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Author Topic: Numerical notations on Ptolemy I Soter’s gold staters  (Read 15974 times)

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Offline Altamura

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #75 on: October 15, 2020, 12:15:56 pm »
...  However, it is an IBE argument: inference to the best explanation, and there is nothing inherently wrong with such arguments.  The question is: Is your explanation of the phenomenon the best available? ...

The best explanation of all those lying on the table not automatically has to be the correct one. If it is not plausible and convincing, then I prefer to leave a question open than to believe in speculations.

Regards

Altamura


Offline PtolemAE

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #76 on: October 15, 2020, 01:53:25 pm »
As you can see, also in the text reported in the penultimate post we return a sampi, the archaic letter with which the number 900 was expressed, which confirms that we are in the presence of numbers, exactly as happens with the elephant gold stater

Did anyone else notice the T's are rather different ('roof' top and 'umbrella' top) ?  Maybe that's related to the papyrus (with the 'umbrella' T) dating from over 600 years later than the coin. Of course, even if they don't look the same they *could* nevertheless mean the same thing. The great strength of this theory is no one can disprove any of it :)

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Offline PtolemAE

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #77 on: October 15, 2020, 02:00:11 pm »
...  However, it is an IBE argument: inference to the best explanation, and there is nothing inherently wrong with such arguments.  The question is: Is your explanation of the phenomenon the best available? ...

The best explanation of all those lying on the table not automatically has to be the correct one. If it is not plausible and convincing, then I prefer to leave a question open than to believe in speculations.

Regards

Altamura



Plausible and convincing would definitely be helpful. Not to mention, falsifiable.


PtolemAE

Offline FEDERICO D

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #78 on: October 15, 2020, 03:15:00 pm »
...  However, it is an IBE argument: inference to the best explanation, and there is nothing inherently wrong with such arguments.  The question is: Is your explanation of the phenomenon the best available? ...

The best explanation of all those lying on the table not automatically has to be the correct one. If it is not plausible and convincing, then I prefer to leave a question open than to believe in speculations.

Regards

Altamura



it is clear that prudence is never too much but when there are many and many clues that lead us in one direction it would be negligent on our part to go in the opposite direction. A very strong clue in the direction of the numbers can for example be taken from the coinage of Massalia: look at how well these monograms reported on this issue of drachms are explained as a numerical sequence

Offline FEDERICO D

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #79 on: October 15, 2020, 03:19:48 pm »
Do you have doubts that the monograms on Massalia's coins are numbers? Then look what's on this other Massalia drachm..
on the right bottom, the sign interpreted like the letter  :Greek_Pi_3:  by Depeyrot and like  :Greek_Tau: :Greek_Lambda:
by Charra. But this sign is none other than a symbol, widely certified in ancient papyri, of the
talent’s monetary unit, corresponding 6,000 drachms. Practically, rather than indicating in figures
the first group of 6,000 drachms to mint in the new issue, it is preferred to introduce the astute
variation to indicate the symbol of the talent, which corresponds to 6,000 drachms.
To be sure that the talent symbol is correctly interpreted on the reverse of the coin no.1,
fig.no.31, the expression :Greek_Tau: :Greek_Alpha: :Greek_Lambda: is shown that, for once, is not a number but the initial part of the
word   :Greek_Tau::Greek_Alpha: :Greek_Lambda: :Greek_Alpha: :Greek_Nu: :Greek_Tau: :Greek_Omicron: :Greek_Nu:, “talent”, that is an alternative way to reaffirm the amount 6,000 drachms which
the mint was working on at the moment: more clearly than that…

