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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?

Short answer

Miles

The Greek Milos of 4800 pous and

the Roman Milliare of 5000 pes and

The English Myle of c 49 BC - 1593 AD

are 8 stadions, stadiums, furlongs of 185 m.

Stadions

The ordinary Mesopotamian sos or side at 6 iku and 180 meters

was the basis for the Egyptian minute of march

the Egyptian minute of march at 183 m and 350 royal cubits

was the basis for the stadion of the Greek Milos

The stadion of the Greek Milos at 6 plethrons or 100 orguia and

600 Atic pous of 308.4 mm at 185 m

was the basis for the stadium of the Roman milliare

The stadium of the Roman Milliare at 625 pes of 296 mm

was also 185 m and at 1000 passus of 5 pes

was the basis for the furlong of 625 fote of the English Myle

Leauges

3 Milos of 4800 pous = 24 stadions = 14,400 pous = 1 leauge = 4440 m

3 Milliare of 5000 pes = 24 stadiums = 15,000 pes = 1 leauge = 4440 m

3 Myles of 5000 fote = 24 furlongs = 15,000 fote = 9375 English cubits = 1 leauge = 4440 m

3 Miles of 5280 feet = 24 furlongs = 15,840 feet = 9900 English cubits = 1 leauge = 4828 m

7.5 milliare = 1 schoeni = 1 kapsu = 2 parasang = 60 furlongs = 11.1 km = 1/10 degree

1 degree (eec) = 1 itrw = 10 schoeni = 20 parasangs = 600 furlongs = 21,000 royal cubits

Divisions of the Milos, Milliare, Myle and Mile into areas

1 square Milos of side 4800 pous = 1 Knights fee

64 square stadions of 360,000 square pous,

34,225 square meters, 368,554 SF

576 aroura of 40,000 square pous, 3802.78 square m, 40,950.46 SF

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

2304 square plethrons of 10,000 square pous,

950.6 square meters 10,237.64 SF

640,000 square orquia of 36 square pous, 3.4 square meters, 36.85 SF

1 square Milliare of side 5000 pes

64 square stadiums of 390,625 square pes,

34,225 square meters, 368,554 SF

25 square actus of side 1000 pes with 25 acres or 20 heridia

1 Heridia was 1.25 Roman acres so there were

20 Heridis to a square Actus

625 areas of 40,000 square pes, 3802.78 m, 40,950.46 SF

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

1 square Myle of side 5000 fote or 8 furlongs

64 square furlongs of side 625 square feet

in a square acre there were 40,000 square feet or fote

each acre had a side of 200 fote

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

8 hydis = 480 English acres

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

Old English or Anglo Saxon units derived from the Greeks and Romans

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

the hide is 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, half a knights fee

but it was typically between 80 and 120 acres, 1/4 knights fee

Its actually 60 modern English, and 70 old Roman acres

We are told that the bovate is 1/8 of a carucate,

which also appears in the Domesday Book originated as a Danish measure

and it is found in the northeastern English counties

constituting the Danelaw.

Lets allow a carucata or carucate, like

1 hide, is approximately 120 acres and

like the bovate was found in the Danish counties.

Lets allow 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. (see definitions of Sumerian areas)

We are told the plowland compares with the knight’s fee

which we have established originates with the Milos

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) used as a measure of area in Saxon counties.

30 acres is 1/4 sulong

We have the Arpent AS a unit of length =~ 191.8 feet and

the (square) arpent used as a unit of area, area

(180 old French 'pied', or foot) used in France, Louisiana, and Canada.

approximately .845 acres, or 36,802 SF

Clearly derived from 1000 square orguia = 36,850 SF

which is itself derived from 1 sos = 10,000 square orguia.

We have the Morgen a unit of area =~ .6309 acres. or 27, 482 SF

used in Germany, Holland and South Africa, as 3/4 the Arpent

derived from the German word Morgen ("morning").

It represented the amount of land that could be plowed in a morning.

