Coin without any number/figure?

"CoinCorgi", maybe, you just joked, but, even if yours was a joke, you are really close to the solution, also to the generalized version. We'll come back to your answer, later.

"Chrisild", thanks for answer, for sharing knowledge about "token", but, I found this

strange. If defining the coin this way (if the private issued, it is not coin) is being done by the coin community in general, it doesn't fit my understanding the coin. If coin is a form of money, and I claim so, its main criteria is mathematics (not private or state issue.)

While we are at it, while re-visiting that website about "math-money", I need to say these also now.

Emphaty. I can do some. Some may say "it is not a fair competition as we don't know about you Erol, we don't know how much knowledgable about the math you Erol are, etc." - OK, first of all, I need to say this, this is not a competition, however, still, it is better to tell a little about my background specifically related to such things so that understanding each others can be easier and this is probably what Dale too may need to know. I am not a mathematican. But, I had used some math including some theoretical math (for example, Lie point symmetry group) when I was pursuing PhD about chaos, mathematically, computationally and experimentally (turbulence in flows), but, these were before at least two decades ago and PhD was incomplete, left the research field/university for "money", went to the industry & engineering & trade in the world. Anyway, I left the chaos, but, the chaos didn't leave me. Then, I focused on "money" in general, "coin" in particular. Anyway, this is not about Erol, all these are about "money" in general, about "coin" in particular.

So, let me tell about my some experiences in last years as I focused on these things. When I've shown some coins, in from local bazaar to global market, from totally illiterate people to high level scholar people, from kids to olds, all people have laughed, have made fun of, some few have got angry, etc.. Why? Because. People's reactions are about the function of money, about what those coins are used for, etc. That's, main interest of people is "function" or "purpose" or "what is used for", "utility", etc which are related to "economy", the field "money is related to somethings else". These are general view of people of whole world from little kids to old people.

Okay, what is wrong in all these? Lets remember what everybody knows, "money is a tool." But... what mistake people are doing is, if we say in engineering language, people are using this tool WITHOUT knowing the tool well enough... This means, people, from illiterates to scholars, from poors to riches, from kids to olds, etc., all people do NOT know what the money itself is. Since it has been used for tousands of years, it is like a joke, such a joke that I too laughed at myself for living years, after 40 years of living without knowing the money. So, first thing to do is to learn what the money really is and this is purely mathematics, that's, without relating it to somethings else that's economy. Hence, I wrote this generalized pure math formulae for coins, i.e., without relating them to the economy. Here again, generalized version:

k.A + l.E + m.I + n.O + p.U + .... (etc) = T(otal) .... Solve k, l, m, etc., and A, E, I, etc... (k, l, m, etc are numbers of coins and A, E, I, etc are face values of coins.)

Okay, where will all these end up? When we solve this equation we will have learnt the money in general and the coin in particular. So, for a contribution to this solution, a mathematican was needed and she/he must have had also some interests in the coin. I've not searched the net a lot, but, I am sure there are only a few and found one, http://web.olivet.edu/~hathaway/math_money.html , that's, sufficient. (Ok, late here. Later, after Monday.)

 

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I'm out

 

It is late on Monday and coins sent are already delivered to the math professor at a USA university who is also a coin collector.
He might be surprised, they are not old coins, just new coins with no any mathematican depicted on any of them and there is no any mathematics on any of them, either. So, why were they sent while some pictures could be enough? It is because I followed an old saying "until wheat is in silo, wheat is not mine." Similarly, until money is not in one's pocket, it is not belong to him. So, coin is in his pocket of a math prof now as well as in his pocket of an old engineer who is over 80. Now, lets back to the topic here in this thread. Where were we at? Ok, lets start with that generalized coin math problem:

----

k.A + l.E + m.I + n.O + p.U + .... (etc) = T(otal) .... Equation 1.

where k, l, m, etc are numbers/quantities of coins and A, E, I, etc are face values on coins. Total amount is any amount.

Solve k, l, m, etc., and A, E, I, etc.

