‘Even the Obvious Can be Proved’(0)

2 October, 2013

It was a truth universally acknowledged, that a simple fact in conformity with Roman ways must not be written down. In itself a simple fact in conformity with Roman ways this truth was never written down because it mustn’t necessarily be point it out. However, when it comes to studying Roman ways, the quote and the simple statement highlights the difference between disciplines such as Archaeology and History. Moreover, suspending 19th c. humanities between paraphrasing Jane Austin and quoting something perhaps Oscar Wilde seems fair.

Consider the following example: some Roman times it was important to know the weight of one’s silver ware – the weight of a pair of cups or a plate – and to demonstrate importance by writing it down on the items themselves. Why not make it simple and write ‘1 lb, 3 oz and 5 dr’ – one pound, three ounces and five dram – on the bottom of the object if that was its weight? Often the inscriptions seem to mean just that, but when checked, the expected simplicity is not there. Seemingly something wrong is there instead.

In the original inscription by the silversmith on the Achilles plate from Kaiseraugst is says that the weight is 15 pounds. Later when the weight was checked, the plate weighed 17 pounds, 4 ounces and 15 scripulae. In grams its weight is 4642.9. Although the plate is not well-preserved we cannot accept a loss of that would once have made it weigh 15 pounds. Irrespective of the weighers referring to the light calculation pound, the logarike litra, (ll.) or the heavy canonical libra (cl.) fifteen pound, c. 4834 or 4912 grams, is too much. There you are: if the plate doesn’t weigh fifteen pounds how come it weighs more than seventeen? The conformity with Roman ways is obvious: the silversmith tells us the weight of the object and someone checks it, but the simplicity of the definition, the simple fact, is not there. Instead something is the matter with the plate, the Romans, the text, the reader, or any possible combination of these four entities.

To the conventional historian this is the end of the inscriptions on the Achilles plate – his scissors will clip out the text but there’s nowhere paste its contradiction into his history of the Roman world except to ridicule the Romans and being conventional rather than a member of the flying circus he wouldn’t do that. There are no more weight definitions to read and no logic, based solely on the expressions, will make them compatible. Archaeologists, nevertheless, may view things differently. Literally they look at ‘things’ as contexts, and find that important, because studying material culture they believe that things being contexts carry meaning. This is to say that primarily, the objects mirror a meaningful series of action. The actual weight definitions, whatever their purpose, are principally speaking secondary. Looking at three pairs of silver cups, already discussed on the reading rest, will illustrate this point. https://floasche.wordpress.com/2012/06/11/accipe-me-sitiens-forte-placebo-tibi-looking-for-the-missing-warren-cup/

On the silver cups from Hoby there are two kinds of inscriptions one dotted and four graffiti. The dotted one resembles the writing style adopted by the silversmith when he signed the cups. Dotted inscriptions are his statements. The four graffiti make up two pairs one on each cup. On one cup there is a weight description and the name SILIUS. On the other SILIUS overwrites the weight description. Silius is considered to be the owner of the cups. The weight descriptions are identical.

The dotted description says:  II . P V S ==-  SU ==- One cups weighs 975,46 gr. The other has lost a handle, but since we know the weight of the three other ones we can estimate its original weight as c. 956,7 gr. Since the logarike litra. weighs 322.32gr and the canonical libra. 327.45 gr, the total weight is somewhere between five and six pounds. II therefore means ‘Two cups’. The dot [.] means ’together’, i.e. ’The pair is’. Then follows the weight description: P V means ’five pounds’; S is ‘one semis’; ==– is ‘five units of which six make up a semis’; SU is ‘one semuncia’ and the last ==– means ‘five units of which six make up a semuncia’. This doesn’t mean that the pair weighs something definite. Instead it means that the pair weighs less than six pounds and more than 5 pounds, namely: one semis (i.e. half a pound), five unciae (i.e. 5 ounces), one semuncia (i.e. half an ounce) and five demida sextulae (ds.). The inscription mirrors an additive weighing procedure that didn’t go further than the ds. If the silversmith had wanted to he could have written ds. DCCCLXIII since 5+(11×6)+72+(144×5) = 863. He could not have written 864 ds. since that would have been six pounds and he didn’t think the pair weighed that much. This then is the additive weight description, the silversmith’s statement, which ought to be controlled. Fair enough.

Things get confused when we see that the two graffiti inscriptions, the controller’s statement, are almost identical. Both cups belong(ed) to Silius and one description says I NVII S ==–  and the other NVII S==– . The I is simple enough. It means ‘one cup’, and we may wonder why NVII S ==–  is either 975 or 956 gr. The inscription nevertheless is easy to read – it says: Seven nonus, one half nonus and five of those units of which six make up half a nonus.

