Ref: http://www.physicsweb.org/article/world/17/5/2
The greatest equations ever
Points of View: May 2004 Physics World

What makes a great equation? Robert P Crease seeks your candidates
and criteria

In It Must Be Beautiful: Great Equations of Modern Science, Graham
Farmelo assembled and edited essays on 11 great equations of the
20th century. Six are from physics: E = hf, E = mc^2, Einstein's
general-relativity equation, the Schrödinger wave equation, the
Dirac equation and the Yang-Mills equation. The other five include
the Drake equation on the likelihood of us forming radio contact
with extraterrestrial life, and Shannon's equations on information
transmission.

Farmelo shuns defining greatness in equations, but compares them
with poems. Both are composed of abstractions with which we address
the world, even though many individual terms do not refer to
anything specific. While "poetry is the most concise and highly
charged form of language", he says, equations are "the most succinct
form of understanding of the aspect of physical reality they
describe". We sense greatness in equations as well as poems, even
though we do not have an objective measure for it.

Wardrobe numbers and overcoats Whether a particular equation is
"great" obviously has something to do with the properties of the
equation itself, such as simplicity and symmetry. This would seem to
favour three-letter equations like F = ma, E = hf and E = mc^2.

But clearly other criteria come into play as well. For example, we
have to consider the relationship of the equation with the world -
otherwise it would just remain hieroglyphs. Uniquely, equations do
not refer directly to things but to quantities measured from special
situations staged in the laboratory. Force, energy, time or
acceleration do not lie around like ordinary objects; measurements
of these quantities have to be "read off" from events that have been
specially conceived, prepared and systematized. The relationship
between a measurement and what it measures is thus not like that of
a word to an object, but - as Einstein once remarked - more like
that of "wardrobe number to overcoat". Equations, as it were, link
the wardrobe numbers to one another - what links wardrobe numbers to
overcoats is laboratory preparation and measurement.

To use an analogy of the science philosopher Patrick Heelan, a
laboratory is like a garden where special kinds of things are grown
in an environment that is isolated (although never completely) from
the life outside. The special things that emerge within the
laboratory walls are thus artifacts - like greenhouse orchids -
which may exist only momentarily, but their properties help us to
understand and explain that wider and wilder external life. The
laboratory creates the conditions under which special things appear
that show themselves as structures of the world. Neither the world
inside nor outside the laboratory is a static environment, however;
both are mediated by technology and continually changing, which
allows new things, concepts and interests.

Whether an equation is great, it seems to me, has something to do
not only with the properties of the equation, but also with the
scope and depth of the phenomena to which it refers. This would
favour equations dealing with fundamental things such as space,
time, fields and energy. Great equations can seem to be "wiser even
than their discoverers" about such fundamental things, as Hertz said
of Maxwell's equations, for "we get more out of them than was
originally put into them". This is why, Hertz felt, that
"mathematical formulae have an independent existence of their own".

Cultural flesh Inside and outside science, furthermore, equations
can acquire what one might call a cultural "flesh". That is,
equations are more than bare and abstract scientific tools but can
develop a lore, history and meaning of their own. This can happen to
even the

most elementary of equations. In US high schools, students are often
reminded of Ohm's law using the phrase "Rhode Island equals
Vermont". During the Second World War, faced with the urgency to
churn out radio operators speedily, one radar school outside Chicago
taught it in three versions - V = IR, I = V/R and R = V/I - because
it was faster to teach these equations than it was to teach trainees
how to manipulate equations.

Equations can exemplify epistemological and moral lessons about
science, and appear to be signposts toward entry into nature's
deeper mysteries. The convoluted story of Schrödinger's equation,
and its competition with Heisenberg's matrix mechanics, is sometimes
used to instruct physics students on the different ways of
practising science.

In popular culture, meanwhile, E = mc^2 has come to stand for science
- even human knowledge - itself. It is a staple of popular cartoons
and images of science, and even turned up in the recent movie School
of Rock, in which a washed-out rock musician is stuck teaching
junior-high-school kids.