Offline FEDERICO D

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #80 on: October 15, 2020, 03:27:42 pm »
the acronyms on the coins of this other issue, minted in 150-130 BC, are made up of
two overlapped elements, that clearly indicate that these elements are not letters but numbers and
have to be multiplied together, exactly as it was necessary to do with two numbers found in the
compound numbers in the Attic system (look at the excerpt on the Attic numbers below). The overlapped numbers in the numerical notation on the reverse of the coin no.1
no. 11 are 10 in the Attic system ( :Greek_Delta:) which multiplies with 20 in the Ionic system (K)18 to give as
the result 200 hundreds of drachms, that is 20,0(00) drachms. The numbers on the obverse and
reverse of the coin no.2, instead, are 7 in the Ionic system (Z) which multiplies with 5
in the same system (E); the result is 35 thousands of drachms, equal to 35(,000) drachms. On both
sides of the coin no.3 we have the number 5 of the Attic system ( :Greek_Pi:) x 10 of the same numeral
system ( :Greek_Delta:) with a result of 50 thousands of drachms, equal to 50(,000) drachms. The coin no.4
which closes the sequence always has on both sides the number 1,000 of the Attic system (X) that
multiplies with the number 100 (H) of the same numeral system with the result of 100,000 drachms,
the final issuing number.


if you want to read the whole article:
https://www.academia.edu/34086494/Federico_De_Luca_Alphabetical_numbering_and_numerical_progressions_on_drachms_and_Massalia_s_small_bronze_coins_Revue_Numismatique_OMNI_n_11_07_2017_p_74_111

Offline glebe

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #81 on: October 15, 2020, 05:43:39 pm »
This last post illustrates one of the obvious weaknesses of this whole number theory, namely the arbitrary scaling up of numbers by various factors of 10.

Thus coin 1 is read as  :Greek_Delta: :Greek_Kappa: = 10 x 20 = 200 = (magically) 20,000. And so on.

Anyway, if the engraver had wanted to say 20,000 why didn't he just put  :Greek_Kappa:  :Greek_Chi: = 20 x 1000?

The other major problem is the use of large numbers of different monograms to represent the same number.

With the Ptolemy I staters the first monogram used for 1,000,000 is  :Greek_Chi:  :Greek_Alpha: = 1000 x 1000, which seems reasonable (if you don't mind mixed alphabets), but then a whole bagful of complicated monograms are also supposed to mean the same number (with help from some extra 0's - see e.g. coins 25, 31, 33). Why?

(Curiously, with coin 34 we wind up back with our good old standby  :Greek_Chi:  :Greek_Alpha: for 1,000,000).

Ross G.

 

Offline FEDERICO D

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #82 on: October 15, 2020, 06:09:20 pm »
This last post illustrates one of the obvious weaknesses of this whole number theory, namely the arbitrary scaling up of numbers by various factors of 10.

Thus coin 1 is read as  :Greek_Delta: :Greek_Kappa: = 10 x 20 = 200 = (magically) 20,000. And so on.

Anyway, if the engraver had wanted to say 20,000 why didn't he just put  :Greek_Kappa:  :Greek_Chi: = 20 x 1000?

The other major problem is the use of large numbers of different monograms to represent the same number.

With the Ptolemy I staters the first monogram used for 1,000,000 is  :Greek_Chi:  :Greek_Alpha: = 1000 x 1000, which seems reasonable (if you don't mind mixed alphabets), but then a whole bagful of complicated monograms are also supposed to mean the same number (with help from some extra 0's - see e.g. coins 25, 31, 33). Why?

(Curiously, with coin 34 we wind up back with our good old standby  :Greek_Chi:  :Greek_Alpha: for 1,000,000).

Ross G.

 


This happens because with the basic numbers that you learn on school books you can compose an infinite number of numerical combinations as you please and like. Each numerical sequence has its own logic that must be understood case by case. The variety of ways in which the Greeks could express the same quantity was something that helped them to differentiate the coins obtained from minting marked with different monograms: the more different the monograms were, the easier it was to distinguish the resulting coins and the easier it was therefore to count them.
Even in the common language  the figures were expressed in tens (dekades),
hundreds (hekatontades), thousands (chiliades), tens of thousands (myriades) and hundreds of
thousands (dekakismyriades). For example, Lucian (Scytha 10) to nominate “the ten Attic orators”
says “ē Attikēdekas, which means “the Attic ten”; Plato (Phaedrus257) to indicate the 9,000 year
figure uses the expression “ennea chiliades etōn”, that means “nine thousand years”; Herodotus
(Histories 3,91) speaks about “myrias medìmnōn, “a myriad of medimnoi of wheat” to indicate “ten
thousands medimnoi of wheat”; in the Book of Daniel the Prophet has a vision of God in which
“thousands upon thousands (chiliai chiliades) were attending Him, and myriads upon myriads
(myriai myriades) were standing before Him” (Dn. ι,10); Plutarch (Marius 34) uses the expression
“myriadōn epta ēmisous priasthai”, “buy for seven and a half myriads (of drachms)”.


