Talk:Ancient weights and measures

Contents

1 Miles 2 Western bias 3 Ancient accuracy 4 When did Erich von Däniken start editing? 5 Irrational Ratio 6 Iranian nationalism?

Miles

While inches and feet have remained pretty constant, the riddle that puzzles me is to trace the history of the various miles. There seem to be at least 4 species:

• The ~10 km Egyptian mile, carried on in the Greek scoinios. No Roman equivalent? Must surely be the origin of the ~10 km Norwegian and Swedish land miles.
• The ~6-7 km mile. Why the change? Presumably to get it in accordance with degrees. When did this happen? Did the Greeks do this at some stage? The German geographical mile and Nordic sea miles at ~7.5 km must be related? Is Goethe connected to this (he was a pioneer of land measurement)? For navigation at sea, it was significant to have a measure which related directly to the degree. On land, not so important.
• The ~1.6 km UK/US mile, with origins from the 1000 paces is a pure Roman invention.
• The ~1.8 Nautical mile, based on the ~1.8 km geograpical miles. Why two different equatorial miles? Which came first?

The various leagues at ~4km also enters the picture, but these seem to have a simple, pedestrian origin. The French league later connects it to the meridian.

Egil 13:49 Feb 13, 2003 (UTC)

I don't know about Goethe, but Ole Rømer was a big player in the 4-minute geographical mile.

Elizabeth I added the 280 ft to make an 8-furlong mile. Gene Nygaard 17:52, 4 Feb 2005 (UTC)

The above questions are very old, and I believe I have found some answers: I have yet found no clear connection between the Egyptian mile (river measure) and anything else, but the Persian parasang is also interesting. The geographical ~7.5 km mile, land and sea, is the brainchild of Ole Rømer - the Prussian king later adopting it. The British nautical mile may have been due to a want of having a sea mile in the same order of magnitude as their land mile? The relationship between the Roman and British land miles are, as you note, well documented. -- Egil 08:48, 9 Feb 2005 (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)

When did Erich von Däniken start editing?

The introduction now contains stuff like:

Modern researches in historical metrology proved that all the ancient measures in the "Old World" are related by simple ratios.

This is totally mind-boggling patent nonsense. For instance, it is claimed:

Even the Japanese Shaku (= 30.24 cm) is exactly 4 seventh of the New Egyptian Royal Cubit (= 52.92 cm).

This is totally outrageus - I am only waiting to hear about aliens in flying saucers who facilitiated the communications between these civilisations.

'In the Antiquity, the units were well defined to a high precision and standards of measurement were generally excellent.

Again, nonsense. Some units were of excellent precision and repeatability, some, like the stadion and the Roman weight units, were horrible.

I will clean up this mess, but can someone figure out a plan for how to keep this page free from these things. -- Egil 17:15, 4 Feb 2005 (UTC)

Hi Egil,
your intervention evoked my smile with sympathy for you. It's a good and sane reaction of scepticism, if one never heard of the results of these - however serious - reseaches, published since the 1960th.

Soon, I will adding here forward arguments, referring explicity to your objections.

I saw, you have contribued a lot for this article, in a constructive and documented manner.

Only this reflection now: Isn't it logical, that cultures with close relationships, commercial and cultural, wouldn't could say: "Oh, I know: One Roman pound is exactly 3/4 of a Greek mine or 600 Greek feet equal 625 Roman feet." And that since the beginning of civilisation in the "crescent fertile" about 8000 years ago?
Paul Martin 23:24, 4 Feb 2005 (UTC)

There are "connections" of various sorts all throughout history, some strong, some weak, some speculative. In particular, names were often borrowed for similar-sized units, and various attempts at reconciling different systems of measurements, often with adjustments of size in one or both systems, have taken place throughout history. It's when you get into notions of unadulterated transference to the present, or some god-given natural units to which we keep returning, that you get labeled quite justifiably as a crackpot. Gene Nygaard 00:15, 5 Feb 2005 (UTC)

Hi Gene,
Partially you misunderstood. I never suggest any value of a hypothetic "god-given natural unit", neither I propose a return to any old system of measurement. (You can't go behind the great attainment of the metric system: able to handle it in a advanced positional arithmetic system. Even if, like it seems me, the metrological culture is not achieved with decimal SI. But that's an other subject.)

