Mutual Discussion of M&D(0): sigma & samekh

[Matthew P Wiener]

jp4321 at idt.net (jporter) writes:

>The Greeks mistakenly called "S" samekh (Hebrew "X") which transliterated
>became sigma, S. So, from early on, alabetically speaking, there was a
>confusion between *the names* for S and X.  [...] But, the original
>Greek confusion, notwithstanding, the phoneme for which the Greeks
>mistakenly borrowed S is symbollized in Hebrew by X., i.e., it is the
>same. Phonetically, Greek S = Hebrew X, given the vagaries of trans-
>literation, samekh to sigma. [...]

Hmmm.  There seems to be some confusion here, partly mine for reading in
media res.  Best to just give a correct summary.

"Samekh" is the Hebrew letter, "sigma" is the Greek letter.  Both are s-like
sibilants.  Samekh for two millennia has been printed as a round loop with
a serif on the upper left.  The Greek sigma (majuscule) looks like a capital
M tilted 90 degrees counterclockwise.

Despite the phonetic similarity, they are distinct letters historically.  The
Greek sigma evolved from the Semitic protosin, which looked like a kind of W.
The Greeks turned it on the side, the Hebrews made it look like an E lying on
its back, with one arm waving left, and two arms waving right.  The _name_
sigma seems to be a Greek corruption of samekh, though.

The Semitic protosamekh, in contrast, was a triple-barred T.  I have no idea
how this became the later samekh.  In Greek, however, it became the xi, simply
by leaving out the vertical bar.  This is pretty much the same k-s `x' that
we use in English.  The cross symbol--our modern `X'--was sometimes used, but
this was permanently attached to chi in Greek.  But the Etruscans took up the
minority k-s X-symbol, from whence it ended up in Latin and eventually English.

Much much later, the Greeks developed their minuscule alphabet.  The small sigma
came in two forms, ordinary and terminal.  The ordinary small sigma looks much
like a backwards samekh, a loop with a serif on the upper right.  This too may
well have been a borrowing, from the "wrong" Hebrew sibilant.  But by then, the
alphabets had long gone their separate ways, so it's only a "mistake" in a purely
academic sense.
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>But the glorious symbol chosen for the cover seems to harken back to the
>Latin Epsilon of Et, the first letter of the latin *and*.

The Latin letter is named "E", no more.

>And to what other uses have Epsilons, of the capital variety, been put?
>Well, (funny you should ask) mathematically speaking, to signify the
>process of summation

No, that's a sigma.

>		       of all the sector'd subintervals of an area under a
>curve- as the number of subintervals increases toward infinity (or, the
>limit of the expanse of each subinterval approaches zero), i.e., integration.

No.  _Any_ summation, involving the finite, infinite, or infinitesimal, is
denoted with the capital sigma.

>Early on, the process of taking limits became internalized and
>automatically assumed, emphasis being placed on the summing of the infinite
>subintervals. Then, the symbol for the Limit, and the sum of the limits, E,
>were subsumed into the elegant and elongated Sigma of Leibnitz. The symbols
>for the whole process becoming sigmated.

Actually, the process of taking limits was not identified as such until more
than a century after Newton and Leibniz.  One could say limits were exhumed,
not subsumed.

>Is it strange that the ampersand faces left to right, and so by convention,
>seems to extend that tongue Eastward?

No.
--
-Matthew P Wiener (weemba at sagi.wistar.upenn.edu)