Numerical notations on Ptolemy I Soter’s gold staters

[Molinari]

I wonder if an examination of earlier Near Eastern craft workshops would be useful for understanding the inner workings of later Greek mint workshops?  We know surprisingly very much about how the Mesopotamians operated from extant cuneiform tablets—how raw materials were deposited at a workshop, how they moved within a workshop, and how they exited.  The tablet envelopes usually have the seal of the major domo (administrative head) as well as the type of goods all written on the “exit” envelope. Not sure what the inner tablets said (mine is still sealed), but presumably the exact quantity of goods so that whoever was in charge of delivery couldn’t rewrite the inscription in the clay.

[n.igma]

But then can you explain to me what was the point of reporting the symbol of talent on that coin? Please write down a hypothesis ..

That is what you interpret it to be. Equally as much it may be just another mint mark composed of Greek letters, an abbreviation of a name or some other word.

[n.igma]

Let's do something. I have presented an explanation of the monograms. You do not like? I'm sorry I can't help it. I tried my best to demonstrate what I say as precisely as possible and my absolute good faith in conceiving this theory of mine. I only receive piqued criticisms, not based on any historical data, document or specific currency (in fact, here we are talking about coins).
If my theory does not convince you, I am sorry but I will certainly not make an illness of it because my satisfaction has already consisted in writing it and this topic can be closed here.
You persist in saying that "it would have been better", "it would have been more logical ..."; in short, you want to explain the facts with a mental order longed for in your mind.
I also have the feeling that here I can post the impossible because it is not read so it is perfectly useless for me to continue doing it. You don't agree with my statements?
I'm not asking you to counter point by point, image by image to what I said, but at least post an ancient text, an image, a coin that confirms what you say and I will believe you.

I am simply responding to each of the questions/challenges you post in reply to my observations.

[FEDERICO D]

I wonder if an examination of earlier Near Eastern craft workshops would be useful for understanding the inner workings of later Greek mint workshops?  We know surprisingly very much about how the Mesopotamians operated from extant cuneiform tablets—how raw materials were deposited at a workshop, how they moved within a workshop, and how they exited.  The tablet envelopes usually have the seal of the major domo (administrative head) as well as the type of goods all written on the “exit” envelope. Not sure what the inner tablets said (mine is still sealed), but presumably the exact quantity of goods so that whoever was in charge of delivery couldn’t rewrite the inscription in the clay.

if we could find such information for the Greek world, we would stop arguing here

[FEDERICO D]

But then can you explain to me what was the point of reporting the symbol of talent on that coin? Please write down a hypothesis ..

That is what you interpret it to be. Equally as much it may be just another mint mark composed of Greek letters, an abbreviation of a name or some other word.

No comment.

[FEDERICO D]

Let's do something. I have presented an explanation of the monograms. You do not like? I'm sorry I can't help it. I tried my best to demonstrate what I say as precisely as possible and my absolute good faith in conceiving this theory of mine. I only receive piqued criticisms, not based on any historical data, document or specific currency (in fact, here we are talking about coins).
If my theory does not convince you, I am sorry but I will certainly not make an illness of it because my satisfaction has already consisted in writing it and this topic can be closed here.
You persist in saying that "it would have been better", "it would have been more logical ..."; in short, you want to explain the facts with a mental order longed for in your mind.
I also have the feeling that here I can post the impossible because it is not read so it is perfectly useless for me to continue doing it. You don't agree with my statements?
I'm not asking you to counter point by point, image by image to what I said, but at least post an ancient text, an image, a coin that confirms what you say and I will believe you.

I am simply responding to each of the questions/challenges you post in reply to my observations.

No challenge. Since the time of the Greek philosophers if a person disputes a thesis he must provide an alternative, complete, detailed and exhaustive thesis to explain these same phenomena analyzed by the first man. Otherwise we only have a broken down series of no ..

[FEDERICO D]

OK stop. I give up. I acknowledge that I have not convinced you. Excuse me again if I disturbed you. Forgive me.
Shall we kindly end this topic? Thank you
Good life.

[glebe]

I agree with n.igma – I don’t see how labelling tranches of coins with the number of coins helps much with accounting.

And even if it did you wouldn’t do it in the obscure, varying and inconsistent manner assumed by Federico – you would surely mark the first 10,000 coins (or more likely the first talent weight of coins) as A, the second as B, and so on, plus maybe the symbol for 10,000 or whatever.

Or at least something simple and straightforward like that.

Ross G.

