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Irrational Ratio

"The Egyptian System" says:

Note also the cubit and remen which has a ratio that constitutes an irrational number.

This sentence is ungrammatical and difficult to decipher. If it is supposed to say

Note also that the ration of the cubit to the remen is an irrational number

the statement is nonsense, since an irrational number is one that canNOT be expressed as a ratio.

I hesitate to just delete it, since there seem to be very serious editors of this topic. Perhaps they can clarify what the sentence means. --Craigbutz 01:13, 8 May 2005 (UTC)

One way to deal with irrational numbers is to use unit measures that are related irrationally. Not precisely as modern mathematics would demand, but to close approximations which are more than sufficient for all practical measurement.

Setting one measure equal to the circumference of a circle and another to its diameter 22:7

• Egyptian circle

An Egyptian architect from the 3rd millenium BC left a sketch which shows how a series of different heights at a unit spacing can be used to define an arc. The heights are given in fractions of royal cubits and therefore its logical to assume the spacing is in royal cubits also, but Egyptian mathematics can be subtle. If the spacing is set as units of an ordinary cubit of 6 palms instead of 7, the arc described is best described as circular.

or the 3:4:5 proportions of a right triangle, where the hypotensuse is a remen of 5 palms and the run a quarter of three palms, the rise is a foot of four palms.

Another way to do this is to relate a length to a volume as its side.

An irrational number is one that can't be expressed as a ratio of two integers. The statement is still nonsense, but just because all ancient measurements are approximate (as opposed to modern, highly technical definitions involving cesium atoms and whatnot), and therefore any ratio between them must be approximate, and therefore the ratio can't be expressed with an infinite degree of specificity, which is what an irrational ratio would require.

In any case, there's no way anyone's actually proven anything like this irrational. Only a handful of things have been proven irrational: certain radicals, π, e, maybe φ. I say remove the statement—it's completely ludicrous. —Simetrical (talk) 05:26, 8 May 2005 (UTC)

These relationships are often rational when they are matters of definition, not otherwise. There is now a rational relationship between a pound and a kilogram, something that wasn't true 150 years ago. But, for example, the ratio between circular mils and square mils is a matter of definition, but not rational.

The ratio of the diagonal of a square to its side is the square root of 2. Not a rational number. So the statement is correct. Gene Nygaard 05:58, 8 May 2005 (UTC)

I think User:24.5.64.20 did a nice job of rewording this idea. Gene Nygaard 19:53, 8 May 2005 (UTC)

Iranian nationalism?

The section on Persian units claims a pre-existing Persian stadion and skhoinos. Both words are Greek, from Greek roots. Stadia are Greek units, found in Greece; schoinoi are Egyptian units, known to us by a Greek word meaning "rush" or "reed". Since the Egyptian symbols for thousands and ten-thousands can both he so described, and the schoenus is several thousand cubits, there's no reason to suppose the "Persian" units ever existed. Septentrionalis 20:56, 15 May 2005 (UTC)

Rktect 8/1/05: Some of the best evidence for pre-existing Persian Units is

Their doubling Egyptian units just as described by Herodotus

The Persian increments of Guz of Gudge are found in places

that weren't reached by the Greeks until the time of Alexander

but that were included in the Persian Empire

These units don't match Greek units but do closely double Egyptian units

Consequently rather than a wide range of different values without any discernable system

you have a great or royal, long, median and short form of the guz

equivalent to the double of Egyptian units making the Persian parasang

actually equal the schoenus because it has half as many units that are twice as long

Persakh, or Para- Persia. 6000 gudge of 42" = 21,000 feet

unit name	"bd"	"rmn"	?	"mh"	?	"rc"	"nibw"
Egyptian half	11.81"	14.5"	?	17.7"	?	20.62"	23.62
Ideal Double	23.62	29"	?	35.4"	?	41.24"	47.24
Persian Region	dbl foot Guz	dbl remen Gueza	dbl cubit Zer	dbl Gudge
India
Bengal	?	?	?	36"	?	?	?
Bombay	?	27"	?	?	?	?	?
Madras	?	?	33"	?	?	?	?
Persia	25	?	?	36.4"	?	40.95"	44"
Arabia	24"	?	?	37"	?	?	(Bassorah)

Herodotus Book 2

Chapter 6

1 Further, the length of the seacoast of Egypt itself is sixty "schoeni" -- of Egypt,

that is, as we judge it to be, reaching from the Plinthinete gulf to the Serbonian marsh,

which is under the Casian mountain -- between these there is this length of sixty schoeni.

2 Men that have scant land measure by feet; those that have more, by miles;

those that have much land, by parasangs; and those who have great abundance of it, by schoeni.