Otherwise you are right, "names were often borrowed". This, because a pace is a pace (generally 5 feet), a foot is a foot (± 30 cm), a span is a span (2/3 foot) and the digit has always been 1/16 foot (< 2 cm), like the inch is 1/12 foot. Only the ell has two meanings: the "natural ell" of 3/2 foot and the the meaning of a more practical "trade cubit" (for cords, ropes, drapery etc.) The values of the trade ells changed with their different definitions: Sometimes simply two feet, sometimes: from the middle of human body to the extremity of the hand (3 feet), sometimes even 4 feet (from the haunch to the fingers of opposite side with outstretched arm). The Egyptian Cubit measured 1.75 feet or 28 digits.

But not only the names of the units were borrowed. Like we can see (Egyptians borrowing the Nippur Cubit), also the values of units are generally taken over by ancient neighbour civilisation. But, often they created their own systems of subdivisions. Centuries later, one of these subdivision-units was not seldom considered to be a main unit and overtaken by others, who still created an other system of subdivisions, and so on.

In the opposite to the European Middle-Ages, science was highly developped in Antiquity (See Eratosthenes, Heron and many others before) and international relationships were omnipresent. Ancient metrological scientists were preeminent. What gives you the arrogance to presume that they worked with corrupted standards?
Later more. What do you say thereto?   So long Gene,  Paul Martin 12:07, 5 Feb 2005 (UTC)

That you have confirmed my impression that you are a crackpot, something already evident from a liberal sprinkling of "exactly" and impossibly precise numbers. Gene Nygaard 17:37, 5 Feb 2005 (UTC)

That's all you have to say?  It's not really argued. Your cheap invectivenesses, I needn't comment. Readers will judging on themselves.

On the topo: Professor Dr. Rolf C.A. Rottländer of the University of Tübingen measured hundreds of real existing ancient archeological scales, regrouping this with the architectural values (which can still be measured) of ancient monuments, stades etc. He found values for the ancient measures with a scientific coefficent of faith less than 0.2 percent. The conventional, rounded values now used in historical metrology are within this coefficient of faith. The recent reseaches of Professor Dr.-ing Dieter Lelgemann, Director of the Berlin Geodesic Institut, accomplished with Eberhard Knobloch, Professor of History of Science and Technology at the Technical University of Berlin and Vicepresident of the French Académie Internationale d’Histoire des Sciences confirme – inter alia – the now established fact, that all the ancient measure systems are related !

The colleagues will be delighted to be vilified as "crackpots" by Mister Gene Nygaard (lol thrice).

Paul Martin 21:52, 5 Feb 2005 (UTC)

Q.E.D. Note that 0.2% cannot give you 6 or more significant digits. Gene Nygaard 22:24, 5 Feb 2005 (UTC)

I count four digits.  52.92 centimetres (0.2%, admittedly :  ≤ 0.11cm).  But if you prefer, you can consider that the conventional foot of Carthage is defined equal (529.2 mm × 5/9 =) 294 mm. Three digits. 0.2% of 294 mm = 0.588 mm. That you satisfy?

(You seem to cleave excessively to the number of decimal digits. This have generally its sens, admittedly. But, if you take, for example, a conventional value of 1/7 of an arbitrarily unit (six recurring digits!). This will not signify that your exactitude is less then 0.0007%. It's only a practical rounding.)
Paul Martin 23:57, 5 Feb 2005 (UTC)

Postscript: Dazzled by your own ignorant arrogance as well as by your repeated impoliteness paired with your pseudo-scientific airs and graces, you don't even see: Like it is clearly indicated in the article (if you ever read it attentively), it's the matter of an defined conventional value. Defined values can have the number of significant digits they want, in the opposite to values obtained by experiences or measurements. This you seem to ignore.

Thus the value 294 mm ± 0.17% (=0.4998 mm) defines also the values 529.2 mm, 370.44 mm, 518.616 mm as like the values 484.0416 mm for the Salamis Cubit (14/15 of Nippur Cubit) and the Pergamon Cubit of 520.93125 mm (15/16 of Babylonian Cubit = 555.66 mm, i.e. 518.616 × 15/14) and dozens of well-known (but untasted by you) other ancient measures.

A definition can't be right or false, only be adequate or not to attain the aim, wherefore it has been formulate. Beyond a definition can be largely accepted or not. Many eminent scientists working in historical metrology do it, like me I do. But, helas!, that's not the case for Mr G.Nygaard.

