Yahoo Tuning Groups Ultimate Backup tuning Pythagorean

Carl,

Now now, we all have to learn everything one or two
items at a time. There's no need to act superior.

When I was 50 years old I was at a party north of
Santa Cruz eating sushi for the first time. A young
woman of about 20 asked me if I wanted some wasabi.
What's wasabi?, I asked. Looking disgusted and
raising her voice so that everyone would hear, she
fairly shouted, "YOU DON'T KNOW WHAT WASABI IS?!!!!!

Mark

--- Carl Lumma <carl@lumma.org> wrote:

> --- In tuning@yahoogroups.com, "Paul Poletti"
> <paul@...> wrote:
> >
> > BTW, over at the Stanford University Encyclopedia
> of Philosophy,
> > they have a really interesting article on our old
> buddy Mister P.
> > Turns out most of the stuff attributed to him,
> including harmonic
> > proportions and the famous triangle theorem, was
> most likely not
> > anything he himself ever did, nor any of the other
> members of his
> > sect. Seems as though both ideas had been floating
> about for some
> > time and he just took them up and wove them into
> his particular
> > brand of religious fanaticism.
>
> You didn't know that?
>
> -Carl
>
>

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🔗Carl Lumma <carl@lumma.org>

🔗Paul Poletti <paul@polettipiano.com>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> You're right, Mark, that was a useless comment on
> my part. Sorry Paul. I've deleted that message from
> the archives. -Carl

That's OK Carl, I'm pretty thick-skinned. Plus I seem to be in good
company in my previous ignorance. Just today I was looking at two
relatively new e-books on acoustics, one in English and one in
Catalan, and both dish out the same old Pythagorean mythology about
how "he" made experiments with strings and discovered that length was
proportional to interval size, and how "he" only found 5ths and 4ths
to be consonances etc etc etc . It pernicious in the acoustics
literature, and its just one of those things I'd never taken the time
to go check up on, until now.

Ciao,

🔗David Beardsley <db@biink.com>

🔗Mark Rankin <markrankin95511@yahoo.com>

Paul,

Somewhere in the mountains along the north coast of
California locked in an old office trailer there is a
book by Morris Klein which was published perhaps in
the 1950's and was entitled "The History of
Mathematics", or some such. As long as I live, I will
never forget reading the opening sentence of the first
paragraph of chapter one. It's a short declarative
sentence and it goes like this:
'Mathematics was invented by the Greeks'.

Fifty years have passed, and it is starting to look as
if alot of what was attributed to the ancient Greeks,
Pythagoras et al, in fact came from the ancient
Babylonians, and some of what has been attributed to
the ancient Babylonians in fact came from the even
more ancient Sumerians.

The duplatio doubling system of the ancient Egyptians,
also called duplation, may seem funky to moderns like
us, but they were able to make good use of it to
achieve the results of multiplication and division.

Today it looks as if the opening sentence of Klein's
book should probably have read: 'Mathematics was
*not* invented by the Greeks!'.

Mark Rankin

--- Paul Poletti <paul@polettipiano.com> wrote:

> --- In tuning@yahoogroups.com, "Carl Lumma"
> <carl@...> wrote:
> >
> > You're right, Mark, that was a useless comment on
> > my part. Sorry Paul. I've deleted that message
> from
> > the archives. -Carl
>
> That's OK Carl, I'm pretty thick-skinned. Plus I
> seem to be in good
> company in my previous ignorance. Just today I was
> looking at two
> relatively new e-books on acoustics, one in English
> and one in
> Catalan, and both dish out the same old Pythagorean
> mythology about
> how "he" made experiments with strings and
> discovered that length was
> proportional to interval size, and how "he" only
> found 5ths and 4ths
> to be consonances etc etc etc . It pernicious in the
> acoustics
> literature, and its just one of those things I'd
> never taken the time
> to go check up on, until now.
>
> Ciao,
>
> P
>
>

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🔗Mayank Chaturvedi <mayank_chatur@hotmail.com>

Hello List Members:

Please check out the following books:

Crest of the Peacock: Non European roots of Mathematics.

