Talk:Ancient Roman units of measurement

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Please see ancient weights and measures for previous edit history and discussions wrt this article.

Newer discussions:

Archive 1   -- Paul Martin 18:39, 4 October 2005 (UTC)
Archive 2   -- Paul Martin 12:02, 30 December 2005 (UTC)
Archive 3   -- Paul Martin 13:14, 17 August 2006 (UTC)


Contents

[edit] League = 1.5 miles or 3 miles?

Just a question out of curiosity. The article states that 1 mile is equivalent in Ancient Rome to 5000 ft, while 1 league is 7500 ft. Hence: 1 league is 1.5 mile. However the article League states that 1 league is 3 miles in Ancient Rome (quote: "The league was used by Ancient Rome, which defined it as being 3 miles."). Which is true? Brynnar 14:42, 14 August 2006 (UTC)

The league was originally used by the Gauls, and later picked up by the Romans during their conquests. Their interpretation of it was that a league was about 1,500 paces, or 7,500 feet. I'm not entirely sure how it came to mean three miles, but I'm fairly certain it wasn't used that way in Rome. --Xanzzibar 23:23, 15 August 2006 (UTC)

Problem fixed at both pages.  League and League (unit).  Paul Martin 13:18, 17 August 2006 (UTC)

A Roman mille passus or thousand paces derives from the Greek mia chillios or one thousand. The thousand is a measure of a field (aroura) laid out boustrehedron or as the ox plows in ten rows of one hundred orquia. Greek measures have short median and long forms so mia chillio of 8 stadia, (4800 ft), one aroura (5000 ft) and one nauticle mile (6000 ft); are referenced in the literature. Roman degrees of 25 leauges, 75 milliare or 110 km, are the same length as Greek degrees of 600 stadia. 69.39.100.2 (talk) 14:21, 15 February 2008 (UTC)

[edit] Mass units

Talent (weight) notes that the Roman talent was a cubic (Roman) foot of water, or about 25.99 kg. It goes on to state that there were 100 libra in a talent, making the Roman pound about 260 grams, much smaller than the figure in this article. Somethng needs fixing. Rhialto 01:53, 12 February 2007 (UTC)


Thanks Rhialto for your advice,

If the Greek talent (= 60 greek mines) was indeed of about 26 kg, this also indicates that Greeks, here, used the old, later-called Roman-digit for their talent-definition, since the third root of 26 gives 2.9625 dm. The Roman foot. The Roman libra was attestedly 3/4 Greek mina.

If the statement that Romans called 100 Roman libra a talent is true (sources?), this would mean, that this hypothetical Roman talent is 1/60 * 3/4 * 100 = 1.25 "water-foot" Greek talent.

I'll see what I can find out, Gluck 123 18:36, 11 June 2007 (UTC).

Mina in their ancient Mesopotamian form have both sacred and profane values so their volume varies. A [Talent] is the cube of a linear measure 69.39.100.2 (talk) 14:29, 15 February 2008 (UTC)

[edit] Roman foot and Nippur cubit

The Roman foot is defined to be 16⁄28 of the Nippur cubit.
"Is that their official definition, or simply a coincidental equivalent value?"

Neither, nor.
Western Roman Empire is dissolved for 476, Eastern for 1453. So, there is no one to give modern "official definition" for Roman measures.

It's nor a "simply a coincidental equivalent value", but the current, widely accepted standard theorie in the science of the historical metrologie.
According to newer – especially German – researches since WW2, we know nowadays that the Roman digit (=1/16 RF) results from
an old Egyptian division per 28 of the sumerian Nippur Cubit. They needed 28 parts, because 20 · √2 = 28.284...

Certainly, Egyptian geometers knew that with their construction-remen, the digit of their 20-digit-catheti was not strictly the same digit,
than the digit in their 28-digit-hypotenuse, but the small error of 1% was satisfying in practice. [1].

However, the digits of the hypothenuse belong to the so-called "Old Egyptian Cubit" of about 523.9 mm. Whereas the digits of the catheti are the later-called Roman digits.
Ancient precisions are generally better than 0.17%.