Perhaps you are high-school student in science, but with your dismissive narrow-mindedness, unable to hold an argued, fair and respectful discussion, I'm not very optimistic for your scientific future.

Note that 294 mm to the nearest millimeter is not a "defined value".

No matter how precise your conversion factor is, using it cannot give you one iota more precision in your result than you had to start with. After using the conversion factor, you must round appropriately. Gene Nygaard 17:03, 6 Feb 2005 (UTC)

I insist: All these values (294 as 518.616 like 529.2 and 296.352 mm) are defined values. The first Nippur Cubit found by archaeological excavations, now in a museum of Istanbul, has a measured length of 518.9 mm, 0.1% more than the value found by statistical methods [[1] (http://www.uni-tuebingen.de/uni/afa/projekte/rottl/codetab.html)] and 0.05% more that the defined value. If Rottländer gives however 294.00 for the Carthaginian foot and not 293.9 like Lelgemann, it's because Röttländer distinguish a real and a corrected Gudea foot, whereas Lelgemann [[2] (http://www.fig.net/pub/athens/papers/wshs2/WSHS2_1_Lelgemann.pdf)] identifies directly the Pous Italikos (= 25/28 of Roman foot) to the Gudea foot. This one is in the Louvre Museum in Paris and measures 264.6 mm (or 264.55 mm like Lelgemann prefers).

The great advantage of the defined value of 518 616 mm exactly one for the Nippur Ell, that's 2³ × 3³ × 7⁴ micrometers. A defined value, a chosen value, a pitched value, but a good value. Therefore, this value is now preferred in the historical metrology. It gives generally "round" values for nearly all other units (except for the Arabic systems, where it is a very simply recurring decimal fraction). Easy, practical, without risk for error by not clearly documented decimal rounding, retaken again as new input values. Admittedly: Not "one iota more precise" than other values, but more practical. After calculations you can round appropriately as it has been done in the Roman measures table in the article (296.352 to 296.4 mm). But you don't "must". At least if it is clearly indicate that's the matter of defined values.

Rottländer specified in his article. In historical metrology, you have to give the values for the ancient digit-measures with at least four significant decimal digits. Because, if not, the values for the leagues are completely corrupted. This not means, he wrote, that ancient cultures could determinate measures in the magnitude of micrometers.

Rounding appropriately, it's obvious with measured values, not with defined values. Even if, I repeat me: Admittedly, you don't gain in precision, but only in practicability.

Paul Martin 20:46, 6 Feb 2005 (UTC)

Ancient meteorology (and even not-so-ancient) is a wonderful mixture of sometimes very admirable standards and methods of tracking, and sometimes outright sloppiness. The Egyptians couldn't care less about mathematical theorems, but in practical arithmetic and meteorological skills they were true masters. Totally in contrast to the Greek, who were totally brilliant theoretical mathematicians, but left practical matters such as meteorology at a state of laissez-fair. (Their definition of a stadion being a case in point, it left antiquity in a state of confusion about distances). It is thus totally impossible to draw any conclusions about relationships between units of measurement among cultures without some additional understanding of the underlying cultures. Most of the claims made by Paul Martin, to the degree I can say I understand what his claims really are, seem to be quite Däniken, or perhaps numerology. For instance, a claim that 600 Greek feet is by definition equal to 625 Roman feet is simply totally meaningless. Firstly, there is no practicality at all in this claim. Adding up 600 Greek feet is easy enough, but how would the Romans go about diving this distance into 625 in an accurate manner to get their Roman foot? Secondly, there is no such thing as one Greek foot, simply because the definition varied from city state to city state and from time to time. Not as bad as in medieval Europe, perhaps, but still bad enough. Twisting numbers to find connections where none exist is simply a worthless exercise. Some of the data points are indeed very accurate, but this must not lead to the conclusion that they all are. But I will certainly take time to review the "VORMETRISCHE LÄNGENMASSEINHEITEN" by Rolf C. A. Rottländer. His connection to Universität Tübingen is not clear to me, and it may be we have yet another Däniken here, but let me give him the benefit of a doubt. -- Egil 09:17, 7 Feb 2005 (UTC)

