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Anu wrote: "We use the decimal system because there are ten fingers on our hands."
This might be one of the reasons. However, there are mathematical reasons that made people use it: The decimal system is much more practical than the hexagesimal system the Babylonians used or the duodecimal one. At least for human beings - computers are much more comfortable with either the binary system or the ...dunno... 0-to-F system (FF being 255 in "real numbers" ;-)
We can add, multiply... numbers in a most elegant and easy way using the decimal system, much easier than in any other system. Try and calculate 7% of 20 Euros or Dollars using the decimal system and then do the same using the decimal system or the binary system :-)
However, considering the poor performance of way too many young people when it comes to most basic calculations as the one mentioned above none of the system seems to be working. How come? :confused:

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Decimal arithmetic is comfortable for us because we're used to it. If you had done your times tables in duodecimal or hexadecimal you'd probably find the decimal system confusing.

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Hi Carsten - welcome.

I think Carsten's got a point myself, Faldo - after all, the ease of moving the decimal point outweighs all the rote learning I did as a kid learning the old British duodecimal currency system, may it rest forever in a pit of half-congealed school custard.


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What was that money called, mav? A shilling was one part of it, right?

Here's a link to a Dozenal Society:
reminds me of Save the Apostrophe

Also--is our duodenal system so called due to some relationhip to the number 12?

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Our crazy old currency, complete with farthings, ha’ppennies, pennies, tuppences, thre’penny bits, tanners, shillings or bobs, two-bobs, half-a-crown, crown, pound, and guinea was generally known as ‘the duodecimal system’ ~ but only once we had started discussing then implementing the alternative…

¼ penny = farthing (obsolete from waybackwhen)
½ penny = “ha’pence” or “ha’penny”
1 penny = 1d
2 pennies = “tuppence” or “tuppeny piece”
3 pennies = “thre’penny bit” or “thre’pence”
6 pennies = “sixpence” or “tanner”
12 pence = 1 shilling (1/-) ~ also known as “a bob”
24 pence = 2 shillings (2/-) ~ in single coin, known as “two-bob”
30 pence = 2 Shillings 6 pence (2/6) ~ also known as “two-and-six” or “half a crown”
60 pence = 5 shillings = crown (rarely in circulation)
120 pence = 10 shillings (10/-) ~ also known as “ten-bob note”
240 pence = 20 shillings (20/-)* = 1 pound (£1/-/-)* ~ also know as “a quid”
252 pence = 21 shillings = 1 guinea (ancient terminology beloved of lawyers)

*I can’t actually remember this notation accurately.

Can you see why it was so indigestible? And speaking of which:

Duodenum
[med.L. (so called from its length, = duodénum digitorum space of twelve digits, inches, or finger's breadths), f. duodéni twelve each (see duodene). Used in Fr. in 1514 (Hatz.-Darm.).]


© OED v2

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Faldage is right. It's not the decimal point being part of the ten based system, it's the system you are used to.

Consider a nonal system:

1
2
3
4
5
6
7
8
10.

If you move the nonal point one over to the left, you get 100. But that is actually nine nines, or 81 decimal. In nonal, it's 100 (and you can call it a hundred if you want to, since that's just a name for a number that's your base plus one. One of nice things about a nonal system is you can take a square root of the base and have an even number: 3 x 3 = 10 (nine decimal).

It really is just that the decimal system is what you are used to. And you can use any base you want to. If it's higher than 10 you just have to come up with new symbols (or recycle familiar ones) to represent the numbers from 1 to your new 10. Don't think of your 10 as ten in decimal, (you can call it that if you want to); you have to train yourself to think of it in terms of your base.

For example, if you use base 16, the convention is to use 1 through 9, then A, B, C, D, E, and F to represent what we think of as 10 through 15 in base ten. 10 is not ten, it's F plus 1. And 100 is 10 times 10, but if you convert it it comes out to 256 in our decimal system. Makes for compactness when dealing with large numbers, and works really well on the computer.

The one I'd like to see is a trinary system for computers. Binary of course is 1s and 0s. Ons and Offs. But in a trinary system, you would have plus charge, minus charge, and neutral, at least the way I put it together in my mind. In fact, though I've thought of it before, this may well be the first time I've actually told anyone about it. It just seems to me that you can make computations a LOT faster than you can in binary, since information would flow 50 percent faster. Though not being a computer whiz I'll admit that's speculation on my part.

