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Paul Martin,
On what basis do you hold that the Roman foot is exactly 296 1/3 milimetres? The metre is based on the speed of light in a vaccuum and the period of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. Is this what the Romans used to define their foot?
Also, I not convinced of the following ...
Since the Roman cubit measures 17.5 English inches exactly one, the English foot is sixteen twenty-eighth of the Mesopotamien cubit. Thus the Roman foot measures 35 lengths of the English barleycorn. This table retains the value of the English barleycorn issue of the foot of the compromise 1959, even if a modern value, increased by 0.533 µm, would be better than the current 8,466.667 µm.
... not convinced ... well it doesn't actually make any sense. Jimp 07:05, 1 December 2005 (UTC)
Paul,
There is a vast difference between those different pounds and these different feet. All those pounds are based on the same base unit: the grain. The English foot is based on the metre which in turn is based on the speed of light and the second with the second being based on the frequency of the aforementioned radiation. This is not the basis of the Roman foot. It seems that you are redefining the Roman foot to your liking. What people want to know is what the actual historical Roman foot was they aren't going to be interested in what you call the "modern defined value of the Roman foot".
I don't doubt that the ancients "respected this simple primary number ratios." and "'took references' to already known standards applied by neighbour nations." I'd not be surprised to find simple interger relationships between the units of various ancient systems. However, what you're suggesting is something more. You're suggesting simple interger relationships between ancient units and modern ones. The Romans didn't have the benifit of the modern SI definitions to base their units on. We can't just go around and redefine their units for them.
A side point: in my opinion, the inch would be better redefined as exactly 25 mm. Why redifine something to fit in nicely with a long obsolete ancient system instead of the current international standard? Jimp 2 December 2005
Talk:Ancient Roman units of measurement/Hexadecimal foot/Archive 1#A very crazy proposal
Talk:Ancient Roman units of measurement/Hexadecimal foot/Archive 1#The new hexadecimal metric system
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
I await your reply. You will forgive my haste in reverting your changes to the table but for the reasons above I felt it necessary and saw little reason to hold out any longer. Also you will have noticed that I have left a mention of the fact that one Roman foot is about 35 English barleycorns in the paragraph at the bottom of the section. I hope that this kind of compromise might be acceptable to you. I did also note, however, that one Roman foot is approximately 34/35 of an English one as well and that this approximation was just as valid. Surely you'd agree. This is certainly interesting trivia but trivia should be presented as such and not masquerade as a defintion. Jimp 8 December 2005
What is the rational for putting equivalence in English barleycorns? This is nothing short of absurd. How many people use barleycorns as a unit of measurement today? How many even know what one is? Jimp 07:23, 1 December 2005 (UTC)
Given that the Roman foot is exactly 35 English barleycorns then, yes, this reference is useful ... to some. However, most of those who still use feet & inches wouldn't have a clue what a barleycorn is supposed to be. Now, instead of simply replacing barleycorns with more familiar units, why not have both? Of course, this is all supposing that the Roman foot is exactly 35 English barleycorns which is the point we're debating above. If, as I contend, the Roman foot is not exactly 35 barleycorns, then this will still be an interesting but rough conversion and still worth a mention. Jimp 2 December 2005
I await your reply. You will forgive my haste in reverting your changes to the table but for the reasons above I felt it necessary and saw little reason to hold out any longer. Also you will have noticed that I have left a mention of the fact that one Roman foot is about 35 English barleycorns in the paragraph at the bottom of the section. I hope that this kind of compromise might be acceptable to you. I did also note, however, that one Roman foot is approximately 34/35 of an English one as well and that this approximation was just as valid. Surely you'd agree. This is certainly interesting trivia but trivia should be presented as such and not masquerade as a defintion. Jimp 8 December 2005
Since the Drusian pygme – equal 18 Roman digits – is 18/28 of the Nippur cubit : | (518.583 / 28) x 18 | = | 333.375 mm |
The Babylonian cubit is a nibw of this attested Drusian pygme seen as a pygon : | (333.375 / 20) x 32 | = | 533.400 mm |
The Hashimi kus is a 30-digit-measure of 32/28 Babylonian cubit (seen as neilos) : | (533.400 / 28) x 32 | = | 609.600 mm |
The Hashimi nibw is the 32-digit-measure of precisely this Hashimi kus measure : | (609.600 / 30) x 32 | = | 650.240 mm |
Talk:Ancient Roman units of measurement/Hexadecimal foot/Archive 1#Related topos
Paul,
"The aim is not to find any ratio," you insist "but the plainest, most simple one !" This is where we rather disagree. 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. "34 Eng. ft. ≈ 35 Roman ft." is no less accurate than "35 Eng. ft. ≈ 36 Roman ft." Noting this in no way vindicates the theory that "the English foot is derived from the other ancient measures by a 34-digit-cubit". All it is is a rough approximation it does not imply anything about the derivation of the English foot.
