Numbers and angles
Ian A. York
Sorry if this has already been posted. I haven't been following this
froup closely for some time.
My son's grade 4 teacher sent home a powerpoint presentation that she
thought (and apparently the kids also thought) was amazing. The opening
is "I shared this with my students today and they really found it
interesting. They wanted me to forward it to you so they could share it
at home!" but it's signed with the wrong initial (J instead of C) so
I'm pretty sure even that part is part of the forwarded email. The next
line has four exclamation marks (!!!!), a serious warning sign.
The powerpoint purports to explain the origin of Western numerals, as
arising from the number of angles in each number. There's a version of
it at http://www.scribd.com/doc/13244252/Number-Story .
The misspellings in the ppt were my first flag, and the explanation
didn't fit with what I remembered for the early shapes of the numbers,
so I looked for something to refute it. I found
A history of mathematical notations, Volume 1, By Florian Cajori
published in 1928-29
http://books.google.com/books?id=7juWmvQSTvwC&lpg=PR1&pg=PA64#v=onepage&q=&f=false
p. 64.
"96. Fanciful hypotheses on the origin of the numeral forms"
[A fine, dismissive tone is struck, including the potential motto "they
were as convinced of the correctness of their explanations as are
circle-squarers of the soundness of their quadratures."]
He explicitly dismisses the angle theory:
"A French writer, P. Voizet[2], entertained the theory that originally a
numeral contained as many angles as it represents units, as seen in Part
V. He did not claim credit for this explanation, but ascribed it to a
writer in the Genova Catholico Militaire."
Part V is one line in a table of XIII fanciful hypotheses, neatly
matching the explanation given in the powerpoint.
The footnote [2] refers to
"Les chiffres arabes et leur origine," La nature (2d semestre, 1899),
Vol. XXVII, p. 222
An earlier reference to the fanciful hypotheses, less detailed but even
more dismissive (and even more elaborately phrased), is
The Hindu-Arabic Numerals By David Eugene Smith, Louis Charles Karpinski
1911
"Of absolute nonsense about the origin of the symbols which we use much
has been written. Conjectures, however, without any historical evidence
for support, have no place in a serious discussion of the gradual
evolution of the present numeral forms."
They also cite Monsieur Voizet, though in this case apparently not for
the angles theory but for his own "strokes" idea.
In any case, it seems that this notion, though entertaining, is pretty
much a load of dingos' kidneys, so feel free to contemptuoulsy mock your
children when they prattle merrily about this.
(I am closing my Panix account, regretfully, so if anyone needs to
contact me I'm now at iayork.com.)
Ian "getting bent" York
--
Ian York (iay...@panix.com) <http://www.panix.com/~iayork/>
"-but as he was a York, I am rather inclined to suppose him a
very respectable Man." -Jane Austen, The History of England
R H Draney
I remember seeing that explanation back in the 60s in that bastion of vectors,
Readers Digest...it seemed stupid and contrived to me even then....
However, there *is* a definite correlation between the first three positive
integers and the shape of their representation in Chinese numerals...the Chinese
character for "four" uses five strokes, although it *is* square....
R H "there are thirty-nine letters in this internym" Draney
--
A pessimist sees the glass as half empty.
An optometrist asks whether you see the glass
more full like this?...or like this?