mean that I don't like silver solder, vacuum wax, or ENGINES.
And I married an engineer!
I am a mathematician. I only found physics clear when it was presented as pure math with mathematical clarity. When,appeal was made ( by hand-waving) to experimental or heuristic, it always got confusing.
The physical intuition must be there--and it is properly placed in the axioms--which are suggested by experiment. This was Galileo's, Newton's, Maxwell's approach. What math does best is get the maximum clarity from physical axioms.
Dear Erik,
What distaste for engines? I distaste hand-waving arguments or
unsupported formulae. I LOVE engines--grew up doing experiments, build a betatron when I was 14--from the wonderful column in Scientific American by Strong. I was a radio ham as a teenager--with an interest in homebrew high
frequency circuits.
Just because I like mathematical clarity, doesn't mean that I don't like silver solder, vacuum wax, or ENGINES.
And I married an engineer!
Penny (not verified) | 07/25/08 | 18:36 PM
Dear Erik,
Carnot's dad was a mathematician. He himself was a student of the mathematicians Ampere and Poisson. And the whole POINT of his work on the Carnot cycle etc, was to produce clear and rigorous mathematical proofs in thermodynamics.
He was inspired by engines--and constructed axioms--and proved theorems that among other things showed the existence of the most efficent cyclic engine--and this theorem is proved
brilliantly by him.
Clausius was a mathematician ( and physicist) who studied under the mathematician Dirichlet. His proofs are excellent, based on his excellent axioms.
Lord Kelvin was also a mathematician--and prof of mathematical physics. His proofs are excellent.
They all loved engines, they all loathed hand-waving and I
agree with them.
They all constructed rigorous proofs.
And, yes, they also liked experiments--as do I.
best
Penny
Carnot's dad was a mathematician. He himself was a student of the mathematicians Ampere and Poisson. And the whole POINT of his work on the Carnot cycle etc, was to produce clear and rigorous mathematical proofs in thermodynamics.
He was inspired by engines--and constructed axioms--and proved theorems that among other things showed the existence of the most efficent cyclic engine--and this theorem is proved
brilliantly by him.
Clausius was a mathematician ( and physicist) who studied under the mathematician Dirichlet. His proofs are excellent, based on his excellent axioms.
Lord Kelvin was also a mathematician--and prof of mathematical physics. His proofs are excellent.
They all loved engines, they all loathed hand-waving and I
agree with them.
They all constructed rigorous proofs.
And, yes, they also liked experiments--as do I.
best
Penny
Penny (not verified) | 07/25/08 | 18:52 PM
Dear Erik,
You wrote:
here are few physicists who ever discovered anything uselful by surrounding themselves in adventures in pure mathematics.
Well, I suppose that James Clerk Maxwell--mathematician--and professor of math doesn't count--but, I think that the radio wave was a fairly important consequence of his mathematics.
Faraday ( whose axiomatic work on flux tubes was a precursor
to modern topology--and no mean feat of mathematics, also conjectured electromagnetic waves--based on his math.)
It was Maxwell who gave a pde type proof. Faraday also
liked experiments--to set up his axioms--but he didn't find
electromagnetic waves by experiment.
It was years after Maxwell that Hertz did the experiment.
There are many other examples--such as Einstein's ( who was a physicist) mathematical derivation of :
Gravitational Time Dilation
Greater bending of light by gravity
Einstein Rings
Frame Dragging
from his field equations which were not even motivated by
an experiment.
Be also got:
the precession of the orbit of mercury
Also, the Mathematician Schwartzchild predicted black holes from Einstein's equations.
The physicist Robert Oppenheimer ( and Synder) predicted
Degenerate matter aka Neutron stars. This was done by mathematics.
I could go on and on.
You wrote:
here are few physicists who ever discovered anything uselful by surrounding themselves in adventures in pure mathematics.
Well, I suppose that James Clerk Maxwell--mathematician--and professor of math doesn't count--but, I think that the radio wave was a fairly important consequence of his mathematics.
Faraday ( whose axiomatic work on flux tubes was a precursor
to modern topology--and no mean feat of mathematics, also conjectured electromagnetic waves--based on his math.)
It was Maxwell who gave a pde type proof. Faraday also
liked experiments--to set up his axioms--but he didn't find
electromagnetic waves by experiment.
It was years after Maxwell that Hertz did the experiment.
There are many other examples--such as Einstein's ( who was a physicist) mathematical derivation of :
Gravitational Time Dilation
Greater bending of light by gravity
Einstein Rings
Frame Dragging
from his field equations which were not even motivated by
an experiment.
Be also got:
the precession of the orbit of mercury
Also, the Mathematician Schwartzchild predicted black holes from Einstein's equations.
The physicist Robert Oppenheimer ( and Synder) predicted
Degenerate matter aka Neutron stars. This was done by mathematics.
I could go on and on.