----

Professor and et al, if this problem setup is properly set up, then, lets go ahead. How can this (Equation 1) be solved?

 

It seems that our mathematican and old engineer will not contribute to the solution. Ok, here is an attempt. In this Equation (1), all parameters are unknown and their numbers can be as big as infinity and it is only one equation. So, of course, it is unsolvable as number of unknown is more than number of equation. But, we know a thing, this Equation (1) is about the money in general and about the coin (for simplicity) in particular.

So, we have two options:

Option 1. Money does not exist (all parameters; k,l,m, etc and A,E,I, etc are equal to "0", zero. Then, Equation (1): 0=0. Lets throw this option away as the reality is the money exists.

Option 2. Money exists. (all parameters; k,l,m, etc and A,E,I,etc are "variables"... EXCEPT one of them which is a "constant", I emphasize/I highlight, CONSTANT...

That's enough for the moment.

 

Rewriting the Equation 1:

k.A + l.E + m.I + n.O+p.U+...=T(otal) ... Equation (1)

Lets divide the both (lefthand and righthand) sides by, lets say, by "O"

k.A/O + I.E/O + m.I/O + n.O/O + p.U/O + ... = T/O ... Equation (1.1)

Lets rename new variables: A/O=Ao, E/O=Eo, etc. Then,

k.Ao + I.Eo + m.Io + n.1 + p.Uo + ... = To ... Equation (1.2)

Now, we have a number in the equation and it is "1", a "constant".

We can rewrite the Equation (1.2) as:

n.1 + Summation of [variables*] = To ... Equation (1.3)

(* these variables can change from zero to infinity, but, taking "0", zero, too should satisfy the generalized coin equation.)
So, this simplified equation below is also valid

n.1 = T ... Equation (1.4)

Then, n = T, that means

T.1 = T ... Equation (1.5)

What was "1"? It was "face value" on the coin, and "1" is "unit value". It doesn't matter whether you call its name "cent" or "agora" or "penny" or "kurus" or "X"... So, mathematically, we arrived at what "CoinCorgi" said above. Note that calculation of variables in [ ] is in the field of "optimization" science subfield that takes parameters of the economy into account and this is not our topic here.

So,

Conclusion: 1cent (or 1penny or 1agora or 1kurus or 1x or 1whatever, let me call it 1coin) is NOT a variable, is a CONSTANT, is a NECESSITY, is an OBLIGATORY. This means, 1coin can NOT be considered as NEGLIGIBLE...

But, economy is neglecting 1coin? Yes, we know it is so, but, then, If so, then, forget about all mathematics, throw all mathematics into the garbage, stop doing all mathematics and all related sciences from physics to engineering, etc, in which mathematics is used. If we humans are to keep doing all these sciences, we need to stick to 1coin, otherwise, economy keeps being dictatorship over mathematics and other sciences. So, we can say that economists do not know what to do, can't we? Yes, we can, they don't know, either. Still, we can be helpful to them also. Hint: 1coin is CONSTANT... (ok, late here, good evening.)

 

Scooby snack coming my way!

 

Indeed so, but, soon, scooby snacks (those saying "we are rich, 1cent is a no need") may knock your door too, you coin collector, to question you that "hey, where/why/etc have you hided all those 1coins!!? Give us some "1cent"!, etc". So, we need to prepare ourselves not to face any such troubles. Lets go on doing some more little math, by doing a simplified version of all those symbolic math to partically numerical math so that everybody, also those who are not familiar with symbolic math, can be familiar with what math is done above, in previous posts. Of course, all these are not a rocket science, but, you know even a space rocket too requires "money" and here we are not inventing a new thing, we may call it a discovery, and that discovery may cause some changes even in rocket science.

Ok, lets do an example or two with partially numerical and partially symbolic math.

Lets use "cent" as the name of coin here as (I guess) majority of people here are familiar without questioning it for a second. Its unit is 1cent. (I'm omitting half cent here. If doing this is not acceptable, we will have to redefine the unit cent as 1halfcent, and this will cause some extra notations, but, at the end, nothing will change as the unit number will still be "1" on the coin.)

