Russ Abbott's comments are interesting. They remind me of a science fiction
movie I saw in my ancient past. A member of a very advanced civilization
encountered some earthlings, one of whom was a hotshot mathematical physicist.
I found it unbelievable that the Martian -- let's call him that-- could look at
the scribbles and immediately say something like, Hmmm . Very interesting ( Why
not give that comment a German accent , Hmmm wery eenteresting!)
Why was that response of the Martian so surprising? The sheet of paper
consisted of nothing but mathematical formulas. No definitions, showing the
meanings of the symbols and no explanation of their context in a consistent
theory. But , we're expected to conclude, the Martian was, after all, a very
advanced intellect.
.
The point is that this would not have helped even that Martian:No definitions,
no context. No embedded concepts.
The mathematics is not expected to stand alone in physics. Concept and symbols
together.
In quantum mechanics, to take an example, the mathematics works. The problem
today is not with the symbolic representations of quantum ideas but with the
otherwordliness of that microscopic domain; It lies below our experience of
this everyday world. Below a certain point, there are no satisfactory metaphors
for the behaviors in the microscopic world. Without the mathematics, we
couldn't ven have gone there-- or imagined that particular "there".
No question that it works. Our present technology, based on quantum mechanics,
works famously well. The concepts are described by the equations. Medical
devices, cell phones-- everywhere you turn-- you see evidence that the
equiations are concept connected.
E.O Wilson's domain in biology, mentioned by Russ, is driven somewhat
differently. But, only to touch on another example from biology: Understanding
of DNA itself, embedded in modern microbiology, depends on quantum mechanics
and its equations. The discovery and exploitation off DNA depend on quantum
mechanics, and concept goes hand in hand with the math.
Even Newton's laws of motion, described by simple equations, demonstrate that
the equations do not stand alone if they are to have any meaning, in the manner
described above. And I could now sail into the deep waters of poor education in
even simple algebra, and waht that means for the unnecessary "two cultures" we
are faced with.
I hear again, in response, the refrain that this is not enough. Which makes us
tempetd to recognize all that has already been said in these e-mail exchanges.
Best New Year to all,
Jack
--- Original Message -----
From: [email protected]
To: [email protected] ; 'The Friday Morning Applied Complexity Coffee
Group'
Sent: Saturday, December 27, 2008 11:03 PM
Subject: Re: [FRIAM] art and science
A fascinating discussion. E.O. Wilson made much the same point in his book
Consilience: The Unity of Knowledge, where he argued that a narrow reliance on
mathmatics had destroyed philosophy in particular, while in general an
increasing reliance on specialization and mathmatics had handicapped
scientists, limiting new hypothesis to variation of current thinking in a
particular discipline.
http://www.amazon.com/Consilience-Knowledge-Edward-O-Wilson/dp/067976867X/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1230443706&sr=8-1
cjf
Christopher J. Feola
President
nextPression, Inc.
www.nextPression.com
------------------------------------------------------------------------------
From: [email protected] [mailto:[email protected]] On Behalf
Of Russ Abbott
Sent: Saturday, December 27, 2008 11:45 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] art and science
Hi Jack,
I'd like to take advantage of your post to raise an issue that is
related--but not directly--to what you are discussing.
You wrote, "What has made mathematics so important in science, especially
physics, is the need for replacing word-fuzziness with precision in
prediction."
Although no one can doubt the importance of mathematics to physics and the
other sciences, what do you think of this somewhat contrary position. The
damage mathematics has done to science is that it has substituted numbers for
concepts.
Mathematics is a language of equations and numbers. Of course equations
operate within frameworks, which themselves involve concepts--such as
dimensionality, symmetry, etc. These are important concepts. But the equations
themselves are conceptless. They are simply relationships among numbers that
match observation. I suspect that this is one of the reasons the general public
is turned off to much of science. The equations don't speak to them. I would
say that the equations don't speak to scientists either except to the extent
that they manage to interpret them in terms of concepts: this is the strength
of this field; this is the mass of this object; etc. But the concepts are not
part of the equations. And (famously) quantum mechanics has no concepts for its
equations! The equations work, but no one can conceptualize what they mean. So
how should one think about quantum mechanics? As a black box with dials one can
read? What should the public think about quantum mechanics if that's the best
that scientists can do?
I can think of two primary goals for science: to understand nature and to
give us some leverage over nature. Equations give us the leverage; concepts
give us the understanding.
-- Russ
On Sat, Dec 27, 2008 at 7:33 PM, Jack Leibowitz <[email protected]> wrote:
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