Penny (not verified) | 07/25/08 | 19:05 PM
Erik,
Also recall that is not just "smelly engines" that gave us
electric power but the work of the mathematician
Charles Proteus Steinmetz. Steinmetz used differential equations to make AC practical.
He was known as the Wizard of General Electric.
He is also widely credited with the method of phasors--but
actually, this was already invented by the mathematician
Euler--for differential equations in mechanics.
Also recall that is not just "smelly engines" that gave us
electric power but the work of the mathematician
Charles Proteus Steinmetz. Steinmetz used differential equations to make AC practical.
He was known as the Wizard of General Electric.
He is also widely credited with the method of phasors--but
actually, this was already invented by the mathematician
Euler--for differential equations in mechanics.
Penny (not verified) | 07/25/08 | 19:14 PM
Erik,
Once again, I do stress that experiments matter--no neutron
, no neutron stars.
Once again, I do stress that experiments matter--no neutron
, no neutron stars.
Penny (not verified) | 07/25/08 | 19:17 PM
Dear Robert,
I will give that URL to my students, who learn Clifford Algebra using the math text of Michelson and Lawson.
The version at that URL is more intuitive in some ways, though very elementary for a mathematician--and
reminds me of the treatment of Cartan in his book Spinors.
Clifford algebra is very important in physics, and in pure math. Nice Site!
For Erik, I should also mention the mathematician ( Lucasian
Prof of Math) Paul Dirac--who used Clifford Algebra to derive Dirac's equation. This was not a matter of experiment, and there was already a relativistic field equation--the Klein-Gordon Equation. Dirac's mathematicial intuition asked for a first order system.
Result--the prediction of fine order spectral effects and
of .....antimatter.
Both, confirmed later by experiment.
I will give that URL to my students, who learn Clifford Algebra using the math text of Michelson and Lawson.
The version at that URL is more intuitive in some ways, though very elementary for a mathematician--and
reminds me of the treatment of Cartan in his book Spinors.
Clifford algebra is very important in physics, and in pure math. Nice Site!
For Erik, I should also mention the mathematician ( Lucasian
Prof of Math) Paul Dirac--who used Clifford Algebra to derive Dirac's equation. This was not a matter of experiment, and there was already a relativistic field equation--the Klein-Gordon Equation. Dirac's mathematicial intuition asked for a first order system.
Result--the prediction of fine order spectral effects and
of .....antimatter.
Both, confirmed later by experiment.
Penny (not verified) | 07/25/08 | 19:24 PM
Erik,
And to complete the circle--Dirac probably was motivated by the quaternionic form of Maxwell's equations--in...Thompson and Tait's physics book.
That's Will Thomson...aka
Lord Kelvin.
And to complete the circle--Dirac probably was motivated by the quaternionic form of Maxwell's equations--in...Thompson and Tait's physics book.
That's Will Thomson...aka
Lord Kelvin.
Penny (not verified) | 07/25/08 | 19:31 PM
Dear Erik,
You wrote:
Pure math also precludes the use of creative thought, because it is so highly axiomatic
Funny, I could argue that pure mathematics is the most creative thought of mankind, often because it is highly axiomatic.
Consider Group Theory, or Wiles and Taylor's Proof of Fermat's
Conjecture, or Perleman's proof of the Poincare Conjecture.
Does the G minor Fugue or the Mona Lisa fall in the same class?
Once could argue the point.
You wrote:
Pure math also precludes the use of creative thought, because it is so highly axiomatic
Funny, I could argue that pure mathematics is the most creative thought of mankind, often because it is highly axiomatic.
Consider Group Theory, or Wiles and Taylor's Proof of Fermat's
Conjecture, or Perleman's proof of the Poincare Conjecture.
Does the G minor Fugue or the Mona Lisa fall in the same class?
Once could argue the point.
Penny (not verified) | 07/25/08 | 19:38 PM
Many typing errors due to typing in a dark room to rest eyes, and typing too fast.
"Once" should be "One".
That's the worst of the typos.
"Once" should be "One".
That's the worst of the typos.
Penny (not verified) | 07/25/08 | 19:41 PM
Dear Erik,
You wrote:
In nearly all cases, advancements in math went alongside an observation or problem posed in the phsyical sciences.
Like number theory, algebraic geometry, differential geometry,
abstract algebra, algebraic topology, differential topology,
, category theory, point set toplogy?
All of which had NO roots in physics.
All of which ( except maybe number theory--but stay tuned to
zeta regularization and quantum dynamical systems) have had major effect on physics.
You wrote:
In nearly all cases, advancements in math went alongside an observation or problem posed in the phsyical sciences.
Like number theory, algebraic geometry, differential geometry,
abstract algebra, algebraic topology, differential topology,
, category theory, point set toplogy?
All of which had NO roots in physics.
