Talk:Ancient Roman units of measurement/Archive 2

message: :I summarise: Because the English system of measurement is now the last surviving variant of the 5000 years old ancient system of measurement, we have to calculate the Roman foot in the English standards. Since the English foot is identified to be 36/35 Roman foot, we know that the Roman foot is 35 English barleycorns. Then we have to convert these values faithfully into decimal SI, since 36 English barleycorns equal 0.3048 meter.
:Even if – that's clear – Romans never heard of "speed of light" nor had a NIST with measure knowledge and know-how up to nanometers and above. Despite this fact, the chosen procedure is – in my humble opinion  – the only accurately one.'''
:Paul Martin 15:09, 2 December 2005 (UTC)
thread_title: Summary

message: Paul,
You note that "the needs of accuracy in ancient times were very less exigent than in modern times."  You point out that Roman foot sticks are found to range in length "from about 295.7 mm to about 296.7 mm". "Furthermore", as you also note, "a Roman foot of 296.0 mm is not more correct than a Roman foot of 295.9 mm or 296.1 mm for example."
Yes, I agree with what you're saying here.  What I'm trying to bring to your attention to is the fact that what you've put into the article is rather at odds with this.  The value you give in the article is 296.3 mm.  By your own very logic this cannot be more correct than 296.3 mm or 296.4 mm.
Indeed since the Roman foot ranged from about 295.7 mm to about 296.7 mm precission to the nearest tenth of a milimetre is plain nonsense.  What belongs in an encyclopædia are the facts.  The fact, as you've explained here, is that the Roman foot is 296.2 mm ± 0.17 %.  This is the fact that belongs in the article.
You agree that "We can't just go around and redefine their units for them." What I'm putting to you, Paul, is that this is exactly what you're doing.  If the Roman foot ranged from about 295.7 mm to about 296.7 mm, you can't just pick a value within that range and call this the true Roman foot (at least not for the purpose of writing an encyclopædia).  By choosing 296 1/3 mm you are redifining the Roman foot.
I appreciate your motives for choosing this value.  Yes, a Roman foot of exactly 35 barleycorns is a nice round foot but it's your Roman foot not the  Roman foot.  Similarly 296.352 mm exactly may be nice too but this is your friend's Roman foot.  I've got an idea: how about we make the Roman foot 296.32 mm exactly then ten Roman stadions will be excatly one international nautical mile (our friend Rktect would love me)?  Or how about making it 2-1.75 m (approximately 297.301779 mm): the perfect height for an A4 sheet?  Surely you'll like my Roman feet ... well the second is a little large ... but they are my Roman feet.
What readers want to know is the length of the true historical Roman foot.  In short, the article must be editted to reflect the facts rather than your preference.  This article is Ancient Roman units of measurement not Paul Martin's modernised Roman units of measurement.  I'm reverting your edits to the length table.
Jimp 5 December 2005
: Hi Jimp, I saw your modifications in this article and this reply. I'll answer you within the next few days. So long, Paul Martin 09:55, 7 December 2005 (UTC)
thread_title: The new Roman foot

message: Thanks for your answer Jimp.
Even if you are an agreeable knowledgeable talk partner, I think we should not eternalise our discussion.
There are points in your version – even if I see it differently – however I can live with.
*Your millimetre rounded mean value is one of these points. We can let it in the table.Nevertheless I consider, giving this value you redefine not only the Roman foot to 296 mm, but also the English foot to be 304 16/35 mm, i.e. – 0.1135 % of the 1959 value.A Nippur cubit of 518 mm exactly one, seems me to be a short Nippur cubit. However it's a Nippur cubit!
*The barleycorn conversions of each Roman unit of length in table is not necessary. You are right, to read that the correct length of the Roman stadium is 21,875 English barleycorns don't give anyone a vision of the length of this stadium.
*Some minor format modifications are also acceptable.
Concerning some other points we are still in disaccord.
*For the A4 mention you write: "Perhaps it would help readers visualise the length of a Roman foot." This is not consistent. The Roman foot is about 29.6 cm. Everybody can imagine a 30 cm ruler. Subtracting in mind four millimetres (or surely some decimals less) than you have a very good visualisation of the Roman foot length.