Lets take Total=91cent. How this total can be obtained by different coins?
(available coins are: half dollar=50cent, quarter=25cent, dime=10cent, 5cent and 1cent)

91cent = k.50 + l.25 + m.10 + n.5 + p.1 (where k,l,m, etc are quantities of each coins.) Solve k,l,m,etc. (*)

One of solution that you can easily see is k=l=m=n=p=1, i.e. one piece from each coin.

Now, lets say that none of these coins (half, quarter, dime, etc) are available. So, we will have to make a new setup of coin face values. (for example, instead of 5cents, our new coin can be with a face value of 7cent.) So, in this case, face values are "variables" and I will use same notations for them, i.e., capital wovel letters, A, E, I, O, U. Now, lets obtain 91cents again by taking 1 piece from each new coin.

91cent = 1.A + 1.E + 1.I + 1.O + 1.U (where A, E, etc are variable face values of coins.) Solve A, E, etc. (**)

Since majority of people are not familiar with this (unknown face values) solving A, E, etc may be a little difficult for them. However, still, with an insight view, at least one of them can be easily known as the total is 9"1" cent. So, face value in one of terms on the right side must be "1"cent. Lets chose "O"=1cent (not to get confused with numerology which takes A=1). Then, 91cent can be written as

91cent = 1.1cent + 1.(A+E+I+U)... Here, indeed, A, E, etc can be any value, so, variables (for ex. 7cent, 12cent, 27cent, and 44cent) which are left to be determined by economists as the money is related (as a function) to the economy. Our topic here, even before economy, is the math, pure math, regarding money itself.

In both equations (* and **) above, what is clearly seen? It is "1cent" which is unit value of money. It has to exist... Obligatory... Necessity... Math of money tells this...

If people object this result, then, they are against basic of math, meaning that they are also against advanced math, also against all math. Then, those economists neglecting "1cent" should not use any math in their economy science also. Engineers should not use any math in their designs. Teachers should not teach any math to children. Etc.

So, if that this "obligatory of 1cent", that "1cent" is a "fixed" value, is clear to everyone, and I guess everybody agrees in that, then, we can go ahead...

What should economists (also anyone who sees money as economy item only) do? It is hard for them, for any person, not to neglect 1cent in economy comparing with, say, a house price, say, $1million which is equal to 100 million cents. But, we saw from its math of money that "1cent" is non-negligible. Indeed, this self-contradictory problem is a hard problem and this is why 1cent or small valued coins have been neglected and phasing out all over the world in all history including today. It is such a big big complicated problem. So, people are either with the math or with the economy, not with the both, if they don't find a solution to "1cent" in economy as well like it is done here about its math.

Ok, herafter, it will be about "1cent & economy".
(But, that's enough for the moment, I need to go out.)

 

1cent & economy ... without giving up the mathematics, that's not been done by economists and by almost all.

What economists and all who listen to them "want" from 1cent?
They want its circulation of 1cent...

Ok, but, 1cent is constant... as shown above, in previous posts.

A constant, mathematically or physically, can NOT circulate...
Circulation of a constant is against its nature of the constant...

(Some may say "take Moon, it is circulating/cycling/turning around Earth". No, it is not exactly really so. Rotation of Moon around Earth is not a real smooth rotation, it is a rotation by "slipping", somethings like a race car's slipping when turning around a corner. That's why we always see the same/constant face of Moon. Anyway, maybe, this Moon example wasn't a good example to explain why a constant can not circulate. It is not so easy to explain it especially if you are not a linguist. However, you can still understand, with an insight view, that the constant can not travel/rotate/circulate. Having said these, lets go on)

So, now, we have these requirements/conditions:

1. Mathematicallly, 1cent DOES exist and physically, 1cent coin DOES have to exist...
2. 1cent is Constant, therefore, NON-negligible...
3. 1cent can NOT circulate in the economy as it is constant...

