Talk:History of measurement/Archive 2

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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)

rktect 7/24/05 I know of no reason why they couldn't say that and
can point you to where the Roman Surveyor Hygenius Gromenicus did say that
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)
rktect 7/24/05
The transferences are not unadulterated but they are tracable

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.)

rktect 7/24/05 its ironic in a way because the oldest system I know of
has a hand of 100 mm and an ordinary cubit of 500 mm

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.

rktect 7/24/05
The problem is that they would borrow a unit, rename it,
revise the subdivisions and just keep the value so to track those changes
can take more research than most people want to invest


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.

rktect 7/24/05
The defined value is only as good as the standard that defines it

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 [[2]] 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 [[3]] 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.
True

The Egyptians couldn't care less about mathematical theorems,

False: They had theorems but not for general cases

but in practical arithmetic and meteorological skills they were true masters.

True: Their skills included developing a system of calculation based on unit fractions
Their system was still in use in the middle ages and included
formulas for the divisions of 2 by the odd numbers 3 to 101
unit fraction tables
division of the numbers 1-9 by 10
formulas for the area of a rectangle
formulas for the area of a triangle
formulas for the area of a circle
formulas for the volume of a cylindrical granary
equations of the first and second degree
geometric progressions
arithmetric progressions
formulas for the seked of a pyramid
formulas for the volume of a truncated pyramid
formulas for the surface area of a semicylinder
formulas for the surface area of a hemisphere
squares and square roots
the pythagorean theorem
continued fractions

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.

True but misleading. The Greeks tended to copy first and theorize afterwards.

(Their definition of a stadion being a case in point, it left antiquity in a state of confusion about distances).

False. Its not their definition that is the problem
(600 pous= 6 plethrons = 100 orguia)
The problem is that we don't understand their system very well
because the plethora of individual pous confuse us.

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.

True with the stated caveat

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.

Thats actually well documented.
World of Measurements" H. Arthur Klein p 69
The Milos, The Milliare and the Myle are all 185 m.

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?

Both systems are essentially the same in terms of overall length but
the pous and pes vary.
The Attic Greek pous is 308.4 mm, The Ionic Greek Roman pes is 296 mm
600 Attic pous of 308.4 mm = 625 Ionian pous Roman pes of 296mm
The real difference is in the calculation of areas.
The Greek system is based on the Mesopotamian iku,
side 100 great cubits of 600 mm
The Roman system is based on the Egyptian st3t,
side 100 royal cubits of 525 mm
the conversion from sexigesimal to septenary systems
keeps both systems feet the same at 300 mm
The Mesopotamian - Greek system provides 9 aroura to a stadion and
64 stadions to a square Milos
The Egyptian - Ionic Greek system initially
provides 9 ares of side 200 pous
Then the Romans modify the stadion of 600 pous to be
a stadium of 625 pes
When the Milliare becomes 5000 pes
A square Milliare now has an area of 25,000,000 pes
The area of the square stadium becomes 1/64 of that or 390,625 SF or
aproximately 9 acres

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.

True but misleading, you learn to recognize which are short feet, which median and which long
A short Ionian pous of 296 mm, a longer Attic pous of 308.4 mm and a long Athenian pous of 316mm

Not as bad as in medieval Europe, perhaps, but still bad enough.

Medieval Europe is easiest to understand if you split it up historically to begin c 800 BC
east of the Rhine Greek pous
west of the Rhine Roman pes

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 remen is originally an Egyptian unit of 5 palms,
The Romans made it 15" or 381 mm
Gillings says the double remen was
the length of the diagonal of a square
whose side was one cubit."
Using the royal cubit you get a double remen of 29.1"
The remen = the hypotenuse of a 3:4:5 triangle
where one side is the mh of 4 palms,
The mh is the Egyptian foot of 300 mm,
the other side is the quarter of 3 palms

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%.
rktect 7/24/05
Its hard to carry its value out to hundredths of a cm when
the length of Egyptian rulers is as often as not 21 inches
rather than 20 something.
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.
False (see above)

I have not investigated if there are evidence that the Egyptian knew that the 'Remen digits' were different from the 'Cubit digits'.

Many ancient civilizations had finger and thumb variables but
SFAIK the Egyptians did not
I do also not know if it has been shown that the Egyptians knew of the Pythagorean theorem nor the concept of irrational numbers.
The evidence of their use of the Pythagorean theorem
is adressed in Gillings who remains unconvinced.
Other authors make a much better case.
They certainly used 3:4:5 right triangles, pythagorean triples and
the fibonacci series.
There is good evidence that they worked around irrationals
by using ratios like 256/81 (Rhynd Papyrus) if not 22/7
In unit fractions 3 '8 '64 isn't bad either for practical applications

I've seen statements that they did not, but it is clear that their neighbors in Babylon knew [4]. 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.
Mesopotamia traded with Iran, India and Afghanistan both overland and by water
The extent of its trade routes are probably best viewed by looking at the Persian empire.
China came into the picture with the silk road.
There was sea trade throughout the southern oceas from Madagascar to Han China
The best proof is Probably Ptolomys Geography

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). [5]

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.

The Same System

The same system of weights and measures has continued throughout history, despite a number of different civilisations making their own adjustments to serve their own purposes.
Goes the article ... the same system? I very much doubt it. Jimp 15Jul05
Wikipedia could use an exposition of Gilling's, Piazzi Smyth's, system etc of unifying all measures, ancient and modern, but to present them as consensus is bosh.
Its a little strange to lump Gillings in with Piazzi Smyth
I will support all efforts to state the apparent values of ancient measures, and then a separate section for the pseudoscience. Septentrionalis 22:06, 17 July 2005 (UTC)
I would have much less problems with this anonymous additions, which at least all come from the same IP User:69.164.70.243 (lndnnh.adelpia.net), if they used correct Wiki mark-up (esp. definition lists) and good wording, but they look just like randomly copied text from some other source
They may indeed look like something randomly copied.
Most of my writing starts with a lot of reading

then jotting down notes, some field measures to verify, some spreadsheets to analyse and then more reading.