But then can you explain to me what was the point of reporting the symbol of talent on that coin? Please write down a hypothesis ..
Let me understand you see the symbol of talent on the papyrus and believe it is the symbol of talent; you see it on the coin and it is no longer the symbol of talent. But what coherence is it?
And if by chance, in a rush of objectivity, you would like to recognize that on the coin there is precisely the symbol of talent, a mathematical symbol therefore, isn't it a logical consequence to ask ourselves about its meaning, which seems to suggest a numerical solution? Tell me why at this point maybe I think I'm really crazy and draw conclusions at random ...

OK, how about this - the talent sign indicates a tranche of 1 talent weight of coins - about 10,000 of these light Massalia drachms, if they used the Attic talent.

This immediately suggests that each tranche was normally struck from only one set of dies, apart from occasional breakages, with perhaps the reverse dies individually marked to distinguish each tranche. It would be interesting to see some die statistics for these types.  

At last we have testable hypothesis.

Ross G.

[PtolemAE]

But you're the one proposing that coin counting via mathematical gymnastics to identify "groups" of coins "make it possible to verify that the entire quantity of precious metal received at the beginning of the minting of the issue was transformed into coins."

But as shown by the example, it does no such thing!

It is weight of the total striikng not numbers of coins that affords such an opportunity of verification.

but in fact I have never ruled out checks on the weight of the coins too, which is one of the main functions of the monetary magistrates. Monograms intended as numbers facilitated them in this task because thanks to the division of the issue into groups identified by different monograms they immediately had an eye on the control of the completed issue and in this way they could devote themselves better to weight checks, perhaps with random checks carried out in front of the authority to which they delivered the completed issue

Now seek to move the goal posts as well!

Methinks you are seeking to defend the indefensible hypothesis.

It was certain the critical analysis of this theory's astonishing weakness would be joined.

The more that skeptical scrutiny slices away at what little is left of this 'theory', the more strenuous its author's defense. Cognitive dissonance can make it hard to cede even the obvious.

Nevertheless, the author can defend it ad infinitum because it can't be disproved and no amount of cogent argument to the contrary will suffice. These kinds of 'theories' are encountered in other fields as well, and their adherents are almost never dissuaded by critical scrutiny.

As for the weights of gold coins, there is actually some evidence about them we can theorize about. A huge die study of some Ptolemaic gold coin types (in RBN a few years ago by Olivier and Lorber) has weights of hundreds, spanning very narrow ranges (my recollection is many vary by  much less than 1%). Just a notion, but you could balance finely divided tiny gold shot (used by goldsmiths to this day), filings or dust with a single fixed weight to create almost exactly equal allotments of metal to melt into beads of almost exactly equal weight for striking. It would be hard to 'lose' much that way. The real gold coin weights are so close that it seems immaterial whether they were counted or weighed to account for the gold input. Simple to just do both

PtolemAE

[Mark Fox]

Dear Mr. De Luca and Board,

You may or may not know me as the person who reviewed your Ptolemaic stater paper as a KOINON submission.  As you rightly described, there has been a torrent of discussion here concerning your theory, but we do not seem to be making much progress in the direction(s) we are going.  Personally, I (and maybe Ross to a certain extent) are impressed with your possible talent symbol discovery.  It does seem like you are on the trail of something fascinating, but what lies ahead is most likely not the picture you have labored in great detail to illustrate in your writings.  I say this based my editorial critique of your work, which raised a couple of points I failed so far to see discussed in this thread, but which I feel are of utmost importance to the validity of your core arguments.   Perhaps I simply missed them (quite possible), but I did not see any of the alluded concerns with you research addressed in the later published OMNI version of your paper.  With that in mind, I would be grateful if you could now address my points (reproduced below among others you are probably tired of hearing!) and shift this whole discussion in a hopefully more fruitful direction.
  
"We will begin with the most problematic.  In his plates, we have six gold (not golden!) staters of Ptolemy I Soter bearing the obverse die 'O8' (Nos. 12-14 & 20-22), coupled with five reverse dies, each of which represents a new, increasing numerical sequence, according to De Luca's interpretations.  The obverse of the first coin (#12) bears a die chip on the forehead of the king, which is obviously not present on #21.  Likewise, we have a very noticeable die chip in front of Ptolemy's nose on coin #13 which is nowhere to be found on #20 and probably #21.  In terms of overall obverse die wear, nos. 20 & 21 look the most fresh to my eyes.  None of this should be the case if the different numerical lettered/monogrammed reverses are supposed to denote increasing values.

