Wikipedia talk:Articles for deletion/Mile Standards

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[edit] Mile Standards

Lots of original research from what is believed to be the same author. Most of it is irrelevant for the suggested title, copies of his contributions that is constantly being added to a number of other articles. This article is not needed. If there is anything of value here wrt. Mile Standards, it should be entered into Mile. -- Egil 15:05, 4 August 2005 (UTC)

  • Delete barring MASSIVE cleanup. Explodicle 16:33, 4 August 2005 (UTC)
  • Delete per Explodicle. Ken 17:11, August 4, 2005 (UTC)
  • Delete. Non-verifiable, confused beyond cleanuppability. --DrTorstenHenning 17:14, 4 August 2005 (UTC)

Rktect 6:03, 5 August 2005 (EST)

No portion of this collection of source material is original research
All of it is directly relevant to the topic
All of it is easily verifiable
The cited material is widely available on the web and
discussed on the ancient weights and measures page
For those who object that it should be entered into the topic Mile
That topic appears to be concerned with the statute mile which did
not exist until it was redefined by statute in 1593.
The Mile standards under discussion here go back six millenia.
For those who object on the grounds that massive cleanup is required
the appropriate place to raise those issues would seem to be the discussion page
For those who are confused about definitions of the mile or are
experiencing cognative dissonance or would like to state what they find confusing
the discussion page would seem to be the appropriate place to do so.
Looking at unit standards of measure comparatively by cultures
makes it much easier to see who shared measures with whom.
Mile standards are used by cultures going back to the Sumerians.
The documentation of this is not original research just a collection of facts
cited by both classical and contemporary experts.
Miles are always related to stadia and stadia are always related to degrees.
Miles are divided into stadia which are generally used as the sides of fields
They are further divided into ropes or cords, chains, rods, paces, fathoms, yards
all with primary agricultural or nautical measuring and navigational function
used to define large distances and areas.
At the level of the cubit,remen, foot, hand and palm the larger units are
corelated to the units used to measure bread and beer and other commercial
consumables. Those are two separate but related sytems.
Iron age standards are probably the best place to look at the consensus of opinion
about how to define the Mile because iron age standards are different than
copper age, bronze age or medieval standards in that their relation to the degree
is discussed in classical documents in considerably more detail.
Because this is the period when the Greek and Roman and for that matter
Phoenician empires are heavily engaged in trade with Europe and a period
when traders moved overland, up rivers and along coasts which they surveyed.
Many Greek, Roman and Phoenician geographers of the period have data
which they provide about the distances between places in Europe.
As the Greek and Roman traders moved into into Germany well in advance of
any conquering armies they carried with them standards of measure for
commerce and agriculture.
These Greek and Roman units are already well established in the popular literature
as opposed to obscure technical publications written in dead languages
for copper and iron age units so they are much easier to document
and have much more accessible web sources.
As to giving their values to the nearest whole mm rather than to several
decimals of mm, iron age standards are not precise to decimal mm
or variant to 10's of mm and generally best established to +/- 1 mm per foot.
For those cultures for whom there is a written contemporary primary reference
to sharing a standard (as with Ptolomy;s geography) which was cited on the
discussion page for ancient weights and measures, there are long term
investigations of the units involved and the results
are now considered basic historical fact.
In the past many people have applied an ethnocentric perspective
to "their measures" stating that they are "Anglo Saxon", "German",
"Danish" French or "English" when they actually have much longer
histories that have been explored in the literature.
Being able to see the connection broken down by conventional archaeological
period rather than simply lumped to gether as ancient makes the similarities
and differances much clearer
The objection that these studies are original research is invalid
as their original sources have been cited on the discussion page and
in some cases transcriptions of the original ancient language with
translations given in English

[edit] 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?

[edit] 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.

http://bible-history.com/isbe/W/WEIGHTS+AND+MEASURES/

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

[edit] Divisions of the Milos, Milliare, Myle and Mile into areas

Milos
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
Milliare
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
Myle
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

[edit] 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

[edit] 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.