After a couple of decades of running the numbers

I tend to see a lot of things that I sort of agree with but might phrase a little differently so there aren't many sources I can cite without commentary.

(Gillings maybe, not findable on Google).
Try Googling

Richard J. Gillings, Mathematics in the Times of the Pharoahs. (1972; rpt. New York: Dover, 1982)


I meant that I did not find your formulations, which otherwise would have been an indication for copy-and-pasting. Christoph Päper 15:28, 19 July 2005 (UTC)
Can you clarify what you are looking for
in the way of "formulations"?
At the moment I'm just listing standards of measure
I therefore now cleaned the article by moving much of that bad styled content here. I'm using my last edit, because I don't want to clean up the newly messed-up paragraphs. Christoph Päper 02:45, 18 July 2005 (UTC)
I'm a little new to Wiki mark-up but willing to clean it up
Okay, show me! Everytime you edit there is a link to “Editing help” below the edit window. Read that! (Or Wikipedia:Lists.) So far all your edits have made the article less readable.
I will consider that an attempt at constructive criticism
allow it is valid and attempt to comply
Not much of your knowledge comes across, much is unclear, seems contradictory (often by ambiguity), is repititive, speculation or just irrelevant for an encyclopedia or this particular article. Christoph Päper 15:28, 19 July 2005 (UTC)
You can speak the truth and say nothing, or tolerate some ambiguity

and discuss what is repetitive, what is speculative, what is irrelevant for the discussion page.

Listing measures seems pretty straightforward
I can see where someone who doesn't have familiarity with a measure
would want to be pointed toward the source material with a cite, but
If your standard of proper grammar is what I see above
maybe we should look for a new standard.

Units

Units were often defined to a high degree of accuracy
by tying the units of length and area to units of volume.
This example, uses English measures as a base and
Egyptian and Roman measures as units of comparison:
English inch := 25.4 mm
English finger := 20.32 mm
That would be 4/5", I've only seen 3/4" or 7/8"
given for English digit/finger(-breadth) so far.
1/16th of a foot (¾") would be consequent, not 1/15th.
Break out your Stanley Tape measure and look for the diamond at 19.2"
It comes right after the arrow at 16" which is used by carpenters
to frame studs so that a 4' x 8' sheet of plywood
will land on the studs.
19.2 " divides eight feet into five parts instead of 6
An English cubit of 19.2" has 6 palms and 24 fingers of 20.32 mm or .8"
Egyptian finger (dj) :≈ 18.75 mm
Egyptian palm (ssp) := 4 dj ≈ 75 mm
Egyptian hand (spd) := 5 dj ≈ 93.75 mm
1 cubic foot (12″): = 1 ft³
1 cubic remen (15.12 "):≈ 2 ft³
(an Egyptian measure of ≈14.5" adopted by Romans as ≈15" )
1 cubic short cubit (17.307"):≈ 3 ft³
1 cubic ordinary cubit (17.575"):≈ π ft³
1 cubic English cubit (19.2″) :≈ 4 ft³
1 cubic royal cubit (20.52") :≈ 5 ft³
1 cubic cubit (6 spd = 21.8″) :≈ 6 ft³
6 spd/cubit × 5 dj/spd × 18.75 mm/dj / 25.4 mm/in ≈ 22.15 in/cubit
1 cubic cubit (31 dj = 22.96″) :≈ 7 ft³
24″ × 24″ × 24″ := 8 ft³
1 cubic meter : = 7 royal cubits³
360 Mesopotamian ku (500 mm) :≈ 180 m
350 Egyptian royal cubits := 1 minute of march ≈ 183.3 m
1 stadion := 600 Attic pous (308.3 mm) ≈ 185 m =
1 stadium := 625 Ionian pous = 625 Roman pes (296 mm) ≈ 185 m
10 stadia :≈ 1 nautical mile
I respectfully disagree with this comment by my editor
"1 English furlong : ca. 200 m - This Anglo-Saxon unit hasn't changed in length (significiantly) for centuries. It was said to be 1/8th of a (Roman) mile since that was reintroduced in Britain, but in fact it is only exactly 1/8th of the English statute mile of 1593 (QE1). 5280 milliari = 5000 statute miles (132:125).
Rktect 7/30/05
I looked at some of the "Anglo-Saxon" European units
from Romania, Norway, Norman France, Germany, Denmark,
Finland, Spain, Scotland, Finland, France, and England
All of them are transparent multiples of Greek and Roman units.
I found a couple of similar statements on websites
Generally I would characterise such statements as uniformed
Especially since you can as readilly find the correct information
with the same web search
The following is from a web page which cites Klein
"The "ell" is an ancient measure of length,...
mentioned explicitly in the Magna Charta,...
reluctantly signed by King John on 15 June 1215.
This document contains sixty-three pledges or clauses;
the thirty-fifth is the "measurements" pledge.
Translated from the medieval Latin into modern English,
this clause reads: "Throughout the Kingdom
there shall be standard measures of wine, ale, and corn.
Also there shall be a standard width of dyed cloth, russet,
and haberject; namely a width of two ells within the selvedges.
Weights also are to be standardized similarly."
One of the earliest of all tables of English linear mesures,
Richard Arnold's Customs of London, c. 1503,
contains the following sequence ...
The length of a barley corn 3 times make an ynche [inch] and
12 ynches make a fote [foot] and
3 fote make a yerde [yard] and
5 qaters [quarters] of the yerde make an elle.
5 fote make a pace.
123[125 in Klein] pace make a furlong
and 8 furlong make an English myle [mile]
Sources:
The World of Measurements, by H. Arthur Klein,
736 pages, Simon and Schuster, New York, 1974, SBN 671215655
http://www.littletechshoppe.com/ns1625/nshist03.html
600 Roman/Greek stadia 111 km, 60 nautical miles
or 75 Roman miles (milliare))
The comment was added " one degree of Earth" which is meaningless
Its one degree of the earth's equatorial circumference.
The discussion of such calculations can be found in Ptolomy's geography
The following question seems a bit naive.
My metrology knowledge in fact is better after mediæval times than before or even inside, but what reason would QE1 have had to increase the number of feet or yards in (and the length of) a mile, if not making eight existing furlongs its new size?
Every time a standard of measure is changed, somebody benefits economically. Someone's acres get larger and they own more land and can charge more in rent or tithes or taxes. Queen Elizabeth clearly had advisors who stood to gain if they suceeded in changing the standards of measure. When they sold her that bill of goods they set the stage for Napoleon and the metric system.
The mile has always been divided in 8 stadions, stadiums and furlongs
The Romans also divided the stadium into 5 actus of 125 pes
When the Milos was 4800 pous the stadion was 600 pous and 185 m
In a square Milos there were 64 square stadions and 576 aroura
The Bodelian manuscript dates from this period
14 acres maketh a yerde of land
5 yerdis maketh a hyde of land which is 70 acres
8 hydis maketh a knights fee which is 560 acres of land
Look at the confusion
the redefinition of the Greek Milos by the Romans and
The redefinition of the Milliare by the Elizabeathans, and
The redefinition of the Mile by the Metric system brings to Europe.
Virgate - An old English unit of area,
equal to one quarter of a hide = 1.25 yerdis = 17.5 acres
The amount of land needed to support a person.
The hide is at its root a German word for household.
In the Saxon counties of southern England,
it referred to the land sufficient to support one family,
  • which equaled what the family plowed in a year.
  • Depending on the fertility of the land, the hide varied
  • from as little as 60 to as many as 240 acres,
  • but it was typically between 80 and 120.
  • The bovate, 1/8 of a carucate, also appears in the Domesday Book.
  • Its origin is Danish and it is found
  • in the northeastern English counties constituting the Danelaw.
  • A carucata or carucate, like a hide, is approximately 120 acres and
  • like the bovate was found in the Danish counties.
  • Plowland or plowgate is equal to a carucate or
  • an area eight oxen can plow
  • sufficient for a free family to support itself;
  • its origins precede 1100.
  • The plowland compares with the knight’s fee, which was a larger area
  • sufficient to support a knight’s family
  • (perhaps to allow pasture for animal husbandry).
  • Sulung is a Kentish term for two hides.
  • A yoke in Kent is 1/4 of a sulung.
  • A virgate is a rod in linear measure and 1/4 of a hide
  • (or 30 acres) as a measure of area in Saxon counties.