*I persist: If you give a 34:35 ratio, you also suggest that the English foot historically derived from a 34-digit-cubit. I'll come back below.  But it's with pleasure that I can confirm you that a hypothetical 34:35 ratio would be "no less accurate than" the well-known and accepted 35:36 ratio. 
Both the A4 mention and the 34:35 ratio – like it seems me – have been introduced by you to relativise the pertinency of the 35:36 relationship. Therefore I'm not mad at you. I understand. 200 years of a hegemonic decimal SI system, unlearnt, broke the habit to reason in "ratio relationships", once the only possible one.
*Concerning the Nippur cubit reference: I propose you to mention it briefly like before in the length table, and to add a new, not all too long chapter at the end of the article. I propose me to prepare a version for example at Discussion version: Chapter: History of the Roman foot which we can review together before integrate it into the article.    If you ask for references, I can give you for example this document of Dieter Lelgemann, Acting Director of the Institute for Geodesy and Geo-Information Technology, Technical University Berlin, who works amongst others for the European GPS project called Galileo. This doubtless, serious and eminent scientist recognises, of course like all the knowledgeable colleagues, the real existing historical ratios inside the ancient measure system. Before invention of the decimal digits, this was the only possible manner to evaluate the different measures. (Sadly he even integrates the doubtful "megalithic yard" researches of Thom, even without commentaries. I never studied these in details, but like others, here, I'm very sceptical. In the opposite, since the well-attested, graduate Nippur cubit measure found in several specimens, the relationships are clear.)
==== The plainest ratio is the accurate one. ====
To close this topo of that reply. You wrote: "What I would say is that aim is neither to find just any ratio nor the plainest, most simple one but to find the most accurate ratio." I'll try to illustrate you how the old measure system in ancient times developed by dispersing.
Imagine a smaller, (nowadays we would say) "satellite state" standing former, for example, under influence of the Babylonian Empire, now came under influence of another regional power, say: the Egypt. Several years later, in consequence of the close commercial relationships with the new friend and protector, they decided to change their system of measurements by abandoning the Babylonian main measure and for adopting the Egyptian Royal Cubit of 529.2 mm. But they would say, in this hypothetical illustration example: Okay, our new main measure will be hence the Royal Cubit. However because it's in our babylonian tradition, we'll continue to share the cubit into 30 equal parts. That will better match with our well-known sexagesimal system. So they created a digit of 28/30 Egyptian digit equal 17.64 mm. Some generations later exactly this digit can give a (not attested) foot main measure of 282.24 mm  equal 8/15 Royal Cubit. Those exchanges of main measures could happen even between great powers, for similar reasons or for example by the arriving of an intellectual elite from a declining former important region to the new dominant metropolis. (See role played of slaved Greek teachers at Rome.) Another example of such exchanges can be studied in the case of the  Russian cubit called "arshin" equal 28 English inches.
So, you see, it's well our duty to rediscover "the plainest, most simple ratios" because they are identical to the "most accurate ones". In your logic the excellent ratio of the two prime factors 829 and 853 would have prevalence. (304.8 / 853) x 829 ≥296.224 mm. If you want or not this suggest that the English foot are deduced from the Roman one via fantastic 829- and 853-digit-arpent lengths. Also hypothetical pseudo-ratios of 1481:1524 or 370:381 are only another way to give respectively 296.2 and 296.0 mm exactly one. But that's nothing to understand of the essence of the ancient ratio values. These ones ever also suggested a real historical deduction. Since the 34:35 ratio is not notably better than the widely accepted 35:36 ratio, the second, simpler one is prevalent, because more probable. That's also a principle in modern science.
===== Conclusion concerning these points =====
In conclusion: Let's concentrate, in our further talk to these six or five proposals expressed just above, for obtaining a solution. Other exchanges can be interesting, but they are less urgent.
Paul Martin 18:36, 13 December 2005 (UTC)
thread_title: Paul's new reply

message: To close this topo of that reply. You wrote: "What I would say is that aim is neither to find just any ratio nor the plainest, most simple one but to find the most accurate ratio." I'll try to illustrate you how the old measure system in ancient times developed by dispersing.