Ancient Definitions of Medieval Units

Mesopotamia

1 square iku = 10,000 SF

1 square great iku = 14,400 SF

1 square sos = 360,000 SF

Egypt

1 square khet = 21,780 SF

1 square st3t of remen = 15,064.64 SF

1 square st3t = 29,526.69 SF

Greece

1 square aroura = 40,950.46 SF

1 square plethron 10,237.64 SF

1 square orquia 36.85 SF

Rome

1 square actus 943,090.78 SF

1 square Centuria 4,715,454 SF

1 square Heridia 47,154.54 SF

1 square area 40,950.46 SF

1 square Jugerum 23,577.27 SF

1 square acuna 11788.63 SF

Anglos Saxon use of Roman and Greek Units

1 Myle of 5000 fote became 1 Mile of 5280 feet in 1593

1 square Mile of side 5280 feet divided into 8 furlongs of 220 yards

1 acre = 43,560 SF because it was increased by Queen Elizabeth

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 was 5 square Actus

in a square acre there were 40,000 square feet or fote

each square acre had a side of 200 feet

Longer Discussion

The Greek root is stadios and means to have standing;

to be a landowner.Land measures including both

length and area are based on the size of fields

The base units are the remen, pace, yard, orguia,

fathom, rod, cord, perche and furlong.

Body measures fingers, thumbs, palms, hands, fists, feet, forearms

are related and worked into the system as multiples of the foot.

The Minute of March and the Atur = Itrw or Hour

The mile develops from the minute of march which originally measures the

river journey or itrw which is a unit of 1 hours travel on the river. 21,000 royal cubits works out to about 36,085 English feet or 6.83 modern miles and 7.217 miles prior to the time of Queen Elizabeth

That is 11 km or 7.43 Roman milliare. Since 75 milliare

are a pretty good value for a degree it would appear that the Egyptian value for 10 itrw is a little less accurate and that probably explains the correction.

The Greeks derived their systemized standards of measure from a variety of sources including ancient Europe, Mesopotamia, Persia, Phoenicia and Egypt.

The credit for the first systemized collection and standardization probably goes to the empire builders of Mesopotamia and Egypt but the international commerce of the people who benefited by those great empires, the Greeks and Persians and the Romans who followed them is what really required the system be standardized over such vast areas.

The important thing to recognize is that you can identify the original source

as Mesopotamian or Egyptian depending on whether the system is sexigesimal or septenary and whether the divisions are by palms or feet or both.

Much of the Egyptian system of measurement is based on the Mesopotamian. The Egyptian system in its turn formed the basis of the later Greek and Roman systems while they in turn influenced European Systems.

The Egyptians took a sexigesimal Mesopotamian system and converted it to a septenary Egyptian system by taking an ordinary cubit of five gat measuring 30 sheshi 25 uban(500 mm) and a great cubit of 6 gat measuring 30 uban (600 mm)and making the first 6 Šsp (6 palms with 24 db<= 450 mm) and the second 7 Šsp (palms with 28 db< = 525 mm).

There are generally two or more divisions by size of finger and thumb

and different cultures have a preference for different unit fractions but basically all of it is part of the same system.

Mesopotamian;

1 (little finger) = 1 "shusi" = 14.49 mm = 0.05 feet or podes

Greek;

1 (ring finger)= 1 daktylos = 19.275 mm = 0.06 feet or podes

Roman;

1.33 (thumb or inch)= 1 uncia = 25.64 mm = 0.08 feet or podes

Greek;

2 (daktylos)= 1 condylos = 38.55 mm = 0.13 feet or podes

Roman

4 (daktylos)= 1 palaiste = 77.10 mm = 0.25 feet or podes =(1 palm)

8 (daktylos)= 1 dichas = 154.20 mm = 0.51 feet or podes =(2 palms)

12 (daktylos)= 1 spithame = 231.30 0.76 feet or podes =(3 palms)

Greek;

16 (daktylos)= 1 pous = 308.40 mm =1.01 podes =(4 palms)

20 (daktylos)= 1 pygon = 385.50 mm =1.26 podes =(5 palms = 1 remen)

Roman

24 daktylos = 1 pechya = 462.60 mm = 1.52 podes =(6 palms = 1 cubit)

English;

25 (daktylos )= 1 English cubit = 493.44 mm = 1.62 podes;

Egyptian;

28 (daktylos )=~ 1 Egyptian royal cubit = 539.70 = 1.77 podes =(7 palms)

The Mesopotamians measured their arable land in garden plots or sar and combined them into fields or iku of 100 cubits to a side. The Egyptians measured out the irrigation ditches that bounded their 3ht or fields as strips a cubit wide and 100 cubits long known as kht. Their st3t which was a field 100 cubits to a side is said to have become the Greek Aroura or thousand but when you run the numbers the Aroura seems more likely to have derived from the iku.

