Coin without any number/figure?

Actually, that's not true. A Roman soldier might not be literate in the way we use the word today, but he surely knew exactly how hard and long he had to work for that dupondius. And he would have known every other piece of legit "money" in the marketplace. And the wine merchant would have known exactly how much to charge the soldier.

A merchant in Boston in 1750 would have had no problem taking in an English pound sterling and making change out of the seemingly chaotic mix of Spanish, French, English and even other country's coins in circulation.

You are thinking of coins as some magic, abstract DEFINITION of value. They are not. They arose because it was easier to trade bits of metal instead of having the baker trade you bread for sheep, then having to trade the sheep to the butcher for his dinner roast and the other pieces of meat to the everyone else including the tax man. Coins arose to REPRESENT value.

 

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You can put a number on anything but what can you buy with it?

The OP's statement about coins predate
mathematics is a bit questionable in that we know the Greeks used mathematics to build the first pyramids. How else would they have known how many stones to cut? There would be a pile of cap stones laying around because no one told them that we have enough.

 

@Burton. Soldier is not a good example to see things clear. Ok, lets replace soldier by a simple, say, a building stone worker during Roman time.
Now, lets rewrite your words, combining.

A Roman worker was literate enough to know dupondius coin as he had to work hard for it, he knew it was used in the marketplace.
So, he worked and earned some coin in one day (how much earned? lets say ****** pcs of coin) - then, he went to the butcher to buy a leg of dead sheep (worker paid how much? lets say *** pcs of coin) - then, he went to the baker to buy a bread (worker paid how much? lets say, * pcs of coin) - then, he went to the wine merchant to buy a bottle of wine (worker paid how much? lets say, ** pcs of coin)... So, "how much" did that worker earn and spend? Actually instead of "how much",, it should have been said "how many" and I did this when saying payments as "pieces/pcs" of coins.. What else I can do when there is "no value" on the coin/s... Now, imagine what if he wants to buy a house which costs ******************** pcs of coins which he should carry within a big bag.... So, there must be "values" one the coins, but, in ancient days, there was not any value on the coins... Then, how can these be explained? I can think of these: 1) governmental authority coins were limited to certain cases (such as for soldiers only during a war) 2) and, ordinary folks were using something else in their exchanges/trades or were not using any coin and this is possible as each person was a building stone worker, a butcher, a baker, etc at the same time, so, they didn't need any coin and they were rarely using coins in trades with soldiers, by trading, say, swords and coins given to soldiers by governments of the day.

So, when there is no any assigned value on coins, these happen. Values represented on such coins are not scientific (mathematic etc) values, but, "royal" values. Still, it is not much different today. After all, I claim, in old days and also today, governmental authorities (including central banks) do not know scientific value of coins, hence, national portraits flags etc royal values on the coins in the world are more highlighted than scientific values. People in the world including governments do not know what the coin is...

Edited to say, as a response to Hommer, as I saw his post after posting my this post... Greeks knew some mathematics, but, not the mathematics of coin and no need to blame them, even today, in space age, we know how to send satellites to the space, using some advanced mathematics, but, still, we do not know coin mathematics... If we (world) knew, millions of different coins in last century/millenium wouldn't have come and gone, to the garbage. Coin collectors should be appreciated/awarded by world governments, they have union, UN.. Somethings wrong, isn't it. Maybe, I misunderstood Hommer's last words. My word, coins were before mathematics, was to state/indicate a reality because of no any numeral on old coins. Perhaps, it was because of "royals" who ordered the mints without any numeral/count on the coins, but, with their own royal powers only. Mathematics and coins, among ordinary folks, were hand to hand.

 

I know your this post was to @Kentucky, probably a response to his "2" as base. Yes, we have been using the base 10 for centuries, but, in modern days, for ex, these computers run on base "2", binary numbers, 0 and 1. Anyway, whenever I see 10 in money talk, I remember a story (ok, just checked on the net now, it was 1990). Arafat, sided with a prof, wrote an article claiming that geomerical figure on Israel's new 10 agorot was a map that showed intention of Israel aiming at occupying some lands in the future and he submitted this controversial article to UN. I don't know what happened later. (Is there anyone from Israel here? What minor coins are being circulated in the market there now?)