[edit] 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

[edit] Anglo - 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 was now divided into 8 furlongs of 220 yards
where before it had been 8 stadium/furlongs of 625'
1 acre = 43,560 SF because it was increased by Queen Elizabeth
The side of each square furlong was increased 35'
The area that had been 8 Heridia of 1.25 acres or 9 acres was now divided into 10 acres
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

[edit] Longer Discussion

Stadios

The Greek root stadios means "to have standing"
"to have standing" means 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.
Different classes of citizen and occupation are apportioned
different amounts of land by the community

[edit] Ancient Degree Based Stadia Standards of Measure

Ancient stadia measures were always divisions of the degree
Systemized standards of measure derived from this common standard
Mesopotamia used 600 sos of 180 m = 108 km
Egypt used 10 itrw = 700 "3ht or fields" (of 3 kht of 100 royal cubits) = 110.25 km
Persia used 20 parasangs of 30(furlongs = 185 m) = 111 km
Phoenicia used 500 stadions (of 750 feet = 185 m) = 111 km
Ptolomy and Marinus of Tyre measured in the Persian/Phoenician stadia
Eratosthenes measured in the 700 3ht of Egypt.
The Greeks used 600 stadions (of 600 pous of 308.4 mm) = 111 km
The Romans used 600 stadiums of 625 pes (of 296 mm = 111 km
All of those are accurate divisions of a degree as defined by Ptolomy
Ancient Europe used the same standards because it did business with the same people
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.

[edit] Egyptian Itrw and Atur

The Itrw is an hour of travel on the river = 21,000 royal cubits
The Atur is an hour of march on the land = 21,000 royal cubits
The minute of march is a unit of 1 minutes travel = 350 royal cubits
21,000 royal cubits = 36,085 English feet = 6.83 modern miles
It equaled 7.22 miles prior to the time of Queen Elizabeth
That was 11 km or 7.43 Roman milliare.
75 Roman milliare are a pretty good value for a degree
The Egyptian value for 10 itrw is a little less accurate
and that probably explains the correction.

[edit] Conversions between Mesopotamian and Other Systems

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" = 15 mm = 0.05 feet or podes
Greek;
1 (ring finger)= 1 daktylos = 19.275 mm = 0.06 feet or podes
Roman;
1.33 finger = 1 (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)

[edit] Land cubits and tenure, the Feudal system

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.

[edit] Where the Metric System came from

In 1670 Abbe Mouton suggested a primary length standard
equal to 1 minute of arc on a great circle of the earth.
For this basic length Mouton offered the name milliare.
This was to be subdivided by seven sub units with each one
to be 1/10 the length of the one preceeding or
Milliare = 1 minute of arc = 36524 English feet = 1.11 km
Centuria =.1 minute of arc = 3652.4 English feet = .111 km
Decuria = .01 minutes of arc = 365.24 English feet = 111.1 m
Virga = .001 minutes of arc = 36.524 English feet =11.1 m
Virgula = .0001 minutes of arc = 3.6524 English feet = 1.11 m
Decima = .00001 minute of arc = .36524 English feet = .111 m
Centesima = .000001 minute of arc .36524 = English feet = 113.25 mm
Millesima = .0000001 minute of arc .036524 = English feet = 11.325 mm
Abbe Mouton may or may not have known that
The Milos was based on a stadion equivalent to the Egyptian minute of march.
Sir Issac Newton who attempted to restablish the measures of the ancient world
from the math problems in Kings 1 may not have known that
But its certain that Jomard, one of the French savants accompanying Napoleon
to Egypt entrusted with the measurement of ancient architecture to attempt
to restablish the correct value of ancient measures by measurement
knew that because he cites the Greeks who knew that
"In 1798, Edme-Francois Jomard visited the Great Pyramid
as a young savant on Napoleon's expedition.
The French had the debris cleared away from
the two northern corners of the Pyramid and discovered the corner sockets
where the corner casing stones had apparently originally been placed.
These were ten by twelve foot mortises, perfectly level,
and perfectly level with each other, cut twenty inches into the limestone bedrock.
Although, there were still piles of rubble between them,
Jomard was able to measure the north side of the base to be 230.902 meters (757.5 feet).
For the height, he measured each step. They added up to a total of 144 meters (481 feet).
By means of trigonometry Jomard calculated a slope of 51* 19' 14", and
an apothem of 184.722 meters. Because the casing stones were missing,
these figures were both estimates, but the length of the apothem
looked virtually perfect in light of various ancient classical texts
which Jomard was familiar with."
Diodorus Siculus and Strabo both claimed that the apothem of the Great Pyramid
was one stadium long. The Olympic stadium was 600 Greek feet, and
was supposed to be related to the size of the earth.
Jomard found the stadium of Eratosthenes and Hipparchus to be 185.5 meters,
and thus within one meter of his figure for the apothem. He also found that
distances quoted by the ancients in stadia matched the distances found by
Napoleon's surveyors, if a stadium was taken to be 185 meters.
The ancient stadium was also reported to have been 1/600 of a degree.
When Jomard took the length of a degree at what he believed to be
the mean latitude of Egypt, 110,827.68 meters, and divided it by 600,
he arrived at a stadium of 184.712 meters, which was
within ten centimeters of his figure for the length of the apothem!
In addition, several Greek authors had reported that the perimeter
of the base was equal to half a minute of a degree.
This would mean that a degree of latitude divided by 480 should
equal the length of one side of the base.
Again Jomard used the length of a degree at his mean latitude of Egypt,
110,827 meters, and dividing by 480 arrived at 230.8 meters,
again within 10 centimeters of his measured base.