In just the same way noting that the height of an A4 sheet is about one Roman foot (ignore the 0.3% error for a second) doesn't imply any historical link between them. Is mentioning this unuseful? A4 sheets are quite a common sight these days (I happen to have a bunch sitting in front of me). Perhaps it would help readers visualise the length of a Roman foot. How may of us have rulers with barleycorns marked off lying about these days? "we also could make researches, whose prominent feet size about 44½ and therefore incidentally one approximate Roman foot." Yes, we could but nor do we have these in the drawer of the desk.
Okay, 36 is three dozen is 22×32 and 35 is five sevens whereas 34 is twice seventeen. As bizzarre as the factors between units in traditional systems got you never had 17, sure. And it is a well attested fact the the English units derived from the Roman ones, indeed. And from Nippur cubits to Hashimi nibw then the French feet and the like and all down throught the ages till we land in England. Let's assume that the English foot had been defined as 36/35 Roman foot. It is now redefined as 304.8 millimetres.
We can't pretend that in 1959 the Commonwealth & U.S. legislators redefined the Roman foot. What they did was to redefine the English foot. Certainly the English foot may have once been defined such that it were 36/35 of a Roman one but it had since been redefined and more than once. Changing the definition of a unit doesn't redefine the units it was once based on. The older definition is abandoned and a new one adopted or are you going to insist that the length of the earth's meridian along a quadrant is exactly the distance travelled by light in vacuum during a time interval of 10 000 000/299 792 458 of a second?
I'm glad you agree that we should note "The ascertained margin of ± 0.17 % relative to a statistical value of 296.2 mm." But you also note "we should not confound a mean value neither with originate value nor with best value nor with legal value." Indeed not. However, our ideas of what constitutes original, best and legal vales are leagues apart.
"English foot and its legal definition, as nowadays the only one of the ancient measures still in use, and so makes also authority for the Roman foot, failing with a serviceable value definition of an inexistent Roman standard institute." you write. I cannot agree with this. There is no extant organisation with the authority to define the length of the Roman foot. Roman units of measurement are obsolete. Neither you nor I can redefine them: you agree that would be absurd. Nor can the U.S. government in conjunction with the Commonwealth governments do so. Not even the U.N. can claim the authority to do this. The Roman foot was what it was and cannot be redefined (except, perhaps, by a god but even this would be to change history).
Anyway, you also note my deletion of the Nippur cubit reference. Yes, if it is valid then it belongs here. However, I'd ask you to cite some verifiable sources before we put it back.
Jimp 12Dec05
Talk:Ancient Roman units of measurement/Hexadecimal foot/Archive 1#Hexadecimal feet
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.
Concerning some other points we are still in disaccord.
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.
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.
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)
Talk:Ancient Roman units of measurement/Hexadecimal foot/Archive 1#Hexadecimal foot
And thank you too, Paul, for your responses.
Now I must go. I shall continue my response later. Jimp 14Dec05
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)
Excuse for not having replied in our topo since a long time. This will be come soon. Promised.
Hovever I didn't stay lazy. I prepared you an overview for the
Hexadecimal metric system. So we'll know exactly what we are talking about.
