molder Wrote:
-------------------------------------------------------

> What is special about the Saxon system?
>
> I think that the Saxon system originated through
> the study of astronomy and
> mathematics, starting with the discovery of the
> significance of the number
> 360.

(quiet laugh)

Well, yes... because the Saxons got it from the Romans who got it from the Greeks and Babylonians. (see Saxon language: [omniglot.com]) They were illiterate, so there was no way for them to do math (https://www.worldhistory.org/Saxons/). The monks introduced the Futhark runes (https://omniglot.com/writing/futhorc.htm) and the Roman military with their recordkeeping and so forth undoubtedly introduced some math and astronomy and technology to the area. It doesn't persist there as well as it does in the south and east after the collapse of the Roman empire.

> The Encyclopaedia Biblica (1899–1903) states:
> The division of the day into 12 parts and the
> further development of the
> sexagesimal system as a whole had commended itself
> to the Babylonians
> from their observation that, at the vernal
> equinox, the time between the
> appearance of the first direct ray of the sun and
> that of visibility of the
> entire disk above the horizon amounted to 1/360th
> of the time during
> which the sun was visible in the heavens, or the
> 720th part of a full day
> reckoned from one sunrise to another. (p 1037)

Yep... but the Egyptians divided the day into 12 hours but had no concept of minutes or seconds. They used candles and water clocks (https://www.metmuseum.org/toah/hd/tell/hd_tell.htm) so they aren't the source of any 60/360 metric.

> land measure: the acre.

> To find 360 in the Saxon system, we can look at a
Which is legally defined as how much land a typical yoke of oxen could plow in a day (660 x 66 feet) [www.britannica.com]

> An acre in our present system is 40 rods ×4 rods
> or 660 × 66 imperial feet,
> giving a total area of 43 560 square feet. There
> are 16.5 feet in a rod.

No problem there.

>
> Therefore, to calculate how many acres in a square
> measured in imperial
> feet, square the length of the base and divide by
> 43 560. If the base of the
> Great Pyramid is 755.7 imperial feet, it would
> contain 13.11025 acres
> exactly:
> 755.7 × 755.7 ÷ 43 560 = 13.11025

Boy, howdy (as we say here in Texas) that leads to a bunch of problems.

For instance, there's absolutely NO way to write 13.11025 in Roman numerals (see [en.m.wikipedia.org]) and if anything, Romans were worse at fractions than the rest of the world (they wrote out the name of the fraction ("one fourth") which isn't much good in trying to add things like "one fourth plus one third". They used a 12-based system, by the way. The Saxons and everyone else in Europe wouldn't be able to write that fraction until sometime in the late 1500's, after Stevin introduced decimal fractions to Europe in his books (https://hsm.stackexchange.com/questions/11092/were-decimal-fractions-known-in-europe-before-stevin)

And until fairly recent times (after 1500) none of the world's civilizations (except for the Chinese [en.wikipedia.org]) could write 13.11025

> The architects did not have electronic calculators
> and so calculations took a
> little time. However, using the Saxon system of
> measuring makes finding an
> acre very easy, because there are 36 000 square
> Saxon feet in an acre. The
> base of the Great Pyramid measures 687 Saxon feet
> (755.7 imperial feet).

So... in order to do their system, they ignore the Romans (whose measurements they've been using for construction) and everyone else, hotfoot it down to Egypt to the Great Pyramid (which was being covered by sand... the sand wasn't cleared away from the base until formal excavations started on the Giza plateau), ESTIMATED the true base by running around the perimeter and measuring that and then guessing how much more of the base was under the sand... and then running back to England and saying "voila!" (or "yoiks", since they're English and not French)?


> There are two quick ways to calculate the acreage:
> • The first method is to divide the length of the
> base by 6, square it and
> divide by 1000:
> – 687 ÷ 6 = 114.5
> – 114.5 × 114.5 = 13110.25
> – 13110.25 ÷ 1000 = 13.11025 acres

I'd just measure the area and then divide by 43560 - one operation instead of three - and unlike your calculation will work on things of an irregular size. Or measure the thing in furlongs (because when you're looking at large numbers, we group them into more useful units (why we measure cloth in yards instead of inches or the drive between Dallas and Oklahoma City in miles and not yards)

> It was clear to me that the measure of 36 000
> square Saxon feet in an acre
> was significant, because it contained the number
> 360.

Or a coincidence. Coincidences happen, y'know.

Now...although this may seem harsh, I do believe you are a sincere and dedicated investigator. The problem is that you do investigations the way the rest of the armchair investigators on the Internet do and not like a scientist (which would be several of us who are responding to you.) You accepted what some site on the Internet said (without completely vetting their information) and launched your inquiry from there.

As a scientist, the first thing I do is look at a timeline (who knew what and when did they know it and how do we know this is so (and dive into scholar.google.com, Wikipedia, Internet archives, museum information pages, archaeological reports and so forth.) Once I've got a good idea of the timeline, I next look at the way the world's connected at that time (history of the areas) and who's exchanging information with others (history again) and then the technology (museums, again, and books on technology which would have details from finds across the world.)

So, as you may have noticed, I looked at the maps of the world during each of the times you mention, the history of the peoples you mention, the history of the numbers pi and phi, the history of sacred numbers, sacred numbers of several civilizations (and the timeframe), mathematical texts of the Romans and Greeks and Egyptians and Chinese, trade and information exchange between these groups (not just products but delving into linguistics a bit... looking for creoles and loanwords) and sticking to sources that were reporting on ancient sources (and documenting which source they were using - if they're talking Egyptian math then they'd better show the connection to known translations of math problems from the mathematical papyri).

I encourage you to continue researching and NOT skip the first step of every scientific investigation, which is to learn every darn thing you can about the background of your problem, including the timelines and the big picture of technology. And make sure that those sources can actually point to real texts from the culture and the time you are investigating.

-- Byrd
Moderator, Hall of Ma'at