Postscript: Having investigated the matter a little bit further, it seems pretty obvious that this is all pseudoscience, essentially out to prove the great connectedness of Stonehenge, the Gisa pyramids and, it would seem, probably everything else in antiquity. The theory seems to be founded on a folly by a certain professor emeritus Alexander Thom, called the Megalithic yard. This is certainly Däniken-like territory, and if it should be mentioned somewhere, then perhaps it can be moved to the Megalithic yard article. -- Egil 10:00, 7 Feb 2005 (UTC)

I have now made an attempt to move all the material about the great connectedness of all the magnificent ancient cultures (including Stonehenge and Cheops) to Pseudoscientific weights and measures, so as not to lose any of Paul Martins excellent research into everything the Megalithic yard has led to, in Germany and elsewhere. Hope this is to everyones enjoyment. I will try to do a further review to make sure that I haven't missed the odd theoretical barleycorn. It would for instance seem the precision stated for the Roman units of weigth is completely out of this world, so I will try to find some more realistic figures. -- Egil 15:46, 7 Feb 2005 (UTC)

Hi Egil, I quote one very accurate phrase of you: "There is no such thing as one Greek foot, simply because the definition varied from city state to city state." It's true, an unified "Greek foot" don't exist.

Many exemplars of the two Egyptian cubits were found and are exposed in museums: Graduated rulers always divided into 28 digits. The Nippur Cubit was a widely-used measure in Mesopotamia and around, five thousand years ago. Let's say for simplify, because you prefer "realistic" numbers of digits: The Nippur Ell is 518.5 ±0.5 mm. So, 51.85 cm divided by 28, that's equal 1.85 cm.

Now you have to know that in Antiquity there are (among others) three important (relative) measures. (Like it has been described even by ancient authors.) Firstly a 20 digit-measure, commonly called with the Greek word "pygon", secondly a 18 digit-measure, called "pygme" and lastly a 16 digit-measure called "pous" (foot).

20 × 1.85 cm = 37.0 cm, the length of the measure called "Remen". Then, 18 × 1.85 cm = 33.3 cm, called "Pes Drusianus" (in Middle-Ages sometimes called foot of Charlemagne). This measure is identical to the Chinese "Chi". At last, 16 × 1.85 cm = 29.6 cm. That's the "Roman foot".

The Olympic stade of Athens was constructed to be 500 Remen (or 600 feet, like all Greek stades, but each City State used his own foot). 500 × 0.37 m = 185.0 m. This Athens stade divided by 600 is a little more than 30.8 cm. This is the foot of Athens commonly called "pous of Kyrenaika". 185 m, that's also 625 Roman feet. Q.E.D.

Later more, Paul Martin 13:28, 8 Feb 2005 (UTC)

Let me make it perfectly clear that I am totally open to relationships between the measures of the aniquity (as well as more recent ages), as long as we agree not to involve mystisism. I regretfully do not have the time right now to follow and research all your arguments, but will try to do so in due course.

Beginning in Egypt, a royal cubit is divided into seven palms, each of which are 4 digits, i.e. 28 digits, each digit 1.87 cm. The short (or common) cubit, much used especially prior to the end of the Third Intermediate Period, is divied into six palms, i.e. 24 digits, so they are certainly not all divided in 28. Even though the Egyptian cubit is very well defined in certain times, it has varied a bit over the times, at least by 1%.

The remen is afaik by definition half the diagonal of a royal cubit square, so in reality it consists of 19.799... 'Cubit digits', not 20. I have not investigated if there are evidence that the Egyptian knew that the 'Remen digits' were different from the 'Cubit digits'. I do also not know if it has been shown that the Egyptians knew of the Pythagorean theorem nor the concept of irrational numbers. I've seen statements that they did not, but it is clear that their neighbors in Babylon knew [3] (http://www.tmeg.com/bab_mat/bab_mat.htm). Regardless, it does constitute an error of 1%, which they should have been able to detect.

Units of measure based on artifacts of the human body are very natural to any culture, and even if independently discovered, will probably be within at least a handful of percent of each other (this goes for digits, palms, feet, cubits and others). So you really need to give some real proof that units have been exchanged between cultures. Numbers matching up can just as well be coincidences.