  • Arpent - Unit of length and area used in France, Louisiana, and Canada. * As a unit of length, =~ 191.8 feet (180 old French 'pied', or foot).
  • The (square) arpent is a unit of area,
  • approximately .845 acres, or 36,802 square feet
  • Morgen - Unit of area =~ .6309 acres. or 27, 482 SF
  • It was used in Germany, Holland and South Africa,
  • and was derived from the German word Morgen ("morning").
  • It represented the amount of land that could be plowed in a morning.


  • 560 acres =~ 576 aroura
  • The square Milos has become the Knights fee
  • in a square stadion there were 9 aroura of 40,000 square pous
  • each aroura had a side of 200 pous divisible into 2 plethrons
  • each of the 2304 plethron in a square Milos had a side of 100 pous
  • When the Milliare was 5000 pes the stadium was 625 pes and 185 m
  • In a square Milliare there were still 64 square stadiums but
  • There were also 25 square actus of 25 acres
  • A Heridia was 1.25 acres so there were 20 Heridis to a square Actus
  • Each Jugerum was half a Heridium and Half a Jugerum was an acuna.
  • A Centuria was 100 Heredia or 125 acres or 5 square Actus
  • in a square acre there were 40,000 square pes or pedes
  • each acre had a side of 200 pes
  • When the Myle was 5000 fote the furlong was 625 fote and 185 m
  • Each square furlong was divided into 25 square actus
  • A Heridia was 1.25 acres so there were 20 Heridis to a square Actus
  • Each Jugerum was half a Heridium and Half a Jugerum was an acuna.
  • A Centuria was 100 Heredia or 125 acres or 5 square Actus
  • in a square acre there were 40,000 square feet or fote
  • each acre had a side of 200 feet
  • When the Mile was made 5280 feet the furlong became 220 yards
  • Each square furlong was divided into 10 acres or 8 Heridia
  • each acre measured a perch by a furlong
  • Each square furlong was half a square Actus
  • Each Jugerum was half a Heridium and Half a Jugerum was an acuna.
  • Each Furlong was 16 Jugerum and 32 acuna
  • A Centuria was 100 Heredia, 12.5 square furlongs
  • 125 acres or 5 square Actus was one
  • in a square acre there were 40,000 square feet or fote
  • each acre had a side of 200 feet
  • The Romans conquered (much of) Britain,
  • when it was inhabited by Celts, bringing with them their mile.
  • The Germanic Anglo-Saxons, who were hardly Roman or Greek influenced,
  • How much influence do you think the Greeks had
  • on the people who lived on the Danube
  • arrived later with their furlong and eventually were defeated
  • by the Normans, of Nordic origin but quite “frenchised”.
  • Where is it that you think the furlong originated?
Like the peoples their systems of measurement merged. See also further down. Christoph Päper 15:28, 19 July 2005 (UTC)
  • This comment seems uniformed
  • "This implies that Greeks and Romans, maybe even earlier civilizations, realised that Earth is a sphere"
  • This appears to be cognative dissonance
  • ...calculated its circumference to a pretty high precision and then decided to use that as a base for their measurements.
I just say that it implies that, not that I exclude the possibility. Of course there were people who not believed in Earth as a disc a long time ago, some even calculated its circumference to quite some precision—I'm bad with remembering names, sorry—, but it's a huge step from there to have a system of measurement based on that. Also consider that there is not just one Greek stadium. Christoph Päper 15:28, 19 July 2005 (UTC)
  • This can be cited to Herodotus and Ptolomy.
  • "The 1 "minute of march" seems much more plausible,
  • This appears to be cognative dissonance
  • the rest being coincidence.