Thus, the Roman foot is de facto and really defined 16/28 Nippur Cubit.
I don't know any serious, contemporary scientist for contesting it. Everyone, like for example, Prof. Dr. Eberhard Knobloch for admitting it.

-- Gluck 123 18:36, 11 June 2007 (UTC)


My point was that, unless the Romans themselves knowingly defined their foot in relation to the Nippur cubit (in which case there would be a historical document from Roman days to say so), it incorrect to call that the definition. I can accept that modern analysis of the two units can show there was a coincidental equivalance, but only a historical document from ancient times can be used to demonstrate a definition.
The sidetrack on the Egyptian geometers is fascinating, but we are talking about Romans, not Egyptians here. I don't see how talking about what the Egyptians did has any bearing on what the Romans did. Without a historical document to say the Romans defined their foot that way, you can't properly call it a definition, except post hoc, which isn't really the same thing at all.
Rhialto 21:58, 11 June 2007 (UTC)


Old Romans and old Greeks knew relationships (ratios) between their measures. These ratios were, by the by, the only way of evaluation of their respective measures, since they ignored decimal fractions like 1.25; so, this was always expressed by, here, 5 to 4. The knowledge of these ratios was even necessary for international trading, already very developped in ancient times (even more than in Middle-Ages).

On the other hand:  If in ancient times a changement of a system of measures was operated, we can surely distinguish two different cases.
1. A great, already prosper, ascending state wished to ameliorate their measures and weights, so by studying the performed, established systems in their neighbourship, by adapting it, by creating other subdivisions w.r.t. their own tradition, but by keeping, by taking-over faithfully at least one main measure.
2. Or, a new system was imposed by a conqueror. The conquered state or the new vassal state was obliged to take-over the measure-system of the suzerain. Sometimes, by creating their own variants in subdivisions, at least centuries later, when they reinforced their own sovereign power.

However in no case, never, a measure was "invented". The legend "from the tip of his nose to the tip of his outstretched fingers" is a legend. Later invented for other reasons. Weights and measures, since ancient times, are a too serious topic. Those improbable and ridiculous proceedings, in reality, never existed. Weight and measure systems were always worked out by the souvereign's scientists, the metrologists. Since they were scientists, they took references by operative and existing systems. (Cf. e.g. Troy weights, the system of Troyes, France.)

"I don't see how talking about what the Egyptians did has any bearing on what the Romans did."
You must understand that what, now, we call "Roman digit" was a well-known measure in all the Near-East, Mediterranean region for millennia. Widely used thousands of years before the foundation of Rome.

So, we can't talk about this measure of length, without mentioning, that, attestedly, even Old Egyptians used this same and identical digit of about 18.525 mm, since the beginning of third millennnia BC with their 20-so-called-Roman-digit-construction-remen of about 37.05 cm. We must talk about.

"[... that] the Romans defined their foot that way"
No, of course they didn't!  The Romans defined nothing. The Egyptian geometers did it !  This was thousands of years before the first Roman citizen was ever born! Romans only choised one of the plenty digits already in use for long times, by declaring this digit as their "national" digit. The digit of the Roman Empire.

Romans knew for example, that their foot was exactly 1/25 smaller than the greek foot used in the stadion of Athens. So, to have just the same length of race-track as in the greek capital, they decided to construct, at Rome, a stadion of 625 Roman feet equals 600 Athens feet.

Many other ratios are related by ancient authors. But the term "Nippur Cubit", Romans and Greeks ignored it. You have to realise that the Nippur measure was the domiant measure in Mesopotania and in Egypt 3000 years before Caesar's time. Archivation of memory was not too easy during these times. At the beginning of 3rd Millennary BC writing (archaic cuneiforme and hieroglyphes) existed but rather limited to epigraphs or writings relating some political or economic facts. There are no written scientific workings in no science dating from 30th c. BC. So, Romans, naturally, had forgotten this old relationship. But we, nowadays, thanks to long scientific researches, we rediscovered it. We know it, now.