[edit] The Egyptian Minute of March as Stadion, Stadium, Furlong

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.

[edit] Leauges and the Vestigal Remnant of ther English Cubit on the Stanley Tape Measure

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

[edit] iku, 3kr, 3ht, kht, st3t, aroura, area, are, acre

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.

[edit] Herodotus on the length of ancient measures

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. [2] Men that have scant land measure by feet; those that have more, by miles; those that have much land, by parasangs; and those who have great abundance of it, by schoeni. [3] The parasang is three and three quarters miles, and the schoenus, which is an Egyptian measure, is twice that.
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. [2] If a reckoning is made, only a little difference of length, not more than two miles, will be found between these two journeys; for the journey from Athens to Pisa is two miles short of two hundred, which is the number of miles between the sea and Heliopolis.
IX. From Heliopolis to Thebes is nine days' journey by river, and the distance is six hundred and eight miles, or eighty-one schoeni. [2] This, then, is a full statement of all the distances in Egypt: the seaboard is four hundred and fifty miles long; and I will now declare the distance inland from the sea to Thebes : it is seven hundred and sixty-five miles. And between Thebes and the city called Elephantine there are two hundred and twenty-five miles.
81 schoeni = 608 miles
1 schoeni = 7.5miles = 1/10 degree = 11.1 km

Parasan = 30 furlongs

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
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
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

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 [1]. Regardless, it does constitute an error of 1%, which they should have been able to detect.

Units of measure based on artifacts of the human body are very natural to any culture, and even if independently discovered, will probably be within at least a handful of percent of each other (this goes for digits, palms, feet, cubits and others). So you really need to give some real proof that units have been exchanged between cultures. Numbers matching up can just as well be coincidences.
The connections between Mesopotamia, Egypt, Persia, Greece and Rome are well known, obviously, but when there are claims about China and Japan, we are into deep water unless there is actual proof.
Mesopotamia traded with Iran, India and Afghanistan both overland and by water
The extent of its trade routes are probably best viewed by looking at the Persian empire.
China came into the picture with the silk road.
There was sea trade throughout the southern oceas from Madagascar to Han China
The best proof is Probably Ptolomys Geography

The same goes for numerical relationships like the 600:625 of Greek vz. Roman feet. There has to be a very good rationale why this should be the case. Playing the number games with values which are of uncertainty 1% or so, there is simply no end to the common factors one can come up with. -- Egil 16:59, 8 Feb 2005 (UTC)


Excuse for not having answered before.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Actually, they merely confirm a connection, if at all. By themselves they say not much about the direction of such cultural transfer, if it happened indeed. Christoph Päper 16:34, 1 Mar 2005 (UTC)
East-Asian civilisation, culture and history is old, very old. But not as ancient as Mesopotanian-Egytian culture and history. If these measures and graduated rulers are attested in the Fertile Crescent since at least the beginning of the third millenary BC and not in Far-East, the sense West-East seems me to be more than probable. -- Paul Martin 10:03, 2 Mar 2005 (UTC)

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

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

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

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

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

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

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

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

Secondly: It's established that the Great Pyramid was constructed with a length of 440 Old Royal Cubits (= 230.5 m) and 440 Remen (= 163.0 m) from the centre to the corners. The length of the Oueen's Pyramid of Giza is 120 Remen (= 44.5 meters) with a diagonal between two corners of 120 Royal Cubits (= 62.9 meters). [2]

[edit] 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

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)

[edit] Iranian nationalism?