"To arrive at the numerical values for the letters and monograms found on the gold staters presented in the article, De Luca has relied on not one, but three different Greek numbering systems.  In some cases, all three are purportedly represented on a single coin.  In support of this astonishing claim, he cites a few, albeit very intriguing, written examples (on page 8 of his article) where numbers and calculations were indeed apparently expressed sometimes in more than one Greek numbering system.  Although I have not investigated the matter to my satisfaction, there nevertheless seems to be logical geographical and cultural relationships underpinning the the use of the numbering systems in those examples.  I am not so sure if such (or similar) traditions and practices can be applied so evenly across the whole Greek world as De Luca seems to suggest when his body of research on numerical letters and monograms is taken as a whole.  Whether he is talking about the letters and monograms on Massalian drachms (in a different article) or Ptolemaic staters, he interprets them in the same basic way, where the die cutters would regularly utilize more than one numbering system in a seemingly less than standardized manner.  When it comes to Ptolemaic and Roman Egypt, there is a considerable surviving corpus of papyrus scrolls, some of which no doubt record ancient mathematical calculations.  Has he consulted this vast resource to discern which numbering system(s) were in common use in that part of the Greek world?        

"My apologies in advance if I have misunderstood De Luca or missed a relevant passage, but from the article in question, he seems to envision the minting process of the Ptolemaic staters in a very linear fashion, with little room for more than one pair of dies being put into service at a time.  I would think one of the number one priorities at any mint, ancient or modern, is to get the job done as quickly as possible, without needlessly dragging the process on.  However, if De Luca's reasoning is true, then I would see difficulties in having more than one team of minters at work at the same time.  Would they all be striking coins within the same sequence, or would one team skip ahead to the next one?  Or perhaps there were two independent lines servicing two separate orders for coins at the same time.  But, if this is the case, then the ability for us to determine roughly how many coins were minted of a single issue falls apart, because we suddenly no longer know if, say, 300,000 staters was the end goal or 600,000.

"And, to top everything off, I fail to see the explicit need to publicly mark all the dies of a coin issue so as to keep track of how many were minted.  If the mint knew how much raw metal they started out with each time, then they would have a good idea of many coins it would produce.  Moreover, if mint workers were really packing the coins in labeled bags, a theory that De Luca could well be correct about, then that further decreases the need to mark every coin with a complex system of numerical symbols---unless there was a more important reason for their existence."

For convenience, here is the link again to De Luca's OMNI paper:
https://www.academia.edu/43928165/F_De_Luca_Numerical_notations_on_Ptolemy_I_Soter_s_gold_staters_Revue_Numismatique_OMNI_no_14_08_2020_pp_31_69

Also, since writing this review, I am not as certain about the existence of the obverse die chip on coin no. 12, but my other coin die observations remain to be explained.

Thank you for your time and effort in trying to make sense of this poorly understood field of numismatics.  If your motive for doing so is to get to the truth of the matter, then you will never be truly disappointed where the trail of evidence will lead you.  
    

Best regards,

Mark Fox
Michigan  

[FEDERICO D]

Dear Mr. De Luca and Board,

You may or may not know me as the person who reviewed your Ptolemaic stater paper as a KOINON submission.  As you rightly described, there has been a torrent of discussion here concerning your theory, but we do not seem to be making much progress in the direction(s) we are going.  Personally, I (and maybe Ross to a certain extent) are impressed with your possible talent symbol discovery.  It does seem like you are on the trail of something fascinating, but what lies ahead is most likely not the picture you have labored in great detail to illustrate in your writings.  I say this based my editorial critique of your work, which raised a couple of points I failed so far to see discussed in this thread, but which I feel are of utmost importance to the validity of your core arguments.   Perhaps I simply missed them (quite possible), but I did not see any of the alluded concerns with you research addressed in the later published OMNI version of your paper.  With that in mind, I would be grateful if you could now address my points (reproduced below among others you are probably tired of hearing!) and shift this whole discussion in a hopefully more fruitful direction.
  
"We will begin with the most problematic.  In his plates, we have six gold (not golden!) staters of Ptolemy I Soter bearing the obverse die 'O8' (Nos. 12-14 & 20-22), coupled with five reverse dies, each of which represents a new, increasing numerical sequence, according to De Luca's interpretations.  The obverse of the first coin (#12) bears a die chip on the forehead of the king, which is obviously not present on #21.  Likewise, we have a very noticeable die chip in front of Ptolemy's nose on coin #13 which is nowhere to be found on #20 and probably #21.  In terms of overall obverse die wear, nos. 20 & 21 look the most fresh to my eyes.  None of this should be the case if the different numerical lettered/monogrammed reverses are supposed to denote increasing values.

