Sunday, April 1, 2012

end of Canada's penny. on obsolete coins. # systems

In Canada, we are finally phasing out the penny. I have always used coins of value 1,5, 10 and 25 cents of value. More recently, we introduced 1 and 2 dollar coins.
But this was not always the # basis for change.


Great Britain and the United Kingdom Main article: Shilling (British coin)
The common currency created in 1707 by Article 16 of the Articles of Union continued in use until decimalisation in 1971. Before decimalisation, there were 20 shillings per pound and 12 pence per shilling, and thus there were 240 pence in a pound. Three coins denominated in multiple shillings were also in circulation at this time. They were:

the florin, two shillings (2/-), which adopted the value of 10 new pence (10p) at decimalisation;
the half-crown, two shillings and sixpence (2/6) or one-eighth of a pound, which was abolished at decimalisation;
the crown (five shillings), the highest denominated non-bullion UK coin in circulation at decimalisation (in practice, crowns were commemorative coins not used in everyday transactions).
At decimalisation, the shilling coin was superseded by the new five-pence piece, which initially was of identical size and weight and had the same value, and inherited the shilling's slang name of a bob.


D - we moderns don't feel like 12x20=240 makes a logical basis for a currency system, but it was considered acceptable, once upon a time.
I just want to point out how easy it is to assume that our modern math and measurement system is the only one that can work.

For example, imagine a # system based on hexadecimal, with #s 1 to 8 A small and 'capital letter' version - or my hexadecimally based binary system - could use it.
But why hexadecimal?
...the primary use of hexadecimal notation is a human-friendly representation of binary-coded values in computing...
It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F (or alternatively a–f) to represent values ten to fifteen.
One hexadecimal digit represents a nibble, which is half of an octet (8 bits).
Alfred B. Taylor used "senidenary" in his mid 19th century work on alternative number bases, although he rejected base 16 because of its "incommodious number of digits.
Hexadecimal is sometimes used in programmer jokes because some words can be formed using hexadecimal digits. Some of these words are "dead", "beef", "babe", and with appropriate substitutions "c0ffee". (Found in Java, C++ in references.)

(D - it, too found traditional use in a measurement system.)

Use in Chinese cultureThe traditional Chinese units of weight were base-16. For example, one jīn (斤) (approximately 256 grams) in the old system equals sixteen liǎng (兩) (16g).

And England.
avoirdupois weights 16 drams = 1 ounce
16 ounces = 1 pound
The avoirdupois pound is the pound in general use today. As its name implies, it was intended to be used for weighing heavy goods. This pound is of 7000 grains, and is split into 16 ounces (each, therefore of 437.5 grains). Each ounce is divided into 16 drams (which my calculator makes of 27.34375 grains each - much more fun than metric isn't it?).

D - makes you wonder if we would have used 14 then 8 base # systems if we had 1 less finger per hand...
D - also makes me wonder about any possible benefit of a 8 or 16 base system, given their compatibility with a power-of-2 approach. For computer memory, for example.

The kilobyte (symbol: kB) is a multiple of the unit byte for digital information. Although the prefix kilo- means 1000, the term kilobyte and symbol kB or KB have historically been used to refer to either 1024 bytes or 1000 bytes, dependent upon context, in the fields of computer science and information technology.

D - a way to denote a 2 or 10 base system would be very useful.
For that matter, a simple way to substitute ANY # to indicate the prefix base would suffice.
In this system:
1) 1000 would be 10 to power 3
2) 1,024 would be (um, 2,4,8,16,32,64,128,256,512, 1024)2 to power 10.
D - I had considered short forms of prefix/ unit names for the purpose of rapid tactical communication. Kilo-metre, for example, could retain the essential KI-lo and MET-re parts to form ki-mets. Of course, we just use "clicks" to address this deficiency.

1 comment:

dino snider said...

IMHO, TEN and not 0&1 is the core of the # naming system. The latter concepts of none&all can be based on the language vs number vocabulary. For example, combing a mid-point "some" with +&- versions of comparative & superlative, with all&none as the extremes of this continuum can use either a 1-to-7 nomenclature, or a +/- version of a 0,1,2,3 system. See CVN. "One" in my # system as a number expresses the concept of ten-to-power-zero. TEN - ten-to-power-ONE - is the ataual default basis.