Also, see the book just published by Princeton Univ.

http://press.princeton.edu/titles/8583.html

M Chaturvedi

> From: Mark Rankin <markrankin95511@yahoo.com>
> Reply-To: "tuning@yahoogroups.com" <tuning@yahoogroups.com>
> Date: Fri, 19 Oct 2007 14:04:44 -0700 (PDT)
> To: "tuning@yahoogroups.com" <tuning@yahoogroups.com>
> Subject: Re: [tuning] Re: Pythagorean - not!
>
> Paul,
>
> Somewhere in the mountains along the north coast of
> California locked in an old office trailer there is a
> book by Morris Klein which was published perhaps in
> the 1950's and was entitled "The History of
> Mathematics", or some such. As long as I live, I will
> never forget reading the opening sentence of the first
> paragraph of chapter one. It's a short declarative
> sentence and it goes like this:
> 'Mathematics was invented by the Greeks'.
>
> Fifty years have passed, and it is starting to look as
> if alot of what was attributed to the ancient Greeks,
> Pythagoras et al, in fact came from the ancient
> Babylonians, and some of what has been attributed to
> the ancient Babylonians in fact came from the even
> more ancient Sumerians.
>
> The duplatio doubling system of the ancient Egyptians,
> also called duplation, may seem funky to moderns like
> us, but they were able to make good use of it to
> achieve the results of multiplication and division.
>
> Today it looks as if the opening sentence of Klein's
> book should probably have read: 'Mathematics was
> *not* invented by the Greeks!'.
>
> Mark Rankin
>
>
>
>
>
>
> --- Paul Poletti <paul@polettipiano.com> wrote:
>
>> --- In tuning@yahoogroups.com, "Carl Lumma"
>> <carl@...> wrote:
>>>
>>> You're right, Mark, that was a useless comment on
>>> my part. Sorry Paul. I've deleted that message
>> from
>>> the archives. -Carl
>>
>> That's OK Carl, I'm pretty thick-skinned. Plus I
>> seem to be in good
>> company in my previous ignorance. Just today I was
>> looking at two
>> relatively new e-books on acoustics, one in English
>> and one in
>> Catalan, and both dish out the same old Pythagorean
>> mythology about
>> how "he" made experiments with strings and
>> discovered that length was
>> proportional to interval size, and how "he" only
>> found 5ths and 4ths
>> to be consonances etc etc etc . It pernicious in the
>> acoustics
>> literature, and its just one of those things I'd
>> never taken the time
>> to go check up on, until now.
>>
>> Ciao,
>>
>> P
>>
>>
>
>
> __________________________________________________
> Do You Yahoo!?
> Tired of spam? Yahoo! Mail has the best spam protection around
> http://mail.yahoo.com

🔗monz <monz@tonalsoft.com>

Hi Mark,

--- In tuning@yahoogroups.com, Mark Rankin <markrankin95511@...> wrote:
>
> Paul,
>
> Somewhere in the mountains along the north coast of
> California locked in an old office trailer there is a
> book by Morris Klein which was published perhaps in
> the 1950's and was entitled "The History of
> Mathematics", or some such. As long as I live, I will
> never forget reading the opening sentence of the first
> paragraph of chapter one. It's a short declarative
> sentence and it goes like this:
> 'Mathematics was invented by the Greeks'.
>
> Fifty years have passed, and it is starting to look as
> if alot of what was attributed to the ancient Greeks,
> Pythagoras et al, in fact came from the ancient
> Babylonians, and some of what has been attributed to
> the ancient Babylonians in fact came from the even
> more ancient Sumerians.

I encourage everyone interested in this topic to
read this online dissertation:

Franklin, John Curtis.
_Terpander: The Invention of Music in the Orientalizing Period_
http://kingmixers.com/Terp.html

Franklin's work supports many of my own speculations.
At any rate, it is beyond dispute that the Babylonians
knew very sophisticated mathematics. And the way the
tablets were written, using Sumerian logograms to
encode all of the important information, strongly
suggests that the Sumerians were the first to write
any of it down, c.2800-2000 BC.

It is clear that the Greeks learned much of their
mathematics (and music-theory!) from the Babylonians,
and it is also clear that the Greeks developed further
upon that during their "Golden Age", the 300s BC.

I have pages about the Sumerians (and the Hurrian Hymn),
which are now indexed in the Encyclopedia. Somewhere
in them you'll find references to this book, which
tells the story in detail:

Otto_Neugebauer.
_The Exact Sciences in Antiquity_.
Princeton: Princeton University Press, 1952;
2nd edition, Brown University Press, 1957;
reprint, New York: Dover publications, 1969.

From the Wikipedia page about him:

>> "By studying clay tablets he discovered that the
>> ancient Babylonians knew much more about mathematics
>> and astronomy than had been previously realized."

http://en.wikipedia.org/wiki/Otto_Neugebauer

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Mark Rankin <markrankin95511@yahoo.com>

Monz, et al,

Somewhere in the mountains along the north coast of
California locked in an old office trailer there is
*also* Otto Neugebauer's "The Exact Sciences in
Antiquity"!

