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, GermanyP.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. -------------------------------------------------------------------- To change your Lit-Ideas settings (subscribe/unsub, vacation on/off, digest on/off), visit www.andreas.com/faq-lit-ideas.html