En Sun, 20 Sep 2009 03:33:47 -0300, Greg Ewing
<greg.ew...@canterbury.ac.nz> escribió:
Hendrik van Rooyen wrote:
In any case, it doesn't affect my point, which was that
I was thinking about something that I didn't have a word,
or even a convenient phrase for.
That is probably true, but on the other hand, it is not totally rubbish
either, as it is hard to think of stuff you have never heard of,
whether you have an undefined word for it or not.
I quite agree that there is *some* interaction between
the language we use and the way we think, but it's a
two-way process. As a species, we're quite capable of
thinking about new things and inventing words to express
them when the need arises.
It's possible that some individuals do this more
frequently than others, e.g. mathematicians and other
people who are in the habit of exploring new ideas may
be less influenced by the constraints of language
than the general population.
Anyway, they're still constrained by the language.
In ancient Greece many wise men made remarkable progress in geometry,
arithmetic, and other areas - but could not develop algebra. Why not?
Algebra requires abstract names for unknowns - x,y,z that we use today.
The greek number system used letters to represent numbers themselves -
α=1, β=2, etc. - so no one would think on using letters for designating
unknown quantities; it was just out of their mental frame.
Diophantus created some kind of algebra notation, so he was able to write
x**n (for 2<=n<=6, basically combining the expressions for x² and x³) and
could express some equations in short (or abridged) form, instead of the
full prose that were used normally. But he was simply not able to develop
symbolic algebra. And nothing happened for 15 centuries in this regard in
Europe.
The Arabians brought the Indian number system (and the idea of zero as a
number) to Europe. And it's not a coincidence that Arabians also developed
symbolic Algebra at the same time [2]; they *could* develop Algebra
because they had a language into which symbolic names could be expressed.
[1] Colerus, Egmont. Historia de la Matemática. De Pitágoras a Hilbert.
Bs. As, Ediciones Progreso y Cultura, 1943
[2] BTW, the very name 'algebra' comes from a book of Abu Ja'far Muhammad
ibn Musa Al-Khwarizmi, "al-jabr w'al-muqabala". And guess where
'algorithm' comes from?
--
Gabriel Genellina
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