Something is telling me I had better return to those
mountains along the north coast and reclaim my books
before someone breaks in and beats me to it.

Thanks for alerting all of us to John Curtis
Franklin's dissertation.

Another person knowledgable on this subject is Ernest
G. McClain.

BTW, a reprint of McClain's book on Islam,
"Meditations through the Quran", with a new 12 page
appendix, will be coming out soon.

Mark

--- monz <monz@tonalsoft.com> wrote:

> Hi Mark,
>
>
> --- In tuning@yahoogroups.com, Mark Rankin
> <markrankin95511@...> wrote:
> >
> > Paul,
> >
> > Somewhere in the mountains along the north coast
> of
> > California locked in an old office trailer there
> is a
> > book by Morris Klein which was published perhaps
> in
> > the 1950's and was entitled "The History of
> > Mathematics", or some such. As long as I live, I
> will
> > never forget reading the opening sentence of the
> first
> > paragraph of chapter one. It's a short
> declarative
> > sentence and it goes like this:
> > 'Mathematics was invented by the Greeks'.
> >
> > Fifty years have passed, and it is starting to
> look as
> > if alot of what was attributed to the ancient
> Greeks,
> > Pythagoras et al, in fact came from the ancient
> > Babylonians, and some of what has been attributed
> to
> > the ancient Babylonians in fact came from the even
> > more ancient Sumerians.
>
>
> I encourage everyone interested in this topic to
> read this online dissertation:
>
> Franklin, John Curtis.
> _Terpander: The Invention of Music in the
> Orientalizing Period_
> http://kingmixers.com/Terp.html
>
> Franklin's work supports many of my own
> speculations.
> At any rate, it is beyond dispute that the
> Babylonians
> knew very sophisticated mathematics. And the way the
> tablets were written, using Sumerian logograms to
> encode all of the important information, strongly
> suggests that the Sumerians were the first to write
> any of it down, c.2800-2000 BC.
>
> It is clear that the Greeks learned much of their
> mathematics (and music-theory!) from the
> Babylonians,
> and it is also clear that the Greeks developed
> further
> upon that during their "Golden Age", the 300s BC.
>
> I have pages about the Sumerians (and the Hurrian
> Hymn),
> which are now indexed in the Encyclopedia. Somewhere
> in them you'll find references to this book, which
> tells the story in detail:
>
> Otto_Neugebauer.
> _The Exact Sciences in Antiquity_.
> Princeton: Princeton University Press, 1952;
> 2nd edition, Brown University Press, 1957;
> reprint, New York: Dover publications, 1969.
>
> From the Wikipedia page about him:
>
> >> "By studying clay tablets he discovered that the
> >> ancient Babylonians knew much more about
> mathematics
> >> and astronomy than had been previously realized."
>
> http://en.wikipedia.org/wiki/Otto_Neugebauer
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>
>
>

__________________________________________________
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🔗monz <monz@tonalsoft.com>

Hi Mark,

--- In tuning@yahoogroups.com, Mark Rankin <markrankin95511@...> wrote:

> Somewhere in the mountains along the north coast of
> California locked in an old office trailer there is
> *also* Otto Neugebauer's "The Exact Sciences in
> Antiquity"!
>
> Something is telling me I had better return to those
> mountains along the north coast and reclaim my books
> before someone breaks in and beats me to it.

I think so. My own library is not now with me where
i live, and it's a pain to be separated from it ...
but at least it's only a fairly short bike ride away.

> Another person knowledgable on this subject is Ernest
> G. McClain.

McClain has been mentioned here several times before,
and it usually starts a subdued-flame war, with
me supporting his ideas and others calling it a crock.

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Mark Rankin <markrankin95511@yahoo.com>

Hygiene,

Monsieur precis, if there is nothing more to
mathematics than proving theorems then you're right,
and Klein makes that very argument if I recall, but
surely you would agree that in the 21st century there
is much more to math than merely proving theorems,
n'est-ce pas?

Mark

--- Gene Ward Smith <genewardsmith@sbcglobal.net>
wrote:

> --- In tuning@yahoogroups.com, Mark Rankin
> <markrankin95511@...> wrote:
>
> > Today it looks as if the opening sentence of
> Klein's
> > book should probably have read: 'Mathematics was
> > *not* invented by the Greeks!'.
>
> If you define mathematics as proving theorems, that
> appears to have
> been invented by the Greeks.
>
>

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