Imagine a smaller, (nowadays we would say) "satellite state" standing former, for example, under influence of the Babylonian Empire, now came under influence of another regional power, say: the Egypt. Several years later, in consequence of the close commercial relationships with the new friend and protector, they decided to change their system of measurements by abandoning the Babylonian main measure and for adopting the Egyptian Royal Cubit of 529.2 mm. But they would say, in this hypothetical illustration example: Okay, our new main measure will be hence the Royal Cubit. However because it's in our babylonian tradition, we'll continue to share the cubit into 30 equal parts. That will better match with our well-known sexagesimal system. So they created a digit of 28/30 Egyptian digit equal 17.64 mm. Some generations later exactly this digit can give a (not attested) foot main measure of 282.24 mm  equal 8/15 Royal Cubit. Those exchanges of main measures could happen even between great powers, for similar reasons or for example by the arriving of an intellectual elite from a declining former important region to the new dominant metropolis. (See role played of slaved Greek teachers at Rome.) Another example of such exchanges can be studied in the case of the  Russian cubit called "arshin" equal 28 English inches.
So, you see, it's well our duty to rediscover "the plainest, most simple ratios" because they are identical to the "most accurate ones". In your logic the excellent ratio of the two prime factors 829 and 853 would have prevalence. (304.8 / 853) x 829 ≥296.224 mm. If you want or not this suggest that the English foot are deduced from the Roman one via fantastic 829- and 853-digit-arpent lengths. Also hypothetical pseudo-ratios of 1481:1524 or 370:381 are only another way to give respectively 296.2 and 296.0 mm exactly one. But that's nothing to understand of the essence of the ancient ratio values. These ones ever also suggested a real historical deduction. Since the 34:35 ratio is not notably better than the widely accepted 35:36 ratio, the second, simpler one is prevalent, because more probable. That's also a principle in modern science.
===== Conclusion concerning these points =====
In conclusion: Let's concentrate, in our further talk to these six or five proposals expressed just above, for obtaining a solution. Other exchanges can be interesting, but they are less urgent.
Paul Martin 18:36, 13 December 2005 (UTC)
thread_title:  The plainest ratio is the accurate one. 

message: In conclusion: Let's concentrate, in our further talk to these six or five proposals expressed just above, for obtaining a solution. Other exchanges can be interesting, but they are less urgent.
Paul Martin 18:36, 13 December 2005 (UTC)
thread_title:  Conclusion concerning these points 

message: And thank you too, Paul, for your responses. 
*I'm glad that you can live with the mean value rounded to the nearest millimetre.  
**However, I don't agree that this is in anyway a redefinition of the Roman foot.  If I were to note that Mount Everest is 8844 metres high, this in no way constitutes a definition of the height of the mountain.  When giving the length of an object it is normal to assume that 296 mm to imply 296±0.5 mm.
**Furthermore, I don't accept that this is a redefinition of the English foot either.  It is not I but you who are insisting that an English barleycorn is exactly 1/35 of a Roman foot.  What I'm saying is that even if it were the case up to 1959 that the English foot had been defined in terms of the Roman one, it is no longer so defined.  The English foot is defined in terms of the metre.  If it were possible to redefine the Roman foot, then the only way to end up with the reationship 1 Roman foot equals 35 English barleycorns exactly would be to choose the definition 2961/3 mm.
**"A Nippur cubit of 518 mm exactly one, seems me to be a short Nippur cubit." you write "However it's a Nippur cubit!"  Nor am I trying to redefine the Nippur cubit.  The same arguement applies but there's more involved here which I'll come to later.
*I'm also glad that you agree that "The barleycorn conversions of each Roman unit of length in table is not necessary."
*"Some minor format modifications are also acceptable." of course.
*With respect to my A4 mention you write "Everybody can imagine a 30 cm ruler. Subtracting in mind four millimetres (or surely some decimals less) than you have a very good visualisation of the Roman foot length."  Yes, this is true.  However 297 mm is still closer to the Roman foot than 300 mm is.  What's going to be easier: subtracting four millimetres in the mind or subtracting one?  However, this is, as I say, nothing more than a little trivia and so I can easily live without its being mentioned.
*"If you give a 34:35 ratio," you persist "you also suggest that the English foot, historically derived from a 34-digit-cubit."  I continue to counter that I do not.  What I have written in the article makes it absolutely clear that this is a rough approximation.  
**Yes, I acknowledge that I had intended to relativise the pertinency of the 35:36.  This was the purpose of my introduction of the 34:35 ratio and my choice of wording for the A4 mention.  Note, however, that I refer to the mention's wording.  It was for the purpose of helping people visualise the Roman foot's length that I mentioned A4 at all.