So long! Paul Martin 14:18, 20 December 2005 (UTC)
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 | Archive 3 | Archive 4 |
Paul Martin,
On what basis do you hold that the Roman foot is exactly 296 1/3 milimetres? The metre is based on the speed of light in a vaccuum and the period of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. Is this what the Romans used to define their foot?
Also, I not convinced of the following ...
Since the Roman cubit measures 17.5 English inches exactly one, the English foot is sixteen twenty-eighth of the Mesopotamien cubit. Thus the Roman foot measures 35 lengths of the English barleycorn. This table retains the value of the English barleycorn issue of the foot of the compromise 1959, even if a modern value, increased by 0.533 µm, would be better than the current 8,466.667 µm.
... not convinced ... well it doesn't actually make any sense. Jimp 07:05, 1 December 2005 (UTC)
Paul,
There is a vast difference between those different pounds and these different feet. All those pounds are based on the same base unit: the grain. The English foot is based on the metre which in turn is based on the speed of light and the second with the second being based on the frequency of the aforementioned radiation. This is not the basis of the Roman foot. It seems that you are redefining the Roman foot to your liking. What people want to know is what the actual historical Roman foot was they aren't going to be interested in what you call the "modern defined value of the Roman foot".
I don't doubt that the ancients "respected this simple primary number ratios." and "'took references' to already known standards applied by neighbour nations." I'd not be surprised to find simple interger relationships between the units of various ancient systems. However, what you're suggesting is something more. You're suggesting simple interger relationships between ancient units and modern ones. The Romans didn't have the benifit of the modern SI definitions to base their units on. We can't just go around and redefine their units for them.
A side point: in my opinion, the inch would be better redefined as exactly 25 mm. Why redifine something to fit in nicely with a long obsolete ancient system instead of the current international standard? Jimp 2 December 2005
Talk:Ancient Roman units of measurement/Hexadecimal foot/Archive 1#A very crazy proposal
Talk:Ancient Roman units of measurement/Hexadecimal foot/Archive 1#The new hexadecimal metric system
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
I await your reply. You will forgive my haste in reverting your changes to the table but for the reasons above I felt it necessary and saw little reason to hold out any longer. Also you will have noticed that I have left a mention of the fact that one Roman foot is about 35 English barleycorns in the paragraph at the bottom of the section. I hope that this kind of compromise might be acceptable to you. I did also note, however, that one Roman foot is approximately 34/35 of an English one as well and that this approximation was just as valid. Surely you'd agree. This is certainly interesting trivia but trivia should be presented as such and not masquerade as a defintion. Jimp 8 December 2005
What is the rational for putting equivalence in English barleycorns? This is nothing short of absurd. How many people use barleycorns as a unit of measurement today? How many even know what one is? Jimp 07:23, 1 December 2005 (UTC)
Given that the Roman foot is exactly 35 English barleycorns then, yes, this reference is useful ... to some. However, most of those who still use feet & inches wouldn't have a clue what a barleycorn is supposed to be. Now, instead of simply replacing barleycorns with more familiar units, why not have both? Of course, this is all supposing that the Roman foot is exactly 35 English barleycorns which is the point we're debating above. If, as I contend, the Roman foot is not exactly 35 barleycorns, then this will still be an interesting but rough conversion and still worth a mention. Jimp 2 December 2005
I await your reply. You will forgive my haste in reverting your changes to the table but for the reasons above I felt it necessary and saw little reason to hold out any longer. Also you will have noticed that I have left a mention of the fact that one Roman foot is about 35 English barleycorns in the paragraph at the bottom of the section. I hope that this kind of compromise might be acceptable to you. I did also note, however, that one Roman foot is approximately 34/35 of an English one as well and that this approximation was just as valid. Surely you'd agree. This is certainly interesting trivia but trivia should be presented as such and not masquerade as a defintion. Jimp 8 December 2005
Since the Drusian pygme – equal 18 Roman digits – is 18/28 of the Nippur cubit : | (518.583 / 28) x 18 | = | 333.375 mm |
The Babylonian cubit is a nibw of this attested Drusian pygme seen as a pygon : | (333.375 / 20) x 32 | = | 533.400 mm |
The Hashimi kus is a 30-digit-measure of 32/28 Babylonian cubit (seen as neilos) : | (533.400 / 28) x 32 | = | 609.600 mm |
The Hashimi nibw is the 32-digit-measure of precisely this Hashimi kus measure : | (609.600 / 30) x 32 | = | 650.240 mm |
Talk:Ancient Roman units of measurement/Hexadecimal foot/Archive 1#Related topos
Paul,
"The aim is not to find any ratio," you insist "but the plainest, most simple one !" This is where we rather disagree. 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. "34 Eng. ft. ≈ 35 Roman ft." is no less accurate than "35 Eng. ft. ≈ 36 Roman ft." Noting this in no way vindicates the theory that "the English foot is derived from the other ancient measures by a 34-digit-cubit". All it is is a rough approximation it does not imply anything about the derivation of the English foot.