3 The parasang is three and three quarters miles, and

the schoenus, which is an Egyptian measure, is twice that.

In other words there are 10 Egyptian scoenus (or itrw of 21,000 royal cubits) to a degree

and there are 20 Persian Parasangs of 3.75 miles or 75 Persian miles.

Chapter 7

1 By this reckoning, then,

the seaboard of Egypt will be four hundred and fifty miles in length.

Inland from the sea as far as Heliopolis, Egypt is a wide land, all flat and watery and marshy.

From the sea up to Heliopolis is a journey

about as long as the way from the altar of the twelve gods at Athens

to the temple of Olympian Zeus at Pisa.

2 If a reckoning is made, only a little difference of length,

not more than two miles, will be found between these two journeys

for the journey from Athens to Pisa is two miles short of two hundred

which is the number of miles between the sea and Heliopolis.

Chapter 9

1 From Heliopolis to Thebes is nine days' journey by river, and

the distance is six hundred and eight miles, or eighty-one schoeni.

2 This, then, is a full statement of all the distances in Egypt

the seaboard is four hundred and fifty miles long; and

I will now declare the distance inland from the sea to Thebes

it is seven hundred and sixty-five miles. And

between Thebes and the city called Elephantine there are two hundred and twenty-five miles.

In other words the two cities are three degrees apart.

Chapter 109

1 For this reason Egypt was intersected.

This king also (they said) divided the country among all the Egyptians

by giving each an equal parcel of land, and made this his source of revenue,

assessing the payment of a yearly tax.

2 And any man who was robbed by the river of part of his land

could come to Sesostris and declare what had happened

then the king would send men to look into it and calculate the part

by which the land was diminished, so that thereafter

it should pay in proportion to the tax originally imposed.

3 From this, in my opinion, the Greeks learned the art of measuring land

the sunclock and the sundial, and the twelve divisions of the day

came to Hellas from Babylonia and not from Egypt.

Chapter 168

1 The warriors were the only Egyptians, except the priests, who had special privileges

for each of them an untaxed plot of twelve acres was set apart.

This acre is a square of a hundred Egyptian cubits each way,

the Egyptian cubit being equal to the Samian.

12 Egyptian acres of side 100 of the cubit = to the Samian, the mh t3 or land cubit

would be equivalent to 6 English acres

Version of IP 69.164.70.243

This article became worse since 2005, February 7th. Now it is really bad ! The low point is attained. --Paul Martin 5 July 2005 12:35 (UTC)

I agree—well, I have not checked whether the 2005-02-07 version was the best one and whether there have been useful edits as well since. Anyhow, I do not care enough about it to be doing more than adding the templates at the top. Christoph Päper 5 July 2005 14:59 (UTC)

Surely there should be some justified changes since then. But at present, this article is higgledy-piggledy. For the rest, I'am always waiting for Egil's reply to my intervention of Feb. 28th below, concerning: "Great Pyramid of Giza was built to a precision of 0.015 m over sides that are 235 meters." etc.
--Paul Martin 5 July 2005 16:37 (UTC)

Western bias

I hate to say it, but... Western bias? Anyone reading this would think half the world never measured anything. 129.2.211.72 22:18, 23 Nov 2004 (UTC)

1. The page is quite large already, but the main reason is probably, 2. there just hasn't been any edits by somebody with non-western sources...

Who can say that the Greek and Roman weight systems were "main" systems and the Persian one was not, while the text itself asserts that the Persian system formed the base and was the forerunner for the Greek and Egyptian and Arabic ones. I changed that in the list.

--Mani1 18:16, 27 Dec 2004 (UTC)

Ancient accuracy

Someone, out of the blue, added this sentence:

Thus, the precision of some of the values given here -- four or five significant digits -- is completely ridiculous.

I suggest said person resaerches the subject better before burping up a comment like that. In many cases, esp for units that are a few houndred years old, these units are in fact tracable to a good number of digits. I would suggest said person who made this comment enlighten himself by reading about the state of the sciences throughout history. He will then find it was in fact quite advanced, also in practical fields such as measurement techniques. Look for instance at the article that quotes the actual measurements of rules found among ordinary people in Pompeius. Obviously, the offical rules were even better. The Great Pyramid of Giza was built to a precision of 1.5 cm over sides that are 235 meters, that would indicate that the Egyptians were able to measure at an accuracy of 5 significant digits. Four and a half thousand years ago.

In some cases ancient units are rather erratic, for instance in the case of Roman units of weight, and in such cases this should be stated. -- Egil 02:19 Feb 13, 2003 (UTC)