"To arrive at the numerical values for the letters and monograms found on the gold staters presented in the article, De Luca has relied on not one, but three different Greek numbering systems.  In some cases, all three are purportedly represented on a single coin.  In support of this astonishing claim, he cites a few, albeit very intriguing, written examples (on page 8 of his article) where numbers and calculations were indeed apparently expressed sometimes in more than one Greek numbering system.  Although I have not investigated the matter to my satisfaction, there nevertheless seems to be logical geographical and cultural relationships underpinning the the use of the numbering systems in those examples.  I am not so sure if such (or similar) traditions and practices can be applied so evenly across the whole Greek world as De Luca seems to suggest when his body of research on numerical letters and monograms is taken as a whole.  Whether he is talking about the letters and monograms on Massalian drachms (in a different article) or Ptolemaic staters, he interprets them in the same basic way, where the die cutters would regularly utilize more than one numbering system in a seemingly less than standardized manner.  When it comes to Ptolemaic and Roman Egypt, there is a considerable surviving corpus of papyrus scrolls, some of which no doubt record ancient mathematical calculations.  Has he consulted this vast resource to discern which numbering system(s) were in common use in that part of the Greek world?        

"My apologies in advance if I have misunderstood De Luca or missed a relevant passage, but from the article in question, he seems to envision the minting process of the Ptolemaic staters in a very linear fashion, with little room for more than one pair of dies being put into service at a time.  I would think one of the number one priorities at any mint, ancient or modern, is to get the job done as quickly as possible, without needlessly dragging the process on.  However, if De Luca's reasoning is true, then I would see difficulties in having more than one team of minters at work at the same time.  Would they all be striking coins within the same sequence, or would one team skip ahead to the next one?  Or perhaps there were two independent lines servicing two separate orders for coins at the same time.  But, if this is the case, then the ability for us to determine roughly how many coins were minted of a single issue falls apart, because we suddenly no longer know if, say, 300,000 staters was the end goal or 600,000.

"And, to top everything off, I fail to see the explicit need to publicly mark all the dies of a coin issue so as to keep track of how many were minted.  If the mint knew how much raw metal they started out with each time, then they would have a good idea of many coins it would produce.  Moreover, if mint workers were really packing the coins in labeled bags, a theory that De Luca could well be correct about, then that further decreases the need to mark every coin with a complex system of numerical symbols---unless there was a more important reason for their existence."

For convenience, here is the link again to De Luca's OMNI paper:
https://www.academia.edu/43928165/F_De_Luca_Numerical_notations_on_Ptolemy_I_Soter_s_gold_staters_Revue_Numismatique_OMNI_no_14_08_2020_pp_31_69

Also, since writing this review, I am not as certain about the existence of the obverse die chip on coin no. 12, but my other coin die observations remain to be explained.

Thank you for your time and effort in trying to make sense of this poorly understood field of numismatics.  If your motive for doing so is to get to the truth of the matter, then you will never be truly disappointed where the trail of evidence will lead you.  
    

Best regards,

Mark Fox
Michigan  

Dear  Mr. Fox, thanks for your speech.
Not even I am sure that on my coin no. 12 there is a die chip that is not present on coin no. 21. instead, the clearly visible dot on coin no.13 is not visible on coins no.20 and 21 but is clearly visible on no.22. This can easily be due to my misinterpretation of the monograms. For example, the monogram TI present on coin n.21 and which I have dissolved as 300 (T) x 10 (I) = 300,0(00) staters, perhaps in reality, however, it should have been understood as 30,00(0) staters. In this new interpretation, therefore, the sequence should be reviewed and coins # 20 and 21 placed at the beginning of the sequence. But the general discourse changes little because the sequence could be wrong but not the final limit of the issue, its final edition. My mistake could be a consequence of the difficulty of interpreting monograms and this case makes it very clear how difficult it is to do it. I have often been accused in this discussion of adjusting the numbers to my liking and surely this episode will give my critics fresh breath. To those without prejudice, however, I hope that paradoxically it is a confirmation of my good faith, because the possible error calls into question the order of the numerical sequence but not the numerical sequence itself and its supposed limit, which is not questioned.
In conclusion, this is a (possible) error that does not undermine the whole system of theory or "theory" as some insist on pointing out.