The connections between Mesopotamia, Egypt, Persia, Greece and Rome are well known, obviously, but when there are claims about China and Japan, we are into deep water unless there is actual proof. The same goes for numerical relationships like the 600:625 of Greek vz. Roman feet. There has to be a very good rationale why this should be the case. Playing the number games with values which are of uncertainty 1% or so, there is simply no end to the common factors one can come up with. -- Egil 16:59, 8 Feb 2005 (UTC)

Excuse for not having answered before.

You are in right: The Egyptian Trade Cubit measured 24 digits of the New Royal Cubit.

Then, we have to distinguish the "Remen" (a measure of 20 digits) and the "Construction Remen": A set square with sides of 20 engraved digits and a base of exactly 28 digits. As you remarked accurately, the digits of the sides are not equal to the digits of the base. A difference of about 1%. But that's not an error!

Even if this is not attested: We can suppose that Egyptian geometers, when they developed their sophisticated Construction Remen, they first took the Nippur Cubit as base (about 51,8 cm = 28 × 1.85 cm). Therefore the original Nippur Cubit has been divided into 28 equal parts (and not into 30 digits like Mesopotanian did it).

But anon, they preferred to seize the sides of their Construction Remen as 20 × 1.85 cm = 37.0 cm. Since, the base of the Construction Remen has the attestable length of around 1.87 cm × 28 = 52.4 cm. This is also the length of Old Royal Cubit.

But, as you say it justly: Egyptian geometers were not silly. They knew that the length of the digits of the sides of their Construction Remen wasn't exactly identical to the length of the digits of the base. However, in praxis, they judged that this difference of about 0.2 mm per digit is - in the majority of cases - acceptable. So, even without logarithmic tables or pocket-calculators, they could treat the radix of number two, often encountered by geometers.

Many, many centuries later the Egyptians decided to modify their Construction Remen. As like they did it with the hypothetical experimental Construction Remen, they carried-over 20 digits of the base of their "Old Construction Remen" to the sides of their "New Construction Remen". Since the New Royal Cubit measures 1.89 cm × 28 = 52.9 cm or - exactly one - hundred 98th of the Nippur Cubit.

But unlike you say this is not an "error of 1%" neither "it has [arbitrarily] varied a bit over the times, at least by 1%" nor this "values [...] are of uncertainty 1%". In the contrary. It's the matter of two well-defined and accurate measures. Each one was used in its well-known and good determinate epoch.

The Old Royal Cubit equal 20√2 / 28 Nippur Cubit.
The New Royal Cubit equal 20√2 / 28 Royal Cubit = 100/98 Nippur Cubit.

One can clearly distinguish the early times, when the ORC was used, and the later times, when the NRC measured 52.92 cm.

You can be sure that, like you, I abhor to involve mysticism in science. I know since more than 20 years the (certainly justified) reputation of M. Däniken. So I never read one line of his commercial, absurd publications. (I don't have time to waste.) Even among the serious researches in the historical metrology, there are several points, where I'm sceptical or I don't agree.

Surely: This or that relationship between two measures could also be a simple coincidence.
(For example: If we didn't know the real history of the definition of the decimal meter, someone would pretend: "The SI-meter is exactly one the yard of the Roman Pygme: 3 × 18 × 1.85 cm = 100 cm." But we know, the decimal meter was originally thought as the ten millionth part of the quarter of an Earth meridian, measured by modern triangulations. Here, it's a clearly established coincidence!)
But because all the ancient measures are related by (more or less) simple ratios. It's not possible that all this relationships are coincidences!

Beyond, it's logical: International trade relationships need factors of conversion and "to take reference" is a criterion of all serious, scientific metrology. This, ancient metrologists knew it and heeded it.

Whereas, undisputed, the European Middle-Ages was not a very scientific epoch.

For example: The Norwegian foot is said to be the Old Danish foot which is said to be the Rheinfuss. Surely, it is so. But never anyone has found any ratio to the ancient measures. It's about 106 % of a Roman foot, but 106 is 53 twice. The number 53 is a primary number, never used anywhere as ratio. Other relationships to the ancient systems have not been found. For the Middle-Ages you can find many, many examples like this: Local measures without relationships to the old systems.

Do you know at least one example of an ancient measure of length not-related to the Mesopotamian, Egyptian, Persian, Roman and the different Greek systems? If this is the case, this would be very interesting for the modern scientific research. Communicate-us this singulary case if you have found one.

