[lit-ideas] Re: Pons Asinorum
- From: karltrogge@xxxxxxxx
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Thu, 11 Jun 2009 12:47:37 +0200
On 10-Jun-09, at 9:02 PM, Robert Paul wrote:
'Pons asinorum,' literally 'bridge of asses' was scholarly cant for
the fifth proposition of the first book of Euclid's Elements. It was
so called because inept students ('dumb asses') had difficulty
understanding its proof, i.e., getting across it. It's been
generalized to mean any intellectual difficulty which separates the
inept from the ept.
Thank you Mr Paul - this is more in line with what I thought I was
remembering about 'pons asinorum'. This is why I was wondering why Mr
Speranza was associating it with 'Euclid's famous proof' (sic) of the
shortest distance between two points being a straight line. From what
little I remember of Euclidean geometry this is not proven but is
AXIOMATIC (and this was why I asked Mr Speranza to tell us where in
Euclid the PROOF of which he speaks is to be found).
Rushing in perhaps where angels fear to tread, I will go further. In
(some?)non-Euclidean geometries IT IS NOT THE CASE THAT the shortest
distance between two points is a straight line. If I remember
correctly, (some of?) these geometries arise from rejecting Euclid's
postulate concerning parallel lines. My parenthetical queries (some?
some of?) indicate my ignorance and I would be grateful for advice
about the relationship between the AXIOMATIC shortest-distance-
straight-line (which given or assumed) and the POSTULATE (which is
proved).
Further to 'pons asinorum': in German an ESELSBRÜCKE (donkey's bridge)
is an aid to remembering some formula or series - a mnemonic. For
example, in German, to remember the tuning of violin strings from low
to high: Geh Du Alter Esel - GDAE; in English, to remember the lines
of the treble staff: Every Good Boy Deserves Fun - EGBDF. It seems
that the meaning has 'wandered' from 'any intellectual difficulty
which separates the inept from the ept' to 'an aid which helps the
inept overcome some such intellectual difficulty'.
Karl Trogge
Hamburg, Germany
P.S. It appears that I apologized unnecessarily for double-posting -
it turns out it was only to myself (owing to the way in which I set up
my rules for managing e-mail) that two copies of my post were
delivered. (I mention this just in case someone was wondering what on
earth I was going on about.) As Goethe says, "Aller Anfang ist
schwer" (all beginning is difficult, or roughly: the first step is the
hardest). I ask for patience while I find my feet.
Karl T.
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