Its probable that farmers measured out the land their community allowed them to plow in return for digging the ditch by pacing it off and built up an enclosure for it with the stones they found in their furrows.

The community would give the fields out in pairs, one to be plowed and one to remain fallow which were planted in rotation. As beasts of burden were domesticated and yoked to the plow the amount of land under cultivation increased, and a third field was added to be planted in hay or fodder for the plow animal. The side of this cluster of fields became standardized at 350 cubits or one minute of march.

The Milos was based on a stadion equivalent to the Egyptian minute of march.

In Egypt the minute of march was 350 royal cubits long and an hour of march or itrw was 21,000 royal cubits long. The Greeks tell us they noted their measures of 6 plethrons and 8 stadions, were both the equivalent of the Apothem or slant side of the Great Pyramid. The modern pre Euro nautical mile was ten times the length of that Apothem.

Using unit measures like the Stadion, Stadium and Furlong which were originally used to lay out fields and only gradually became defined as areas like the Aroura or thousand square royal cubits, the empire builders measured out their roads.

The Greek Milos was originally 8 stadions or 600 Greek pous x 8 = 4800 pous The Pous came in long short and median variations so depending on which one you used the number of pous would vary even as the length of the stadion and Milos remained the same. 600 Attic pous were equal to 625 Ionian pous but both stadions were 185 meters long

The Romans standard pes was the Ionian pous of 296 mm so they made their stadium of 185 meters egual to 625 pes or 1000 passus and that made their Milliare 5000 pes

What makes that a great system for empire builders is that the passus is now a measure of the pace at which the army moves. If such standards of measure are well suited to controlling the movements of armies with milestones related to how much distance can be covered in a set period of time they are equally servicable to the needs of commerce.

Just as the farmer can use the stone walls that border his field to help him restablish its boundaries after a flood, the community can establish its bounds in terms of how much land it needs to irrigate to sustain its population and the lugal or narmr (chief farmer)can determine how many men he needs to dig the irrigation system and how much land to alot to each oinkos, gene and phratre in return for their service. its all very feudal.

The city state is based on a market or agora that serves a number of communities which are spaced about as far apart as a man can walk in a day driving a team of oxen pulling a cart.

When it takes more days to get the goods to market than it takes for the crops to spoil you need a new market.

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.

Pull out your standard everyday run of the mill Stanly tape measure and you should

see a diamond at 19.2" That is the ancient ordinary English cubit and its the basis of the English League of three modern miles or anciently in the time when a mile was 8 furlongs of 600 feet, 14,400 ft and 9,000 diamonds.

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)

She added the 280 feet to make a mile of 8 furlongs of 660 feet be a mile of 80 perche instead of a mile of 8 furlongs of 625 feet. The perche was not a Roman measure.

Trying to lay out a knights fee with a mile that measured 75.75 perche to a side was what led to the confusion as to how many acres were in a hyde and yerde.

In a modern square mile there are 640 acres making 10 acres to a square furlong.

In the ancient square Milos there were 576 Aroura.

Greek Aroura would be measured with a side of 200 Attic pous of 308.4 mm.

That means there would have been 9 Aroura to a square stadion and

576 to a square Milos of 23040000 square pous.

Those would have been derived from

a Mesopotamian iku of 100 cubits of 600 mm rather than

a st3t with side 100 Egyptian royal cubits of +/- 525 mm.

An iku of side 100 great cubits of 600 mm has

a side of 196.85 modern English feet and

an area of 38750 SF. It would have had

a side of 202.7 Ionian pous or Roman pes of 296 mm

An Egyptian st3t with side 100 royal cubits

would measure 171.83 modern English feet to a side and

contain 29526.69 SF. While thats about half of a modern acre and

anciently fields were farmed in pairs that's 169.83 Attic pous and

With 28841.37 square pous not enough square pous in an Aroura

to multiply out to a square mile of 4800 pous to a side.

When people began to harness domestic animals to the plow

they added a third field which probably became

the basis for the Roman jugerum.