Egyptian volume

  • See Gillings’ “Mathematics in the time of the Egyptians” is a good benchmark for discussions of Egyptian mathematics and their systematic calculations of length, area and volume.
  • hekat, hk3t := 1/30 Royal cubit³, 4.8 l, used for grain, was divided into fractions of ½, ¼, 1/8, 1/16, 1/32 and 1/64 by an "Eye of Horus" rule.
  • Gillings says the hk3t was 1/30 royal cubit. If we take the royal cubit as 5 cubic feet that would mean that 6 hk3t = 1728 in³ and the hk3t is 288 in³ (4.72 l). Gillings says, Chace gives it as 292.24 in³ (4.79 l).
  • Since the divisions of the hk3t are clearly a doubling system similar to the English systems and since ancient weights and measures often have long, median and short forms, it might be interesting to see what would happen if the divisions of the cubic cubit would follow the same system.
  • For purposes of accuracy allow a Bronze Age variation in the length of the cubit, 20.62" ± 1/16" or 523.75 mm ± 1.6 mm.
  • Comment by my editor
  • above it is only said to be <= 525 mm
  • The variance in actual cubit rules is +/- 1/16" at a minimum
  • If we set the hk3t at 1/32 of a royal cubit with side 20.7" and volume 8876 in³ and divide by 32 we get 277.36 in³.
  • For comparison purposes:
  • 1 ounce := 1.44375 in³, i.e. side 1.13"
  • 1 gill := 5 ounces = 7.21875 in³, i.e. sides 1.93"
  • 1 pint := 4 gills = 28.875 in³, i.e. sides 3.06" = 1 palm
  • 1 quart := 2 pints = 57.75 in³, i.e. sides 3.86"
  • 1 (US/wine) gallon := 231 in³ = 4 quarts,
  • i.e. side 6.14" = 2 palms = 1/38 royal cubit, 1/24 ordinary cubit
  • 1 imperial gallon := 277.42 in³
  • 1 peck := 2 wine gallons = 462 in³, i.e. sides 7.73" or
  • volume 1/12 ordinary cubit and 1/19 royal cubit of side 20.62
  • 1 kenning := 2 pecks = 924 in³, i.e. sides 9.74 in = 1/6 ordinary cubit
  • 1 bushel := 8 gallons = 4 pecks = 2 kennings = 1/3 ordinary cubit
  • Volume = 1848 in³ = sides of 12.27" = 312 mm
  • 6.4 hk3ts of 288 in³ but 6 2/3 hk3ts of 277.36 in³
  • 1 firkin := 9 gallons, 2079 in³, side 12.76 in, 7.5 hk3ts of 277.36 in³
  • 1 kilderkin := 18 gallons = 4158 in³ = side 16 in, 15 hk3ts of 277.36 in³
  • 1 wine barrel := 36 gallons = 8316 in³ (height 34 7/8",
  • area 238.45 in², diameter 1 Roman cubit ≈ 30 hk3ts of 277.36 in³)
  • 1 beer barrel := 38 gallons = 8778 in³ (height 34 7/8",
  • area 252 in², diameter 1 biblical cubit ≈ 32 hk3ts of 277.36 in³)
  • 1 beer hogshead := 54 gallons = 12474 in³ ≈ 45 h3kts of 277.36 in³
Dimensions of real barrels from a winery
Capacity Stave thickness Head diameter Head circumference Belly diameter Belly circumference Height Bung hole diameter
53 gallon 0.937" 21.25" 66.8" 25.7" 80 5/8" 34 7/8" 2"
59 gallon 0.987" 22.687" 71.27" 27.53" 87" 34 7/8" 2"
65 gallon 0.937" 22.687" 71.27" 28" 88" 34 7/8" 2"
1 quarter
= 8 bushels = 14,784 in³
1 puncheon
= 84 wine gallons = 19404 in³
1 hogshead
= 2 barrels = 72 gallons = 16632 in³
1 butt
= 126 wine gallons = 29106 in³
1 tun
= 3 puncheons = 252 wine gallons = 58212 in³
1 chaldron
= 32 bushels = 256 gallons = 59136 in³
1 last
= 80 bushels = 640 gallons = 147840 in³
1 oipe, ipet
= 4 hekat
1 jar
= 5 oipe
1 hinu
= 1/10 hekat, used for perfume as well as grain
1 ro
= 1/32 hinu
1 des
≈ 0.5 l, for liquids
secha
for beer
hebenet
for wine

Roman area

  • Why do you put semicolons in front of and behind each sentence?
  • It makes the text bold. On the other hand the text doesn't need to be bold so I took them out
Please, please read up on Wikipedia mark-up, before making any other edits. Christoph Päper
  • Your reduplication for emphasis raises an interesting point about standards of measure. Whenever one system duplicates another it

repeats what was said before and then adds on something more besides. rktect 7/19/05

  • What does Egyptian stuff do here?
  • The Egyptian measures are the earliest form of the Roman measures.
  • The acre (Egyptian 3kr, the land itself) was first defined
  • as the area of a farmers fields or 3ht.
  • In Mesopotamia the iku was 100 cubits to a side.
  • The Mesopotamian measures are the earliest form of the Egyptian measures.
  • In Egypt the kht was defined as the side of an 3ht. The kht measured 100 cubits long by 1 cubit wide. It originated as the length of the irigation ditch that brought water to the field. At first fields were farmed in pairs with one field left fallow and the other plowed.
  • A field with side 100 ordinary cubits of 450 mm (17 2/3 in)
  • has sides of 147.29 English feet,
  • its area is 21,693 ft² or about half a modern English acre of 43,560 ft².
  • its exactly half an acre if the Egyptian ordinary cubit is 17.7"