Offline FEDERICO D

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #83 on: October 15, 2020, 06:11:44 pm »
and how to explain the handover between these two "monetary magistrates" which always occurred at the same point but under different sovereigns (Demetrius I king of Bactria and his successor Euthydemus II)? Numbers, more numbers ...

Offline FEDERICO D

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #84 on: October 15, 2020, 06:21:40 pm »
Does issues of millions of drachms seem excessive to you? So how do you explain that certain ancient coins are still common today? In ancient times, much more money was minted than we can imagine and the monograms on the coins, interpreted as numbers, can help us understand better ..

Offline n.igma

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #85 on: October 15, 2020, 06:43:59 pm »
Please not that I intend  the following comments as constructive suggestions for consideration:

Mathematics
I think the key to understanding whether or not the hypothesis presented is plausible lies in a better explanation of the mathematics behind it in terms of what we know of the history of mathematics.

The hypothesis interprets the monograms as numerals to be multiplied in a decimal (base 10) algebraic system. https://en.wikipedia.org/wiki/Decimal

Yet the ancient Greeks used a sexagesimal system (base 60) that had its foundation in geometry. https://en.wikipedia.org/wiki/Decimal


The paper need needs to address these issues and reconcile the discrepancy in the mathematics.


Ancient accounting and the written sources
Another aspect to consider is that the ancient Greek sources consistently refer to expenditures in terms of talents (weight) of precious metal (silver or gold), an Attic talent being about 26 kg rather than quantities of drachms. https://en.wikipedia.org/wiki/Attic_talent

Under the circumstances the need for the mint to count drachms rather than to weigh the quantity of struck coinage is problematic in my opinion.

This discrepancy between written records of expenditures (talents) and the hypothesis (number of drachms) needs to be addressed in the paper.

Mint Process and controls
The primary concern of the mint was to strike coinage to the requisite standard (metal purity) and quantity (talents) specified by the king in a process that was so tightly controlled as to prevent malfeasance (precious metal pilferage, debasement etc). With gold at 10 times the value of silver this became a more substantial when striking gold coinage. It was a non-issue for low value bronze which as explained below is why bronze coinage does not exhibit the mint mark complexity of precious metal coinage and why it is frequently encountered that gold coinage has more mint marks than silver coinage.

In this context, the reconciliation of inputs (bulk precious metal) to output (struck coins) was the paramount concern and means of control. This could be achieved by simply weighing the output of coined metal on a daily basis and comparing it to the weight of precious metal allocated to a striking team on a daily basis.  No need to count coins - input and output weights is all that counts. Moreover, the volume to be coined at the requisite weights standard was specified by the king in weight (talents) of precious metal (be it gold or silver)

In the case of multiple anvils it would be necessary to identify with absolute certainty which coins were struck by which striking team to ensure valid reconciliation on a team by team basis. Hence the need for an additional mint mark (monogram, or symbol, or numeric dot sequence) designating each team and purpose cut reverse dies for use on each anvil. This explains the multiplicity of obverse die links observed in multi-anvil a striking for the obverse dies formed a shared inventory that can be used by different striking teams on different days, while reverse dies (i.e. bearing secondary and/or tertiary mint controls) are restricted use to a specific striking team each under supervision of an individual official designated by a discrete mint control (monogram, letter, symbol, or even a number sequence of dots). This explains Lorber's observations on the gold Ptolemaic coinage. For a more detailed exposition of this phenomenon in two eastern Alexander mints  https://www.academia.edu/37022091/The_Damaskos_Mint_of_Alexander_the_Great
and
https://www.academia.edu/37029265/The_Earliest_Alexander_III_Tetradrachm_Coinage_of_Babylon_Iconographic_Development_and_Chronology

Thus we end up with multiple mint marks - one designating the mint, one designating the most senior mint official and one designating the official over-sighting the striking on a specific anvil in a multi-anvil striking operation.