It would be 1, 2, 10, 11, 12, 20, etc. 10 would be our decimal 3, 20 our decimal 6, and 100 our decimal 9.


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Quote:



Also--is our duodenal system so called due to some relationship to the number 12?




Did we not read our A.W.A.D. today??

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>you can take a square root of the base and have an even number: 3 x 3 = 10 (nine decimal).

a less confusing way to say that is that the square root of the base (10) is a whole number (3), 3 being odd. : )

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> It really is just that the decimal system is what you are used to.

yeahright. So what's 17 and a half percent of 15 guineas 18 shillings and sevenpence three-farthings?

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Quote:

Our crazy old currency, complete with farthings, ha’ppennies, pennies, tuppences, thre’penny bits, tanners, shillings or bobs, two-bobs, half-a-crown, crown, pound, and guinea was generally known as ‘the duodecimal system’ ~ but only once we had started discussing then implementing the alternative…





I remember the changeover (and even the date, Feb 15th 1971). My sister and I had a game called "decimal snap". It was just the card game Snap, but you were allowed to call "Snap!" if you put down (for instance) 1 new penny, followed by 2.4 old pennies (as they were equivalent). Highly educational.

Getting back to the topic of words, the system was sometimes referred to as LSD which is an abbreviation for Libri, Solidi, and Denari (latin) I think (from memory). I assume the old pence symbol "d" was because of this, and the pound symbol is a stylised L. I look forward to being corrected if I'm wrong!

One of the claimed advantages of the LSD system was that 240d in the pound had many integer divisors: 2,3,4,6,8,10,12,20, 30... So much more flexible than the decimal system :-) Of course, as someone says below, calcuting 10% of some arbitrary sum was tricky.

Alan


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> It really is just that the decimal system is what you are used to.

yeahright. So what's 17 and a half percent of 15 guineas 18 shillings and sevenpence three-farthings?




And people who used this monetary system once had a globe-girdling empire? Just think what you mighta been able to do if you had had a decimal monetary system and hadn't been wasting a third of your GDP doing really ugly arithmetic. That's the real reason the colonies borke away, innit? c'mon, 'fess up. Well that and the terrible habit of putting udder drippings into your tea.


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And people who used this monetary system once had a globe-girdling empire? Just think what you mighta been able to do if you had had a decimal monetary system and hadn't been wasting a third of your GDP doing really ugly arithmetic. That's the real reason the colonies borke away, innit? c'mon, 'fess up. Well that and the terrible habit of putting udder drippings into your tea.

Pistols at dawn, TEd. Name your second.

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Today's word is nifty because it can be divided by 1, 2, 3, 4, and 6

But I like 36 because you can divide it by 1,2,3,4,6,9,12,18. However, imagine the size of the multiplication table

http://www.wordwizard.com/ch_forum/topic.asp?TOPIC_ID=17971&SearchTerms=36

However, one very neat advantage of the HEXATRIGESIMAL system is that it uses all the digits and all the letters of the alphabet: 0, 1, 2, 3, ....9, A, B, C,...Y, Z, 10

Where "10" reps 36


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Quote:

> It really is just that the decimal system is what you are used to.

yeahright. So what's 17 and a half percent of 15 guineas 18 shillings and sevenpence three-farthings?




The problem with that monetary system is not that it wsn't base ten; it's that it wasn't base anything consistent.

Four farthings to the penny.
Twelve pence to the shilling.
Twenty shillings to the pound.

And that's not even counting things like crowns (five shillings) or guineas (one pound and one shilling). If you'd had thirteen pence to the shilling and thirteen shillings to the pound and scrapped those silly crowns and guineas and learned your times tables in base thirteen you'd shake your head in wonder at how anyone could work in something as silly as base ten.

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you've put your foot on it, and I think we're inching towards understanding.


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> your times tables in base thirteen you'd shake your head in wonder at how anyone could work in something as silly as base ten.

yeahright and had to take your socks off to count when in your formative years!

Alan, forgive these rude buggers - a warm welcome, especially as you may help to redress the cross-pond perspective! Yes, you're right of course - in daily use it was called "the LSD sytem".