  • Some people may not know that before the time of Queen Elizabeth
  • Anglo- Saxon English measures derived from the Greek and Roman
IOW some people believe in the one-system-everywhere theory and don't accept variations.
IMHO everything anyone believes is a bias against the alternative.
Perhaps two measures with the same name and value would be a coincidence.
With an entire system with the same name and value coincidence is harder to support.
  • Queen Elizabeth added 280 feet to the old Roman Milliare or Myle
  • so that a furlong would measure 10 perche and be 10 acres so
  • that 64 square furlongs would egual a square mile.
  • In an Anglo - Saxon Myle there were 625 acres
  • Those acres are measured as 40,000 pes with 625 to a square Milliare
  • (of side 5000 pes) That was the Myle c 49 BC - 1593 AD
  • The Furlong of that Myle was 625 fote.
  • Before that c 800 BC - 49 BC there was a Milos of 600 pous
  • There were 9 aroura to a square stadion and
  • 64 square stadions to a square Milos (of side 4800 pous)
  • meaning that their aroura was 40,000 sq pous.
  • The Anglo Saxons derived their measures from the Germanics
  • and the Germanics East of the Rhine used the Pous
I'd like to see a proof for that. And an explanation. Until then I regard this as a result of deliberately misinterpreted statistics. Christoph Päper 15:28, 19 July 2005 (UTC)
Take a look at the page on Medieval Measures.
Look at the values broken down by German city.
How many are evenly divisible by subdivisions of a Greek Milos?
  • The important fact about the Egyptians is that their
  • 3kr or measure of the land itself was derived from
  • the Mesopotamian iku and so was the Greek aroura or thousand.
  • Although initially fields had measured a half acre
  • with sides of 100 ordinary cubits of 17.7"
  • they had always been plowed in pairs and
  • the pair of fields had measured an acre
  • The Egyptians called the field (3ht) and
  • the field of side 100 royal cubits, a st3t.
  • Later as domesticated animals began being used to plow the fields a third field was added and planted in hay or fodder for the beasts of burden.
  • The field of side 100 royal cubits of 20.5" had an area of 29,040 SF so * three st3t was 2 acres.
  • The Greeks called the st3t an aroura or thousand.
  • I would be very suprised if the Roman acre is a squared Roman arpent
  • or that there was a Roman arpent equal to 14400 ft²
  • or about 0.126 ha or "more exactly almost" 1264.673 m².
  • The reason is that none of those measures of area
  • are evenly divisible into a square Roman Milliare and
  • every measure the Romans adopted is if nothing else systematic.
  • 625 pes = 500 remen = 1/8 milliare, 1 milliare = 5000 passus
  • 1 square milliare = 625 acres of 40,000 pes
  • 25 square acres = side 1000 pes, 1 area side 100 pes
  • 600 stadia = 75 miliare = 1 degree


Proof of the same-system hypothesis

I'd love to see your proof that "the same system has been used throughout
history and traced back to a sngle system." All I say is that until it appears,
refrain from making such claims in the article.
Jimp 20Jul05

rktect 7/20/05

  • Thesis: The same system of measures has been used throughout History.
  • Antithesis: The same system of measures has not been used throughout History.
  • Synthesis:* Either the Thesis is correct or the Antithesis is correct
Reword your antitheis: There is no one system which has been used
throughout history.
Jimp 23Jul05
Rktext 7/29/05 I respectfully disagree and suggest
that rather than start with the conclusion,
we proceed to test the hypothesis.
I'm not trying to start with the conclusion. All I'm suggesting
is clearer wording.
Jimp 6Aug05
  • Proof by Testable Hypothesis:
  • 1.) For Mesopotamia, Egypt, Greece, Rome, Europe
The World is bigger than this. What of the Aztecs, what of Japan,
what of Tasmania? You've not even really taken into account
ancient Scandinavia.
Jimp 23Jul05
Rktext 7/29/05 The system originated with civilization.
Scandanavian is a nice mix of Roman and Greek Measures

What of the Aztecs? What of Japan, What of Tasmania?