This is a very simple and fool proof system that identifies who was responsible for the struck coinage and in so doing provides the means for accurate reconciliation of inputs and outputs. Accurate identification of those responsible for the coinage at each stage of the operation acts as a deterrent against malfeasance and pilferage which was the mint's primary concern in acting on the king's instruction for coinage.


Suggestion
For the purpose of improved credibility, I think the paper on the numeric hypothesis of reading mint marks needs to canvas and reconcile to the background of ancient Greek mathematics, the written sources on the matter of expenditures and payments and competing theories of mint operational processes and controls.  

All historical inquiry is contingent and provisional, and our own prejudices will in due course come under scrutiny by our successors.

Offline Brennos

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #86 on: October 15, 2020, 07:16:24 pm »
Do you have doubts that the monograms on Massalia's coins are numbers? Then look what's on this other Massalia drachm..
on the right bottom, the sign interpreted like the letter  :Greek_Pi_3:  by Depeyrot and like  :Greek_Tau: :Greek_Lambda:
by Charra. But this sign is none other than a symbol, widely certified in ancient papyri, of the
talent’s monetary unit, corresponding 6,000 drachms. Practically, rather than indicating in figures
the first group of 6,000 drachms to mint in the new issue, it is preferred to introduce the astute
variation to indicate the symbol of the talent, which corresponds to 6,000 drachms.
To be sure that the talent symbol is correctly interpreted on the reverse of the coin no.1,
fig.no.31, the expression :Greek_Tau: :Greek_Alpha: :Greek_Lambda: is shown that, for once, is not a number but the initial part of the
word   :Greek_Tau::Greek_Alpha: :Greek_Lambda: :Greek_Alpha: :Greek_Nu: :Greek_Tau: :Greek_Omicron: :Greek_Nu:, “talent”, that is an alternative way to reaffirm the amount 6,000 drachms which
the mint was working on at the moment: more clearly than that…

Yes but with this TΑ monogram οn the obverse, you have a TAΛ monogram on the reverse  but also a ΑΖΑ, a ΕΔΒ, a ΠΗΑ, a ΗΑΤ, a ΚΠΤ, a ΛΑΔ...
How do you interpret them ?

Offline glebe

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #87 on: October 15, 2020, 10:12:32 pm »
It's worth noting (as Federico does in his main article) that not all the Ptolemy I staters have monograms on the reverse.
Coins 37 (below) and 38 have laurel(?) branches in the exergue instead.

Ross G.


Offline n.igma

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #88 on: October 15, 2020, 11:28:37 pm »
As Callatay says on the matter of interpreting mint controls context is everything:
 https://www.academia.edu/2350185/Control_marks_on_Hellenistic_royal_coinages_use_and_evolution_towards_simplification_Revue_belge_de_Numismatique_158_2012_p_39_62

And context (circumstances) in any mint was continuously evolving.

His concluding remarks in this definitive study are most instructive.
All historical inquiry is contingent and provisional, and our own prejudices will in due course come under scrutiny by our successors.

Offline FEDERICO D

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #89 on: October 16, 2020, 04:43:26 am »


Ancient accounting and the written sources
Another aspect to consider is that the ancient Greek sources consistently refer to expenditures in terms of talents (weight) of precious metal (silver or gold), an Attic talent being about 26 kg rather than quantities of drachms. https://en.wikipedia.org/wiki/Attic_talent

Under the circumstances the need for the mint to count drachms rather than to weigh the quantity of struck coinage is problematic in my opinion.

This discrepancy between written records of expenditures (talents) and the hypothesis (number of drachms) needs to be addressed in the paper.


