US dollar and its strangeness

[retina]

Originally Posted by masser

Sooo... you are telling me that I can shake my ...money-maker?

Sure, If you like. Just not in my direction thank you.

[a1call]

From a mathematical point of view a denomination structure based on binary values ($1, $2, $4, ...coinage) would be the optimally inefficient model.

What would be the most efficient?
On the second thought the most inefficient would be denomination of $1 only.

ETA Depending on how we define efficiency, it could be a coinage with denominations for every integer upto some anticipated maximum. That way there would be a single coin that world be equal to any value. So you could always (if you wanted to) carry around all your wealth as a single coin, regardless of how wealthy or poor you are.

[Batalov]

Back in the USSR, we had 1, 2, 3, 5, 10, 15 (!!). 20, 50 cent coins and 1, 3 (!!), 5, 10. 25 (!!). 50, 100 roubles.

15 cent piece comes all the way back from Czarist Russia; there was even a word for it, a "pyatialtynnyj", where "altyn" is 3 cents (nobody has likely ever heard these words in modern Russia)

[ewmayer]

Originally Posted by Batalov

Back in the USSR, we had 1, 2, 3, 5, 10, 15 (!!). 20, 50 cent coins and 1, 3 (!!), 5, 10. 25 (!!). 50, 100 roubles.

15 cent piece comes all the way back from Czarist Russia; there was even a word for it, a "pyatialtynnyj", where "altyn" is 3 cents (nobody has likely ever heard these words in modern Russia)

Here's a pic of a 5-rouble from 1902:

[GP2]

Originally Posted by a1call

From a mathematical point of view a denomination structure based on binary values ($1, $2, $4, ...coinage) would be the optimally inefficient model.

What would be the most efficient?

Originally Posted by Batalov

Back in the USSR, we had 1, 2, 3, 5, 10, 15 (!!). 20, 50 cent coins and 1, 3 (!!), 5, 10. 25 (!!). 50, 100 roubles.

Apparently coins of powers of 3 would be the most efficient, in the sense of using the fewest coins to reach a total, assuming that your transaction counterpart also has coins to provide change. So the 3 rouble coin actually makes sense.

[Batalov]

Fiji has a 7 dollar bill.

[LaurV]

The most efficient would be coins in golden ratio
This can be mathematically proven, hehe, but it would depend of how you define "efficient".

During our youth, under "commi" government, we had denominations similar to what Serge said, at the time you could still buy something (like a candy, a small copybook, a pretzel, a ballpoint pen refill tube, etc) with the "15 bani" - a value of 2-3 US cents in the '70s.

[firejuggler]

should you use odd value only, it should be 1-3-7, the objective being using 3 denomination of the same order at max for all the value inside the range it. say, for example, you want a half of a baguette ( yes, i'm french) with exact change.It cost 48 cent(all taxes included) .

1-3-7
10+30+7+1 : 4 coins
1-2-5
5+2+1+20*2 : 5 coins
1-5-10-25-50
25+10+10+5+1*3 : 7 coins

1,2,3,5,10,15,20,50
3+10+15+20: 4 coins


now I know in N America, the price would be 50 cent, without taxes... but that is not the point ;p

[retina]

Originally Posted by firejuggler

now I know in N America, the price would be 50 cent, without taxes... but that is not the point ;p

Actually I think that might be the very point here. If you make the money too efficient then people couldn't justify adding those two more cents.

So to keep the profits rolling in we can add two cents and say we are helping the buyer to make life easier for them. It is totally for the buyers benefit, we promise. It isn't so we can make more profit. But if we have to suffer with more profit then okay we will do it if it helps the buyer.

[a1call]

You will not find any bakeries in my neck of the woods in N. America that will sell you half of a baguette. Judging by how much we weigh on average, that is no surprise.
It is difficult for me to formulate the constraints that would define an efficient denomination structure.
It should be something along the lines of:
* Minimum number of sub-dollar denominations that would allow you to have optimally minium number of coins, if you were to have the exact change for any value from 1¢ to 99¢.

ETA With the current North American structure you would need:
3x25¢+2x10¢+1x5¢+4x1¢
Total of 10 coins.

With a binary structure you would need:
1¢+2¢+4¢+8¢+16¢+32¢+64¢
Total of 7 coins.

With a 3 based structure you would need:
2x1¢+2x3¢+2x9¢+27¢+81¢
Total of 8 coins.