[FEDERICO D]

But you're the one proposing that coin counting via mathematical gymnastics to identify "groups" of coins "make it possible to verify that the entire quantity of precious metal received at the beginning of the minting of the issue was transformed into coins."

But as shown by the example, it does no such thing!

It is weight of the total striikng not numbers of coins that affords such an opportunity of verification.

but in fact I have never ruled out checks on the weight of the coins too, which is one of the main functions of the monetary magistrates. Monograms intended as numbers facilitated them in this task because thanks to the division of the issue into groups identified by different monograms they immediately had an eye on the control of the completed issue and in this way they could devote themselves better to weight checks, perhaps with random checks carried out in front of the authority to which they delivered the completed issue

Now seek to move the goal posts as well!

Methinks you are seeking to defend the indefensible hypothesis.

The only thing astonishing is your stubbornness in criticizing me without bringing a shred of evidence to back up your claims

[FEDERICO D]

But you're the one proposing that coin counting via mathematical gymnastics to identify "groups" of coins "make it possible to verify that the entire quantity of precious metal received at the beginning of the minting of the issue was transformed into coins."

But as shown by the example, it does no such thing!

It is weight of the total striikng not numbers of coins that affords such an opportunity of verification.

but in fact I have never ruled out checks on the weight of the coins too, which is one of the main functions of the monetary magistrates. Monograms intended as numbers facilitated them in this task because thanks to the division of the issue into groups identified by different monograms they immediately had an eye on the control of the completed issue and in this way they could devote themselves better to weight checks, perhaps with random checks carried out in front of the authority to which they delivered the completed issue

Now seek to move the goal posts as well!

Methinks you are seeking to defend the indefensible hypothesis.

It was certain the critical analysis of this theory's astonishing weakness would be joined.

The more that skeptical scrutiny slices away at what little is left of this 'theory', the more strenuous its author's defense. Cognitive dissonance can make it hard to cede even the obvious.

Nevertheless, the author can defend it ad infinitum because it can't be disproved and no amount of cogent argument to the contrary will suffice. These kinds of 'theories' are encountered in other fields as well, and their adherents are almost never dissuaded by critical scrutiny.

As for the weights of gold coins, there is actually some evidence about them we can theorize about. A huge die study of some Ptolemaic gold coin types (in RBN a few years ago by Olivier and Lorber) has weights of hundreds, spanning very narrow ranges (my recollection is many vary by  much less than 1%). Just a notion, but you could balance finely divided tiny gold shot (used by goldsmiths to this day), filings or dust with a single fixed weight to create almost exactly equal allotments of metal to melt into beads of almost exactly equal weight for striking. It would be hard to 'lose' much that way. The real gold coin weights are so close that it seems immaterial whether they were counted or weighed to account for the gold input. Simple to just do both

PtolemAE

The only thing astonishing is your stubbornness in criticizing me without bringing a shred of evidence to back up your claims

[FEDERICO D]

I agree with n.igma – I don’t see how labelling tranches of coins with the number of coins helps much with accounting.

And even if it did you wouldn’t do it in the obscure, varying and inconsistent manner assumed by Federico – you would surely mark the first 10,000 coins (or more likely the first talent weight of coins) as A, the second as B, and so on, plus maybe the symbol for 10,000 or whatever.

Or at least something simple and straightforward like that.

Ross G.

But then can you explain to me what was the point of reporting the symbol of talent on that coin? Please write down a hypothesis ..
Let me understand you see the symbol of talent on the papyrus and believe it is the symbol of talent; you see it on the coin and it is no longer the symbol of talent. But what coherence is it?
And if by chance, in a rush of objectivity, you would like to recognize that on the coin there is precisely the symbol of talent, a mathematical symbol therefore, isn't it a logical consequence to ask ourselves about its meaning, which seems to suggest a numerical solution? Tell me why at this point maybe I think I'm really crazy and draw conclusions at random ...

OK, how about this - the talent sign indicates a tranche of 1 talent weight of coins - about 10,000 of these light Massalia drachms, if they used the Attic talent.

This immediately suggests that each tranche was normally struck from only one set of dies, apart from occasional breakages, with perhaps the reverse dies individually marked to distinguish each tranche. It would be interesting to see some die statistics for these types.  

At last we have testable hypothesis.

Ross G.

And how do they verify the weight of these 10,000 coins? they certainly could not load them on a truck and take it to the weighbridge...

[FEDERICO D]

I agree with n.igma – I don’t see how labelling tranches of coins with the number of coins helps much with accounting.