The above questions are very old, and I have found some answers

I have yet found no clear connection between

the Egyptian mile (river measure) and anything else,

The Egyptian minute of march is 350 royal cubits.

The itrw is 60 minutes of march or a one hour river journey and

measures 21,000 royal cubits.

The key to understanding Egyptian measures is that they are septenary

and based on multiples of the palm rather than multiples of the hand.

but the Persian parasang is also interesting.

For that you go to Herodotus (and Ptolomy)

Herodotus explains that the Persian stadia are 500 to a degree

rather than 600 so their stadion is 222 meters rather than 185 and

based on 750 Persian feet rather than 600 Greek feet.

The geographical ~7.5 km mile, land and sea, is the brainchild of Ole Rømer - the Prussian king later adopting it.

VI. Further, the length of the seacoast of Egypt itself is sixty “schoeni”1 --of Egypt, that is, as we judge it to be, reaching from the Plinthinete gulf to the Serbonian marsh, which is under the Casian mountain--between these there is this length of sixty schoeni. Men that have scant land measure by feet; those that have more, by miles; those that have much land, by parasangs; and those who have great abundance of it, by schoeni. The parasang is three and three quarters miles, and the schoenus, which is an Egyptian measure, is twice that.

VII. By this reckoning, then, the seaboard of Egypt will be four hundred and fifty miles in length. Inland from the sea as far as Heliopolis, Egypt is a wide land, all flat and watery and marshy. From the sea up to Heliopolis is a journey about as long as the way from the altar of the twelve gods at Athens to the temple of Olympian Zeus at Pisa. If a reckoning is made, only a little difference of length, not more than two miles, will be found between these two journeys; for the journey from Athens to Pisa is two miles short of two hundred, which is the number of miles between the sea and Heliopolis.

IX. From Heliopolis to Thebes is nine days' journey by river, and the distance is six hundred and eight miles, or eighty-one schoeni. This, then, is a full statement of all the distances in Egypt: the seaboard is four hundred and fifty miles long; and I will now declare the distance inland from the sea to Thebes : it is seven hundred and sixty-five miles. And between Thebes and the city called Elephantine there are two hundred and twenty-five miles.

81 schoeni = 608 miles

1 schoeni = 7.5miles = 1/10 degree = 11.1 km

Parasan = 30 furlongs

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)

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 ] 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 ] 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 2 × 3 × 7 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 . 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 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).

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)

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

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

• Egyptian circle

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

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

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

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

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

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

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

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

Iranian nationalism?

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

Version of IP 69.164.70.243

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

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

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

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

• Misplaced Pages 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 Misplaced Pages: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 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).

• • 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 and
• 12 ynches make a fote and
• 3 fote make a yerde and
• 5 qaters of the yerde make an elle.
• 5 fote make a pace.
• 123 pace make a furlong
• and 8 furlong make an English myle

• 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

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 Misplaced Pages 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 7/190/05

• 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.

• 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)

• 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

All Cubits Great & Ordinary

I've just moved the following from the article page.

--

 *My editor asks
 *Is one the ordinary cubit à 30 shusi (500 mm)
 *and one the great cubit à 30 uban (600 mm)
 * short answer: No.

 *Both were split into 15 digits (shusi not uban) and hands qat 
 *The Gudea rule is divided into two parts of 15 pieces each, with two ends 
 that extend beyond the division marks. Until the early 20th century the ends 
 were erroneously counted as digits.

--

69.164.70.243,

The normal thing to do is to keep such comments here in the talk page. Also note that Crissov is hardly your editor. He's editing this page but it's not your page ... unless you own Misplaced Pages.

Jimp 19Jul05

• I have rewritten the introduction and removed the disputed tags

removing the references to pyramids, irrationals, remains to be proven

uncited conjecture. As per instructions I am commenting here.

I propose that before we change the main page again we discuss

some of the issues and attempt to identify what items are

questionable and why.

69.164.70.243 20Jul05

69.164.70.243,

Please sign & date your comments otherwise this talk page gets very hard to read.

For example, who wrote what in the section above? It's also helpful to use indentation

(I've taken the liberty to add some to your comments above).

69.164.70.243, you continue to delete the "disputed" and "cleanup" templates

on this article. Thank you for putting a comment here this time. However more

in the way of a discussion or explanation was what I'd had in mind.