May I call your attention to the fact, that also, for example, Dieter Lelgemann pdf, former Director of Berlin's Institute for Geodesy uses well the term: definition.

If Rolf Rottländer for 40-50 years recollected especially ancient, archaeological, graduated rule sticks for his statistical researches, Dieter Lelgemann, several years ago, measured with his students, six race-tracks of preserved ancient Greek stadions.

According to Lelgemann, in this context, especially eight old measures are important.
With old highly composite number-orientated measures 7-smooth-numbers are very important. See: de:Historische Metrologie. Because old systems used selected numbers (never all in the same system) e.g. in the suite 16, 18, 20, 21, 24, 27, 28, 30, 32 digits = 2 feet, I prefered the defined, modern 7-smooth-value for the length of the Nippur Cubit, an over-all-rounding.


Symbol
 Name of the measure
Deduction 
Idealistic value
× 10-7 metre      
NC
 Nippur Cubit
 by 7-smooth:
=  518.6160 mm
  =  24 × 33 × 51 × 74
R
 Remen
(20 / 28)  NC
=  370.4400 mm
  =  24 × 33 × 52 × 73
ORC
 Old Royal Cubit
Root 2  ×  R
~  523.8813 mm
  =  25 × 33 × 52 × 73  × √2  
OTC
 Old Trade Cubit
(24 / 28)  ORC
~  449.0411 mm
  =  26 × 34 × 52 × 72  × √2
RTC
 Remen Trade Cubit
(20 / 28)  OTC
~  320.7436 mm
  =  26 × 34 × 53 × 71  × √2
RC
 Royal Cubit
(50 / 49)  NC
=  529.2000 mm
  =  25 × 34 × 53 × 72
BC
 Babylonian Cubit
(30 / 32)  RC
=  496.1250 mm
  =  21 × 34 × 54 × 72
BTC
 Babylonian Trade Cubit
(27 / 32)  RC
=  446.5125 mm
  =  20 × 36 × 53 × 72
All the idealistic values  – excepting of course ORC, OTC and RTC –  are plain values, not-rounded,
because the Nippur Cubit is a defined 7-smooth value, inside the scientific coefficient of variation.


Stadion Measured   Length of the stadion
Deduction
of the foot
Ideal length
of the foot
Ideal length
of the stadion
Relative
deviation
Olympia 192.27 m = 600 Remen trade cubits
(20/28) OTC
~ 320.7436 mm
~ 192.4462 m
– 0.092 %
Epidauros 181.30 m = 600 Epidauros feet
(16/28) RC
= 302.4000 mm
= 181.4400 m
– 0.077 %
Priene 191.39 m = 600 Priene feet
(20/28) BTC
= 318.9375 mm
= 191.3625 m
+ 0.014 %
Milet 177.36 m = 600 Milet feet
(5/6)(20/28) BC
= 295.3125 mm
= 177.1875 m
– 0.097 %
Delphi 177.55 m = 600 Roman feet
(16/28) NC
= 296.3520 mm
= 177.8112 m
– 0.147 %
Athens 184.96 m = 600 Kyrenaika feet
(20/24) R
= 308.7000 mm
= 185.2200 m
– 0.140 %


One knows that in ancient times a lack of precision of ± 0.17 % must be considered as normal, without any problem. (Nowadays often (tolerances in industrial production, building construction, etc.) not better than this. Of course, now, much better in very high-level accuracy and with top-level scientific measures.)  So, all the values are good.

This can not be, like you said, a "coincidental equivalance", but arises from the well-known deduction of these measures, ones from the others.
Example:
You took on a 18-digit-pygme, but you decide to use – exactly this measure – as a 16-digit-standard-foot. So, your new digit is exactly 18/16 old digits. It grew-up by exactly 12.5 %.