At last we have testable hypothesis.

Ross G.

And how do you explain everything else, all the other monograms, coin sequences etc? For years I have exhausted myself looking everywhere, since August 30 I have been struggling with this topic and you with this simple statement have solved all the puzzles? But well ..

[FEDERICO D]

I agree with n.igma – I don’t see how labelling tranches of coins with the number of coins helps much with accounting.

And even if it did you wouldn’t do it in the obscure, varying and inconsistent manner assumed by Federico – you would surely mark the first 10,000 coins (or more likely the first talent weight of coins) as A, the second as B, and so on, plus maybe the symbol for 10,000 or whatever.

Or at least something simple and straightforward like that.

Ross G.

But then can you explain to me what was the point of reporting the symbol of talent on that coin? Please write down a hypothesis ..
Let me understand you see the symbol of talent on the papyrus and believe it is the symbol of talent; you see it on the coin and it is no longer the symbol of talent. But what coherence is it?
And if by chance, in a rush of objectivity, you would like to recognize that on the coin there is precisely the symbol of talent, a mathematical symbol therefore, isn't it a logical consequence to ask ourselves about its meaning, which seems to suggest a numerical solution? Tell me why at this point maybe I think I'm really crazy and draw conclusions at random ...

OK, how about this - the talent sign indicates a tranche of 1 talent weight of coins - about 10,000 of these light Massalia drachms, if they used the Attic talent.

This immediately suggests that each tranche was normally struck from only one set of dies, apart from occasional breakages, with perhaps the reverse dies individually marked to distinguish each tranche. It would be interesting to see some die statistics for these types.  

At last we have testable hypothesis.

Ross G.

And how do you explain everything else, all the other monograms, coin sequences etc? For years I have exhausted myself looking everywhere, since August 30 I have been struggling with this topic and you with this simple statement have solved all the puzzles? But well ..

[Molinari]

Here is the Garsana workshop.  Now reimagine with different metals and each branch (like an officina) within the workshop is charged with a different series or denomination.  You'd have room for the major officiant's title (here Adad-tilati) but also the "officina" head, (here Ana-Ili for leather).  This would allow for many different names to be included on the varieties via monograms. And yet, it might also allow for numbers to be included as well. My question is: would there be some practical use for having the number of coins issued on the coins themselves?  The immediate practical concern for theft is solved by n.igma's explanation.  But what about accounting records for an empire?  Would it be useful on the marco-level, in other words, to have the coins themselves carry that number?

Just thinking about some common ground among all the different theories I am reading here--which I admit, I am too stupid to fully understand!

[PtolemAE]

...

... Since the time of the Greek philosophers if a person disputes a thesis he must provide an alternative, complete, detailed and exhaustive thesis to explain these same phenomena analyzed by the first man. Otherwise we only have a broken down series of no ..

Compounding the nonsense doesn't improve it.

The analysis is astonishingly weak, so the theory is not believable. It's that simple.

PtolemAE

[FEDERICO D]

...

... Since the time of the Greek philosophers if a person disputes a thesis he must provide an alternative, complete, detailed and exhaustive thesis to explain these same phenomena analyzed by the first man. Otherwise we only have a broken down series of no ..

Compounding the nonsense doesn't improve it.

The analysis is astonishingly weak, so the theory is not believable. It's that simple.

PtolemAE

Then the Greeks had nothing better to do than put letters haphazardly on the coins, that is to say in a space of a few centimeters ...

[FEDERICO D]

Here is the Garsana workshop.  Now reimagine with different metals and each branch (like an officina) within the workshop is charged with a different series or denomination.  You'd have room for the major officiant's title (here Adad-tilati) but also the "officina" head, (here Ana-Ili for leather).  This would allow for many different names to be included on the varieties via monograms. And yet, it might also allow for numbers to be included as well. My question is: would there be some practical use for having the number of coins issued on the coins themselves?  The immediate practical concern for theft is solved by n.igma's explanation.  But what about accounting records for an empire?  Would it be useful on the marco-level, in other words, to have the coins themselves carry that number?

Just thinking about some common ground among all the different theories I am reading here--which I admit, I am too stupid to fully understand!