In just the same way noting that the height of an A4 sheet is about one Roman foot (ignore the 0.3% error for a second) doesn't imply any historical link between them. Is mentioning this unuseful? A4 sheets are quite a common sight these days (I happen to have a bunch sitting in front of me). Perhaps it would help readers visualise the length of a Roman foot. How may of us have rulers with barleycorns marked off lying about these days? "we also could make researches, whose prominent feet size about 44½ and therefore incidentally one approximate Roman foot." Yes, we could but nor do we have these in the drawer of the desk.
Okay, 36 is three dozen is 22×32 and 35 is five sevens whereas 34 is twice seventeen. As bizzarre as the factors between units in traditional systems got you never had 17, sure. And it is a well attested fact the the English units derived from the Roman ones, indeed. And from Nippur cubits to Hashimi nibw then the French feet and the like and all down throught the ages till we land in England. Let's assume that the English foot had been defined as 36/35 Roman foot. It is now redefined as 304.8 millimetres.
We can't pretend that in 1959 the Commonwealth & U.S. legislators redefined the Roman foot. What they did was to redefine the English foot. Certainly the English foot may have once been defined such that it were 36/35 of a Roman one but it had since been redefined and more than once. Changing the definition of a unit doesn't redefine the units it was once based on. The older definition is abandoned and a new one adopted or are you going to insist that the length of the earth's meridian along a quadrant is exactly the distance travelled by light in vacuum during a time interval of 10 000 000/299 792 458 of a second?
I'm glad you agree that we should note "The ascertained margin of ± 0.17 % relative to a statistical value of 296.2 mm." But you also note "we should not confound a mean value neither with originate value nor with best value nor with legal value." Indeed not. However, our ideas of what constitutes original, best and legal vales are leagues apart.
"English foot and its legal definition, as nowadays the only one of the ancient measures still in use, and so makes also authority for the Roman foot, failing with a serviceable value definition of an inexistent Roman standard institute." you write. I cannot agree with this. There is no extant organisation with the authority to define the length of the Roman foot. Roman units of measurement are obsolete. Neither you nor I can redefine them: you agree that would be absurd. Nor can the U.S. government in conjunction with the Commonwealth governments do so. Not even the U.N. can claim the authority to do this. The Roman foot was what it was and cannot be redefined (except, perhaps, by a god but even this would be to change history).
Anyway, you also note my deletion of the Nippur cubit reference. Yes, if it is valid then it belongs here. However, I'd ask you to cite some verifiable sources before we put it back.
Jimp 12Dec05
Talk:Ancient Roman units of measurement/Hexadecimal foot/Archive 1#Hexadecimal feet
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.
Concerning some other points we are still in disaccord.
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.
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.
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)
Talk:Ancient Roman units of measurement/Hexadecimal foot/Archive 1#Hexadecimal foot
And thank you too, Paul, for your responses.
Now I must go. I shall continue my response later. Jimp 14Dec05
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)
Excuse for not having replied in our topo since a long time. This will be come soon. Promised.
Hovever I didn't stay lazy. I prepared you an overview for the
Hexadecimal metric system. So we'll know exactly what we are talking about.
So long! Paul Martin 14:18, 20 December 2005 (UTC)