-- Gluck 123 11:33, 13 June 2007 (UTC)


Since these ancient metrologists apparently knew the precise relationships, no doubt there should be a cite from at least one of them to state the mathematical relationship between them, yes? You provide over 2 screens full of data, but without a single cite to show that the Romans (as opposed to more modern metrologists) were aware of the relationship, it just isn't relevant. Rhialto 14:13, 13 June 2007 (UTC)


I saw during my necessary corrections, you replied. I'll answer you soon. Gluck 123 15:16, 13 June 2007 (UTC)
PS. Just a thing, later more, it isn't that a fact is ignored by s.o. at a specific time (here, the ignorance of Romans), this doesn't prouve that a fact is not true. No? *
There are many ancient authors like Eratosthenes, Heron and Ptolemy describing well-known ratios. But all these ancients ignored the Nippur cubit.
The first specimen was found by archeological excavations in 1916, but, meantime, we have understood its high importance.
 *  It isn't because Columbus thought to be in India, that the Americas are identical to India.
The knowledge progresses. Sometimes even, old, entombed cognitions must be regained. (Cf. Copernicus).
In short:  It is not because s.o. at a specific time isn't aware of s.th. (here, the ignorance of the Romans) that it isn't true.
If, now, we know that the definition of the "Roman foot" is via the Egytian Remen, 16/28 of the Nippur measure, it doesn't matter that the Romans ignored it. It is so, anyway!

((This was my prepared continuation before your reply below. I'll write you s.th. later on w.r.t. your new arguments. Thanks.))


Just to answer that specific point... you're right that absence of evidence isn't proof that something is not true. But equally, it isn't proof that something is true. And the official standard of wikipedia is to only say something is proved to be true if you can actually provide a cite which says so. I'm more than happy to acknowledge that modern metrologists have noted the relationship between the various ancient units. But this is froma time period in which written records are reasonably common.
If the Romans were directly aware of the relationship between their units of measurement and the Nippur/Egyptian/etc units of measurement, why are there no cites from notable Romans to demonstrate this? For example, we can say the metre was defined as xyz because someone somewhere made a formal statement about its relationship with xyz. For us to say that the Romans defined their foot as 16/28 of a Nippur cubit, somewhere there needs to be a Roman metrologist making a formal statement about its relationship with the Nippur cubit. Since I haven't seen any cite to say that the Romans defined it, I strongly feel the most we can say is that modern metrologists have found the Roman found to be 16/28 of a Nippur cubit.
Also in your long text, you noted that the Romans had in fact lost information about the Nippur cubit, as written records from taht long ago no longer existed. If the Romans really had no direct knowledge of the Nippur cubit, I put forward the hypothesis that the claim that they defined their foot as 16/28 of a Nippur cubit MUST be obviously untrue. You can't define something relative to something you don't know about. Although in this case, I would accept that there must be some intermediary unit whioch there were aware of, and that the Romans presumably defined their foot relative to that intermediary unit.
Rhialto 15:53, 13 June 2007 (UTC)


Here, my reply to your new thoughts:

  1. Not an "absence of evidence", but an absence of knowledge, of cognition.  But you are right  – the other way round –  also, this must be proofed.
    At least as "to be the current, widely accepted standard theory."  That's the case.  (By Lelgemann, Knobloch, Huber, BI-SMH  a.m.o.m.)
  2. You are right:  "Modern metrologists have found the Roman found to be 16/28 of a Nippur cubit."
    After long trials and tribulations especially at the end of 19th c. beginning of the 20th century with alltoo complicated, very doubtful theories (cf. Pseudoscientific metrology),
    now for several decades it is standard theorie in the historical metrology, that the Near-East, Fertile Crescent, Mediterranean weights and measures are all related by easy
    7-smooth  – also called humble numbers –  deductions.
    Since 2003, the hexadecimal BI-SMH  – as the antagonist to the decimal BIPM –  even proposes a conventional, 7-smooth over-all-rounding of the values themselves.
    But if these modern metrologists are right, not only themself, we nowadays know that the later called Roman foot is defined 16/28 NC, but also these old Egyptian geometers operating this definition about 5000 Jears ago were aware using a mesopotamian measure to define a new measure, a new digit by 16/28 NC. This is it, what really counts.
    We contemporary human beings know it. Old Egyptian geometers knew it. Between long time of ignorancy. Nevertheless it is so.
  3. One more:  Not the Romans, but the old Egyptian geometers defined the  – later called –  Roman foot 16/28 NC.
  4. "that the Romans presumably defined their foot relative to that intermediary unit"  You are partially, widely right. Romans passed by an "intermediary unit".
    But they never defined anything, they simply took over a well-known  – since millennia –  already and widely used unit.
  5. Ancient scientists referred  – of course –  to the various Greek measures, than also to the Egyptian measures. But old metrologists ignored the lost missing link, the Nippur cubit.