Then, what should be done, in practice? ("practice" here can be read as "economy" by those who prefer so.)

Ps: I stop here, to give some time for those who may need to think and who may have any objection to anything said above.
Good evening.

 

In ancients having coins without their value appearing in either word or number form is common. Here is an example, a denarius of C. Lentulus from the era of the Roman Republic.



It has legends but no mark of value appears anywhere on the coin, but it does not matter as the ancient Romans would have known it was a denarius based on size and weight. And they would have known 4 bronze sestertii were worth one denarius even though most sestertii coins had no mark of value either. And they could tell a bronze sestertius apart from a bronze As coin due to size and weight, even if both shared similar designs, and known 10 As were a denarius...and if one can't figure that out, just get a scale and let the weight sort things out for you. Its not that complicated to have a currency system without marks of value on most coins as long as the system maintains consistent metal weights and sizes for the coins.

 

"Sallent", yes, it was my first post and it was to learn first whether the ancient coins have numerals or not on them and thanks for your post. I've looked at many pictures (at google) of world ancient coins from east to west and with my novice eyes in this field, I've not seen any single ancient coin with any face value. Beside some earlier posts in this thread, your this post too verifies this.

Ok, in so old days, as you said, their currency system, aparting/sorting out the coins, were based on their different materials and different sizes and maybe also some art/pictures differences as well, but, NO numerals at all even though they knew they were using numerals such as V(=5), X(=10), XX, etc, but, these were related to "vota/vows" of those so called legends/kings/royals. Aparting coins by their materials and sizes are still done even today. No need to mention blind people who use their fingers to sort out coins. In general, people in the world still do not look at the numerals on the coins, they just look at their colors which reflects materials, sizes, pictures on them. This approach can also be seen in naming 5cent by folks in USA as "nickel." So, about coins, today is not much different than those old days, people are not about the mathematics, but, more about materials, sizes, and so called legends on the coins.

Ok, while we are at it again, let me write that ancient Roman currency coin system here that I found via google:

Roman coins around 200BC (in the same era/years when the governmental authority was same):

1aureus(gold) = 2quinarii(gold, smaller size) = 25denarii(silver) = 50quinarii(silver, smaller size) =100sestertii(bronze) = 200dupondii(bronze, smaller size) = 400as(copper) = 800semisses(copper, smaller size) = 1600quadrans(copper, more smaller size.)

If these numeral values which were not depicted on these coins were not a "speculation" by experts/numismatists of our days, then, they were "guessed" values based on some findings. Ok, I'll take these as true and I'll cointinue.

In that era, c200BC, when there were all those coins above in the same region at the same time, what was their coin mathematics? First question to be asked related to this question is what was their "most important" coin? I can think of, any person even today can answer/say "their most important coin was 1auerus" as it was biggest value coin (at least, in this list above.) This answer maybe correct in economy, but, can be wrong in mathematics. In mathematics, "most important coin" is not about "biggest valued coin", it is about "unit value". So, in this old Roman currency system, I take "1quadran" as "unit value" and that 1quadran is the most important coin as it is in those all coins; quandrans, semis, as, dupondii, sestertii, quinarii, denarii and aureus and they didn't know either that their most important coin was 1quadran.

Its equivalents of 1quadran of old Romans in our days are: 1 cent in USA/Europe, 1penny in England, 1yen in Japan, 1agora in Israel, 1kurus in Turkey, 1kopik in Russia, and so on. Now, it may be realized that I said:

"most important money" is "unit value" of money and it is "1x" and it is usually a coin with 1x value today... (x=name of any coin, name is not important in the universe of mathematics that is equaivalent to universe of people in the world.)

This (mathematical approach) DOES contradict with economical approach of people that doesn't care about "unit value" in money...

Then, question arises: shall we keep doing mathematics in economy?