The identified numerical notations on the coins always indicated amounts of money expressed in drachms, even if they were engraved on coinswith a higher value than a drachm (like tetradrachm) or even lower (like obol). That it dealt with drachms and not other monetary units 8as the talent) is confirmed by the complete reconstruction of issues (thefigures appear to be compatible with the number of dies belonging to the issue and with the numberof coins from those presumably generated) and also by the fact that in common parlance the largedigits used without any specification were implicitly referred to amounts in drachms. Thus in The Knights  (829) of Aristophanes, Paphlagon threats to denounce the Sausage-seller because he stole "treis myriades", that means thirty thousand (3 x 10,000) drachms: in fact, the expression treis myriades  implies drachmōn  that means "of drachms". The same does Plutarch in
 Marius  (34) using the expression "myriadōn epta ēmisuos priasthai" (buy for 7 myriads and a half) that implies "drachmōn" ("of drachms").

Offline FEDERICO D

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #90 on: October 16, 2020, 04:45:00 am »
Please not that I intend  the following comments as constructive suggestions for consideration:


Ancient accounting and the written sources
Another aspect to consider is that the ancient Greek sources consistently refer to expenditures in terms of talents (weight) of precious metal (silver or gold), an Attic talent being about 26 kg rather than quantities of drachms. https://en.wikipedia.org/wiki/Attic_talent

Under the circumstances the need for the mint to count drachms rather than to weigh the quantity of struck coinage is problematic in my opinion.

This discrepancy between written records of expenditures (talents) and the hypothesis (number of drachms) needs to be addressed in the paper.



The identified numerical notations on the coins always indicated amounts of money expressed in drachms, even if they were engraved on coins with a higher value than a drachm (like tetradrachm) or even lower (like obol). That it dealt with drachms and not other monetary units (as the talent) is confirmed by the complete reconstruction of issues (the figures appear to be compatible with the number of dies belonging to the issue and with the number of coins from those presumably generated) and also by the fact that in common parlance the large digits used without any specification were implicitly referred to amounts in drachms. Thus in The Knights  (829) of Aristophanes, Paphlagon threats to denounce the Sausage-seller because he stole "treis myriades", that means thirty thousand (3 x 10,000) drachms: in fact, the expression treis myriades  implies drachmōn  that means "of drachms". The same does Plutarch in
 Marius  (34) using the expression "myriadōn epta ēmisuos priasthai" (buy for 7 myriads and a half) that implies "drachmōn" ("of drachms").

Offline FEDERICO D

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #91 on: October 16, 2020, 05:26:02 am »
Please not that I intend  the following comments as constructive suggestions for consideration:

Mathematics
I think the key to understanding whether or not the hypothesis presented is plausible lies in a better explanation of the mathematics behind it in terms of what we know of the history of mathematics.

The hypothesis interprets the monograms as numerals to be multiplied in a decimal (base 10) algebraic system. https://en.wikipedia.org/wiki/Decimal

Yet the ancient Greeks used a sexagesimal system (base 60) that had its foundation in geometry. https://en.wikipedia.org/wiki/Decimal


The paper need needs to address these issues and reconcile the discrepancy in the mathematics.




Sexagesimal calculus was used in geometry but in the case of numerical notations on coins we have simple numerical notes, with methods widely attested in current practice. For example, the fact that two numbers side by side must be multiplied with each other, as widely assumed in my article is attested  by a schoolboy on a wax tablet in the VI-VII century AD, transcribed in fig.no.21. On this wax tablet, for example, the simple combination of the number  :Greek_Xi: (60) to the number  :Greek_Beta: (2) indicates that they are multiplied between each other giving the  :Greek_Rho: :Greek_Kappa: (120) result, reported immediately later; the juxtaposition of the number  :Greek_Xi: (60) to the number  :Greek_Gamma: (3) indicates that they multiply together with the  :Greek_Rho: :Greek_Pi_3: (180) result, diligently annotated on the side, and so on.

