[lit-ideas] Re: Pons Asinorum
- From: Jlsperanza@xxxxxxx
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Wed, 10 Jun 2009 10:30:39 EDT
"Peregrine..began to read Euclid..but he had scarce advanced beyond the
Pons Asinorum, when his ardor abated."
Smollett
"He never crossed the bridge of asses"
Suppose the name of our ass is "Mike"
MIKE
.
.
.
. - - - - - - - - - - - -> fodder
"Mike" reasons, "Surely it's shorter to use the hypothenuse". He learned
all that in a barn.
In a message dated 6/10/2009 10:02:39 A.M. Eastern Daylight Time,
karltrogge@xxxxxxxx writes:
I would be very interested in hearing from Mr Speranza an explication
of this famous proof, which seems to have been left out of my education!
In German, the term ESELSBRÜCKE seems not to share this curious
etymology (which makes no reference whatsoever to a bridge). And the
term 'Pons Asinorum' as I have learned it is applied in Euclidean
geometry at some other point than this proof of the shortness of
straight lines joining points (but as that seems to be strangely
lacking in my education, perhaps this was left out as well). Could Mr
Speranza please show us the sources for this interesting account?
----
Sure. Actually, I learned it from M. Zeleny, recently. In a post to the
forum CHORA, he was talking 'pons asinorum'. I replied publicly that according
to the OED there is some dispute about the origin.
Let me see if I can retrieve M. Zeleny's interesting post from the CHORA
archives:
----
Zeleny is using Proclus:
[Proclus] further relateed that the Epicureans
used to ridicule this theorem as being evident even
to an ass and requiring no proof. They claimed that
the theorem was "known" (gnorimon) even to an ass
that can invariably be seen choosing to walk towards
his fodder in a straight line, in lieu of traversing the
two sides of the triangle formed by an outlying point.
Suppose I call this Ass, "Mike":
MIKE . . . . . . . . . . . . > fodder
On the other hand, an Euclidean "Mike" would go triangular:
MIKE
.
.
.
.
.
. . . - - - - - - - - - - - - -> fodder.
Geary explains, "It's the mystique of the hypothenuse".
---
Zeleny continues:
In his response, Proclus pointed out that
perceiving the truth of the theorem is at a far remove
from understanding its proof as a reason why it is true.
His focus on proof remained at the foundation of
geometrical knowledge. . . .
The mediaeval tutors, frustrated by the resistance of
their charges to the idea of a geometrical figure being
congruent with its own mirror image, paid an homage to
Epicurus by deeming this proposition the
pons asinorum, the bridge of asses.
Cheers,
J. L. Speranza
Buenos Aires, Argentina
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