The first point to make is the one that says that the description doesn’t mean eight nonus. And since we already know that the weight is close to three pounds we may draw the conclusion that 8 nonus equals 3 libra. The description tells us that there are 6 units in a half nonus and thus 12 in a nonus, which means that there are 8 x 12 = 96 units in 3 pounds or 32 units in 1 pound.

If we use the ll. the smallest unit in the description is 322,32/32 = 10,0725 gr and a cup thus 10,0725 x 95 = 956.89gr that is very near the reconstructed weight of the ‘light’ cup (c. 956.7 gr). If we use the cl., the calculation results in 327.45/32 = 10.23 x 95 = 972.12 gr and a weight slightly below the actual weight of the cup – 975.46 gr. It is fair to say that the controller’s definitions follow the formula: ‘more than x and less than x+1’.

The second point has to do with the integrity of the controller vis-à-vis the silversmith – the point being that the descriptions must be referred to two different series of analytical action. The controller doesn’t take the silversmith’s procedure for granted, but shows it to be reasonable.

The weight descriptions on the Hoby cups are not simple facts. They require us to follow the procedure of the silversmith and the controller respectively. The former was Greek and from the weight of the three handles we gather that as a craftsman he used a mina system when he divided his silver and created his cups. But he was given 3 + 3 Roman pounds of silver to make them. Tacitly, the dotted description refers to two different pounds and his description of each of the cups would obviously have differed from that of the controller, who was satisfied with a description down to a relatively large weigh unit a little above 10 gr. Rather elegantly, nevertheless, the controller pointed out that the silversmith was given two different pounds of silver and consequently asked to make a heavy and a light cup formally weighing the same. This implies that there is a ‘heavy’ and a ‘light’ scene in the pair.

*

In the Menander hoard there are two pairs of inscribed cups: Cups M5+6 and M7+8. There are two inscriptions on M7 and one on M8. The inscription on M5 refers to both M5 and M6 and runs:

M5:       II   P    VII    SS )   ’II

This should be read: Two cups. Each or ‘this one’ weighs: 1 pound + 7 uncia + 2 sicilicius +  ‘ (i.e. circa) 2 semisextula. Only the inscription on M5 has been preserved.

*

M5 weighs 528gr., i.e., close to the original weight. M6 weighs 517 gr., i.e. not the exact original weight. The weighing procedure, based on the ll., starts with a pound and contains four steps ending up in a rest of circa a number of units:
Step One:        the total weight minus 1 Pound:          528.00 – 322.32 = 205.68 gr
Step Two:        the rest minus 7 uncia:                      205.68 – 188.02 =   17.66 gr
Step Three:      the rest minus 2 sicilicius:                    17.66 –  13.43  =   04.23 gr = ’II
Step Four:        the rest which is c. semisextula-
Comment. If the rest had been 2 semisextula then it would have been the same as a Sextula, i.e. 1/6th of an uncia. Together with the two sicilicus the rest above the 7 uncia would have amounted to one semuncia. Then the definition would have been: P VII IV, i.e. 1 Pound (but not 2), 7 uncia (but not 8) and 4 sextula (but not 5). As it happens the definition reads: 1 Pound (but not 2), 7 uncia (but not 8), 2 sicilicius (but not 3) and c. 2 semisextula. The weight 4,23gr is indeed c. 4,476 gr, i.e. 2 semisextula.

*

M8 weighs 445 gr. Dotted inscription: AUREL . AUGUR[ . . .  . . .]
M7 weighs 445 gr. Dotted inscription: AUREL . AUGUR . II . P . III . )X
The first part  AUREL . AUGUR . II .  reads: ‘By Aurelius Augur-inus, -ans, -ianus, -is or -ius   (i.e. the silvermith). Two cups; each weighing:’ The second part, P . III . )X reads: ‘ one pound, three suscuncia and c. 10 siliqua.’
The weighing procedure has three steps ending up in a rest:
Step One:        the total weight minus 1 pound:                     445,00 – 322,32 = 122,68gr
Step Two:       the rest minus 3 suscuncia:                            122,68 – 120,87=   001,81gr
Step Three:     the rest which c. 10 siliqua, i.e. c. 1,87 gr. And 1.81 gr is indeed c. 1.87 gr.

The reason we may defend this interpretation of the total divided by two rests with the graffiti definition on each of the two cups.