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

Rktect 8/1/05: Some of the best evidence for pre-existing Persian Units is
Their doubling Egyptian units just as described by Herodotus
The Persian increments of Guz of Gudge are found in places
that weren't reached by the Greeks until the time of Alexander
but that were included in the Persian Empire
These units don't match Greek units but do closely double Egyptian units
Consequently rather than a wide range of different values without any discernable system
you have a great or royal, long, median and short form of the guz
equivalent to the double of Egyptian units making the Persian parasang
actually equal the schoenus because it has half as many units that are twice as long
Persakh, or Para- Persia. 6000 gudge of 42" = 21,000 feet
unit name "bd" "rmn" ? "mh" ? "rc" "nibw"
Egyptian half 11.81" 14.5" ? 17.7" ? 20.62" 23.62
Ideal Double 23.62 29" ? 35.4" ? 41.24" 47.24
Persian Region dbl foot Guz dbl remen Gueza dbl cubit Zer dbl Gudge
India
Bengal ? ? ? 36" ? ? ?
Bombay ? 27" ? ? ? ? ?
Madras ? ? 33" ? ? ? ?
Persia 25 ? ? 36.4" ? 40.95" 44"
Arabia 24" ? ? 37" ? ? (Bassorah)


Herodotus Book 2
Chapter 6
1 Further, the length of the seacoast of Egypt itself is sixty "schoeni" -- of Egypt,
that is, as we judge it to be, reaching from the Plinthinete gulf to the Serbonian marsh,
which is under the Casian mountain -- between these there is this length of sixty schoeni.
2 Men that have scant land measure by feet; those that have more, by miles;
those that have much land, by parasangs; and those who have great abundance of it, by schoeni.
3 The parasang is three and three quarters miles, and
the schoenus, which is an Egyptian measure, is twice that.
In other words there are 10 Egyptian scoenus (or itrw of 21,000 royal cubits) to a degree
and there are 20 Persian Parasangs of 3.75 miles or 75 Persian miles.
Chapter 7
1 By this reckoning, then,
the seaboard of Egypt will be four hundred and fifty miles in length.
Inland from the sea as far as Heliopolis, Egypt is a wide land, all flat and watery and marshy.
From the sea up to Heliopolis is a journey
about as long as the way from the altar of the twelve gods at Athens
to the temple of Olympian Zeus at Pisa.
2 If a reckoning is made, only a little difference of length,
not more than two miles, will be found between these two journeys
for the journey from Athens to Pisa is two miles short of two hundred
which is the number of miles between the sea and Heliopolis.
Chapter 9
1 From Heliopolis to Thebes is nine days' journey by river, and
the distance is six hundred and eight miles, or eighty-one schoeni.
2 This, then, is a full statement of all the distances in Egypt
the seaboard is four hundred and fifty miles long; and
I will now declare the distance inland from the sea to Thebes
it is seven hundred and sixty-five miles. And
between Thebes and the city called Elephantine there are two hundred and twenty-five miles.
In other words the two cities are three degrees apart.
Chapter 109
1 For this reason Egypt was intersected.
This king also (they said) divided the country among all the Egyptians
by giving each an equal parcel of land, and made this his source of revenue,
assessing the payment of a yearly tax.
2 And any man who was robbed by the river of part of his land
could come to Sesostris and declare what had happened
then the king would send men to look into it and calculate the part
by which the land was diminished, so that thereafter
it should pay in proportion to the tax originally imposed.
3 From this, in my opinion, the Greeks learned the art of measuring land
the sunclock and the sundial, and the twelve divisions of the day
came to Hellas from Babylonia and not from Egypt.
Chapter 168
1 The warriors were the only Egyptians, except the priests, who had special privileges
for each of them an untaxed plot of twelve acres was set apart.
This acre is a square of a hundred Egyptian cubits each way,
the Egyptian cubit being equal to the Samian.
12 Egyptian acres of side 100 of the cubit = to the Samian, the mh t3 or land cubit
would be equivalent to 6 English acres

[edit] 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)

[edit] The Same System

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

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

After a couple of decades of running the numbers

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

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

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


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

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

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

[edit] Units

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


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


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

[edit] Egyptian volume

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

[edit] Roman area

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

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

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


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

[edit] 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 Wikipedia.