A personal question: Where you are Rhialto?  Me, roughly at 48° 52′ N, 02° 21′E.
-- Gluck 123 18:09, 13 June 2007 (UTC)

((First, here above, my older prepared reply. Later on, w.r.t. your new arguments below, with these funny postpostements ;-))  However have a good day to you, Rhialto.


"If, now, we know that the definition of the "Roman foot" is via the Egytian Remen, 16/28 of the Nippur measure, it doesn't matter that the Romans ignored it. It is so, anyway!"
That is a spurious argument. By that logica, we can say, with teh benefit of some future historian, that the metre, far from being defined as a cfertain fraction of the teh distance light travels in a second, is in fact some fraction of the diameter of Pluto. It woudl of course be technically correct to define it that way, just as it is technically correct to say the metre is defined as slighlt less than half my height. But that would not be the definition that modern scientists use.
Beg pardon. The meter was defined as being a fraction of the size of the earth. Later it was changed to a number of wavelengths of a certain colour of light. Estimates can vary about the size of the earth, but wavelenths of light are assumed to be constant. The distance light travels in a second is a secondary measure, and comes out at an awkward amount, usually rounded off to 300 m/sec.Mariya Oktyabrskaya 04:18, 5 October 2007 (UTC)
Similarly, although with hindsight, we can say the Roman foot was some fraction of teh Nippur cubit, that would not be teh definition that they used. Rhialto 16:50, 13 June 2007 (UTC)


This argumentation is invalidated by the fact (and only, if that theorie is true):  The old Egyptian geometers consciously took the Nippur measure to create their construction-remen digit.
Later called Roman digit. They knew what they did. If this is true, we modern human beings, we rediscover. So, if this is the case, your argumentation above is invalid.
-- Gluck 123 18:23, 13 June 2007 (UTC)


If it is true that they consciously took that Nippur cubit, we should be able to come up with a Roman scholar on record as saying as much. It's not as if written records from Roman times are lost to modern day scholars. I see your point that the Romans were using a unit that was defined by the Egyptians. But that simply pushes the date and culture of the people doing the defining. If we can't find a historical document saying it was defined as such, the best we can do is reconstruct the definition from the evidence available, and make a best guess as to the definition.
I am going to amend the article to note that modern scholars have found (re-discovered?) that 16/28 relationship. Rhialto 19:34, 13 June 2007 (UTC)


According to Rottländer this digit is attested at least since the third dynasty of Egypt, i.e. roughly 2650 BC. From this time, by the preserved hieroglyphic textes we only know the names of the pharaons, some few political facts. In no case there exist e.g. philosophical, theoretical textes, nor any scientific dissertation. However in practice, we know that the Old Egyptians were good and competent geometers.

More than 2000 years later, scholars like Eratosthenes were content to discribe relationships with the measures in use during their life-time, including those used in the hellenistic Egypt.

In conclusion:  I can live with your current amendement and I thank you for our interesting discussion.
-- Gluck 123 07:18, 14 June 2007 (UTC)

[edit] Important Error.

There is an important error in this article, in the table of ancient Roman dodecimal fraction-names. Semis means not 2/12 but 6/12. Sextans means not 6/12 but 2/12. I'm sure about this, but I suppose I should find a reference-- here we go: Gullberg, Jan: Mathematics from the Birth of Numbers, Norton, 1997, p. 16.

Mjhrynick (talk) 18:13, 5 April 2008 (UTC)