The French intellectual Roland Barthes observed that while
photographs of Einstein often show him next to a blackboard covered
with impenetrable symbols and equations, cartoons often portray him,
chalk in hand, next to a clean blackboard on which he has written
down this particular formula as if it had just come to him. Barthes
observed that this equation restores the image of "knowledge reduced
to a formula?science entirely contained in a few letters". It has
become a Gnostic image symbolizing knowledge at once ultimate and
esoteric: "The unity of nature, the ideal possibility of a
fundamental reduction of the world, the unfastening power of the
word, the age-old struggle between a secret and an utterance, the
idea that total knowledge can only be discovered all at once, like a
lock that opens after a thousand unsuccessful attempts."

The critical point Equations were not always as prominent in, nor as
identified with, scientific methodology as they are now. At the
beginning of modern science, laws such as Galileo's law that we now
express in the form of equations (d = 1/2at2) were expressed through
proportionalities (d α t2). One may well wonder about the role
played by the increasing centrality of equations in the advance of
science.

The equations in Farmelo's book are all from the 20th century. Which
equations would be on the list if it were expanded to include the
greatest equations of all time? I invite you to send me your
candidates, the reasons why they deserve to be on the list, and what
value, if any, you find in discussing their greatness. I shall
report on the results in a future column.

• What is your shortlist of the greatest equations in science,
and what makes them great? Send your thoughts to Robert P Crease at
the address or e-mail given below, or by fax to +1 631 632 7522.

Author
Robert P Crease is in the Department of
Philosophy, State University of New York at Stony
Brook, 213 Harriman Hall, Stony Brook, NY
11794-3750, US, e-mail


Copyright © IOP Publishing Lt

"Sam Wormley" wrote in message
...
| Ref: http://www.physicsweb.org/article/world/17/5/2
| The greatest equations ever
| Points of View: May 2004 Physics World
|
| What makes a great equation? Robert P Crease seeks your candidates
| and criteria
|
| In It Must Be Beautiful:

Q_vac = +,- sqrt(hbar*c)

You can't get much prettier than that. A wonderful thing of beauty.

FrediFizzx

Sam Wormley wrote in message ...
Ref: http://www.physicsweb.org/article/world/17/5/2
The greatest equations ever
Points of View: May 2004 Physics World

What makes a great equation? Robert P Crease seeks your candidates
and criteria

e^{i pi } = -1

Four of the more important numbers we know, in one equation.
Oh, you wanted physics content? Well...
Socks

Sam Wormley wrote:

Ref: http://www.physicsweb.org/article/world/17/5/2
The greatest equations ever
Points of View: May 2004 Physics World

What makes a great equation? Robert P Crease seeks your candidates
and criteria

[snip]

• What is your shortlist of the greatest equations in science,
and what makes them great? Send your thoughts to Robert P Crease at
the address or e-mail given below, or by fax to +1 631 632 7522.

Author
Robert P Crease is in the Department of
Philosophy, State University of New York at Stony
Brook, 213 Harriman Hall, Stony Brook, NY
11794-3750, US, e-mail


The most significant equation in the history of mankind is the
compound interest equation. Societies that encouraged investment with
proportionate reward grew to rule the world, and their citizens
enjoyed every possible pleasure of the mind and flesh. Those
societies mandating charity or denying payback remained poor and crude
no matter how vast their raw income generation.

England was resource poor but aggressively invested. Spain enjoyed a
river of New World plunder pouring across its borders for almost 80
years. In the end, England ruled the world and Spain was nothing.
The present day implications are obvious, staggering, and unwlecome.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!

