

Feynman the Babylonian - TriinT
http://golem.ph.utexas.edu/category/2009/08/feynman_the_babylonian.html

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10ren
I get the idea, but I wish the blogger had explicitly defined the
"'Babylonian’ approach". I think he's saying that it's a mistake to take one
theory, with one notation, and imagine that just because it is correct and
covers all the cases, it is the one "truth". It sounds like solipsism: wanting
a predicable and self-contained world that is safe and controlled. But there
are a few strange things about different notations that mean the same thing:

\- notations have usability. Each one makes it easier or harder to do certain
things. One notation might be good at one task, and poor at another; whereas
another notation vice versa, even though both are equally "true". Notations
also make it harder or easier to think/reason about certain things, in the way
that language tends to shape our thoughts (not determine them, Dr. Whorf).

\- notations are similar or different to related concepts and notations,
making some connections easier to see, and some harder.

\- notations generalize differently, having different suggestions for the
"obvious" next step.

A particular notation is then just a shadow of the truth - a one dimensional
projection, capturing only a plane of the unseen reality. It seems that
mathematicians and scientists routinely invent new notations for new domains
(not necessarily good ones). The advantages of different notations is what
Alan Kay was talking about when he said that "point of view is worth 80 IQ
points". Notation is a form of point of view.

 _It was based on a few things from the past like how smart you had to be in
Roman times to multiply two numbers together; only geniuses did it. We haven't
gotten any smarter, we've just changed our representation system. We think
better generally by inventing better representations; that's something that we
as computer scientists recognize as one of the main things that we try to do_
<http://ecotopia.com/webpress/futures.htm>

~~~
andrewl
10ren - Interesting points. I've always liked what Alfred North Whitehead says
about notation:

"By relieving the brain of all unnecessary work, a good notation sets it free
to concentrate on more advanced problems, and, in effect, increases the mental
power of the race. Before the introduction of the Arabic notation,
multiplication was difficult, and the division even of integers called into
play the highest mathematical faculties. Probably nothing in the modern world
would have more astonished a Greek mathematician than to learn that ... a
large proportion of the population of Western Europe could perform the
operation of division for the largest numbers. This fact would have seemed to
him a sheer impossibility ... Our modern power of easy reckoning with decimal
fractions is the almost miraculous result of the gradual discovery of a
perfect notation. [...] By the aid of symbolism, we can make transitions in
reasoning almost mechanically, by the eye, which otherwise would call into
play the higher faculties of the brain. [...] It is a profoundly erroneous
truism, repeated by all copy-books and by eminent people when they are making
speeches, that we should cultivate the habit of thinking of what we are doing.
The precise opposite is the case. Civilisation advances by extending the
number of important operations which we can perform without thinking about
them. Operations of thought are like cavalry charges in a battle -- they are
strictly limited in number, they require fresh horses, and must only be made
at decisive moments."

\--from An Introduction to Mathematics, 1911

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ntownsend
For an excellent treatment of how doing mathematics is a subtle and dynamic
interplay of the "Greek" and "Babylonian" approaches I recommend Imre Lakatos'
"Proofs and Refutations"
([http://books.google.ca/books?id=EjQqJT4Z-VoC&lpg=PP1&...](http://books.google.ca/books?id=EjQqJT4Z-VoC&lpg=PP1&dq=proofs%20and%20refutations&pg=PP1#v=onepage&q=&f=false)).
It's presented as a Socratic dialog and is simply fantastic.