In my opinion, to solve the enigma of these monograms one should not ask oneself if it is logical to write numbers on the coins or if it was no longer logical to bear the bill in mind or if it was cumbersome as a system. We must start from the objective reality of the monograms and ask ourselves, even before WHAT THEY WERE FOR, WHAT THEY WERE. I'm killing myself to convince you that they are numbers and appear to be numbers on the basis of various objective elements. After seeing that they can be numbers we have to move on to ask ourselves what they were for and I propose that they were used to:
-they helped to carry the bill of coins gradually minted;
-having the quantitative control of the coins that were included in the issue, by randomly checking only some coins, it was also easy to check the validity of the weight of the coins (and therefore the absence of
 theft was checked)
-presenting the issue divided into distinct groups characterized by different monograms, it was easier to allow the final control on the issue entirely minted by the authority in charge.


I've been waiting for a better explanation than this since August 30th.
We have to start from the objective data, from the monograms, not from what they could serve in our opinion.
I'll give you an example. When these small vessels from the Bronze Age were found to understand their function, we did not start from "in my opinion" but from scientific analyzes
A group of researchers verified with chemical investigations that in some containers with this characteristic shape, found in burials of children dating back to the Bronze and Iron Ages, there was milk: very likely, therefore, that they were part of the kit for the feeding those little ones.
and it turned out that they were baby bottles. It was not said "according to me it is impossible that they are baby bottles because it was too much for the Bronze Age", but some analyzes have been made, understand? In the case of monograms, is that sign a sampi? Yes? then they are numbers, not being able to do scientific tests at least let's try to remain objective! Am I asking too much??

[glebe]

Dear Mr. De Luca and Board,

You may or may not know me as the person who reviewed your Ptolemaic stater paper as a KOINON submission.  As you rightly described, there has been a torrent of discussion here concerning your theory, but we do not seem to be making much progress in the direction(s) we are going.  Personally, I (and maybe Ross to a certain extent) are impressed with your possible talent symbol discovery.  It does seem like you are on the trail of something fascinating, but what lies ahead is most likely not the picture you have labored in great detail to illustrate in your writings.  I say this based my editorial critique of your work, which raised a couple of points I failed so far to see discussed in this thread, but which I feel are of utmost importance to the validity of your core arguments.   Perhaps I simply missed them (quite possible), but I did not see any of the alluded concerns with you research addressed in the later published OMNI version of your paper.  With that in mind, I would be grateful if you could now address my points (reproduced below among others you are probably tired of hearing!) and shift this whole discussion in a hopefully more fruitful direction.
  
"We will begin with the most problematic.  In his plates, we have six gold (not golden!) staters of Ptolemy I Soter bearing the obverse die 'O8' (Nos. 12-14 & 20-22), coupled with five reverse dies, each of which represents a new, increasing numerical sequence, according to De Luca's interpretations.  The obverse of the first coin (#12) bears a die chip on the forehead of the king, which is obviously not present on #21.  Likewise, we have a very noticeable die chip in front of Ptolemy's nose on coin #13 which is nowhere to be found on #20 and probably #21.  In terms of overall obverse die wear, nos. 20 & 21 look the most fresh to my eyes.  None of this should be the case if the different numerical lettered/monogrammed reverses are supposed to denote increasing values.

"To arrive at the numerical values for the letters and monograms found on the gold staters presented in the article, De Luca has relied on not one, but three different Greek numbering systems.  In some cases, all three are purportedly represented on a single coin.  In support of this astonishing claim, he cites a few, albeit very intriguing, written examples (on page 8 of his article) where numbers and calculations were indeed apparently expressed sometimes in more than one Greek numbering system.  Although I have not investigated the matter to my satisfaction, there nevertheless seems to be logical geographical and cultural relationships underpinning the the use of the numbering systems in those examples.  I am not so sure if such (or similar) traditions and practices can be applied so evenly across the whole Greek world as De Luca seems to suggest when his body of research on numerical letters and monograms is taken as a whole.  Whether he is talking about the letters and monograms on Massalian drachms (in a different article) or Ptolemaic staters, he interprets them in the same basic way, where the die cutters would regularly utilize more than one numbering system in a seemingly less than standardized manner.  When it comes to Ptolemaic and Roman Egypt, there is a considerable surviving corpus of papyrus scrolls, some of which no doubt record ancient mathematical calculations.  Has he consulted this vast resource to discern which numbering system(s) were in common use in that part of the Greek world?        

"My apologies in advance if I have misunderstood De Luca or missed a relevant passage, but from the article in question, he seems to envision the minting process of the Ptolemaic staters in a very linear fashion, with little room for more than one pair of dies being put into service at a time.  I would think one of the number one priorities at any mint, ancient or modern, is to get the job done as quickly as possible, without needlessly dragging the process on.  However, if De Luca's reasoning is true, then I would see difficulties in having more than one team of minters at work at the same time.  Would they all be striking coins within the same sequence, or would one team skip ahead to the next one?  Or perhaps there were two independent lines servicing two separate orders for coins at the same time.  But, if this is the case, then the ability for us to determine roughly how many coins were minted of a single issue falls apart, because we suddenly no longer know if, say, 300,000 staters was the end goal or 600,000.

