Newsgroup sci.archaeology 47175

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In article , petrich@netcom.com says...
>
>
>        [A lot of stuff on unit-fraction decompositions...]
>
>        A rather interesting curiosity, but hardly Euclid's _Elements_. I 
>think it interesting that Mr. Whittet has yet to claim any Egyptian 
>originals for the _Elements_, any Egyptian text that looks as if the 
>_Elements_ had been copied from it.
>-- 
>Loren Petrich                           Happiness is a fast Macintosh
>petrich@netcom.com                      And a fast train
>My home page: http://www.webcom.com/petrich/home.html
>Mirrored at: ftp://ftp.netcom.com/pub/pe/petrich/home.html
>
>
Date: Mon, 23 Sep 1996 18:34:33 -0700 (PDT)
From: Milo Gardner 
To: Steve Whittet 
Subject: Re: Euclid's Book VII and Unit Fractions
Hi Steve:
A 3-term series is an improvement over a 5-term series,
especially with the last terms being so small.
Congratulations. I'll pass along to Kevin Brown
these comments:
On Mon, 23 Sep 1996, Steve Whittet wrote:
> At 01:46 PM 9/23/96 -0700, you wrote:
> 
> ...snip...
> 
> Hi Milo,
> 
> I will respond to the rest later, but I thought this expansion
> 1/6 + 1/17 + 1/102 = 4/17 was ok, basically Sylvesters method
> as you point out, a little practice probably helps you learn
> some axioms to go along with the basic algorithm
> 
> >> 4/17 - 1/17 = 3/17
> >> 17/3 = 5 2/3
> >> 5 2/3 > 6
> >> 3/17 - 1/6 
> >> 6*17= 102
> >> 18/102 - 17/102 = 1/102
> >> 
> >> 1/6 + 1/17 + 1/102 = 4/17
> >>
Let me see if any of my algorithms produce your series.
1. n/p = 1/a + (na -p)/ap
3/17 = 1/6 + (18 - 17)/(6*17)
     = 6' 104' 
is it an improvement on the Egyptian value from
the table? 
Yes, a value that would have been know by the author of the
Akhmim P. I have no idea why the u.v value was chosen. 
(Just showing off, I suspect).
n/17 Akhmim P. Value Ideas from 1650 BC Egyptian Fractions 
------------------------------------- 
 2/17 12' 51' 68' 2 a - p = 7 [a = 12, divisors 4, 3]
 3/17 12' 17' 51' 68' 2/17 + 1/17 
 4/17 12' 15'17' 68' 85' (1/3 + 1/17)(1/4 + 1/5) or  (1/a + 1/p)(1/u+ 1/v)*  
                                                 or (1/3 + 1/17)(1/4 + 1/5) 
That is to say, this analysis only read the contents of the
Akhmim P. and did no evaluate the smallness issue -- as
you have pointed out.
Thanks for the comments,
Milo
steve