 

I'm not saying a mark of value was never present. Sometimes Romans did put marks of value on coins, but the practice was very inconsistent and most coins would not have had it. Here is an example of a coin that does have a mark of value, the X below Roma's chin is the Roman numeral 10, showing this coin was worth 10 As. By 146 BC when this denarius was minted, the As was suplanting earlier Republican era small denomination coinage.


M. Junius Silanus
AR denarius (146 BCE)

By the imperial era, the As was the most basic coin (but I would not compare it to a penny). It could probably buy you a glass of cheap wine or a cheap meal at a dodgy restaurant in a back alley. So the smallest coin in the imperial system could probably be best compared to a $10 note today.


Emperor Claudius
AE As (Cir. 47 AD)

In an era with no supermarkets, no packaged goods, few finished non-luxury goods, no mass consumer culture like what we have today, and with people being more handy and used to buying raw goods by weight, etc., smaller is simply not necessary. Which is why it's dangerous and difficult to compare ancient coins and ancient economies to our modern currencies and mass consumer societies.


Emperor Marcus Aurelius
AE Sestertius

However, Romans tended to use the sestertius as the unit in which they quantified salaries, large transactions, money needed to qualify for a government post, taxes, etc. For example, we know Senators needed to be worth at least 1,000,000 sestertii during the time of Emperor Augustus. They could have said 250,000 denarii, but they put it in sestertii as that's the largest denomination the average public would see in the streets. If someone owed you a denarius, they were most likely to pay you 4 sestertii instead of a denarius coin. So in that sense you could say a sestertius was the $20 bill of the late Republican era and the early to middle Roman Empire, while the denarius (a day's pay for a laborer with some skills) was probably more akin to a $100 bill. An Aurus or any other gold coinage would have simply been foreign to most Romans, except for wealthy and elite Romans engaged in large transactions.

One last thing. Sometimes in coins of similar size and material, the Romans used differences in the busts of the emperors to differentiate the currency. For example, a denarius always featured the Emperor with a laureate wreath.


Emperor Gordian III
AR Denarius

But an antoninianus (double Denarius) always featured the Emperor wearing a radiate crown.


Emperor Gordian III
AR Antoninianus

And don't forget most Romans used a second monetary system besides the imperial system. Most major cities outside Italy also minted their own independent coinage, what we call Roman provincial coinage today. These would have had different values from imperial coinage and would have circulated in a region or province alongside the imperial coinage, which means the average Roman would have had two set of exchange/currency rates memorized. You might pay for something in imperial currency and get change in provincial currency, or the other way around too. Sounds difficult, but people get used to it and manage it well. For a modern example of a two currency system, see Cuba today with their CUP and CUC currencies. When I was there two weeks ago I owed a taxi driver 4 CUC, and paid him with a 10 CUC note, and received change of 150 CUP in return. One CUC is equals to 25 CUP, so even though I received change in another currency, I got my six CUC's worth of change back...albeit in a different form.

Here is a Roman provincial for your viewing pleasure. Notice the Greek legends even though it is a Roman Emperor depicted.


Emperor Trajan
AR Tetradrachm
Tyre Mint
Melqart featured on the reverse.

And here is another provincial


Emperor Probus
AE Tetradrachm
Alexandria Mint
*Metal is probably Potin instead of bronze

 

PS: If any As for a glass of mediocre wine sounds expensive if you are a laborer making 10 As a day, that's because it was. You'd probably spend 40% of your monthly income in food, and most of the rest in rent.

You'd have little left at the end of each month, and clothes were also expensive, so you'd wear your one or two tunics for several years until they started to fall apart before buying another. Fortunately since you didn't live in a mass consumer society, your household wares such as glasses, cups, home furniture, etc, were designed to last you a whole lifetime. You'd slowly buy what you needed and maybe in a few years you'd be set for life as far as those necessities.

What else was there to spend money on? Nothing much really. Maybe some Greek luxury goods imported into Italy, but you'd probably not be able to afford any of that anyway. So I guess a cheap prostitute once a month might have been your idea of entertainment and luxury.