**I can accept a change of wording here.  I can also accept that we drop the mention of 34:35.
**"200 years of a hegemonic decimal SI system, unlearnt, broke the habit – once the only possible one – to reason in 'ratio relationsips'." Yes but I'm not the only one with this broken habit.  Other readers will be in the same habit as I.  Decimals are what readers will be expecting these days.
*Thank you for the link to the document of Dieter Lelgemann's.  I have read it.  
**I too was dismayed that he unblinkingly incorporates the megalithic yard.  On the one hand: who am I to refute the research of such an eminent and serious scientist?  On the other: how can I take this seriously when he also says the the megalithic yard was based on the same Nipur cubit?  
**Another point: perhaps I've overlooked something but I don't quite see anywhere where he states that the Roman foot was defined as 16/28 of a Nippur cubit.
**However, I'm sure that you'd be able to find plenty of other sources if it is as you say such a "good, not-controversial definition of the Roman foot"
**Then, on the other hand, you write "Roman foot is 16/20 of the Egyptian Remen and thus 16/28 Nippur cubit".  So which is the definition of the Roman foot.  For comparison consider the English foot. It is exactly 304.8 mm but this is not its definition.  The definition of the English foot is one third of a yard which is, in turn, defined as 0.9144 metres.
**I look forward to reading your "new, not alltoo long chapter" regarding the definition of the Roman foot.
Now I must go.  I shall continue my response later. Jimp 14Dec05
==== Is the plainest ratio the accurate one? ====
Paul, 
You write "it's well our duty to rediscover 'the plainest, most simple ratios' because they are identical to the 'most accurate ones'."  The logic behind this is that because of the influence of neighbouring states, one ancient society should be expected to have adjusted their system of measurement to be compatible with that of their neighbours.
I can certainly understand the validity of the arguement that the values of the units of measurement used in contemporary societies may be expected to have existed in simple ratios.  Now, if you tell me that the Roman foot was defined such that 24 of them equalled exactly 25 Greek ones, then I'll happily accept this.  However what you're saying is something entirely different.
The arguement you present applies only to contemporary societies.  It could well be extended so as to include the possibility that a unit be based on an older one.  However you cannot base your measurement standard on something that is two millenia yet to come ... at least not unless the causal theory of time is wrong.
Were the English yard defined as 3×36/35 Roman feet, then you could say that one Roman foot was exactly 35 English barleycorns.  The English yard is not so defined.  It is defined as 0.9144 metres.  The simple ratio of 35:36 may once have been valid but the English yard now has a new definition.  This does not force a redefinition of the old Roman foot: it is an abandonment of the ratio.
Take, for example, the nautical mile.  Until 1970 the British nautical mile was defined as 6080 feet.  In 1970 the international definition of 1852 metres was adopted.  It would seem to me, by your way of thinking, then that this would be to redefine the Imperial foot to be 1852/6080 (463/1520 or ~0.304605263) metres.  Of course this is not the case.  The old definition was abandoned for the new one.
"In your logic the excellent ratio of the two prime factors 829 and 853 would have prevalence. ... If you want or not this suggest that the English foot are deduced from the Roman one via fantastic 829- and 853-digit-arpent lengths."  If I don't want to make this suggestion then I have merely to note that this is a rough approximation.  However, no, I wouldn't want to use such mind-boggling ratios ... not when readers will be expecting decimals.
"Also hypothetical pseudo-ratios of 1481:1524 or 370:381 are only another way to give respectively 296.2 and 296.0 mm exactly one."  Okay, but I do not intend to suggest an exact relationship.  What I'm saying is that this kind of precission is not valid.  Giving "296 mm" is not to suggest any exact relationship.  "296 mm" is normally taken to mean "296±0.5 mm" (unless some other range is specified).
You write of ratios suggesting real historical deductions.  I'm afraid, my friend, that in your hands they seem to imply a backwards historical deduction, at least to me they do.  You write of principles in modern science.  One such principle would be that the cause comes before the effect.
No organisation today has the authority to redefine the ancient Roman foot.  If you have a unit which is based on the Roman foot and you redefine that unit based on the metre, then you've abandoned the old definition in favour of a new one.  The two different definitions don't just continue to coexist thence redefining the Roman foot back through time.