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Regarding the difficulties of calculating percentages in non-base-ten systems - don't forget the bias implied in the name. Percent = per centum = per 100 ==> base ten is presupposed. In a base-12 world if you made it "per 144," it would still be written as one-zero-zero and the computations would be just as easy. Likewise the shifting of a (duo)decimal point would be just as easy and other shortcuts in arithmetic probably even easier, because of the multiple factors of the base.

As [whoever-it-was] said above, whatever you're used to is what's easiest and "natural."

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From today's Word:
The first portion of the small intestine (so called because
its length is approximately twelve-finger breadth).
It IS! I tried looking it up yesterday, but could not find why it is called that.

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I think ease of use is a learned thing.

I learned the decimal system in school but also use a duodecimal system at work. Most cases in our industry are packed in twelve or multiples of twelve. A gross is 144 – or, if you prefer, a dozen dozen.

When I first started in sales, and counted inventory of bottles at store level, it would be in multiples of twelve (as in, 2,4,6,8,10, ONE 2,4,6,8,10, TWO 2,4,6,8,10, THREE, and so on.) It was much quicker than counting in multiples of ten then having to divide. It wouldn't have been complicated to divide, but why do that when you can count in the correct multiple and get the correct count immediately.


EDIT: typo

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42? bah humbug! 37!!

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Quote:

The problem with that monetary system is not that it wsn't base ten; it's that it wasn't base anything consistent.

Four farthings to the penny.
Twelve pence to the shilling.
Twenty shillings to the pound.




Before laughing too much at the mote that used to be in someone else's eye, we should consider the some of the logs in our own, e.g.

3 teaspoons in a tablespoon
2 tablespoons in an ounce
8 ounces in a cup
2 cups in a pint
2 pints in a quart
4 quarts in a gallon

What's 17.5% of 3 quarts, 1 pint, 1 cup, 3 tbl, 2 tsp? Please answer in drams.

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> 3 teaspoons in a tablespoon

no wonder my pancakes don't turn out...


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3 teaspoons in a tablespoon
2 tablespoons in an ounce
8 ounces in a cup
2 cups in a pint
2 pints in a quart
4 quarts in a gallon






... and thus I find myself every year bringing my baffled students a cup measure, to convince them that a "cup" is not just any ole cup they might have lying around their houses...

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... and thus I find myself every year bringing my baffled students a cup measure, to convince them that a "cup" is not just any ole cup they might have lying around their houses...




Is there no equivalent in Spain, Marianna? In Brazil we had tea cup (xícara de chá) and coffee cup (xícara de café) for cup and quarter-cup.

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What's 17.5% of 3 quarts, 1 pint, 1 cup, 3 tbl, 2 tsp? Please answer in drams.

What base would that 17.5 percent be in?


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tsu: Thank you for that link. I have fwded it to my No. 1 Son who will appreciate it as he's into that sort of thing

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tsu: Thank you for that link. I have fwded it to my No. 1 Son who will appreciate it as he's into that sort of thing




please pass along also the ironic intent of that post.

(for those who suffer from irony deafness*, the point perhaps being that you could take any number between, e.g., 3 and 57 and develop a similar thesis.)

*this link brought to you by the TTCAAC** committee***

**Those That Celebrate Anu's Aniversaries Committee

***I know, I know...

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great link, t. thanks.


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Quote:

Quote:

The problem with that monetary system is not that it wsn't base ten; it's that it wasn't base anything consistent.

Four farthings to the penny.
Twelve pence to the shilling.
Twenty shillings to the pound.




Before laughing too much at the mote that used to be in someone else's eye, we should consider the some of the logs in our own, e.g.

3 teaspoons in a tablespoon
2 tablespoons in an ounce
8 ounces in a cup
2 cups in a pint
2 pints in a quart
4 quarts in a gallon

What's 17.5% of 3 quarts, 1 pint, 1 cup, 3 tbl, 2 tsp? Please answer in drams.




lol! Great post, Myr. You could also mention the one that we both still suffer from - ok, we don't use rods, perches, chains and all that old guff now, but we still have the ridiculous legacy of inches, feet, yards, miles...! Even worse, in the UK we have a typical British compromise: my mum bought some material for upholstery work, and it was sold as 11 metres of 56" width!