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
One good example might be the slide rule. There are a lot of variations
on it but essentially its a spread sheet, it allows you to set 1x:1y
where x and y can be any two formulas. When you combine that with the Egyptians
use of unit fractions you have continued fractions, fluxions, anything you like.
Another good example would be the tables on a framing square

[edit] Proof of the same-system hypothesis

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

rktect 7/20/05

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

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

Region Foot Name Foot Measure
China che 333.45 mm
Japan shaku 303.02 mm
Korea chok 303.02 mm
Costa Rica tercia 278.64 mm
Aztex Mexico pie 278.89 mm
Ecuador -El Salvador tercia 304.8 mm
Paraguay pie 288.8 mm
Tasmania foot 304.8 mm
And this is supposed to prove ... Your "Tasmanian" foot is
just an Imperial foot (surprise surprise). What of pre-colonial
Tasmania? Similarly your South American feet look suspiciously
Latin. Even Scandinavia ... what about pre-Grecio-Roman
influence? The Far East units are interesting but, as I've
mentioned, simply showing an approximate equivalence
hardly proves that two units are related. We haven't ruled
out coincidence nor have we ruled out different cultures
happening on similar defintions ... or does this count as
the "same theme"?
Jimp 6Aug05
  • 2.) A system of measures organized by increasing length, area, volume exists
Several systems have existed they might be related as the
Imperial and U.S. systems are but even these are not the same.
Jimp 23Jul05
The American system is inarguably derived from the British Imperial System and has only deviated from it in relatively modern times. The Imperial system is in every respect the same system as was used in ancient Greece, Rome, Palestine, Persia, Egypt amd Mesopotamia.
Seems you've dug yourself into a bit of a hole there. The US
system is inarguably derived from earlier English units but not,
as you claim, from the Imperial system. Still, sure, the point
you'd wanted to make is that they share a common ancestor.
However to say that the two systems are derived from one common
source and to say that they are the same are two different
things. The argument applied also to the Imperial system verses
the Roman system. They are related but to say that they are
"in every respect the same system" would be to use language too
strong. Just as there are 4 fluid ounces to a US gill as
opposed to the 5 per Imperial gill, there are 280 extra feet in
the Imperial mile as opposed to the Roman 5000 foot mile.
Similar, sure, but not the same.
Jimp 6Aug05
Then there is the metric system: you'll be stretching it if you
point out that the height of an A4 sheet is one Roman foot. Even
today some use of three different systems is being made.
Jimp 23Jul05
Ancient Measures from Greece, Rome, Mesopotamia and Egypt were the source of the Metric System. Google Jomard and Napoleons French Savants, and/or read your Klein.
  • 3.) Each civilization has a unit measure which corresponds
  • 4.) to a unit measure in each other civilization by
  • 5.) name, position in the system, length, area, volume
  • 6.) Each measure is systematic in that it is part of an iterative sequence
  • 7.) 1 finger, 2 fingers, 3 fingers, palm, hand, fist and so forth
  • 8.) each area is the square of a unit length and you can convert between systems
  • 9.) each voume is the cube of a unit length and you can convert between systems
The Imperial gallon is the cube of what unit of lenght?
Jimp 23Jul05
How about we choose an Egyptian royal cubit as the side of a cube.
Wickopedia cites the British Imperial Gallon as 277.42 cu in
British Imperial Gallon
multiply 32 x 277.42 cu in = 8877.44
take the cube root of 8877.44 = 20.7" = the side of an Egyptian Royal cubit
the cube which is 1/32 Egyptian royal cubit is the hkt measure used with
the Horus eye doubling series to apportion bread and beer in the mathematical
problems of the Rhind papyrus.
Interesting, sure, however the Imperial gallon was originally
defined not to be 1/32 of the cube of an Egyptian Royal cubit
but to be the volume of 10 lb of water (at certain thermodynamic
conditions). Jimp 8Aug05
Try converting to U.S. gallons.
Jimp 23Jul05
Ok, presumably you have never read 1 Kings
homer (= 10 baths) 60 US gallons - mentioned in Ezek 45.11-14
NT metretes = 38 US gallons = side of 1 royal cubit - mentioned in John 2.6
bath (= 1/10 homer = 6 hins; also = 1 ephah of dry measure =6 US gallons 1 Kgs 7.26; Isa 5.10
hin (= 1/6 bath or 12 logs) 1 US gallon Exod 29.40,41; 30.23-25; Num 15.4-10
log (= 1/12 hin or 1/72 bath) 1/3 US pint Lev 14.10,21
1 wine gallon = 8 cubic Athenian pous, and is 1/12 the cube whose side is the Biblical talent.
4 wine gallons = 31 Cubic Attic Greek pous, 30 cubic English feet, 28 cubic Roman pes
Haven't you ever done any of this? Its all the same system but the conversions allow you
to take different unit fractions of the same volume.
The ratio is 5-6 just like mesopotamian ordinary cubit - great cubit
Let's say the side of a royal cubit that contains 32 BIG's is 20.7"
The ordinary cubit is side 5/6 that or 17.7" it contains 20 BIG's and 24 wine gallons
100 ordinary cubits (mh t3 or land cubits) are the side of a square of 1/2 acre
17.7/12 X 100 = 147.5 ft and if you square and multiply x 2 you get 43512.5 SF
The differance is round off error and some inaccuracy in the standards that tends
to creep in when people redefine them.
  • 10) where changes and conversions between systems occur they occur systematically
  • 11) a stadion is 600 pous = 185 m a stadium is 625 pes = 185 m
  • 12) a Milos is 8 stadions, A Milliare is 8 stadiums
You can identify Jupiter as Zeus but you still haven't proven anything about Vishnu.
Jimp 23Jul05

