On 1/3/2013 6:43 PM, matthew lange wrote:
> Why does it have to be
> John: "Teaching ontology by burying the fundamental insights under the
> trivial notation is pedagogical malpractice."
> or
> Leo: "The point of using mathematical (or logical) notation is to make
> your statement precise and unambiguous."
>
> Cannot these perspectives be harmonized?:
> Fundamental principles can be explained in plain language, with
> formalized notation provided for those trained in higher mathematics. (01)
I am strongly in favor of stating the fundamental principles in "plain
language" and then following that with mathematical formulations, and I
think that is the best practice for such papers. But I must confess
that, a few steps into a theory, the "plain language" can become
significantly less than "plain" and easily understood. (02)
> FWIW, I am a life scientist with several years of data/knowledge
> architecture experience. I cringe at the formalist notation--able to
> understand it with my old math books next to me--but view that largely
> as a waste of time if the concept is well explained. If authors only
> care about talking to other mathematicians/logicians then this
> notation is good. If they want to reach a larger audience who can
> leverage their teachings...
>
> ~mc (03)
In my limited contact with the medical and life sciences communities, it
has been my experience that the "plain language" is not by any means
"plain". The language is created by introducing a new term for every
combination of properties that is of interest, either by defining a new
"property", or more commonly by defining a new "class" that inherits
every property but one from some subsuming class and adds the one new
property. The result is a language in which most of the sentences are
fairly simple and structurally easy to understand, but they depend on a
huge proliferation of terms to accomplish that simplicity. The concepts
are no less complex, and it requires looking at 5 definitions to
determine what was said. (04)
This approach is the reverse of mathematical notations, which create a
grammar that allows complex statements to be unambiguously written, and
in turn allows the theory to be conveyed with a smaller vocabulary. (05)
Ultimately, the problem is that we have a world of knowledge that is
considerably more complex than that of our 19th century forebears.
Different disciplines have devised different approaches to conveying
complex theories, but they cannot reduce the intrinsic complexity. Per
Einstein, "we must strive to make things as simple as they are, but no
simpler." (06)
-Ed (07)
--
Edward J. Barkmeyer Email:edbark@xxxxxxxx
National Institute of Standards & Technology
Systems Integration Division, Engineering Laboratory
100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263 Cel: +1 240-672-5800 (08)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (09)
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