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And here I've been thinking that the U.S. was being dangerously progressive ever since they started selling Cokes in two-liter bottles...

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Lousy memory coming back to haunt me. I was on our HS math team.
We had a problem once, a small piece of which required us to know how many teaspoons in a tablespoon. I had never learned this in math or any other part of my school education. However, being a momma's boy, I was always in the kitchen and had asked my mother who told me that 4 tsp = 1 Tsp. So I missed a sure thing.

Anyways, I learnt the meaning of "trust, but verify."

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I recently was part of a discussion with a native of Ireland about cooking using volume instead of weight measurements. He ended up with a gift of measuring spoons. Now I'm saving butter wrappers, to share the magic of measurement-marked packaging.

Leading to the revelation for some of the meaning of a "stick of butter."

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*this link brought to you by the TTCAAC** committee***


... and that codes for what protein, did you say? The one that makes butter, maybe?

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Is there no equivalent in Spain, Marianna? In Brazil we had tea cup (xícara de chá) and coffee cup (xícara de café) for cup and quarter-cup.




Not really, as we mostly see weight measurements in recipes. That's why the kids interpret "cup" as "any cup", and they are surprised that there is a standard.

Fortunately, for this situation we have found an incredibly useful link!

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Weight measures are, of course, far more accurate.

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You'd think so, but most kitchen scales are not that sensitive.

For example, in a recipe for Fungible pudding we once got, (thank you Mav) the measures were in weight. I used a kitchen scale and found that I could add tiny bits and the arrow wouldn't change noticeably.

I think that this non-preciseness would be comparable to volume measures...like when your tablespoon is a little over-filled and the liquid-pressure (I know there is a name for this but can't recall it) is keeping the tablespoon from overflowing.

I did notice the recipe took longer to prepare with the scale though. There's the whole, "add a bit, look, add a bit, look, ooops, remove a tiny bit, ooops, removed too much, add iota. O.k. that's good," thing you have to go through.

With measuring cups and spoons, you scoop, scrape top with a straight-edged knife and voilà, you're done.

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yeah, true bel; but I always find that the first time of trying a recipe - my favourite approach is to read several recipes and then abstract a general sense of what I'm aiming at. I hate the anal thing of 53g of this and .468cl of that!

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... I hate the anal thing of 53g of this and .468cl of that!




What's 17.5% of the net total? I gotta tip my scale.

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...and the liquid-pressure (I know there is a name for this but can't recall it) is keeping the tablespoon from overflowing...



meniscus

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surface tension.. some fluids (like water) have it, and you can ever so slightly over fill a measuring spoon (or a glass) and some fluids don't.

alcohol has less than water, so when measuring flavor extracts (like vanilla) the spoon overflows more easily.

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Ooops, Mav, I hope you didn't think I wasn't grumbling at you...I was thanking you for sending the recipe - it's a fabulous pudding. It is the only recipe I've ever received that measured in weights, so was the only one I could use as an example.

Bec-bec.


----------------------------

Suface tension / miniscus

Thanks ladies. I remember in grade school, the teacher doing the "is this glass full" in front of us kiddies as she kept adding drops of water to the glass, and being awed when looking sideways and seeing the water higher than the glass. Ah, the sense of wonder of little kiddies, eh?

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Quote:

Weight measures are, of course, far more accurate.




Quote:

You'd think so, but most kitchen scales are not that sensitive.




*measures, not *measurers . . . but I get your point.

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I made a steamed pudding once and halved the entire recipe...well almost the entire recipe. I accidently used the full measure of butter. Took nearly twice as long to cook but tasted fabulous.