THE Unworthy Turd wrote:

Sam Wormley wrote:


• What is your shortlist of the greatest equations in science,
and what makes them great? Send your thoughts to Robert P Crease at
the address or e-mail given below, or by fax to +1 631 632 7522.

snip

The most significant equation in the history of mankind is the
compound interest equation.

snip

*science*

snip balance of nonsensical personal observations

Bill Vajk wrote:

THE Unworthy Turd wrote:

Sam Wormley wrote:

• What is your shortlist of the greatest equations in science,
and what makes them great? Send your thoughts to Robert P Crease at
the address or e-mail given below, or by fax to +1 631 632 7522.

snip

The most significant equation in the history of mankind is the
compound interest equation.

snip

*science*

snip balance of nonsensical personal observations

Hey stooopid critic troll Vajk, DCF/ROI. All industrial research is
risk vs. reward. Academic research is not funded, only proposed
results are funded. The world revolves around generated value. You
cannot imagine that, stooopid critic troll Vajk, because you have
never created anything of value. You are wholly unaware of the
history of productivity. You now nothing about econmics, stooooid
critic troll Vajk, or you would know that Henry Ford's greatest
innovation was paying a wage that allowed his workers to buy his
product. Real people call that "velocity of money" - and it requires
granting credit, and that is motivated by interest charged.
*Everybody* ended up wealthier. Capitalism is a hoot.

Gee winkydinks, I don't see your contributed equation, stooopid critic
troll Vajk. ARE YOU TOO ****ING STOOOPID TO VOLUNTEER ONE?

Poor stooopid critic troll Vajk. Hey moron - my credit card balances
are exactly $zero at the end of each month. Are you paying 19% annual
interest on de facto loans when your checking account pays 0.25%
interest on deposits? Ha ha ha. Looks like the compound interest
equation has you by your balls. How important is that? snip balance
of nonsensical chronic mental dysfunction

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!

wrote in message om...
Sam Wormley wrote in message ...
Ref: http://www.physicsweb.org/article/world/17/5/2
The greatest equations ever
Points of View: May 2004 Physics World

What makes a great equation? Robert P Crease seeks your candidates
and criteria

e^{i pi } = -1

Four of the more important numbers we know, in one equation.

hm, I strongly prefer the version:

e^{i pi} + 1 = 0

with five (!) of the more important numbers, and 3 of the more import
operations (+, * and ^).

Oh, you wanted physics content? Well...

Ah yes.
Well indeed ...

Dirk Vdm

THE Unworthy Turd protested:

Note: Warning in advance, the following is a "point of view" but
not on topic regarding the cited Wormley question.

Bill Vajk wrote:

THE Unworthy Turd wrote:

Sam Wormley wrote:

• What is your shortlist of the greatest equations in science,
and what makes them great? Send your thoughts to Robert P Crease at
the address or e-mail given below, or by fax to +1 631 632 7522.

snip

The most significant equation in the history of mankind is the
compound interest equation.

snip

*science*

snip balance of nonsensical personal observations

Your tourettish (or some other reason perhaps?) outburst
doesn't alter the fact that this is sci.physics and
the discussion was about "greatest equations in science."

The details of your views are not only uninteresting but
predominantly incorrect in the several salient points. But
as I am winding down my participation, Al, why don't you,
since you brought up the issues, tell us what your value
related creations to date have been. I know it will be a
very short list. I understand you patented an unmarketable
roach related product.

I know a fellow in Chicago who is a self-proclaimed genius
not very unlike yourself in a number of ways, who has never
actually achieved anything of value. Not only that, but in
his 40's he's still living under his parents' roof and
sponging off his father who is some half century his senior.

That I cannot, and do not, discuss my achievements on usenet
should come as no surprise to anyone ever remotely conversant
with the facts as well as anyone who is familiar with the
ins and outs of what should be called "the usenet culture".
Your disgusting little troll involving one of the brightest
and nicest individuals on usenet, Dr. John Baez is a classic
example against disclosing anything about oneself in this
medium.

Did you manage to get your act together long enough to offer
Dr. Baez your most profuse apology? Is it any wonder people
in academia try to steer clear of you?