If the ratio 36:35 is historically valid, then it deserves a mention.  However, the place for such a mention will be English unit not here.  Such a ratio may once have been valid: it no longer remains so.  Today it is nothing but a rough approximation.  It would certainly be an approximation with historical importance but no less an approximation.
Jimp 15Dec05
Talk:Ancient Roman units of measurement/Hexadecimal foot/Archive 1#One Billion hexadecimal feet
I've disentangled these two different topics.  You'll notice links between this page & the new one (the last of these is right above this paragraph).  By clicking on each of these as you come to them you can preserve the flow of this chat of ours.  Paul, I shall respond again when I find time but now I must go.  Jimp 16Dec05
You made it very well. Me too, I'll reply soon. Paul Martin 09:55, 16 December 2005 (UTC)
thread_title: Jimp's next few words

message: Paul, 
You write "it's well our duty to rediscover 'the plainest, most simple ratios' because they are identical to the 'most accurate ones'."  The logic behind this is that because of the influence of neighbouring states, one ancient society should be expected to have adjusted their system of measurement to be compatible with that of their neighbours.
I can certainly understand the validity of the arguement that the values of the units of measurement used in contemporary societies may be expected to have existed in simple ratios.  Now, if you tell me that the Roman foot was defined such that 24 of them equalled exactly 25 Greek ones, then I'll happily accept this.  However what you're saying is something entirely different.
The arguement you present applies only to contemporary societies.  It could well be extended so as to include the possibility that a unit be based on an older one.  However you cannot base your measurement standard on something that is two millenia yet to come ... at least not unless the causal theory of time is wrong.
Were the English yard defined as 3×36/35 Roman feet, then you could say that one Roman foot was exactly 35 English barleycorns.  The English yard is not so defined.  It is defined as 0.9144 metres.  The simple ratio of 35:36 may once have been valid but the English yard now has a new definition.  This does not force a redefinition of the old Roman foot: it is an abandonment of the ratio.
Take, for example, the nautical mile.  Until 1970 the British nautical mile was defined as 6080 feet.  In 1970 the international definition of 1852 metres was adopted.  It would seem to me, by your way of thinking, then that this would be to redefine the Imperial foot to be 1852/6080 (463/1520 or ~0.304605263) metres.  Of course this is not the case.  The old definition was abandoned for the new one.
"In your logic the excellent ratio of the two prime factors 829 and 853 would have prevalence. ... If you want or not this suggest that the English foot are deduced from the Roman one via fantastic 829- and 853-digit-arpent lengths."  If I don't want to make this suggestion then I have merely to note that this is a rough approximation.  However, no, I wouldn't want to use such mind-boggling ratios ... not when readers will be expecting decimals.
"Also hypothetical pseudo-ratios of 1481:1524 or 370:381 are only another way to give respectively 296.2 and 296.0 mm exactly one."  Okay, but I do not intend to suggest an exact relationship.  What I'm saying is that this kind of precission is not valid.  Giving "296 mm" is not to suggest any exact relationship.  "296 mm" is normally taken to mean "296±0.5 mm" (unless some other range is specified).
You write of ratios suggesting real historical deductions.  I'm afraid, my friend, that in your hands they seem to imply a backwards historical deduction, at least to me they do.  You write of principles in modern science.  One such principle would be that the cause comes before the effect.
No organisation today has the authority to redefine the ancient Roman foot.  If you have a unit which is based on the Roman foot and you redefine that unit based on the metre, then you've abandoned the old definition in favour of a new one.  The two different definitions don't just continue to coexist thence redefining the Roman foot back through time.
If the ratio 36:35 is historically valid, then it deserves a mention.  However, the place for such a mention will be English unit not here.  Such a ratio may once have been valid: it no longer remains so.  Today it is nothing but a rough approximation.  It would certainly be an approximation with historical importance but no less an approximation.
Jimp 15Dec05
Talk:Ancient Roman units of measurement/Hexadecimal foot/Archive 1#One Billion hexadecimal feet
I've disentangled these two different topics.  You'll notice links between this page & the new one (the last of these is right above this paragraph).  By clicking on each of these as you come to them you can preserve the flow of this chat of ours.  Paul, I shall respond again when I find time but now I must go.  Jimp 16Dec05
You made it very well. Me too, I'll reply soon. Paul Martin 09:55, 16 December 2005 (UTC)
thread_title:  Is the plainest ratio the accurate one?