 

There are 10 kinds of people, those who know digital and those who don't

 

Israel has six circulating coin denominations: 10 agorot, half sheqel, one sheqel, and 2, 5 and 10 sheqalim ...

 

First off, I meant what I said, because a Roman soldier was paid the same across the entire empire and that implies a rough ability to assign parity across wide swaths of the ancient world.

Second, you are completely wrong. There is no magic government telling people what things are worth or what to exchange for what. It's an open market. Everybody knows the value of things in terms of other things including coins. The coins are simply a shortcut to effect exchange of these things out of sight.

But I'm done here...

 

I'm not done here, because, as far as I know (I searched the threads), this thread is the only thread related to the math in the coin. So, I'll stay here for a while as my knowledge about world coins is very limited.

Lets rewrite all these in the same unit, agorot, to avoid confusions, to simplify.
10agorot, 50agorot, 100agorot, 200agorot, 500agorot, 1000agorot.
These are circulating coins, right?, in a certain geometrical region, called country, under management of a governmental authority. Lets not go back to history, to Romans, etc. This country is a country counted as one of (scientifically) developed country in our this era. No objection to this. But, just look at the coins circulated in their system. Do you see any order? Any systematics? What I see is randomness. If there is anything, maybe, optimization science, they are optimized according to "open market" in which people are fighting against each others claiming, for ex, "my apple is more valuable than your apple." If it were only about apples, things could have become stable after a while and these coins would stay forever. There are also others saying such as "my art/idea/etc is more valuable than yours".. So, all subjective, subjective values are driving force (as also seen in this coin collecting field which is mainly subjective, as the interest here is more about the art in coins in this collecting field.) If we are to distinguish the fields (art, literature, politics, culture, social sciences, mathematics, etc) according to subjectiveness and objectiveness, we can chose mathematics as objective and all others as subjective fields. So, we need to stick to mathematics mainly when it is about the coin, an item that can not be called as money if there is no mathematics in it. I don't see any systematic/orderly math in those circulated coins in the mentioned country which has high technology, but, poor in coin math. (ps: this is not only about that particular country, about world in general.) How come they have professors, experts in math also!? Well, I don't claim I know math more than them, but, all those professors need to go back to elementary schools to study the coin again, to take missing piece, to integrate/complete their knowledge. ok, good evening, late here.

 

Before the euro was introduced around here, there was some discussion about what could be the best "setup" for the new currency. What is easy to understand, but also questions such as, how many coins or notes are needed to pay any amount between x and y?

Now I am not a mathematician, but apparently a row of denominations that is repeated at each "level" makes most sense. So we have 0.01 - 0.02 - 0.05, then 0.10 - 0.20 - 0.50, then 1.00 - 2.00 - 5.00 and so on. Denominations above €2 are notes.

Back to the example of Israel, they used to have something similar. Using the way you wrote the amounts, that would be 1 - 5 - 10 - 50 - 100 - 500 - 1000. Due to inflation, they then phased the 1 and 5 out (similarly, some euro area countries do not use 1 and 2 cent coins any more). Also, the "200" (2 new sheqalim) coin was added later, about ten years ago. So they had a logical system that got diluted by practical needs.

Christian

 

I was in Europe for a year, but, it was before 1995, probably the year when those Euro coin&note discussions started. I think that those discussions were mainly behind the doors, were not in the public. I don't know what aspects mathematics&economy&etc experts discussed, but, I can say it seems that they reached a mathematically correct (at least, closer to absolute correctness), however, it seems result is practically incorrect. I'm hearing/reading on the net that in the countries/regions (US, EU, Japan, etc) where smallest coins exist in the market, but, they are not circulated enough. If a coin is circulated, mathematically, we can talk about cycle. When there is cycle, we can talk about frequency. In US, EU, etc, whats happening is the smaller value coins the smaller freuency, that's, less return to the market (due to being kept in moneyboxes, etc). I see that US EU etc have been forcing the market to make smaller value coins return/cycle, but, it is not happening, therefore, they have been lunching smaller value coins in quantities more than necessary. So, practically, it too is a fail. Anyway, beside math, these are also about economy, in that there are things like inflation & deflation which are killing the math. How? For ex. neither inflation nor deflation is desired. But, stagnation is not desired, either. So, this logic is absurd and absurd logic is not desired in the math. Anyway, there is/are contradictions and my economy knowledge is not much to discuss these with economists. Lets take pause here, we can talk math&market later, after learning coins better enough.