Life was tough for most people who weren't part of the elites, but if it's any consolation, it was brief. With the abysmal health care available, the poor sanitation, and rampart warfare, the average person would probably be dead before their 48th birthday. If you made it to 55, you'd probably look like a 65 or 70 year old does today, and you'd be the worse for wear after a life of tough manual labor, chronic illnesses and no modern science to cure you or manage the symptoms, etc.

 

"Sallent", thanks for these posts which are very informative. I'll read them slowly and I'll come back and read them from time to time. It is like a library. For the moment, I'm going to touch a thing or two in your posts.

Is that "X" depicted in the coin really 10? It looks to me like a part (handle) of a sword. If it were 10As, while there were also denarius, sessertius, etc., they could have clearly write/add "As" also like "Xas", couldn't they? Even if "as" was not added, still "X" on that coin does not look like numeral "X" (=10 in Roman.) Anyway, if it is really 10, then, it is a singularity in ancient coin domain. Have you seen some other ancient coins with any mark of value?

Ok, I understood/learnt that, even if there was no numeral, no marks of values on different coins (as, denarius, etc), all those coins were related each others mathematically, by invisible mathematics. There were numerical ratios between all those coins, that is, there was a systematic mathematics also in those ancient coins. But, again, like it is happening today, in old days too, there was/is a "non-integrity" in the coin mathematics. This non-integrity or "broken-chain" in money math was/is due to the economy that you told in your posts.

We can compare all those costs and living conditions related to economy of those old days with those of today. But, you say this:

Yes, things in the past and today are not same, not so easy to compare, but, still, it can be comparable using coins of old days and today. Things, living conditions and economy, in those old days and coins depending on these were a "compact" version of things of today. We can simulate these things including coins of old days and today as a chewing gum, contracting/stretching gum, which can be mathematically modelled by "scaling" techniques to find "invariants" between coins of old days and today. One of those invariants I immediately see is "unit value" which was unimportant in those old days and also today.

I need to stay around "unit value" a little more here not to confuse it with "smallest value" coin circulating in the market. For example, as you said, 10As was probably the smallest value coin in some years of those old Roman days. In our day, for ex, in Israel, stiuation is same, smallest value coin there in the market is 10agorots. This 10agorot is not "unit value" of currency in Israel even if it is smallest in Israel economy. Their "unit value" is 1agora even if it does not exist physicially in their economy, it exists mathematically. Hope this is clear. So, as a conclusion, even if bad economies cause "coins with unit values" to disappear in economy, still, mathematically the most important money is the coin with unit value, that's, 1x coin. However, economically the most important coin is the biggest value coins such as 1aureus, 100dollars, etc. So, there is a contradiction between mathematics and economy, and, mathematicans of old days and today have been siding with economists in that challenge, accepting rich economists as their boss also because of those "elegants" on those coins who were/are illiterate in basic mathematics and who were/are siding with wealthies who have contradictions in their words, for ex, "1cent is nothing, it is not needed, we are rich of money." Do you find their this word normal? I don't.

 

Is not "10As", but rather four As coins were worth 1 sestertius coin, and 10 As coins were worth 1 Denarius coin. So just an As, "10As" did not exist unless you got 10 of those coins together.

And yes, it is a mark of value. Check out these coins sold at auction which are perfect obverse die matches to mine.



As you can see, as these coins were struck by hand and were often not centered, so numismatists study many coins of the same type to understand the full design. For the first, the details of the X are not as clear, but in the last one we can clearly see the entire X on the flan (even clearer than on mine) and know it was a solitary x, which means 10, and we also have surviving Roman texts that tell us 10 As coins were 1 denarius, so we are fairly confident this is a mark of value.

Quinarius, which were rarer than Denarius, frequently had a mark of value on them. They were worth half a Denarius and weigh roughly half as much as a Denarius, and they had a solitary V mark on them, which is the number 5 in Latin.

Here is an example of one. The V is behind Roma:


AR Quinarius (Cir. 195 BC)
*Not my coin, credit for the image goes to World Coin Catalog and is shared here for educational purposes under the Fair Use Act.