[Dr Sardonicus]

Originally Posted by ewmayer

So, aside from the lack of a US 2-cent coin and a 25-cent piece in lieu of a 20-center (both differences being at what we in the US call the "chump change" level) the systems are identical. You just answered your "where is the consist[e]ncy" question - it's where it always was, mostly running around in its favorite guise, as the "hobgoblin of small minds". :)

The proper quotation is from Ralph Waldo Emerson's 1841 essay "Self-Reliance:" A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines. With consistency a great soul has simply nothing to do. He may as well concern himself with his shadow on the wall. Speak what you think now in hard words, and to-morrow speak what to-morrow thinks in hard words again, though it contradict every thing you said to-day. — 'Ah, so you shall be sure to be misunderstood.' — Is it so bad, then, to be misunderstood? Pythagoras was misunderstood, and Socrates, and Jesus, and Luther, and Copernicus, and Galileo, and Newton, and every pure and wise spirit that ever took flesh. To be great is to be misunderstood.

Thus, a "foolish consistency" indicates an unwillingness or inability to learn, or to disregard new information for the sake of ideological purity.

You wanna talk real differences, consider weights and measures - though as I've noted in at least one forum thread which I'm too lazy/busy to dig up, there the US system is mostly based on powers of 2 (e.g. for liquids: tablespoon = 1/2 fluid oz, cup = 8oz = 16 tbsp, pint = 2 cups, quart = 2 pints, gallon = 4 quarts, hogshead = 64gal, tun = 4 hogsheads and weighing 2^11 = 2048 lbs if filled with water at sea level), which should make it quite appealing to the computer science types.

Of course I'm glossing over various subtleties with regard to the different kinds of gallon... ;)

Once upon a time, long long ago, I compiled a rather lengthy list of units. Some of them were from a 19th Century arithmetic text.

I refer to it occasionally, as when someone invited me to have a "puncheon" of ale (probably meaning a "flagon"). Among the entries:

1 (U.S.) fluid ounce (fl oz) = 1.8046875 cubic inches (in^3)
1 (U.S.) fluid (liquid) pint (fl pt)= 16 fl oz = 28.875 in^3
1 (U.S.) fluid (liquid) quart (fl qt) = 2 fl pt = 57.75 in^3
1 (U.S.) gallon (gal) = 4 fl qt = 8 fl pt = 128 fl oz = 231 in^3

[Note: the gallon of 231 in^3 is the U.S. standard liquid measure.]

1 British or Imperial quart = 69.354 in^3 = 1.201 U.S. fl qt
1 British or Imperial gallon = 277.42 in^3 = 1.201 U.S. gal

[Note: A British or Imperial pint would be half an Imperial quart, so 1.201 U.S. fl pt, or about 19.2 fl oz. However, the British or Imperial fluid ounce is defined so that a British or Imperial gallon is 160 British or Imperial fluid ounces, as opposed to 128 U.S. fluid ounces in a U.S. gallon. Thus a British or Imperial pint would be 20 British or Imperial fluid ounces.]
--------------------------------------------------------------------------
APOTHECARIES' FLUID MEASURE:
The Apothecaries' fluid ounce, pint, quart and gallon are the same as for
U.S. liquid measure. However, the fluid ounce is subdivided as follows:
1 fluid dram = 60 minims = 1/8 fl oz
1 fl oz = 8 fl drs = 480 minims
Thus 1 fl pt = 128 fl drs and 1 gal = 1024 fl drs.
--------------------------------------------------------------------------
WINE OR LIQUID MEASURE -- used for all liquids except beer, ale and (formerly) milk.
The ounce, pint, quart and gallon are the same as for U.S. liquid measure.
1 gill = 4 oz; 1 pt = 4 gills (gi)
1 barrel (bl) = 31 & 1/2 gal
1 tierce (tr) = 42 gal
1 hogshead (hhd) = 2 bl = 63 gal
1 puncheon (pn) = 2 tr = 84 gal
1 pipe (p) = 2 hhd = 3 tr = 4 bl = 126 gal
1 tun (T) = 4 hhd = 8 bl = 252 gal [sometimes a tun is larger.]
--------------------------------------------------------------------------
ALE OR BEER MEASURE -- for beer and ale (and formerly milk also).
The BEER GALLON is 282 in^3, not the U.S. standard 231 in^3 gallon! It is
divided into 4 quarts, and the quart into 2 pints.
1 beer pint = 35.25 in^3
1 beer quart = 2 beer pints = 70.5 in^3
1 barrel = 36 beer gallons
1 hogshead = 54 beer gallons
--------------------------------------------------------------------------
MISCELLANEOUS CUBIC MEASURES
1 teaspoon (tsp) = 1/6 fl oz, 5 ml approx
1 fifth = 1/5 gal = 46.2 in^3 [usually for distilled liquor]
1 Magnum = a 2-quart bottle of wine or champagne
1 acre-foot = 43560 cu ft (a volume of water 1 ft deep, covering 1 acre.)