Now, from responses here and from no response, I learnt, I arrived at this conclusion that:

with some few exceptions like Sovereign, all coins in modern era (say, in last 2000? years) have had numerical values, numerals on their faces of coins, as figures like "5/V/etc" or as words like "Five/etc", things which I relate to the math - while there was less or no numerals at all in ancient coins.

So, it is necessary now to add this new question to my OQ (original question):

What is the oldest coin on which there is a numeral/face value (such as 5/Five/etc)?

 

I found a coin (a chinese ancient coin, dated 200 B.C., from the collection of Schlosser, Hannover) mentioned in the book, "Number Words and Number Symbols: A Cultural History of Numbers" by Karl Menninger (1969).

I was able to read one page only (at books.google.com). On page 220, figure 48 shows the picture of that ancient coin.
Author of the book says "written numbers on this coin are 10'9" ... Since the book is not about the coin, but, about history of numbers, it is not said anything about what these numbers are. Probably a date or rank nr of a chinese empire. Maybe, I am wrong and it (10'9) is its face value of coin?

I have been unable to find (on the net) any ancient coin with a face value. Btw, i just read an ancient greek literature (Frogs, 400-500 BC) now in that "coin values" were mentioned. It seems that face value started to appear on the coins after 1000s, after "representative money" started. So, previous coins before 1000s AD were "commodity money" which were used to exchange the goods "without" mathematics. I mean, it is subjective valueing things like one saying "gold is more valuable than silver" and another saying "silver is more valuable than gold". Face values gained importance after "fiat money", "let its value be so" money started to appear. But, face values on the coins&banknotes have always been going lower than, say, "gold value". Fiat money we use today is not really fiat money. We see this clearly in coin material value always dictating/exceeding its face value. So, as a conclusion, we in this so called modern era still live in ancient era when it comes to coin values.

Ok, I too am done here.

 

I'm going to "up" this thread as this thread is about "coin is money."

In this thread, I've questioned history of numbers in the coins, but, not the date numbers such as 1820, 1990, etc. I've questioned numbers in coins which make them money. After a long research, result is that the coin has not been seen as money throughout the history, even so today.

What does this mean? People do not know what the money is.

What is money? Money is not an item, a tool, used ONLY to exchange the goods, BUT ALSO, money has mathematics. This makes money differ from other items. However, money is an "imaginary" item, just like mathematics. Coins, banknotes, etc) are physical versions of money. And, basic mathematics is in the coin. (Ok, that's enough for the moment. Soon, I'll write coin mathematics here.)

 

No. Value is the abstraction. Money is the physical manifestation of money.

Originally money was things like cattle, later it became junks of metal, later still it became coins. Only much later did it become pieces of paper. More recently it have become bits in the ether.

 

IF money is like cattle, pieces of metals, coins or papers, bits, etc., you are implying that money is not a single thing, not a unique thing then, then, this contradicts in itself.

So, you claim that "value" is the abstraction, single, unique thing, and money is the physical manifestation of value? Then, lets look at the value.

There are other values such as artistic value, a value which is not countable. Value (I prefer to say value=money) is a countable value when it is money. Art value is not a countable value, it is a subjective value. With money, we are taking "countable values" so that we are relating to money. Those countable values do not necessarily have to be like 1 sheep 2 sheep 3 sheep etc. For example, how do you pay your electricity bill? Electricity is not countable like that, 1,2,3, etc. After some mathematics in electricity field, using similarity rules in mathematics, playing with formulae, we are bringing some quantities together in a one quantity, called energy, in unit wattxhours, now, we obtained a countable value. Only then, it is related to money, as money is a countable value. So, what we are doing actually is to convert things to countable things so that they can be related to money whose main property is countability. If there was no money, we would not have needed to search quantible/countable values like this kwh.

