# [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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