Source: https://www.academia.edu/36962445/F_De_Luca_Monograms_on_Kibyra_s_coins_names_or_numbers_Revue_Numismatique_OMNI_no_12_6_2018_pp_54_84

The nature of “the notes inside the mint” of the numerical notations explain why they were often not immediately comprehensible: it was not necessary that they had to be understood by the coin’s final users because they were not intended for them but only  for the mint staff that was aware of issue’s final edition and, therefore, of the decimal order implied by the numerical notation (for example OP = 1,000[,000] drachms) as well as the numeral system from which the different figures were composed. The inspiring criterion of numerical notations, therefore, was not their intelligibility by most, but their functionality and economy: this is why assembling them some figures could be left out, some others supposed or, with greater ease respect to other contexts, some were expressed using a numeral system and others using another numeral system in order to obtain a brief final figure, suitable for the coin’s limited space. The numerical notations reported on the coins were ultimately services notes like the ones we find today on our shopping lists where, for example, we write:

bread
sugar
3 water

   In this shopping list for “3 water” we actually mean “3 water boxes with 6 bottles for each box for a total of 18 bottles”: as it appears evident, rather than writing such a long expression it is much more practical to write “3 water” on a piece of paper where you write in a hurry without paying much attention to the form. Another thing would have been if the numerical notation would have indicated the coin’s facial value, like the figures brought on modern banknotes: in that case it would not have been conceivable simplifications, approximations or understood decimal orders but we know well that the Greek coin value was represented by its weight and was not indicated by the legend on it.

Offline FEDERICO D

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #92 on: October 16, 2020, 05:30:12 am »
It's worth noting (as Federico does in his main article) that not all the Ptolemy I staters have monograms on the reverse.
Coins 37 (below) and 38 have laurel(?) branches in the exergue instead.

Ross G.




Yes, the coins obtained from the last reverse die do not show a number but a symbol, just to emphasize that they are part of the last group of coins. In the article I report cases of this kind that occurred in other Greek mints

Offline FEDERICO D

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #93 on: October 16, 2020, 05:32:59 am »
As Callatay says on the matter of interpreting mint controls context is everything:
 https://www.academia.edu/2350185/Control_marks_on_Hellenistic_royal_coinages_use_and_evolution_towards_simplification_Revue_belge_de_Numismatique_158_2012_p_39_62

And context (circumstances) in any mint was continuously evolving.

His concluding remarks in this definitive study are most instructive.

it is clear that the context is very important. Indeed, Callatay's article is very instructive, it is a pity that it liquidates the monograms shown on many mints over a substantial period of time in a few pages. After reading this article we don't know much more about monograms ...

Offline FEDERICO D

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #94 on: October 16, 2020, 05:38:40 am »
Please not that I intend  the following comments as constructive suggestions for consideration:

Mint Process and controls
The primary concern of the mint was to strike coinage to the requisite standard (metal purity) and quantity (talents) specified by the king in a process that was so tightly controlled as to prevent malfeasance (precious metal pilferage, debasement etc). With gold at 10 times the value of silver this became a more substantial when striking gold coinage. It was a non-issue for low value bronze which as explained below is why bronze coinage does not exhibit the mint mark complexity of precious metal coinage and why it is frequently encountered that gold coinage has more mint marks than silver coinage.

In this context, the reconciliation of inputs (bulk precious metal) to output (struck coins) was the paramount concern and means of control. This could be achieved by simply weighing the output of coined metal on a daily basis and comparing it to the weight of precious metal allocated to a striking team on a daily basis.  No need to count coins - input and output weights is all that counts. Moreover, the volume to be coined at the requisite weights standard was specified by the king in weight (talents) of precious metal (be it gold or silver)