"And, to top everything off, I fail to see the explicit need to publicly mark all the dies of a coin issue so as to keep track of how many were minted.  If the mint knew how much raw metal they started out with each time, then they would have a good idea of many coins it would produce.  Moreover, if mint workers were really packing the coins in labeled bags, a theory that De Luca could well be correct about, then that further decreases the need to mark every coin with a complex system of numerical symbols---unless there was a more important reason for their existence."

For convenience, here is the link again to De Luca's OMNI paper:
https://www.academia.edu/43928165/F_De_Luca_Numerical_notations_on_Ptolemy_I_Soter_s_gold_staters_Revue_Numismatique_OMNI_no_14_08_2020_pp_31_69

Also, since writing this review, I am not as certain about the existence of the obverse die chip on coin no. 12, but my other coin die observations remain to be explained.

Thank you for your time and effort in trying to make sense of this poorly understood field of numismatics.  If your motive for doing so is to get to the truth of the matter, then you will never be truly disappointed where the trail of evidence will lead you.  
    

Best regards,

Mark Fox
Michigan    

If we look at Federico’s die linkage diagram there are a couple of sequences where crossed  links seem to mean that at least two obverse dies were in use simultaneously, including the sequence Mark deals with.

These crossed links can mostly be eliminated by a relatively simple rearrangement of the coins (e.g, swapping coins 4 and 5, and moving coin 3, which is not die-linked to any other coin, to some later position. Coin 3 is only placed where it is in order to fit the numeric theory).

However we are still left with one problem, namely the coupling of obverse 7 with reverse 19.
Unfortunately this particular coin does not seem to be illustrated in the main article, so it’s hard to verify this link or otherwise.

Ross G.

[Altamura]

... Then the Greeks had nothing better to do than put letters haphazardly on the coins,  ...

Nobody is telling that this has been haphazardly, only your explanation for it is not accepted.

... I've been waiting for a better explanation than this since August 30th. ...

Again: An explanation of a phenomenon does not automatically become true and valid only because there is no better one on the market. If an explanation is not accepted and there is no better alternative, then the phenomenon just goes back into the status "unexplained", that's all  .

Regards

Altamura

[glebe]

I agree with n.igma – I don’t see how labelling tranches of coins with the number of coins helps much with accounting.

And even if it did you wouldn’t do it in the obscure, varying and inconsistent manner assumed by Federico – you would surely mark the first 10,000 coins (or more likely the first talent weight of coins) as A, the second as B, and so on, plus maybe the symbol for 10,000 or whatever.

Or at least something simple and straightforward like that.

Ross G.

But then can you explain to me what was the point of reporting the symbol of talent on that coin? Please write down a hypothesis ..
Let me understand you see the symbol of talent on the papyrus and believe it is the symbol of talent; you see it on the coin and it is no longer the symbol of talent. But what coherence is it?
And if by chance, in a rush of objectivity, you would like to recognize that on the coin there is precisely the symbol of talent, a mathematical symbol therefore, isn't it a logical consequence to ask ourselves about its meaning, which seems to suggest a numerical solution? Tell me why at this point maybe I think I'm really crazy and draw conclusions at random ...

OK, how about this - the talent sign indicates a tranche of 1 talent weight of coins - about 10,000 of these light Massalia drachms, if they used the Attic talent.

This immediately suggests that each tranche was normally struck from only one set of dies, apart from occasional breakages, with perhaps the reverse dies individually marked to distinguish each tranche. It would be interesting to see some die statistics for these types.  

At last we have testable hypothesis.

Ross G.

And how do you explain everything else, all the other monograms, coin sequences etc? For years I have exhausted myself looking everywhere, since August 30 I have been struggling with this topic and you with this simple statement have solved all the puzzles? But well ..

No, I'm just saying the Talent symbol was used in Egyptian papyri to mean the talent weight and there seems to be no evidence that it was ever used as a number.

In Massilia therefore it could also mean a weight.

Ross G.

[FEDERICO D]

ok, ok
bye

[Molinari]

So it really comes down to the sampi.  Is it really a sampi and does the sampi necessarily denote a number? (And I ask this of the group)