Below is another of my Denarius coin with a mark of value (below the chin of Philip V). The X is a little more stylized, but it is still clearly an X. You can see the difference between it and the star on the bottom of the reverse. And like I said, studying other coins from the same type helps to clarify that it is exactly that. It is seldom enough to study one coin of each type alone when dealing with hand engraved dies and coins struck individually by hand.


L. Phillipus
AR Denarius (115 BC)

PS: others may disagree and that's ok as the field of ancient Numismatics is always advancing and we are always learning new and fascinating things (and there is plenty of room for different interpretations), but for me the most important Roman coin was the sestertius as we know state budgets were calculated in sestertius and not Denarius, and the same goes for the qualifications of wealth for holding office.

After around 260 AD though everything becomes a mess as old coin types are discontinued, new coins are introduced, and values are constantly recalculated due to the massive inflation in the late Roman world. I'll leave that time period to the experts in late Roman coins, but here is one just for fun, a follis from the London Mint of Constantine II.

 

When I entered this field (historical coins in general) as a rookie, I was able to track (on the net) coins with values marked till around 300AD. So, I now see, it goes further back, to 195-200BC with "V" (5) mark of value on a coin. I also saw some Chinese ancient coins, claimed to be as old as 800-900BC, but, I have no idea on them, whether there is any mark of value on them or not as I am totally illiterate in Chinese alphabet and number symbols.

Anyway, if these ancient coins with marks of values are rare, and ok, I am convinced about their rarity by your postings, we can say this period (around 200BC) is the beginning period of striking mark of value on the coin and lets stay at this period of Roma coins which have sufficient number of different coins to study invariants between those old days and today. (If those Chinese ancient coins have marks of values on them, then, we can extrapolate them, later.)

Since this topic is about the math in the coin which is also relevant to the economy, "Sallent", if possible, could you write all existing Roman coins of same dates, in a certain short period like 10 year period, say between 190AD and 180AD, in a systematic way like it is done as "1aureus = 25denarii = 50quinarii =100sestertii = 200dupondii = 400as = 800semisses = 1600quadrans = etc." I am confused about the names by calling also "dime", "nickel", etc as it is difficult to see global picture with names which are not systematic.. I'd like to see matematical relations between all those different coins existed in the same short period of Roma days so that we can easierly see global picture of coin&math&economy of those days also.

 

Pose that question on the ancient section of Cointalk. There are far more knowledgeable people who can give you a far more satisfactory answer than I can. As much as I know, there is still a lot I have to learn about Roman economics.

Same goes for your inquiry about ancient Chinese coins. We have some very knowledgeable members on that topic. I do have a Wu Zhu coin from around 100 BC with the value written on it in Chinese old script (5 Zhu), but I know Chinese coins with the value on them are much older than that. So come by the ancient section and let us answer your questions.

 

Thanks, but, I don't prefer my posts here to scatter around the forum and my main interest here is not about the history, it is about the coin&math and economy as well and I guess this fits "coinchat" and it is better to keep the talk restricted to this thread.

Yes, my OP was about numerals/face values also in ancient coins, but, a part of aim was to see also all coins existed in a certain old day in time and in a certain region of old day. Roman period of 100-200BC fits this purpose, which is not to study history of Romans here. I may visit there ancientcoins room later.

Anyway, I guess, it is correct enough to take this scheme which relates different coins, mathematically link to each others:

1aureus = 25denarii = 50quinarii =100sestertii = 200dupondii = 400as = 800semisses = 1600quadrans ...
during 190-180BC of Romans.

Its a similar version today is: (beside 100usd, 20usd, 5usd, 1usd notes)
1usd = 2half = 4quarter = 10dimes = 20nickels = 100cents ...

From mathematical point of view, I already mentioned which the most important one is, i.e., 1quadran, 1cent, etc.