In article , petrich@netcom.com says...
>
>
>        [A lot of stuff on unit-fraction decompositions...]
>
>        A rather interesting curiosity, but hardly Euclid's _Elements_. I 
>think it interesting that Mr. Whittet has yet to claim any Egyptian 
>originals for the _Elements_, any Egyptian text that looks as if the 
>_Elements_ had been copied from it.
>-- 
>Loren Petrich                           Happiness is a fast Macintosh
>petrich@netcom.com                      And a fast train
>My home page: http://www.webcom.com/petrich/home.html
>Mirrored at: ftp://ftp.netcom.com/pub/pe/petrich/home.html
>
>
Date: Tue, 24 Sep 1996 06:13:05 -0700 (PDT)
From: Milo Gardner 
To: Steve Whittet 
Subject: Re: Euclid's Book VII and Unit Fractions
Hi Steve:
The system is easy to learn when considering local rather than
global algorithms. That is to say, Egyptians used several rules,
depending upon the situation --- such as the EMLR's 1/p, 1/pq
and RMP's 2/p and 2/pq and later papyri n/p and n/pq view points.
That is to say, Egyptians, Greeks, Romans and Copts did not use
base 10 decimals, a form of blinders than commonly hides the
beauty/simplicity of Egyptian fractions from modern 'scholars'.
Milo
On Tue, 24 Sep 1996, Steve Whittet wrote:
> Milo Gardner wrote:
> > 
> > Hi Steve:
> > 
> > A 3-term series is an improvement over a 5-term series,
> > especially with the last terms being so small.
> > Congratulations. I'll pass along to Kevin Brown
> > these comments:
> > 
> > On Mon, 23 Sep 1996, Steve Whittet wrote:
> > 
> > > At 01:46 PM 9/23/96 -0700, you wrote:
> > >
> > > ...snip...
> > >
> > > Hi Milo,
> > >
> > > I will respond to the rest later, but I thought this expansion
> > > 1/6 + 1/17 + 1/102 = 4/17 was ok, basically Sylvesters method
> > > as you point out, a little practice probably helps you learn
> > > some axioms to go along with the basic algorithm
> > >
> > > >> 4/17 - 1/17 = 3/17
> > > >> 17/3 = 5 2/3
> > > >> 5 2/3 > 6
> > > >> 3/17 - 1/6
> > > >> 6*17= 102
> > > >> 18/102 - 17/102 = 1/102
> > > >>
> > > >> 1/6 + 1/17 + 1/102 = 4/17
> > > >>
> > 
> > Let me see if any of my algorithms produce your series.
> > 
> > 1. n/p = 1/a + (na -p)/ap
> > 
> > 3/17 = 1/6 + (18 - 17)/(6*17)
> > 
> >      = 6' 104'
> 
> Yes, = 6' 102', right?
> 
> now I begin to see where your algorithim comes from
> 
> n/p = any numerator over any denominator
> a = p/n > 
> (I always had trouble figuring out where the a came from)
> can we simplify as the following so we don't need the "a" term?
> would this be easier to plug into a spread sheet?
> 
> 1. n/p = 1/[p/n>] + (n [p/n>] - p) / ([p/n>] * p)
> 
> > 
> > is it an improvement on the Egyptian value from
> > the table?
> > 
> > Yes, a value that would have been know by the author of the
> > Akhmim P. I have no idea why the u.v value was chosen.
> > (Just showing off, I suspect).
> > 
> > n/17 Akhmim P. Value Ideas from 1650 BC Egyptian Fractions
> > -------------------------------------
> >  2/17 12' 51' 68' 2 a - p = 7 [a = 12, divisors 4, 3]
> >  3/17 12' 17' 51' 68' 2/17 + 1/17
> >  4/17 12' 15'17' 68' 85' (1/3 + 1/17)(1/4 + 1/5) or  (1/a + 1/p)(1/u+ 
1/v)*
> >                                                  or (1/3 + 1/17)(1/4 + 
1/5)
> > 
> > 
> > That is to say, this analysis only read the contents of the
> > Akhmim P. and did no evaluate the smallness issue -- as
> > you have pointed out.
> > 
> > Thanks for the comments,
> 
> Well, I'm interested, just mathematically illiterate,...:)
> My hope is that perhaps there was a fairly uncomplicated system which
> even I can learn...
> > 
> > Milo
> 
steve

I had thought this report was either completely bogus or was a report of a
tomb of a high-ranking nobleman, but Frank Yurco's comment that the tomb
sounds like an early 18th dynasty royal tomb (not 19th dynasty) suggests
an interesting solution:  Ahmes I.  His tomb has never been found, and
certainly lay outside the Valley of the Kings.
It seems unlikely that the occupant is Ahmes.  A mummy labelled as his was
in the TT320 cache.  However, Wente and Harris have cast dount on the
identification of this mummy
Just a thought. 
Chris Bennett
(from my wife's account)

In article ,
Loren Petrich  wrote:
>>Also, there is an Egyptian word for monkey "gf" or "gfu", which might 
>>have been pronounced "gafu", hence the German "Affe" and the English 
>>"ape". 
	And Hebrew kof or qop, also.
>	Old English has apa; I confess I find it hard to imaging a g 
>being dropped so readily.
	I just realized that there *might* be a way for that "k" to drop 
out of Germanic; it has to do with Grimm's Law. That's an Indo-European 
sound correspondence that goes something like this:
Most Indo-European t ~ Germanic th (often becoming d)
Most Indo-European p ~ Germanic f
Most Indo-European k ~ Germanic h or kh
	Examples:
English "that" ~ Greek to ~ Sanskrit tat ~ Russian to
English "foot" ~ Latin ped- ~ Greek pod- ~ Sanskrit pad-
English "heart" ~ Latin cord- ~Greek kardia ~ Sanskrit s'rad- ~ Russian serdtse
English "who, what" ~ Latin qui-, quo- ~ Greek ti- ~ Sanskrit kas, kim ~ 
Russian kto, chto
English "eight" ~ Latin octo ~ Greek okto ~ Sanskrit as'ta
English "hundred" ~ Latin centum ~ Greek hekaton ~ Sanskrit s'atam ~ 
Russian sto
English "hound" ~ Latin canis ~ Greek kuon- ~ Sanskrit s'van-
(some of the k's correspond to s-like sounds in Sanskrit and Russian, but 
that's another matter)
	Thus, if a word like /kop/ got borrowed early enough by some 
speakers of some ancestral Germanic dialect, then by Grimm's law, it 
would have been turned into something like *haf or *hap, and ultimately 
into English ape and German Affe. However, that would require the initial 
h disappearing, which does not seem to happen.
	Conclusion:
	The putative borrowing *kop- > English ape, German Affe, etc. 
would have had to take place among some early Germanic speakers, and even 
then, there are still some sound-correspondence problems, like why not 
English *hafe ?
-- 
Loren Petrich				Happiness is a fast Macintosh
petrich@netcom.com			And a fast train
My home page: http://www.webcom.com/petrich/home.html
Mirrored at: ftp://ftp.netcom.com/pub/pe/petrich/home.html