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

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

Metathesis:

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

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


They have both been abused by people who didn't know
what they were doing, to put it bluntly
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

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

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

[edit] 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?
Rktect 07/29/05 I looked at the Wikipedia definition of original research
It says that if you are posting or citing previously published material
that isn't copywrited or that you have permission to use that's fine
My cites are to previously published non copywrited material
Here is another independant scholar saying essentially the same thing
Clandonia
If it is, posting it
here, I'm afraid, would be against Wikipedia's policy.
Jimp 23Jul05

[edit] 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.


[edit] 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


[edit] 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."
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.

[edit] The apportionment of land according to occupation

Rktect 7/28/05 I've come across a really interesting graduate study of mh t3 (land cubits) and st3t (aroura)which attempts to use a number of ancient Egyptian accounts of fields and their owners taxes to show how different occupations seemed to be granted different unit acerages
There was a comment on Sumerian measures to the effect that there was a question as to whether the fingers might not just be different versions of the same digit 16.666... mm
Sumerian tuning
brick measures
metrum 15/16/17/18
For Sumerian units it appears that both the ordinary cubits of 500 mm and the great cubits of 600 mm were divided into 30 fingers so 16.67 and 20 are in a ratio of 5:6 which gets us two of the four. The other two would be the 5:6 of those or 15 mm and 17.67 mm
še: n., barley; grain; a small length measure, barleycorn = 1/6 finger = 1/30 cubit = 1.67 centimeter in Presarg.-OB period; as a surface area measure = 432 square linear barleycorns = 12 square fingers; as a volume measure = 1/180 gín = 1/3 gín-tur = 1 2/3 sìla = 360 cubic fingers = 1/10800 sar = approx. 1.667 liters; 1/180 of a gín or shekel of silver = ca. 0.0463 grams (cf., še-ga/ge) [ŠE
[šu-si]= 30 fingers = 500 mm
zipaþ, zapaþ[ŠU.BAD] half; a length-measure, span = 1/2 cubit = 15 fingers = 25 cm.
éše, éš[ŠÈ rope; measuring tape/cord; length measure, rope = 10 nindan rods = 20 reeds = 120 cubits = the side of 1 square iku in area = 1,0,0 [602] fingers; a surface area measure, = 6 iku; leash (can be an adverbial suffix like eš) (eš, 'much', + eš, 'much') [ŠE3 archaic frequency: 152].
gín, giñ4 small ax(-head) used as money; shekel (of silver) = ca. 8.333 grams; a surface area measure, 1/60 square nindan (sar) = 180 surface še = 2160 (=36,0) square fingers; a volume measure, = 0.3 cubic meters (Akk. kiinu 'true measure', cf., Orel & Stolbova #1459, *kin- "count") [TUN3 archaic frequency: 96; concatenates 3 sign variants].
kùš ell/cubit = 1/2 meter = 30 fingers [šu-si] = distance from elbow to fingertips; forearm; channel (cf., šu-da) (ku, 'to base, found, build', + many).
niš, neš twenty (ní, 'self, body', + aš, 'one [finger, toe]').
kingusili greater part; five-sixths (5/6) (kíñ, 'task', + sílig, 'hand [of five fingers]').
zipaþ, zapaþ[ŠU.BAD] half; a length-measure, span = 1/2 cubit = 15 fingers = 25 cm. (ŠU.BAD: 'open hand' - approx. distance measured by span of outstretched thumb and little finger).
am-si elephant ('wild ox' + 'horn, ray, antenna'; cf., šu-si, 'finger').
gín-tur a surface area measure, little shekel = 1/60 shekel = 1/3600 square nindan (sar) = 3 surface še = 36 square fingers = surface of the side of a cube of 1 sìla capacity.
ma-na-tur a surface area measure, little mina = 1/3 shekel = 60 surface še = 720 square fingers; as a volume measure, = 60 še.
šu-dù-a length measure of 10 fingers = 16.666 cm. ('hands' + 'to stack').
šu-si finger ('hand' + 'horn, ray, antenna').
šu...túkur to nibble or lick one's fingers ('hand' + 'to gnaw, nibble').
umbin-gud oxen hooves; oxen tracks ('fingernail' + 'ox').
umbin...kud to shave; to shear; to manicure ('fingernail' + 'to cut off').
šu n., hand; share, portion, bundle; strength; control [ŠU archaic frequency: 360].
šika potsherd; shell; rind (hand, portion + mouth).
bùzur hand, palm.
kišib(3) n., hand; fist; seal; sealed bulla; receipt (cf., kéš, 'to snatch; to bind'). v., to seal.
sílig hand.
tibir(2,3,4,5)hand; palm; blow, strike ('life' + 'open, release' ? 'the beggar's open palm'). tíbira, ibira merchant, tradesman (Proverb 3.108 describes how the peddler 'flays' or 'skins' the open hand of the customer).
zipaþ, zapaþ[ŠU.BAD] half; a length-measure, span = 1/2 cubit = 15 fingers = 25 cm. (ŠU.BAD: 'open hand' - approx. distance measured by span of outstretched thumb and little finger).
šu-da hand and forearm, as a unit of measurement, ell/cubit (cf., kùš) ('hand' + 'arm').
šu-dù-a length measure of 10 fingers = 16.666 cm. ('hands' + 'to stack').
šu-ri(2)(-a) one-half ('hand' + 'to take, remove' + nominative).