Region Foot Name Foot Measure
China che 333.45 mm
Japan shaku 303.02 mm
Korea chok 303.02 mm
Costa Rica tercia 278.64 mm
Aztex Mexico pie 278.89 mm
Ecuador -El Salvador tercia 304.8 mm
Paraguay pie 288.8 mm
Tasmania foot 304.8 mm
And this is supposed to prove ... Your "Tasmanian" foot is
just an Imperial foot (surprise surprise). What of pre-colonial
Tasmania? Similarly your South American feet look suspiciously
Latin. Even Scandinavia ... what about pre-Grecio-Roman
influence? The Far East units are interesting but, as I've
mentioned, simply showing an approximate equivalence
hardly proves that two units are related. We haven't ruled
out coincidence nor have we ruled out different cultures
happening on similar defintions ... or does this count as
the "same theme"?
Jimp 6Aug05
  • 2.) A system of measures organized by increasing length, area, volume exists
Several systems have existed they might be related as the
Imperial and U.S. systems are but even these are not the same.
Jimp 23Jul05
The American system is inarguably derived from the British Imperial System and has only deviated from it in relatively modern times. The Imperial system is in every respect the same system as was used in ancient Greece, Rome, Palestine, Persia, Egypt amd Mesopotamia.
Seems you've dug yourself into a bit of a hole there. The US
system is inarguably derived from earlier English units but not,
as you claim, from the Imperial system. Still, sure, the point
you'd wanted to make is that they share a common ancestor.
However to say that the two systems are derived from one common
source and to say that they are the same are two different
things. The argument applied also to the Imperial system verses
the Roman system. They are related but to say that they are
"in every respect the same system" would be to use language too
strong. Just as there are 4 fluid ounces to a US gill as
opposed to the 5 per Imperial gill, there are 280 extra feet in
the Imperial mile as opposed to the Roman 5000 foot mile.
Similar, sure, but not the same.
Jimp 6Aug05
Then there is the metric system: you'll be stretching it if you
point out that the height of an A4 sheet is one Roman foot. Even
today some use of three different systems is being made.
Jimp 23Jul05
Ancient Measures from Greece, Rome, Mesopotamia and Egypt were the source of the Metric System. Google Jomard and Napoleons French Savants, and/or read your Klein.
  • 3.) Each civilization has a unit measure which corresponds
  • 4.) to a unit measure in each other civilization by
  • 5.) name, position in the system, length, area, volume
  • 6.) Each measure is systematic in that it is part of an iterative sequence
  • 7.) 1 finger, 2 fingers, 3 fingers, palm, hand, fist and so forth
  • 8.) each area is the square of a unit length and you can convert between systems
  • 9.) each voume is the cube of a unit length and you can convert between systems
The Imperial gallon is the cube of what unit of lenght?
Jimp 23Jul05
How about we choose an Egyptian royal cubit as the side of a cube.
Wickopedia cites the British Imperial Gallon as 277.42 cu in
British Imperial Gallon
multiply 32 x 277.42 cu in = 8877.44
take the cube root of 8877.44 = 20.7" = the side of an Egyptian Royal cubit
the cube which is 1/32 Egyptian royal cubit is the hkt measure used with
the Horus eye doubling series to apportion bread and beer in the mathematical
problems of the Rhind papyrus.
Interesting, sure, however the Imperial gallon was originally
defined not to be 1/32 of the cube of an Egyptian Royal cubit
but to be the volume of 10 lb of water (at certain thermodynamic
conditions). Jimp 8Aug05
Try converting to U.S. gallons.
Jimp 23Jul05
Ok, presumably you have never read 1 Kings
homer (= 10 baths) 60 US gallons - mentioned in Ezek 45.11-14
NT metretes = 38 US gallons = side of 1 royal cubit - mentioned in John 2.6
bath (= 1/10 homer = 6 hins; also = 1 ephah of dry measure =6 US gallons 1 Kgs 7.26; Isa 5.10
hin (= 1/6 bath or 12 logs) 1 US gallon Exod 29.40,41; 30.23-25; Num 15.4-10
log (= 1/12 hin or 1/72 bath) 1/3 US pint Lev 14.10,21
1 wine gallon = 8 cubic Athenian pous, and is 1/12 the cube whose side is the Biblical talent.
4 wine gallons = 31 Cubic Attic Greek pous, 30 cubic English feet, 28 cubic Roman pes
Haven't you ever done any of this? Its all the same system but the conversions allow you
to take different unit fractions of the same volume.
The ratio is 5-6 just like mesopotamian ordinary cubit - great cubit
Let's say the side of a royal cubit that contains 32 BIG's is 20.7"
The ordinary cubit is side 5/6 that or 17.7" it contains 20 BIG's and 24 wine gallons
100 ordinary cubits (mh t3 or land cubits) are the side of a square of 1/2 acre
17.7/12 X 100 = 147.5 ft and if you square and multiply x 2 you get 43512.5 SF
The differance is round off error and some inaccuracy in the standards that tends
to creep in when people redefine them.
Okay, presumably you've got a modern American translation of the
Bible because you can be pretty damn certain that U.S. gallons
are not mentioned anywhere in the original texts.
Haven't I ever done "any of this"? Any of what: looking for
connexions that don't exist? Sure, I've done that. Guess what
I found: nothing.
The Ezekiel passage you mention is interesting. It talks about
using a single standard. This would seem to indicate that there
were different standards in use at the time of writing. Why
else would the author be insisting on consistancy?
If five of my gallons equal six of yours then we are not using
the same system ... even if this ratio is exact. However in the
case of US verses Imperial gallons the ratio is not five to six
exactly.
Five to six is only an approximation the exact ratio is
4.99674355488 to 6.0008388. To blame this on "round off error
and some inaccuracy in the standards that tends to creep in when
people redefine" them would be rather silly.
Are we talking about what the standards are or are we
talking about what they should be? If we're talking about
what they should be then why should there be any difference
at all between an Imperial gallon and a US one?
Jimp 23Aug05
  • 10) where changes and conversions between systems occur they occur systematically
  • 11) a stadion is 600 pous = 185 m a stadium is 625 pes = 185 m
  • 12) a Milos is 8 stadions, A Milliare is 8 stadiums
You can identify Jupiter as Zeus but you still haven't proven anything about Vishnu.
Jimp 23Jul05

Jupiter is the sky father, Peter, Pitar, Ptah all the same pantheon

... and Vishu? Jimp 6Aug05
  • 13) a sexigesimal cubit of 30 fingers becomes a septenary cubit of 28 fingers
  • 14) they share a system of unit measures fingers, palms, hands, feet, remen, cubits etc;
  • 15) they share the same system
  • Parenthesis: Proof by identity
What is identity proof? Do you mean if you take two measures and show that
they are (approximately) equal or related by simple ratios, you've proven
a connexion? This is a very unscientific approach. There may well be other
explanations for the phenomenon.
Jimp 20Jul05
  • Items 11 and 12 are examples of Proof by Identity, ie; the essence of the scientific method
  • a model is created which is based on a testable hypothesis
  • If the tested results match the predicted results
  • the model works and the hypothesis is proved
  • If the tested results do not match the predicted results
  • the model fails, the hypothesis is disproved and the antithesis is proved
You don't prove a scientific theory.
Jimp 23Jul05
The use of a testable hypothesis to make a proof is the scientific method
This is simply false. You might confirm a scientific
hypothesis or theory but you never prove it. Science
involves inductive logic. Jimp 8Aug05
  • We measure weigh and judge the Similarity and Difference between a proposition and reality
  • to learn its truth
  • Everything which exists changes, if simply by becoming older, but also remains the same.
  • Proof by identity: Things which are the same match.
However not all things that match are necessarily the same. Jimp 8Aug05
  • The Agregate of all Becoming, (which changes constantly) = Being which remains the same
  • One example of Proof by Identity includes synthesis by resolution of paired opposites
  • a minute of march becomes a stadion becomes a stadium becomes a furlong

Metathesis:

  • If there are other different explanations
  • we measure, weigh and judge them against these explanations.
  • Esthesis: The whole is the sum of its parts. QED.
QED? I think not. Here's disproof for you. The Imperial system
and the U.S. system are different. They've both been used.
Different systems have been used in history. QED. Oh, yeah,
the metric system is not even related to either and is the most
used system today and has been for several decades.
Jimp 23Jul05
Not really, they are the same system with some disagreement
about how to define an accurate standard. The argument dates back
first to Elizabeth and some shrewd land speculators that had her ear,
and then to Thomas Jefferson and his redefinition of the wine gallon.
["http://www.unc.edu/~rowlett/units/usmetric.html wine gallon]
gallon "(gal) [1]

a traditional unit of liquid volume, derived from the Roman galeta, which originally meant a pailful. Gallons of various sizes have been used in Europe ever since Roman times. In the United States, the liquid gallon is legally defined as exactly 231 cubic inches; this is equal to the old English wine gallon, which originated in medieval times but was not standardized until 1707, during the reign of Queen Anne. Some scholars believe the wine gallon was originally designed to hold 8 troy pounds of wine. The U. S. gallon holds 4 liquid quarts or exactly 3.785 411 784 liters; a U.S. gallon of water weighs about 8.33 pounds. American colonists were also familiar with the Elizabethan beer and ale gallon, which held 282 cubic inches (4.621 liters). gallon (gal) [2] a historic British unit of dry volume still used implicitly in the U.S. In the U.S., the term "gallon" is not used in dry measure, but if it were it would be equal to 1/2 peck, or 4 dry quarts, or 268.8025 cubic inches, or approximately 4.404 884 liters. This unit is the English corn or grain gallon, standardized during the reign of Elizabeth I in the sixteenth century. The earliest official definition of a dry gallon in Britain is a 1303 proclamation of Edward I, where the gallon is defined as the volume of 8 pounds of wheat; the current U.S. "gallon" contains about 7.5 pounds of wheat. Grain gallons have tended to be larger than liquid gallons throughout the history of British units, apparently because they were based on heaped rather than "struck" (leveled) containers. A container in which grain has been heaped above the top will hold as much as 25% more grain, and the traditional corn gallon is in fact 16.4% larger than the wine gallon. gallon (gal) [3] currently the British use a larger gallon than either of the American gallons. The Imperial Weights and Measures Act of 1824 established a new unit for all volumes, liquid or dry, replacing all the other gallons in previous use in Britain. The imperial gallon, designed to contain exactly 10 pounds of distilled water under precisely defined conditions, holds exactly 4.546 09 liters or approximately 277.4194 cubic inches. The imperial gallon equals 1.20095 U.S. liquid gallons (British wine gallons) or 1.03206 U.S. dry gallons (British corn gallons). gallon (gal) [4] a traditional unit of volume in Scotland equal to 4 Scots quarts. This is almost exactly 3 British Imperial gallons, 3.6 U.S. liquid gallons, or 13.63 liters. "

They have both been abused by people who didn't know
what they were doing, to put it bluntly
Be it use or abuse, whether they knew or knew not what they were
doing the Imperial system and US system have been used. If your
"disagreement about how to define an accurate standard" leads to
differing definitions, then you've got different systems. If
five of my pints are a tad bigger than six of yours, then we're
using different systems. Jimp 23Aug05

The metric system was first used in decimal form in ancient mesopotamia.

Our modern rediscovery of it goes back to when it was first being proposed in the 16th century. Its adoption and definition were based on a survey of ancient measures by Napoleons savants and it was used by the French peasantry as a political tool to overthrow the feudal system

Original research?

This is all very interesting, Rktect, your identity proofs, your
theses, your spreadsheets and such. However, it does sound a
little like original research. Is it not? If it is, posting it
here, I'm afraid, would be against Wikipedia's policy.
Jimp 23Jul05


Rktect 07/29/05 I looked at the Wikipedia definition of original research
It says that if you are posting or citing previously published material
that isn't copywrited or that you have permission to use that's fine
My cites are to previously published non copywrited material
Here is another independant scholar saying essentially the same thing
Clandonia

Does Rktect contend that the material he's posting is consensus among scholars? Because if not, the actual ancient units, on which there often is consensus, ought to separated from the international comparisons, which are not. This would also avoid confusion and reversions. Septentrionalis 15:26, 19 August 2005 (UTC)

I don't like to be contentious but when you cite something from a source like Kleins "World of Measurements' or any of the other cited references then the proper way to dispute it would be to cite a counter source that either says something different or adds on something more besides.

Please answer the question I asked. I am not asking whether you have scholarly support; I am asking if you assert there is a consensus. If not, both PoV should be represented in the article, and separated from the individual measurements, insofar as they are consensus. Septentrionalis 14:21, 20 August 2005 (UTC)

Replacements

rktect 7/20/05

  • I would like to replace this


  • I would replace it with a more accurate update

that looks at the Roman units of area in comparison with equivalents of its peers as well as our modern equivalents and gives some sources.

  • I don't think you get the same British Imperial system

equivancy if you only look at its metric system value and so while you may be telling the truth you are not telling the whole truth.

  • The mile has always been divided in 8 stadions, stadiums and furlongs

The Romans also divided the stadium into 5 actus of 125 pes The Greek Milos was the immediate predecessor to the Roman Milliare It derives its acre or aroura from The Mesopotamia iku which is 100 cubits to a side rather than from the Egyptian st3t which is also 100 cubits to a side