In the case of multiple anvils it would be necessary to identify with absolute certainty which coins were struck by which striking team to ensure valid reconciliation on a team by team basis. Hence the need for an additional mint mark (monogram, or symbol, or numeric dot sequence) designating each team and purpose cut reverse dies for use on each anvil. This explains the multiplicity of obverse die links observed in multi-anvil a striking for the obverse dies formed a shared inventory that can be used by different striking teams on different days, while reverse dies (i.e. bearing secondary and/or tertiary mint controls) are restricted use to a specific striking team each under supervision of an individual official designated by a discrete mint control (monogram, letter, symbol, or even a number sequence of dots). This explains Lorber's observations on the gold Ptolemaic coinage. For a more detailed exposition of this phenomenon in two eastern Alexander mints  https://www.academia.edu/37022091/The_Damaskos_Mint_of_Alexander_the_Great
and
https://www.academia.edu/37029265/The_Earliest_Alexander_III_Tetradrachm_Coinage_of_Babylon_Iconographic_Development_and_Chronology

Thus we end up with multiple mint marks - one designating the mint, one designating the most senior mint official and one designating the official over-sighting the striking on a specific anvil in a multi-anvil striking operation.

This is a very simple and fool proof system that identifies who was responsible for the struck coinage and in so doing provides the means for accurate reconciliation of inputs and outputs. Accurate identification of those responsible for the coinage at each stage of the operation acts as a deterrent against malfeasance and pilferage which was the mint's primary concern in acting on the king's instruction for coinage.


Suggestion
For the purpose of improved credibility, I think the paper on the numeric hypothesis of reading mint marks needs to canvas and reconcile to the background of ancient Greek mathematics, the written sources on the matter of expenditures and payments and competing theories of mint operational processes and controls.  




We don't have to worry about what it should have been based on inductive reconstructions but what appears to our eyes from the coins. The preconceptions must not lead to not seeing the numbers that in some cases jump out of the coins with all evidence and we must ask ourselves the problem of understanding their function.
Then I am not able to solve all the unsolved problems of numismatics and Greek archeology but I bring your attention back to a very limited aspect which, however, if properly understood, can throw light on many aspects still unknown to us.




Offline FEDERICO D

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #95 on: October 16, 2020, 09:00:11 am »
Do you have doubts that the monograms on Massalia's coins are numbers? Then look what's on this other Massalia drachm..
on the right bottom, the sign interpreted like the letter  :Greek_Pi_3:  by Depeyrot and like  :Greek_Tau: :Greek_Lambda:
by Charra. But this sign is none other than a symbol, widely certified in ancient papyri, of the
talent’s monetary unit, corresponding 6,000 drachms. Practically, rather than indicating in figures
the first group of 6,000 drachms to mint in the new issue, it is preferred to introduce the astute
variation to indicate the symbol of the talent, which corresponds to 6,000 drachms.
To be sure that the talent symbol is correctly interpreted on the reverse of the coin no.1,
fig.no.31, the expression :Greek_Tau: :Greek_Alpha: :Greek_Lambda: is shown that, for once, is not a number but the initial part of the
word   :Greek_Tau::Greek_Alpha: :Greek_Lambda: :Greek_Alpha: :Greek_Nu: :Greek_Tau: :Greek_Omicron: :Greek_Nu:, “talent”, that is an alternative way to reaffirm the amount 6,000 drachms which
the mint was working on at the moment: more clearly than that…

Yes but with this TΑ monogram οn the obverse, you have a TAΛ monogram on the reverse  but also a ΑΖΑ, a ΕΔΒ, a ΠΗΑ, a ΗΑΤ, a ΚΠΤ, a ΛΑΔ...
How do you interpret them ?


Source: https://www.academia.edu/34086494/Federico_De_Luca_Alphabetical_numbering_and_numerical_progressions_on_drachms_and_Massalia_s_small_bronze_coins_Revue_Numismatique_OMNI_n_11_07_2017_p_74_111