Now, from economy point of view, before writing coin&economy formula, the most important coin is to be determined.
For this, to take a general picture of economy in a place, lets say, the most important coin is the most circulated one.
In Roman days, what you said was "sestertius" or "As"?. Today in USA, I guess it is "quarter" or maybe, "dime".

 

I was expecting math professor and old engineer to come here for some contribution. Yes, today, they both said they finally received coins sent, but, they didn't have time to read and write here. Maybe, they are viewing here and may say a word or two later.

After coin&math, since it is coin&economy now, let me continue, with the same formula I wrote above.

n.1 + summation of [k.A+l.E+m.I+p.U...] = T(total) ... Equation (2.1)

where k, l, m, etc are quantities of each coins with marks of values A, E, I, etc, where A, E, I, etc are, for ex, "half/sessertius/etc", "quarter/dupondius/etc", "dime/as/etc", etc.

So, k,l,m,etc are "variables" and A,E,I,etc are also variables "actually". The only and only constant is "1" (1cent, 1quadran if it is unit value, etc.)

Economy link of money... connected with T(total): is related/equalized to "somethings else", for example, to assigned or blown value of "apple", eg, for one pound (lb) or 2kg of apple. Lets blow. Money value of 1pound of apple is 91cents = T(otal).

Now, Equation(2.1) becomes an equation of coin&economy as money was related to apple, which is somethings else. Lets rewrite (2.1):

n.1 + Summation of [k.A+l.E+m.I+p.U+...] = 91cents = Cost of Apple ... Eqn (2.2)

Now, "variables" k,l,m,etc and A,E,I,etc are to be determined. How? By following parameters of economy which are also related to some other "somethings else" such as orange value, bread value, car value, tv value, electricity kwh value, etc etc... We already calculated? and have A, E, I, etc (as half, quarter, dime, etc)? Actually, not. They are just randomly chosen coin values without any calculation that should take economy parameters into account, but, didn't.

Not so easy to calculate those "variables" in [ ]... Still, there is hope... But, when the term "n.1" which includes "constant" of money, i.e. "1" is ignored like it has been done, there is no hope... With this way, economy science is a science of blows... So, the very first thing to do is to study what to do with "1cent" which is "unit value" of money in USA.

What happens if we continue like that, like what we have already been doing?
Nothing happens.. except that mathematics and all other sciences using mathematics DO fail...
And, what we have already been living in reality is that.. science failure...
(Then, when science fails, you are free easily to say "we landed on the Moon for mankind"... error... It won't be easy to delete this error in the memory of mankind... To save mankind, this error should be erased and maybe, it can done by doing somethings about "1cent"... Late here, good evening.)

 

Before going further in coin&math&economy, there is an "error", done to the mankind, to be cleaned.

So, lets question/dig first somethings else related to the coin first. I see that one of criteria for a coin to be called "coin" by numismatists is "if a coin issued by govermental authorities, it is a coin."..

Governmental authorities? Scholars, some titled ones, etc and at top of them, they are presidents, monarchy heads, etc. who all represent folks in their countries, they all are heads of states that issue "coins"... Let me call all those state heads "presidents" whether they are elected or not.

I guess, everybody knows this. Now, let me take what I said in one of threads, in "rarest coins issued", here:

I claim, NONE of presidents of the World HAS "1cent/penny/agora/kurus/yen/kopek/etc." in their pockets...

So, numismatists, how can you interpreate this? 1x coin is issued by them, but, they themselves aren't taking it...
Are they all fooling people like Erol!?...

So, numismatists need to change their that criteria...
What makes a coin a coin is not who issued it, what makes a coin a coin is "effort", that's not a thing that the governmental authorities/presidents of the World do have, they showing no any effort to take a coin in their pockets... Their this error needs to be cleaned.

 

My old friend, an old engineer, still working in the industry, may not read such long posts easily due to his age.
Just for him and also for people like him, let me rewrite a sentence above:

I said:

NONE of presidents of the World HAS 1cent (or 1penny or 1agora or 1kurus or 1yen or 1kopik or etc) coin in their pockets...