  • When the Milos was 4800 pous the stadion was 600 pous and 185 m
  • In a square Milos there were 64 square stadions and 576 aroura
  • 560 acres =~ 576 aroura
  • The square Milos became the Knights fee
  • In a square stadion there were 9 aroura of 40,000 square pous
  • each aroura had a side of 200 pous divisible into 2 plethrons
  • each of the 2304 plethron in a square Milos had a side of 100 pous
  • When the Milliare was 5000 pes the stadium was 625 pes and 185 m
  • In a square Milliare there were still 64 square stadiums but
  • There were also 25 square actus of 25 acres
  • A Heridia was 1.25 Roman acres so there were 20 Heridis to a square Actus
  • 1.25 Roman acres is 50,000 pied = side 217.15 Ft area 47,154.54 SF
  • Each Jugerum was half a Heridium and Half a Jugerum was an acuna.
  • A Centuria was 100 Heredia or 125 acres or 5 square Actus
  • in a square acre there were 40,000 square feet or fote
  • each acre had a side of 200 feet
  • When the Mile was made 5280 feet the furlong became 220 yards
  • Each square furlong was divided into 10 acres or 8 Heridia
  • each acre measured a perch by a furlong
  • Each square furlong was half a square Actus
  • Each Jugerum was half a Heridium and Half a Jugerum was an acuna.
  • Each Furlong was 16 Jugerum and 32 acuna
  • A Centuria was 100 Heredia, 12.5 square furlongs
  • 125 acres or 5 square Actus was one
  • in a square acre there were 40,000 square feet or fote
  • each acre had a side of 200 feet
  • The Romans conquered (much of) Britain,
  • when it was inhabited by Celts, bringing with them their mile
  • In Roman Europe The Bodelian manuscript tells us
  • 14 acres maketh a yerde of land
  • If those are Roman acres of 40,000 pied then the yerde is 12 English acres
  • 5 yerdis maketh a hyde of land which is 70 acres 60 English acres
  • 8 hydis maketh a knights fee which is 560 acres of land = 480 English acres
  • Look at the confusion
  • the redefinition of the Greek Milos by the Romans and
  • The redefinition of the Milliare by the Elizabeathans, and
  • The redefinition of the Mile by the Metric system
  • brings to Europe.
  • The Virgate - "An old English unit of area" is actually Roman in origin
  • equal to one quarter of a hide = 1.25 yerdis = 17.5 acres
  • The amount of land needed to support a person.
  • The hide is at its root a German word for household, but also a Roman derived unit
  • We are told that in the Saxon counties of southern England,
  • it referred to the land sufficient to support one family,
  • which equaled what the family plowed in a year.
  • We are told that depending on the fertility of the land, the hide varied
  • from as little as 60 to as many as 240 acres,
  • but it was typically between 80 and 120 acres.
  • Its 60 modern English, 70 Roman acres
  • We are told that the bovate, 1/8 of a carucate,
  • which also appears in the Domesday Book has its origin as Danish
  • and it is found in the northeastern English counties constituting the Danelaw.
  • Lets allow a carucata or carucate, like a hide, is approximately 120 acres and
  • like the bovate was found in the Danish counties.
  • A Plowland or plowgate is equal to a carucate or an area eight oxen can plow
  • sufficient for a free family to support itself;
  • its origins precede 1100.
  • We are told the plowland compares with the knight’s fee,
  • which was a larger area sufficient to support a knight’s family
  • (perhaps to allow pasture for animal husbandry).
  • Sulung is a Kentish term for two hides.
  • Its 120 modern English, 140 Roman acres
  • A yoke in Kent is 1/4 of a sulung.
  • A virgate is a rod in linear measure and 1/4 of a hide
  • (or 30 acres) as a measure of area in Saxon counties.
  • 30 acres is 1/4 sulong
  • We have the Arpent a unit of length =~ 191.8 feet and
  • the (square) arpent is a unit of area, area
  • (180 old French 'pied', or foot) used in France, Louisiana, and Canada.
  • approximately .845 acres, or 36,802 square feet
  • We have the Morgen a unit of area =~ .6309 acres. or 27, 482 SF
  • used in Germany, Holland and South Africa, derived from the German word Morgen ("morning").
  • It represented the amount of land that could be plowed in a morning.


A strange edit

Despite the fact that you've just proposed that before we the main page again we discuss,
Rktect, you've gone and changed it without discussion. Let's now attempt to identify
what's questionable about this and why.

Old version

Many systems ... are related to a varying degree, despite a number of different
civilisations making ... adjustments to serve their own purposes.
The accuracy of definitions improved over time.

New version

Many systems ... are related to a varying degree. Despite a number of different
civilisations making ... adjustments to serve their own purposes, the accuracy of
definitions improved over time.
You do realise that this completely changes the meaning, don't you, Rktect?
The first version says that the systems were related inspite of the adjustments.
The second version says that the accuracy of definitions improved inspite of
the adjustments.
The first version makes sense: the systems are still related
though different. The second is nonsense: how could these adjustements possibly
have reduced the accuracy of the definitions?
Jimp 20Jul05
Think about that...

I think people do need to re-read and self edit from time to time to remove poor phrasing, obvious typos, and bad formating.

Neither of those first two versions is well phrased.

The first is a run on sentence which says.

1. The systems are related to a varying degree.
2. The degree they are related to varies.
3. The accuracy of the definitions improved over time.
4. This was despite adjustments.
5. A number of different civilizations made them.
6. The adjustments were to serve their own purposes.

That's just too many clauses for a single thought.

The second uses two run on sentences to say.
I
1. The systems are related to a degree.
2. The degree they are related to varies.

This has the misfortune of suggesting the degree was a variable standard.

II
3. The accuracy of the definitions improved over time.
4. This was despite adjustments.
5. A number of different civilizations made them.
6. The adjustments were to serve their own purposes.

Perhaps this is a better way to say it.

Many systems of weights and measures, that have been used throughout history, are related. To a varying degree, despite a number of different civilisations making their own adjustments to serve their own purposes, the accuracy of definitions improved over time.

rktect 7/21/05
rather than continue to see a big sign at the top of my favorite article which says this needs attention, unless someone objects I will give it some.
I would like to try and make it clear why the various systems are related

by listing equivalents to each systems units in the units of their peers rather than just modern or metric equivalents.

In the ancient world people measured things by cubits rather than feet or meters. It would be nice to see just how all the cubit systems equate when evaluated in unit fraction fingers or palms rather than just decimal feet inches or mm.
I have had this in spread sheet form for a decade or so but just never bothered to try to prove it systematically.
One place I would like to pay particular attention is the definition of units of length and their development into areas.
dividing measures up by unit and the various unit fraction multiples rather than culture might be interesting.
The finger, inch, ell, palm, hand, remen, ordinary cubit great cubit, pace, fathom, orguia, rod, perch, cord, chain, minute of march, stadion, stadium, furlong, iku, khet, st3t, 3kr, aht, are, aroura, actus, acre milos, milliare, lyle, mile, yerde, hide, knights fee degree
rktect 7/21/05 cleaned up Egyptian units somewhat, have much more to add
rktect 7/21/05 cleaned up Mesopotamian units, added a lot, broke out Akkadian from Sumerian as per an email exchange with John Halloran
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