All of which ( except maybe number theory--but stay tuned to
zeta regularization and quantum dynamical systems) have had major effect on physics.
Penny (not verified) | 07/25/08 | 19:51 PM
Dear Erik,
Forgot to mention:
Mathematical Logic
Set Theory
Tupos theory
Trupical Geometry
Algebraic K Theory
Geometric K Theory
etc.
Forgot to mention:
Mathematical Logic
Set Theory
Tupos theory
Trupical Geometry
Algebraic K Theory
Geometric K Theory
etc.
Penny (not verified) | 07/25/08 | 19:55 PM
Dear Erik,
and
Game theory
Differential Game theory
Mathematical Economics
Linear and Nonlinear Programming
Integer Programming
Projective Geometry
Integral Geometry
Combinatorics
Additive Combinatorics
Recursive Function Theory
Harmonic Analysis on Groups
Arakelov Geometry
Homological Algebra
Crystalline Cohomology
Several Complex Variables
Complex Manifold Theory
It is a strange fiction of engineering education--and
bad applied math programs that all of maths comes from
physics. Most of maths doesn't.
and
Game theory
Differential Game theory
Mathematical Economics
Linear and Nonlinear Programming
Integer Programming
Projective Geometry
Integral Geometry
Combinatorics
Additive Combinatorics
Recursive Function Theory
Harmonic Analysis on Groups
Arakelov Geometry
Homological Algebra
Crystalline Cohomology
Several Complex Variables
Complex Manifold Theory
It is a strange fiction of engineering education--and
bad applied math programs that all of maths comes from
physics. Most of maths doesn't.
Penny (not verified) | 07/26/08 | 02:03 AM
In the case of engineers, it may be because they study a few
years of calculus, baby differential equations, and maybe basic
linear algebra and elementary complex analysis and they think they have a broad math education. They don't even have the basics.
And those "service" courses, are often made palatable to engineers by a song and dance about how math is always inspired by physics.
years of calculus, baby differential equations, and maybe basic
linear algebra and elementary complex analysis and they think they have a broad math education. They don't even have the basics.
And those "service" courses, are often made palatable to engineers by a song and dance about how math is always inspired by physics.
Penny (not verified) | 07/26/08 | 02:13 AM
—
Robert H. Olley
Quondam Physics Department
University of Reading
England
Robert H Olley | 07/26/08 | 03:36 AM
Gee Robert, I really like your last post! You have a wonderful
personality shining through, and you are a very talented writer.
I have exactly the same feeling about the phrase "service courses". Academia capitulated when we allowed "service courses", when we pandered to the students by telling them that maths was all about applications etc., and we are paying the price in spades.
I am very sorry that you department is closing. It is a shame that the country that supported the research of Rutherford
and Hawking should have become so backward.
You know, for all negative statements we make about our educational system here in the USA, things are healthier here, and you might consider relocating to the USA.
We have more diversity because we lots of private universities, and public universities, and redbrick polytechnics. So, it is difficult to destroy science here,
which I fear is what has happened in England recently.
personality shining through, and you are a very talented writer.
I have exactly the same feeling about the phrase "service courses". Academia capitulated when we allowed "service courses", when we pandered to the students by telling them that maths was all about applications etc., and we are paying the price in spades.
I am very sorry that you department is closing. It is a shame that the country that supported the research of Rutherford
and Hawking should have become so backward.
You know, for all negative statements we make about our educational system here in the USA, things are healthier here, and you might consider relocating to the USA.
We have more diversity because we lots of private universities, and public universities, and redbrick polytechnics. So, it is difficult to destroy science here,
which I fear is what has happened in England recently.
Penny (not verified) | 07/26/08 | 09:23 AM
As an Englishman, I wish you well with your war on stupidity, which is what I see you describing...
Sadly the decision-makers often have no clue as what we as a people have achieved, and have pride in, and what we abandon, in the name of economy, only to lose out and play catch-up....
Are ears getting closer as minds narrow? ;-)
Real research seems to have shifted to China, India and such countries, where 'Necessity is still the mother of invention'
Funny, I don't feel that comfortable, that we can afford to cease research - nor do I feel pleased at the offer for you to 'desert the good ship Blighty'
...but such is life where 'being in control' has become an abused phrase
Aitch
Henry Cox | 11/13/10 | 13:19 PM
One needs axioms, and theorems and careful definitions. NOT
just unexplained formulae. Hence, no formulae monkey approach.
That is Newton's approach--and he called it Natural Philosophy.
So, in the example given in the article, one starts with a clear mathematical treatment of single particle motion under Newton's Differential Equation of Motion, and work is just a first integral of this equation after using the chain rule:
dv/dt= dv/dx dx/dt.
Then one generalizes as needed with a clear axiom and theorem based approach.
In short, Physics as PURE maths, not as dumbed down applied maths. ( Applied maths not dumbed down is also done best as Pure maths).