In article <01bb4a59$c47d2060$54c4b7c7@system>, tekdiver@ix.netcom.com 
says...
>
>Dear Frank,
>
>At what point in history did the Polynesians become prodigious navigators?
I would use the term Polynesian to refer to the people who could navigate 
the Pacific out of sight of land. This would include the Lapita but
probably not the Micronesians so lets be conservative and date this
navigation to the 3rd millenium BC which is about when the land snails,
obsidian and Lapita pottery first spread rom the Solomons to the Carolines.
>
>Paul
>-- ...snip...
>Frank Joseph Yurco  wrote in article
>...
>> Dear Steve and Yuri,
>> 
>> The Pacific Islanders, especially the Polynesians and Micronesians, were
>> prodigious navigators. They had learned to navigate by the stars, also
>> used wave patterns, and watched clouds, as well as bird formations.
I think Pauls point may be, did they learn all this at once or did it
gradually evolve that there were more and more recognizable clues to
their position which people were capable of using and teaching others 
to use. In a way this must have been one of the first true sciences.
>>  All these could give signals of undetected islands nearby. 
>> High islands are cloud covered at higher elevations, waves 
>> would bounce off islands, and certain birds were ranging far 
>> out to sea, while others stuck close to land. 
Yes, plus rivers emptying into the sea carry dirt and various
bits of flotsam and jetsam, the water changes color as you
pass over shoals and reefs, different species of fish can be
found in different waters, winds and tides, water temperature,
air temperature, currents, and the position of the sun and moon.
>> So, all these techniques were used in combination to reach and
>> settle new islands.
Yes
 That's how Hawaii was found, Easter Island, as well
>> as New Zealand, all settled by Polynesian navigators.
This I am not so sure about. All these were settled much later than
the rest of Polynesia and may have been found as the result of some
new technique or capability not possessed by earlier generations.
One possibility might be improved ways of rigging sail, another might
be stronger sturdier boats.
>> The old sea-voyaging canoes were large double out-riggered craft, 
>> very capable of long voyages,
What is the earliest evidence of these? I think underwater archaeology
and the investigation of wrecks in the Pacific is just beginning to
get started.I honestly don't know of any wrecks which go back to
the Lapita culture.
>> and the Polynesians stocked such exploratory voyages with food and
>> plants, and water, not only sufficient to supply the voyagers, but 
>> actually enough to plant a new settlement, were an island group 
>>located.
I am not sure there is any evidence of this which predates the 
settlement of the Hawain Islands.
>> Again, recently a recreated voyage was made from Hawaii, with 
>> a navigator trained by traditional methods in Micronesia. He had 
>> never previous travelled outside Micronesia.
That's interesting because Micronesian islands are mostly pretty close 
together. The Hawain islands are a completly different situation.
>> Yet, he was able using the traditional navigation with a
>> reconstructed Polynesian style sea-going craft, to sail from 
>> Hawaii, and plot a course for Tahiti, and make direct landfall 
>> in Tahiti. That program was broadcast on a Nova PBS program 
>> a few years ago, but it was especially impressive, as the group 
>> that made the voyage took along no modern navigational instruments, 
>> but trusted completely the abilities of the Micronesian navigator. 
That program was filmed several years ago. I at first thought you were 
refering to the expedition reported in sci.archaeology last year.
>> Alas, with the advent of modern travel, the old
>> traditions are dying out, even in Micronesia, where they last survived.
>> Fortunately, the Hawaii-Tahiti voyage awoke interest in the traditional
>> sailing methods both in Hawaii and Tahiti, so at the eleventh hour,
>> perhaps the old technique will not be completely lost. Otherwise the
>> arch skeptic would laugh off Polynesian and Micronesian navigation and
>> trans-oceanic sailing abilities. 
I think there is little question about the interest having been revived.
>> These abilities also lead me to believe
>> that it is far more probable that the Polynesians touched South America,
>> and there acquired the sweet potato, that in Pre-Columbian times they
>> then dispersed through certain islands.
I would be more inclined to believe the sweet potato was brought from 
South America to Polynesia and probably rather late, sometime in the
first millenium BC by ocean going raft. Speaking of these it is interesting
to note that the first Europeans to see them commented on their cotton sails.
>>  The Marquesas Island Polynesians
>> are the likeliest to have done this, as the sweet potato then spread in
>> the larger high islands, and eventually became established in Melanesia
>> and especially New Guinea. 
The sweet potato is most closely related to the other species of South
America or Polynesia?
>> 
>> Most sincerely,
>> Frank J. Yurco
steve