RE: virus: Running around in circles

TheHermit (The@Hermit.net)
Wed, 9 Dec 1998 11:55:18 -0600

The Babylonians laid the foundations of the place-value system the number
system they borrowed from the Sumerians, we see two basic ''large ones'':
ten and sixty, from the most ancient clay tablets which have come down to
us, dating to the beginning of the third millennium B.C. We can only guess
where the number sixty was taken from. The well-known historian of
mathematics O. Neigebauer believes that it originated in the relation
between the basic monetary units in circulation in Mesopotamia: one mana (in
Greek mina was sixty shekels). Such an explanation does not satisfy our
curiosity because the question immediately arises: why are there sixty
shekels in a mana? Isn't it precisely because a system based on sixty was
used? After all, we don't count by tens and hundreds because there are 100
kopecks in a ruble! F. Thureau-Dangin, an Assyriologist, gives linguistic
arguments to show that the number system was the primary phenomenon and the
system of measures came second. Selection of the number sixty was apparently
a historical accident, but one can hardly doubt that this accident was
promoted by an important characteristic of the number sixty, namely that it
has an extraordinarily large number of divisors 2, 3, 4, 5, 6, 10, 12, 15,
20, and 30). This is a very useful feature both for a monetary unit (since
its existent money has been evenly subdivided) and for establishing a system
of counting (if we assume that some wise man introduced it, guided
considerations of convenience in calculation).

The mathematical culture of the Babylonians is known to us from texts dating
from the Ancient Babylonian (1800-1600 B.C.) and the Seleucidae epoch
(305-64 B.C.). A comparison of these texts shows that no radical changes
took place in the mathematics of the Babylonians during this time.

The Babylonians computed the circumference and area of a circle using a
value of [pi]=3, which is much worse than the Egyptian approximation.

The Egyptians calculated the area of a circle by squaring 8/9, of its
diameter, a difference of about 1 percent from the value of pi. (from the
Moscow Papyrus which refers to this knowledge as being "common" by around
3,700 BCE).

The reason for 360 divisions is simple, it is based on the physical
measuring instruments which were available to them. In other words, at the
time that the division of the circle became a convention, they could
represent each quadrant with sixty divisions. To go beyond that to 120
divisions was beyond the limits of their technology.

Having familiarized themselves with both the Egyptian and the Babylonian
systems of writing fractions and performing operations on them, the Greeks
selected the Babylonian system for astronomical calculations because it was
incomparably better, but they preserved their own alphabetic system for
writing whole numbers. Thus the Greek system used in astronomy was a mixed
one: the whole part of the number was represented in the decimal
nonpositional system while the fractional part was in the 60-base positional
system--not a very logical solution by the creators of logic! Following
their happy example we continue today to count hours and degrees (angular)
in tens and hundreds, but we divide them into minutes and seconds.

The above is in part derived from chapter 9 of the "The Phenomenon of
Science" by Valentin F. Turchin and the balance from Lancelot Hogben's
Mathematics for the millions. As you can see, we have no need to introduce
Velokovskyian "magic" into the process of figuring things out.

Hermit

> -----Original Message-----
> From: owner-virus@lucifer.com [mailto:owner-virus@lucifer.com]On Behalf
> Of John DePaul Hansen, Jr.
> Sent: Tuesday, December 08, 1998 11:22 AM
> To: virus@lucifer.com
> Subject: Re: virus: Running around in circles
>
>
> December 8, 1998
>
> Dear Erik:
>
> According to Immanuel Velokovsky (and perhaps Zechariah Sitchen also),
> the year used to be 360 days long, back before solar-system catastrophes
> changed its orbit. Thus it seemed natural to divide the circle into 360
> degrees, one degree being the size of arc travelled by the earth in one
> day. 360 also has the virtue of having many factors, thus being capable
> of all kinds of equal subdivisions. (As a member of the Dozenal Society
> [formerly the Duodecimal Society, I have a keen interest in such
> matters.)
>
> According to Graham Hancock in The Mars Mystery, the space aliens are
> aware of the way we have divided the circle, and may even have endowed
> us with this system themselves.
>
> There are better ways to measure the circle, but that is another story.
>
> ***********************************************************
> * John D. Hansen, Jr. * Hansen Softwares *
> * 801 Hillside Terrace, #50 * *
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>
> >From owner-virus@lucifer.com Mon Jun 15 10:58:44 1998
> >Received: (from majordom@localhost)
> > by maxwell.kumo.com (8.8.7/8.8.7) id LAA15018
> > for virus-outgoing; Mon, 15 Jun 1998 11:48:46 -0600
> >X-Authentication-Warning: maxwell.kumo.com: majordom set sender to
> owner-virus@lucifer.com using -f
> >Message-Id:
> <C7EA264064ACD011BE4500805FC1DCA10193BEC0@SATURN.nt.data-io.com>
> >From: "Chelstad, Erik" <chelste@data-io.com>
> >To: "'virus@lucifer.com'" <virus@lucifer.com>
> >Subject: virus: Running around in circles
> >Date: Mon, 15 Jun 1998 09:51:03 -0800
> >X-Priority: 3
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> >Reply-To: virus@lucifer.com
> >
> >Since everyone seems to be talking about circles, perhaps someone
> >might be able to answer a question for me.
> >
> >Why does a circle have 360 degrees?
> >
> >I guess, potentially, the question might be: What is the origin of
> >the degree?
> >
> >Sort of mathematical meme questioning.....
> >
> >eEc
> >
> >> ----------
> >> From: Wade T. Smith[SMTP:wsmith1@camail2.harvard.edu]
> >> Reply To: virus@lucifer.com
> >> Sent: Monday, June 15, 1998 1:55 AM
> >> To: virus@lucifer.com
> >> Subject: Re: virus: getting it
> >>
> >> > Does it matter that a circle is represented
> >> > symbolically as "pi" or does it matter that a person
> >> > understand the pure nature of a circular form?
> >>
> >> Yes.
> >> **********************
> >> Wade T. Smith
> >> wade_smith@harvard.edu
> >> **********************
> >>
> >>
> >
>
>
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