For the question, if the Japanese and the Chinese foot is related to the systems of the "fertile crescent", the cradle of all the human civilisation (at least in the Old World) or not:

The digit of the New Royal Cubit is exactly one 1.89 cm. 16 times 1.89 cm = 30.24 cm. This is the Japanese Shaku. It's not contestable.
The Chinese Chi is as long as the well-known and well-attested "Pes Drusianus" around 1.85 cm × 18 = 33.3 cm. It's a coincidence?

Perhaps. But, as user Crissov advisedly remarked: Trade on the Silk Road was constant and durable in former times. Graduated rulers like the New Royal Cubit (we have beautiful specimens today in museums) are "transportable merchandises". What's strange in the idea that merchants brought this rulers to the Courts of China and Japan? Anybody knows, measures (even in ancient times) have to be exact. If you command a piece, it's necessary that both sides use the same ruler. Accuracy is always required.

If we admit this surely not-digressive idea that merchants brought western graduated rulers to Far-East: It would be logical that eastern metrologists copied truthful this measures. The values of the Japanese Shaku and the Chinese Chi confirm this thesis.

Actually, they merely confirm a connection, if at all. By themselves they say not much about the direction of such cultural transfer, if it happened indeed. Christoph Päper 16:34, 1 Mar 2005 (UTC)

East-Asian civilisation, culture and history is old, very old. But not as ancient as Mesopotanian-Egytian culture and history. If these measures and graduated rulers are attested in the Fertile Crescent since at least the beginning of the third millenary BC and not in Far-East, the sense West-East seems me to be more than probable. -- Paul Martin 10:03, 2 Mar 2005 (UTC)

For the so-called "megalithic yard": I don't know. I never studied this measure. In this time graduated rulers didn't exist. So, all modern researches of the "megalithic metrology" are difficult and approximated hypothesis, and surely many publications about the megalithic yard are not serious and not scientific.

For the Olympic stade: What do you understand by "proof"?
The historical Olympic stadion of Athens measures 185.0 m (In spring 2004 Lelgemann and his students measured 184.96 m at site. This are 600 feet of Kyrenaika.) Undeniably: 185 meter is 10 000 Roman digits or 625 Roman feet.

This frequent relationship, 25 to 24, is already well-known in Antiquity. Plinius (VI, 35) mentioned: “For the way from Syene to Meroe, Eratosthenes counts 625 milia passuum, Artemidoros 600 milia passuum.” According to this, the stadion of Artemidoros equal 625 pous Italikon or 600 pous Nikomedesios. That's almost 165,4 m.

Without further context that translation could just as well mean that they used the same milia passuum, but came to different results. But I assume you know the context and it proves your claim. Christoph Päper 16:34, 1 Mar 2005 (UTC)

What do you understand by "proofs"? These are well-known evidences. These are "facts".

So long, -- Paul Martin 21:53, 28 Feb 2005 (UTC)

P.S. In one point you disappointed me. You retook into the article this false information:
"As a case in point, the Great Pyramid of Giza was built to a precision of 0.015 m over sides that are 235 meters, over four and a half thousand years ago."

Firstly: 1.5 cm of 235 m? It's a precision of 0.006% !!! And that's you who spoke of "realistic values"?

Secondly: It's established that the Great Pyramid was constructed with a length of 440 Old Royal Cubits (= 230.5 m) and 440 Remen (= 163.0 m) from the centre to the corners. The length of the Oueen's Pyramid of Giza is 120 Remen (= 44.5 meters) with a diagonal between two corners of 120 Royal Cubits (= 62.9 meters). [4] (http://www.fig.net/pub/athens/papers/wshs2/WSHS2_1_Lelgemann.pdf)

Second Postscript: I hope, one time soon, you will demand the deletion of Pseudoscientific_weights_and_measures and you will reintegrate the content into the article. The only reproach one can evoke is that the practical, conventional value of 2×2 × 3×3×3 × 7×7 hundredth of centimeters (equal 52.92 cm) for the New Royal Cubit for example, is a "modern, defined value." But put this value to the test. This value delivers the simplest values for all the other values of the ancient measures of length (except the values derivate from the "irrational" Old Royal Cubit of course). Beyond this value is not in contradiction to the values obtained by modern statistical methods. Therefore it's an easy and the good "over-all rounded" value. (Practical, not numerological!) It should be mentioned in the article.

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)

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)