To see what the money is, without looking its "purpose" (exchange property), try to look into money itself only. What is seen there, in money itself, is pure mathematics. Don't look at the paper money, it is mind confusing, they have too much arts which are shadowing science in the money, therefore, look into the coin only, see, the less art the more math.

 

When I searched the net using keyword "coin mathematics" I found these:

1. Probability & statistics (in coin toss, flip flow, 1/2 probability for "head" and 1/2 probability in "tail". This "head & tail" is another topic, actually about "art/literature/etc" and "numbers/math", anyway, I may write some more later about that.)

2. Fair coin & unfair coin (again in the probability field, with geometrical "smoothness")

3. Educational mathematics (counting numbers in elementary schools, and high school level math like this http://www.purplemath.com/modules/coinprob.htm )

4. And, the one that "Chrisild" mentioned in this thread (above), "Before the euro was introduced around here, there was some discussion about what could be the best "setup" for the new currency. What is easy to understand, but also questions such as, how many coins or notes are needed to pay any amount between x and y?..."

---

So, these are all, available on the net, that are related to "coin mathematics" which I can translate it as "coin is money is mathematics." Among those above, 1 and 2 are not really about the coin. 3 is basic basis of coin math. 4 is closer to understanding "coin mathematics." Question "how many coins/notes are needed to pay any amount between x and y?" is not a simple question. When such a question is tried to be answered, many subfields of mathematics enter into the game (from number theory to simple calculus to advanced analytics to statistics to probability to optimization, etc.) And, when a coin is omitted/ignored, all these calculations fail... So, a coin is a necessity...

Ps: ok, this thread has become like a monologue thread, because, perhaps, what is meant here is not understood, yet. Maybe, someones else can participate later.

 

I don't have a clue what you are talking about and I have taught several of the disciplines you refer to at the university level over the years.

 

May I ask which disciplines?

 

Not meaning any disrespect, but perhaps one of the problems is your use of the English language in a way that is minimally comprehensible. My wife is Japanese and sometimes in talking with her, I first have to figure out what it is that she is trying to say, even if I agree with her.

 

You may ask, but I not tell too much. I have already told which part of the country I live in. Too much information will be too revealing in a public place.

 

@sakata: Ok, I retract my question about your disciplines that you have taught at the university level for years. It wasn't a personal question, it was about "language".

@Kentucky: I am well aware of that my use of the English language is not comprehensible enough. However, the "language" I am trying to use here is beyond the English or the Japanese or the Turkish or any other language. When I've told such things in this thread here in this town to fifty tousands people in their native Turkish language, they have not understood, either. Because the "language" that I've been using is a foreign language to them, too. Because it is "language" of mathematics, strictly relevant to money, its basic is coin.

By the way, those fifty tousands people are not only those who are illiterate in mathematics, among them, there were also professors. I've given them some coins, but, they haven't understand its language, either. I've got used to. Quite normal. This is totally a new language that has not been learnt by any people in the world throughout the history. It's not so easy for me too to speak this "language" as this is a new language. I keep trying.

Ok, having said these, lets back to the topic. Step by step.
I'm gonna copy&paste his words of "Chrisild" here again.
His words were:

"during the setup for the new currency, Euro, one of questions was how many coins/notes are needed to pay any amount between x and y?"

Notice here that you do not have any coin in your hand, not available anywhere there in Europe, it is just a "setup". This means that you can not say "hey, I can calculate it easily by using 5 cents, 10 cents, etc" as those coins do not exist before the setup. So, how did they setup? There are many many factors and all those factors are subject to several branches of mathematics, from simple to advanced mathematics. My guess, they had ignored many factors during the setup and they minted 1,2,5,10,etc cent coins to be circulated in their domain. I'm not saying they made an error by minting those coins, but, they made an error by circulating all of them. It's difficult to tell what the error is. Just look at the result. Some of coins are not circulating naturally, but, circulating forcefully, hence, they are disappearing in time.

Btw, I often say here in this thread, mathematics and mathematics and mathematics, bla bla, which I guess it makes many people fear and run away. Those who are not graduated from even elementary school can just look at the result to see somethings wrong. Just ask this question, why have coins been always phasing out and this has been happening everywhere in the world and troughout all time in the history... Somethings wrong, isn't it.