Offline glebe

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #96 on: October 16, 2020, 10:00:55 pm »
Do you have doubts that the monograms on Massalia's coins are numbers? Then look what's on this other Massalia drachm..
on the right bottom, the sign interpreted like the letter  :Greek_Pi_3:  by Depeyrot and like  :Greek_Tau: :Greek_Lambda:
by Charra. But this sign is none other than a symbol, widely certified in ancient papyri, of the
talent’s monetary unit, corresponding 6,000 drachms. Practically, rather than indicating in figures
the first group of 6,000 drachms to mint in the new issue, it is preferred to introduce the astute
variation to indicate the symbol of the talent, which corresponds to 6,000 drachms.
To be sure that the talent symbol is correctly interpreted on the reverse of the coin no.1,
fig.no.31, the expression :Greek_Tau: :Greek_Alpha: :Greek_Lambda: is shown that, for once, is not a number but the initial part of the
word   :Greek_Tau::Greek_Alpha: :Greek_Lambda: :Greek_Alpha: :Greek_Nu: :Greek_Tau: :Greek_Omicron: :Greek_Nu:, “talent”, that is an alternative way to reaffirm the amount 6,000 drachms which
the mint was working on at the moment: more clearly than that…

But a tranche of only 6000 coins sounds unlikely - it would hardly be worth the trouble of accounting for it separately. It seems you need to throw in at least one of those ever useful factors of ten.

Where else by the way can I find the "talent' symbol on the obverse?

Ross G.

Offline FEDERICO D

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #97 on: October 17, 2020, 08:35:00 am »
Do you have doubts that the monograms on Massalia's coins are numbers? Then look what's on this other Massalia drachm..
on the right bottom, the sign interpreted like the letter  :Greek_Pi_3:  by Depeyrot and like  :Greek_Tau: :Greek_Lambda:
by Charra. But this sign is none other than a symbol, widely certified in ancient papyri, of the
talent’s monetary unit, corresponding 6,000 drachms. Practically, rather than indicating in figures
the first group of 6,000 drachms to mint in the new issue, it is preferred to introduce the astute
variation to indicate the symbol of the talent, which corresponds to 6,000 drachms.
To be sure that the talent symbol is correctly interpreted on the reverse of the coin no.1,
fig.no.31, the expression :Greek_Tau: :Greek_Alpha: :Greek_Lambda: is shown that, for once, is not a number but the initial part of the
word   :Greek_Tau::Greek_Alpha: :Greek_Lambda: :Greek_Alpha: :Greek_Nu: :Greek_Tau: :Greek_Omicron: :Greek_Nu:, “talent”, that is an alternative way to reaffirm the amount 6,000 drachms which
the mint was working on at the moment: more clearly than that…

But a tranche of only 6000 coins sounds unlikely - it would hardly be worth the trouble of accounting for it separately. It seems you need to throw in at least one of those ever useful factors of ten.

Where else by the way can I find the "talent' symbol on the obverse?

Ross G.

What sounds strange to us does not necessarily sound strange to them too.
The numerical notations noted on the coin did not follow rigid rules and varied from mint to mint and, within the same mint, from issue to issue. They were conceived with a situational criterion, dictated by the needs of the moment. In the issue studied in my article posted at the beginning of this topic, for example, we have a tranche ranging from 90,000 to 150,000 states marked by a symbol that certainly appears to be numerical. From an abstract logical point of view it would have been better to write "100,000 to 150,000 staters" but in this way, evidently, the 10,000 staters missing to 90,000 to reach the 100,000 staters of our abstract ideal indication remained unaccounted for.
In the case of Massalia's coin from the previous post, the symbol of talent perhaps distinguished the initial part of the issue.
So far I haven't found any other Talent symbols on any other coins.

Offline FEDERICO D

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #98 on: October 17, 2020, 08:47:16 am »
And look at these "monetary magistrates" who sign these gold staters in the name of Alexander the Great minted in Abydos: strangely they always follow one another at the same point. Instead, these are numbers that indicate the progression of the issue: on the second coin of each issue a second symbol (pentagram) is added to the main symbol to underline that we are in the final part of the same.

Offline FEDERICO D

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Re: Numerical notations on Ptolemy I Soter’s gold staters
« Reply #99 on: October 17, 2020, 08:54:55 am »

Do you doubt that on the coins of the previous post the monograms are numbers? Then look at this other stater always coined in Abydos. On the second coin the monogram changes but the indicated figure is always the same. This time to indicate that the monogram shown on the second coin is a number, a point appears, a diacritical mark that warns the reader that it is a number and not a compendium of letters.

 

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