[edit] The Table of Sumerian Measures

rktect 7/29/05 Multiple references give the Sumerian measures as exact unit fractions of a common standard.
sargonic math problems using exact unit fractions of a common standard
The finding of thousands of clay tablets at Ebla which were prepared as
tax audits by scribal accountants recording gifts to the various temples
are compounded by this document which shows them used as ratios
sumerian language translation search

[edit] Time for another split

I am not sure what's up with this subject and with this article, but the article has now moved into a state of total chaos for anyone trying to find out who-did-what and what-can-we-trust, in addition to very bad markup in places, and so on.

Part of the problem is obviously that the subject at hand is most obviously open to controversy, and may I say, sometimes original research. Another part of the problem is the sheer amount of information, making it impossible to maintain and understand.

If we split up in seperate articles for the various systems, i.e. ancient Egypt, Greece, Rome etc then at least there is a better chance of making each portion more maintainable.

Rktect7/31/05
Its pretty easy to see who did what if you look at the history page.
Most of the recent changes that I have made have been to provide you information
in response to your questions.

Due to the controversy of this subject, we also need a strict requirement of documenting references for all information entered, stating which source claims what. (Doing that from the outset is difficult, but let us work against this target).

Rktect7/31/05
There should be no contraversy. The facts either have an acceptable source or they don't.
In many cases I see assumptions that facts don't have an acceptable source
that can be easily addressed by giving the source.

Let me also add that anonymous contributions which also do not cite sources are IMHO worthless, and should be considered void. -- Egil 09:37, 31 July 2005 (UTC)

Rktect7/31/05
That should also apply to questions. If you don't know something, why not check out the topic
and see what has been said by others in the past?

Possible list of new articles:

[edit] Ancient Measures by Culture

Rktect7/31/05
Another way to approach the listing of measures would be to break it up by time and unit
These will eventually compare cultures in a less ethnocentric way (note pre-conquest Americas)
They are a work in progress requiring the names and values of many units be filled in
ideally they would also eventually get their value in increments of their own units.
  • Standards of measure in the Jemdet Nasr
  • Standards of measure in the Copper Age
  • Standards of measure in the Near Eastern Bronze Age
  • Standards of measure in Iron Age Europe
  • Standards of measure in Medieval Europe
  • Standards of measure in the Pre Conquest Americas
  • Standards of measure in the Medieval East
  • Standards of measure in the Modern West