TITLE: Notations, Representations, and Names
AUTHOR: Eugene Wallingford
DATE: June 18, 2019  3:09 PM
DESC: 
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BODY:
 In
<A HREF="http://devlinsangle.blogspot.com/2017/07/the-power-of-simple-representations.html">
   The Power of Simple Representations</A>,
 Keith Devlin takes on a quote attributed to the mathematician
 Gauss: "What we need are notions, not notations."

<BLOCKQUOTE><EM>
 While most mathematicians would agree that Gauss was correct
 in pointing out that concepts, not symbol manipulation, are
 at the heart of mathematics, his words do have to be properly
 interpreted.  While a <STRONG>notation</STRONG> does not matter,
 a <STRONG>representation</STRONG> can make a huge difference.
</EM></BLOCKQUOTE>

 Spot on.  Devlin's opening made me think of
<A HREF="https://twitter.com/proffeynman/status/1129820872955400192">
   that short video of Richard Feynman</A>
 that everyone always shares, on the difference between knowing
 the name of something and knowing something.  I've seen people
 mis-interpret Feynman's words in both directions.  The people
 who share this video sometimes seem to imply that names don't
 matter.  Others dismiss the idea as nonsense: how can you not
 know the names of things and claim to know anything?

 Devlin's distinction makes clear the sense in which Feynman is
 right.  Names are like notations.  The specific names we use
 don't really matter and could be changed, if we all agreed.
 But the "if we all agreed" part is crucial.  Names do matter
 as a part of a larger model, a representation of the world
 that relates different ideas.  Names are an index into the
 model.  We need to know them so that we can speak with others,
 read their literature, and learn from them.

 This brings to mind an article with a specific example of the
 importance of using the correct name: 
<A HREF="https://www.epsilontheory.com/through-the-looking-glass-or-this-is-the-red-pill/">
   Through the Looking Glass, or ... This is the Red Pill</A>,
 by Ben Hunt at Epsilon Theory:

<BLOCKQUOTE><EM>
 I'm a big believer in calling things by their proper names.
 Why?  Because if you make the mistake of conflating instability
 with volatility, and then you try to hedge your portfolio today
 with volatility "protection" ...., you are throwing your money
 away.
</EM></BLOCKQUOTE>

 Calling a problem by the wrong name might lead you to the wrong
 remedy.

 Feynman isn't telling us that names don't matter.  He's telling
 us that knowing <EM>only</EM> names isn't valuable.  Names are
 not useful outside the web of knowledge in which they mean
 something.  As long as we interpret his words properly, they
 teach us something useful.
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