M7 Graffito: P III £ V and M8 Graffito: P III £ V[I]. This means that when the cups are judged individually, one is considered a trifle heavier than the other. In practice they weigh the same and when we look at them as a pair of two identical cups we are entitled to divide the total by 2. So, the dotted weights are the silversmith’s inscription taking the identical pair for granted because it was indeed what he was ordered to do. The graffiti on the other hand is a control of each of the two cups. In the graffiti definition the rest is 5 units (M8) and 6 units (M7) respectively. This means that the c. 10 units in the dotted definition on M8 equals 5 units in the graffiti definition. This implies that the graffiti units are double-siliqua. In the M7 cup the rest is 6 double-siliqua and that is a semisextula since 24 seliqua equals a sextula. We could of course argue that that 22 seliqua divided by two is 11 seliqua, so why not write so in the dotted definition? On the other hand controlling the weights there is a point in the letting the controlled weights match the original definition and having found that M8 weighs exactly what the silversmith had suggested, M7 must logically speaking weigh a bit more. In the units used by the controller this means 6 instead of 5. Whether the silversmith or the controller were the better weigher is impossible to say. Probably they were both overdoing it, but the controller has understood the silversmith and has made an independent analysis in a small series of analytical steps. It is the procedure and the ‘more than x and less than x+1’ convention that makes it possible to understand the additive weight description. If the weigher is sufficiently diligent the description resembles the Achilles and the Tortoise paradox since from the very beginning we are told that there is a weight we will never reach while at the same time we are supposed to come closer and closer to it. The closer we come to the limit, the smaller the units we employ not to reach it.

*

The Obvious 00

Let us return to the Achilles plate. Its weight in grams is 4642.9 gr and it has lost some of its original weight. The dotted inscription says ‘Pausylypos in Thessaloniki 15 Pound’ (Λ IE in Greek). This is the silversmith’s inscription. The two dotted silversmith inscriptions discussed above indicated that when an object was produced a certain amount of silver was lost. It is unlikely that such loss of weight would not have occurred when producing the Achilles plate. Moreover, 4642.9/15 = 309,53gr doesn’t fit a known Roman pound. The inscription therefore says: ‘Made by Pausylypos in Thessaloniki from 15 pound’ of silver. If the smith had the logarike litra in mind the loss of weight would have been 4834.8 – 4642.9 = 191,9 gr. This is quite a lot compared to the two other silversmith inscriptions, but their loss on the other hand was exceptionally small. Probably the point in these description was a wish to show how little silver had disappeared in the production of the cups. In Pausylypos case the difference between the actual weight and the 15 pounds may also have included his salary, since he was probably not a slave.

The controller’s description of the weight is additive telling us that the plate weighed 17 pounds and a little more, but not 18 pounds. The graffiti looks like this:

The Obvious 01

Since we know that the plate was made from 15 pounds of silver and thus weighed less than 15, it stands to reason that the pound referred to by the controller was a smaller one of which 18 pounds were the same as 15 pounds.

This would be the libra metrica (lm.), which relates to a normal pound as 5 to 6, and that is why 18 lm. equals 15 ll. Perhaps the extra line in the Λ means that the controller had lm. in mind. An lm. consists of 12 uncia, but since its weight equals only 10 uncia there are only 20 sextula to the ounce of the lm. Five sextula lm. therefore equals one sicilicius, i.e. 1/4th of an ounce, in this case 5 scripula.

The smallest unit in the additive description is in other words a sicilicius, i.e. 1/4th of an uncia or 1/48th of the libra metrica. Expressed in sicilicius, the additive weight description amounts to 816 + 16 + 3 = 835 sicilicius. A sicilicius equals (322.32/6 x 5) / 48 = x 5.60 gr. The total therefore is 5.59583 x 835 = 4672.2 gr.

Compared to the weight of the plate as we know it today, the controller has arrived at a weight c. 30 gr above the weight of the plate. This suggests that he has made a mistake when he added up the weights or that the plate has lost c. 35 gr of its original weight. This loss is less than a percent, but still perhaps unlikely. In the Achilles case therefore, the material context is difficult to grasp and it may have been misjudged by the controller. The text nevertheless has become relatively clear.

The silversmith didn’t aim at an additive description of the weight. The controller did and distanced himself from the silversmith by not using the same pound as the smith. He could just have said 14 logarike libra, 4 uncia and 5 sextula, which would have been correct in relation to the plate’s present weight, but using this description the controller would have continued in the footsteps of the silversmith – i.e. the formula ‘more than 14 pound and less than 15’. Had he started there, his description would have lived up to that of the silversmith’s description and lost its integrity. Introducing the libra metrica, he demonstrated his role as a controller.

And that is the controller’s point – an independent statement analyzing the silversmith as well as the weight through a series of steps. Skill rather than authority, action rather than fact is the controller’s message and with it he proves the obvious – the in a sense the silversmith was right. The silversmith on the other hand demonstrated his status as an artist and a craftsman. So obviously does his cups and plates.

NOTES
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(0) The Reading Rest has been in China a while and thus predictably been unable to edit or post anything on a WordPress.com blog. Now the Reading Rest is back.

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