What's going on? Just look at this talk page and tell me that there is no dispute

as to the accuracy of the article (particluarly your contributions). Look at the article:

it's a jumble. It badly needs a clean up. Being split into several articles (Roman units,

Greek units, etc.) might not be a bad idea either.

Jimp 20Jul05

7/19/05 rktect (pardon: I thought ID and date was kept on the history page)

 I am posting most of my material to this page in an 
 attempt to ask and answer. Scroll up, pick a measure 
 you disagree with copy it down here and tell me why. 

 As soon as I can I will respond with a cite and as much 
 backup as possible. 

 I don't like to see people making statements that have   
 no leg to stand on. If you want to edit something I wrote 
 by inserting a paragraph that makes it sound like I want  
 to base the history of measures on unproven assumptions  
 and speculations, I would prefer that you do bring it  
 here for discussion first.

Rktect,

ID and date is kept on the history page, yes. However, it's

helpful to include it here as well so that readers don't have to

sift through these history pages just to tell who's writing what.

Perhaps you're perfectly right about Crissov's references to the

pyramids and irrational numbers. Perhaps this does remain to be

proven and perhaps it is uncited conjecture. There seems to be

quite a bit of this flying about on this article (most of which

coming not from Crissov).

I have noticed, however, that gone are claims that the same system

has been used throughout history. Gone also are claims that they

can all be traced back to a single system. Yes, I'd like to see

some discussion, citation and/or evidence before such claims reappear.

Discussion, it seems you agree, is the best way to resolve the dispute.

Edit wars are just a waste of time for both/all parties. Discussion,

however, is a two-way street. It's best not to expect that others

discuss their edits with you whilst you make no effort to yours with them.

"If you want to edit something I wrote ..." you write "... that makes it

sound like I want to ..." This comment has intrigued me to no end.

Edits to this page are not about making you sound like anything.

It's not as if you are credited as the author.

Jimp 20Jul05

I agree with the last. rktect 7/19/05, but would support by cite and by identity proof, that the same system has been used throughout history and traced back to a sngle system.

I don't have a lot of problems with pyramids as evidence for Egyptian standards of measure as long as you include ordinary buildings, inscription grids, all known rulers and rods, fields, nileometers, the volume of h3kts, generally do your homework.

Irrational numbers are irrational, using measures to make them rational along with the classic problems of greek antiquity would be interesting to discuss.

Irrational numbers are irrational. You can't make them rational by using measures.

Not even a god could make an irrational number rational.

Jimp 20Jul05

One way to rationalize an irrational number is to construct a geometric ratio using two units related as the sides of a square to its diagonal or the diameter of a circle to its circumference. Its a somewhat subtle, very Egyptian concept where numbers are not thought of as iterations but rather as individuals as in the seked or ratio of unit rise to unit run so also foot to remen or remen to cubit. ie the ratio is 1x:1y

Look, I can see where you're coming from with this "rationalising

the irrational" but, you surely realise, it's a play on words. In

the mathematical sense of the word there is no rationalising

irrational numbers: a number is either rational or irrational.

There is, of course, the other sense of "rationalise" meaning "to

make sense of". Yes, it would be interesting to look at how

people used measures to do this.

Jimp 23Jul05

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

• 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

• 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.

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

• 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? Try

converting to U.S. gallons.

Jimp 23Jul05

• 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

• 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

• 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.

• 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

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 Misplaced Pages's policy.

Jimp 23Jul05

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

This article needs attention

Rktect,

You might not like seeing the big sign but, of course you'd have to

agree, the question is not whether you like it there or not but

whether it belongs there or not. It looks to me as if the article

is in need of further attention. Why not leave the sign up till we

have something decent here?

Jimp 23Jul05

Rktect 7/23/05 I agree the question is whether it belongs there or not.

It belongs there if work remains to be done and you don't see any improvement.

It doesn't belong there if you don't like something but

don't feel like you have the time to spend fixing whatever it is you object to.

I have collected and continue to collect a lot of information about ancient measures

which I would like to upload.

Today I began working on Hygini Gromatici "De Condicionibus Agrorum"

which discusses a Roman Surveyors discovery that the Measures of Germanica

were Greek and based on feet which were sides of volumes like

the mina and bushel. This in response to someone's claim that

they were Anglo Saxon and removal of the volumes and sides to the discussion page.

