> As far as I know, Zen Buddhism has strongly influenced Japanese culture.
> Since these are areas of my major interest, I've been wondering if it can
> be said that this is true for Japanese mathematics particularly. I mean,
> its history, its flavor... What relation, if any, has had Zen with Japanese
> mathematics? What about Chinese mathematics?
There are many sects of Buddhism in Japan, various ones including Zen
practices. I am not a member of any, but I have studied the socio/cultural
history of such. I think it is important to understand that forms of Zen
and other Buddhist practices coming to Japan were and perhaps are always
filtered through a sense of social consciousness and political purpose that
stems from centuries of native Shinto belief and practice. As such, I think
the phrase "strongly influenced Japanese culture" has to be seen within the
context of just how much Buddhist practices were adapted and compromised as
they found their way here. I would also suspect that such filtering (within
the complementary extant systems of any particular culture) is also a major
factor in development of "Zen" practices which have found their way to the
West.
Historically, I can find no mention of a "Zen Mathematics" in Japan, and
records showing any kind of relation between methods of "Zen" and
development of mathematics are nil as far as I can determine. Mathematics
was used by some priests in divination, and knowledge of Chinese
mathematics played a part in the curriculum some Zen priests provided in
their schooling of members of the imperial house from at least Heian times
onward. Recreational mathematical games with Chinese origins appear to have
been a part of activity of some Buddhist sects, Zen and otherwise, though
there is little evidence of "originality". More abstract mathematics, like
many areas of science, seems to have been studied more by "commoner" than
those in academic or religious power through most of Japan's history. I can
speak to these aspects relative to my own research into the development of
astronomy in Japan, but I do not think such is appropriate for this list.
On mathematical development in East Asia, the following may be valuable:
Sugimoto, M. and Swain, D.L. (1989) Science and Culture in Traditional
Japan. Charles E. Tuttle Co. Inc., Tokyo.
In Japanese:
Endou, T. (1960) Zoushuu: Nihon Suugakushi (History of Japanese
Mathematics; Enlarged and Revised). Kouseisha Kuseikaku, Tokyo.
Katou, H. (1967, 1968) Nihon Suugakushi (History of Japanese Mathematics).
Numbers 1 and 2. Maki Shoten, Tokyo.
For China, perhaps still very valuable is Needham's now classic:
Needham, J. (1959) Science and Civilization in China, Vol. III; Mathematics
and the Sciences of the Heavens and the Earth. Cambridge University Press,
Cambridge.
and a more recent general discussion of mathematics in Chinese antiquity...
Cullen, C. (1996) Astronomy and Mathematics in Ancient China: the Zhou Bi
Suan Jing. Needham Research Institute Studies. Cambridge University Press,
Cambridge.
The past decade has seen more and more work shared by scholars from the
PRC, but I am not familiar with much of this yet. I'm sure others on this
list can provide many more sources.
> The next is not a historical question, but it might be adequate to the
> context. I have no experience with koans, because I'm a practitioner of
> the Soto Zen tradition, but when I read about it I often see a sort of
> parallelism between the work with koans and the work with mathematical
> problems. Say,
>
> Rinzai Experience Mathematical Experience
> ----------------- -----------------------
> Dealing with a koan Dealing with a mathematical problem
> The zafu / the bus The chair of your office / the bus
> Satori Solution becomes suddenly clear in your mind
>
> More than this, mathematical solution is not always a discursive one, but
> a sort of intuition...
>
While I think it would be fruitless to argue with Xavier's last thought in
this context, it seems odd to me that Soto Zen seems to be so popular in
the West, something also somewhat amazing to my colleagues here in Japan.
Lately, on some "academic" lists, I have noticed a proclivity to link "Zen"
to epistemological issues in a number of areas. Discussions I have seen on
this so far have been far from fruitful; they seem to lead to nothing but
"don't you see?" sorts of arguments accompanied with "if you don't see,
then I can't show you" and other forms of "true belief" rather than any
kind of communicable "knowledge" or "methodological" base.
I have only been on this list for about a month, and I have thoroughly
enjoyed the rigor with which topics are approached. I do hope that if "Zen
Mathematics" becomes a topic on this list, that we can have the input of
actual scholarship on the subject rather than mere speculative and/or
ego-based argument.
I say the latter hoping no disrespect is shown to anyone or to any belief
system... and also with the hope that my comments are appropriate to the
context of this mailing list.
Regards,
Steve Renshaw
---------------------------------------------------------------------
Dr. Steven Renshaw stever@gol.com
Kochi University Kochi, Japan
Astronomy in Japan Page: http://www2.gol.com/users/stever/jastro.html
---------------------------------------------------------------------