Following that you posted like some unfamiliar sane and
decent man for two days, Tuesday and Wednesday, yet it was
late Thursday and you had already recovered your old form
and format. No one in their right mind would give you, or
others much like yourself, any ammunition with which to fuel
their internal hatred and loathing of themselves as well as
humanity in toto.


Hey stooopid critic troll Vajk, DCF/ROI. All industrial research is
risk vs. reward. Academic research is not funded, only proposed
results are funded. The world revolves around generated value. You
cannot imagine that, stooopid critic troll Vajk, because you have
never created anything of value. You are wholly unaware of the
history of productivity. You now nothing about econmics, stooooid
critic troll Vajk, or you would know that Henry Ford's greatest
innovation was paying a wage that allowed his workers to buy his
product. Real people call that "velocity of money" - and it requires
granting credit, and that is motivated by interest charged.
*Everybody* ended up wealthier. Capitalism is a hoot.

Gee winkydinks, I don't see your contributed equation, stooopid critic
troll Vajk. ARE YOU TOO ****ING STOOOPID TO VOLUNTEER ONE?

My work remains classified and probably will be for the foreseeable
future. You don't like it? Tough. Demonstrate a "need to know" to
the appropriate authorities and then you can get at it.

Here's a clue: it never had anything remotely to do with roaches, so
it is unlikely you'd understand it anyway. I mean you actually
believe a "measurement" can be absolute when measurement is
conceptually, in all cases, a relationship.

Poor stooopid critic troll Vajk. Hey moron - my credit card balances
are exactly $zero at the end of each month.

Easy to do when the limits are zero. LOL

Are you paying 19% annual
interest on de facto loans when your checking account pays 0.25%
interest on deposits? Ha ha ha.

You are an idiot. My checking account pays 6% per annum.

Looks like the compound interest equation has you by your balls.
How important is that? snip balance
of nonsensical chronic mental dysfunction

I'm glad you cut off posting even more of your chronic mental
dysfunction, Al.

But here's the same clue a second time: The subject was (and you
*can* read it above) "the greatest equations in science." Now
it seems pretty clear to me that compound interest isn't science
in any legitimate definition of the word.

P.S. Your clay feet have been turning to mud again, otherwise
we wouldn't even be having this (ahem) discussion.

In article , writes:
Sam Wormley wrote in message ...
Ref: http://www.physicsweb.org/article/world/17/5/2
The greatest equations ever
Points of View: May 2004 Physics World

What makes a great equation? Robert P Crease seeks your candidates
and criteria

e^{i pi } = -1

Four of the more important numbers we know, in one equation.

I prefer to write it as

e^(i pi) + 1 = 0

which makes it "five of the most important numbers". And, yes, I'll
second the nomination of the above as the most beatiful identity (it
is an identity, not an equation).

Mati Meron | "When you argue with a fool,
| chances are he is doing just the same"

Sam Wormley wrote in message ...
Ref: http://www.physicsweb.org/article/world/17/5/2
The greatest equations ever
Points of View: May 2004 Physics World

What makes a great equation? Robert P Crease seeks your candidates
and criteria

In It Must Be Beautiful: Great Equations of Modern Science, Graham
Farmelo assembled and edited essays on 11 great equations of the
20th century. Six are from physics: E = hf, E = mc^2, Einstein's
general-relativity equation, the Schrödinger wave equation, the
Dirac equation and the Yang-Mills equation. The other five include
the Drake equation on the likelihood of us forming radio contact
with extraterrestrial life, and Shannon's equations on information
transmission.


Hamilton's Matrix 1= [b]*[H]

where [b] is the matrix sufficicient.

Hamilton's matrix in this formulation is a differenatial.


The operation, *, here, is the reinverted symmetry. It may be
performed by a common matrix multiplication followed by addition to
the [h] particulars.

The symmetry of the real number is seen to be just that. And the
integer of Socrates a beautiful counting of the constant [b] apon all
such matricies self evident.



Douglas Eagleson
Gaithersburg, MD USA