"They measure in plinthides ,the parcel of land that feeds a household,

square centuries, each is six thousand square feet

(77 Roman, 75 English feet to a side = 1.3 acres ) including

the strips of uncultivated land enclosing the individual parcel,

250 jugerums in total."

"The Praeterea is the foot Ptolomeicus called the mina foot.

So therefore 250 eris, as they measure, is 10 x 24.

The 24 part of the mina foot is the iug of 356.

A strip of uncultivated land called the quattuorus

marks the bound of the plowed land.

"Its width measures out at six times the sides of the cube

that contain one Greek bushel of dry measure.

The measure of plowed land in Cyrenica is a jugerum of the mint.

In Germany the foot of the Drusianus is the mint foot and

their stadia is one-eighth of their Myle."

"Wherever outside of our boundaries the law of the Romans extends,

I don’t care if its to the people of the rus, I shall bring out of Italy

whatever requires to be examined and from our standard of measure the nequid,

we shall determine what may be with respect to the praeteriss of the foot.

The foot Ptolomeicus called, the mina foot lays out as a standard of 100

to the sides of the fields I have become acquainted with."

• [http://www.forumromanum.org/literature/hyginus_gromaticusx.html

Now, to really appreciate that you also have to read Ptolomies "Geographies" and

realise that Ptolomy and Marinus, the Tyrian geographer he was reviewing,

were measuring in Persian stadia that were 750 feet long and 500 to the degree

because that was the standard of measure that the Persians brought to Phoenicia and Egypt.

Rktech,

I'm not sure whether I see improvement but surely the "clean up" tag

should stay until the job's done even though there be improvement.

No, it's not a question of taste either:

whether or not I may happen to like something is not important.

Nor, however, is it important whether I have time to clean it up.

If you think that the article is fine as it is, then it makes sense that

you don't believe that the "clean up" tag belongs there.

But if that's what you think, then we disagree.

There, of course, remains the question of disputed factual accuracy.

This is the other sign that you've been constantly removing.

Suppose that you are perfectly correct and throughout history

all people have indeed used one and the same system of measurement.

Does your being correct entail that there need be no sign up there

stating that the content is disputed?

Surely the question is not who's right but whether there is any dispute.

Is there no dispute? It seems that there is.

You may indeed be the expert here but I'm still to be convinced

of even the watered down version of your theory that appears in the introduction.

... throughout History ... is your claim however you don't seem to be

dealing with all of history but a section namely Egypt,

the Middle East and Europe. The intro seems to imply that

there be some underlying theme, some basic system.

What does this mean? One system can in part be based on another.

Do they share the same theme therefore?

I could go on but I'd mainly be repeating myself.

The point is that dispute exists thus the sign belongs there.

Jimp 25Jul05

rktect 7/26/05 Though I'm not big on labels,

I'm inclined to weight the title expert very heavily

toward what you know is what you do.

Any farmer knows more than I do about what size his field is.

Furthermore since you are at least one person

who clearly feels strongly these labels should be there,

I propose that you do put them back up.

I would hope you would then feel some responsibility

to identify what you think needs to be cleaned up or

what you think should be disputed.

If you will do that then we can take care of

whatever the problems are and then remove the disputes.

When I talk about history I talk about that portion of

mankind's experience which has been recorded and preserved

by whatever means.

I definitely do not limit that experience to any geographical area and

certainly agree that the study of metrology can be extended

to include Asia, Oceanasia, Sub Saharan Africa, The Americas, and the Artic.

Klein is a great source for some of those and more can be googled and put up.

I happen to have better knowledge of the ancient near east

than I do the Dong Song drum culture, the Lapita or the Inuit but

I can give you access to the numbers 1-10 in 5000 languages and

divide them into groups by counting methodology.

As to the underlying theme of measures I think it is property,

generally people measure, weigh and judge the lengths, areas, volumes and times of

the things they care about and they don't like to have other people devalue them

by changing the standards they are measured by.

The constant used to keep the measures the same appears to be the same

in all the areas of the world which were reached by ancient navigators

which according to Plato was an ocean empire larger than Libya, Asia and Europe combined

(because it included all the oceans which encircled them).

By the Time of Hygini Gromatici, if not Claudius Ptolomy and Marinus,

there were Roman coins circulating from Britain to China.