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>Ooops, Mav, I hope you didn't think I wasn't grumbling at you...I was thanking you for sending the recipe - it's a fabulous pudding. It is the only recipe I've ever received that measured in weights, so was the only one I could use as an example.
Bec-bec.
~~~~~~~~~~~~~~~
No, not at all, sweet thing - I don't think I didn't not think for scarecely not any time at all that you weren't not grumbling at me... or was that yes?

and anyway, that was a fun conversation it sparked, realising how much measurements vary across our globe, wasn't it?

bec~bec a toi aussi

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Quote:

Quote:

...and the liquid-pressure (I know there is a name for this but can't recall it) is keeping the tablespoon from overflowing...



meniscus




I injured my knee last year and, after an X-ray, the doc said I had a torn meniscus. I think. I'm not sure. Anybody know enough about anatomy/etymology to tell me if it's the same word and if, so, what's the connection?

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meniscus in physics (the water thingy) is called that because it is shaped like a crescent moon. The same for the medial and lateral meniscuses (menisci)(menisca) in your knees. They are chunks of cartilage that keep the femur from wearing away the head of the tibia. Or is it the fibula. The larger of the two bones in the lower leg, I think, is the one that articulates with the lower end of the femur. Right near the cruciate ligaments, which, as you might imagine, are cross-shaped.

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¼ penny = farthing (obsolete from waybackwhen)





I'm not that old but I can remember farthings from my childhood. Black Jacks were originally a farthing each, and then became 4 for a penny.


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i remember farthing too, my dear mr bingley, from my childhood trip to ireland.. i don't remember what 'penny' (US Penny) candies were available in the 'shop', but there were candies available..

(what i like best, was when my mother in her muddled confusion, would give us shillings (12 pence) instead of dimes. back then,(1960) the pound was about $5.75 US dollars, and a shilling was a small fortune to a child!)

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So "farthing" from "fourth" or "quarter"

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This may or may not tickle your literary fancy, but the number twelve plays a vital role in the Western musical scale.

There are twelve half-steps in an octave (which gets its name from there being eight notes in the major scale). On a fretted instrument such as the guitar, there are twelve frets to an octave. The length of a vibrating string fretted at the twelfth fret is half as long as the length of the open string. This difference (and similarity) in wavelength and frequency is perceived by the listener as one octave, such as middle C and the C above that, or the opening guitar riff of The Knack's "My Sharona," or the bass guitar riff in Led Zepplin's "Immigrant Song" for you rock and roll fans.

The distance between frets on a guitar is related to the number 12 as well. For a given scale length, such as 25 inches, the first fret is placed at a distance that is the twelfth root of (0.5). (i.e. the number which when multiplied by itself twelve times equals 0.5, which happens to be 0.943874.)

Thus the first fret is placed at 25-25(0.943874) = 1.403142 inches from the nut at the top of the guitar neck, or 23.596857 inches from the bridge.

The second fret is placed at the same relative interval to the remaining length. It is placed 23.596857 * 0.943874 inches, or 22.272467 inches from the bridge.

This iterative process leads to the result that, at the twelfth fret, we have arrived at a point that is 1/2 the distance of the whole string, in this case 12.5 inches.

The musical notes that we experience when we listen to music are our brains' representation of mathematical differences and similarities in wavelength and frequency. Other cultures and musical traditions may divide the scale in other ways, and their music sounds as harmonious to them as Western music sounds to my Western ears.

An online fret calculator used by musical instrument makers is available HERE, and allows you to enter your scale length and the total number of frets on the neck (not the number of frets in an octave--it's hardwired for a 12-step scale).

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Thanks!

(perhaps mathematics, here, is a representation of what we perceive)

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Yes, I too remember blackjacks and fruit salads at 4 for a penny and two for ha'pence, but the farthing went obsolete in 1956.

I had forgotten to mention the sovereign and 'half sov' ~ and now I stop and think again, I remember my grandad telling me about some of the oddities, like the silver tuppence...

Hey, Bing and OT, you remember the groat, too? and the noble, angel and mark?!

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farthing might have gone from UK in 1956, but in ireland, they lingered..

as for noble's angel's and mark's, i have only read about them in historical novels...
*************************************************

another '12th' cycle are the tides, that move by rules of '12th's' --i always forget exactly how, but the volume of water that 'moves' increases by 12ths (1/12, 2/12, 3/12, 6/12th, is the progression, i think-- (and the reversed, 6/12th, 3/12th,..)

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From mav's link:
mark obsolete medieval denomination
more common in Scotland

Did Scotland used to be related to Germany?

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Quote:

Before laughing too much at the mote that used to be in someone else's eye, we should consider the some of the logs in our own, e.g.

3 teaspoons in a tablespoon
2 tablespoons in an ounce
8 ounces in a cup
2 pints in a quart
4 quarts in a gallon




I think that presenting the measuring system that way you're obscuring some sense of order that is really there. Look at it this way:

For liquid measurement:
16 tablespoons to a cup
16 cups to a gallon

A quart, being a quarter gallon, is naturally 4 cups.
A pint, being an eighth of a gallon, is 2 cups.
A firkin (honest!), being 9 gallons, at first appears to be a strange unit, but 9 gallons is equal to 144 cups.

As for tablespoons and ounces:
2 tablespoons to an ounce = 2^1 tablespoons
8 ounces to a cup = 16 tablespoons = 2^4 tablespoons
16 ounces to a pint = 32 tablespoons = 2^5 tablespoons
32 ounces to a quart = 64 tablespoons = 2^6 tablespoons
128 ounces to a gallon = 256 tablespoons = 2^8 tablespoons

Traditional dry measurement units also have an orderly progression:
1 quart = 2 pints = 2^1 pints
1 gallon = 8 pints = 2^3 pints
1 peck = 16 pints = 2^4 pints
1 bushel = 64 pints = 2^6 pints

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Well that's very odd. 1956 was the year before I was born, but I definitely remember my grandfather giving me some farthings and I'm pretty sure I spent them on blackjacks.


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You are right, Bing – although the coin was last minted in 1956 it stayed in legal tender until 1960. I should have checked my facts on an English rather than American site!

http://www.tclayton.demon.co.uk/farth.html

It’s also worth remembering that there were fractional farthings minted in the previous century: half-farthing, third-farthing, and quarter-farthing coins were minted at various times during the 1800s, but circulated only in particular British colonies and not in the UK itself for the most part. The exception was the half farthing, initially issued in 1828 for use exclusively in Ceylon but in 1842 it was made legal tender in the UK despite moans about it being far too tiny a coin to be useful. Although it only lasted until 1869 it must have been in common use since I had several examples amongst a simple coin collection as a kid.

To return to a language point, I have also been reminded that the ‘LSD system’ was not unique to Britain. At some point prior to the revolution (I don’t know when, YCLIU!) a similar pre-decimal system operated in France, also based on the Roman currency, consisting of the livre (L) sol (s) and denier (d).

http://en.wikipedia.org/wiki/Roman_currency

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Quote:

I think that presenting the measuring system that way you're obscuring some sense of order that is really there. Look at it this way:




On the other hand, you've just ignored the tricky parts, which was the point.

Here I have a simpler system.

1 pound = 1 pound.

That's it. What could be easier. Now my poor grandmother doesn't have go back to school to learn about powers of two to use all the recipes she's made for 80 years ... of course, now she can only make pound cakes but that's a small price to pay for such an elegant system of measurement

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Exactly what tricky parts have I ignored? I don't think I've ignored the tricky parts at all. I've presented them in a working context that makes them seem less tricky in the first place.

There is no denying the appeal of a metric system where each unit is an order of magnitude different from its neighbor, but when it comes to cooking, the old system's units tend to be easier because you can use 1 tablespoon instead of 15 mL, or 1 cup instead of 237 mL. So there's a practical advantage because the units are sized for household work. A milliliter is too small a unit for cooking. A liter is too big. Do you want to measure out 2.37 deciliters of milk or one cup?

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While I agree with the first para in your post whole-heartedly, Alex, I think the second is a little tongue-in-cheek?

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> when it comes to cooking, the old system's units tend to be easier

Having been schooled old time and come later to metric systems, I can as a keen cook firmly disagree with this view Alex. The metric units make no difference since you just get as empirically used to the look of 200g of pasta as you might to 4 cupfuls or whatever of rice; but the clear advantage with metric systems comes whenever you need to scale the quantities in a recipe. It's far easier to make a mistake when you have to change the unit of measurement rather than just the numerical value.

Then there is the additional advantage of ease of communication, since most of the civilised world uses the superior system! Of course I wouldn't want to make an American blush by mentioning communication problems, so I will avoid all discussion of failed mars landing probes due to cocked up arithmetic in a mish-mash of units...

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Which leads us to the burning question, is Mars metric?

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No, but Ares is.


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Having worked for a few years as a baker, converting family-sized recipes to a restaurant-sized recipes from time to time, I can say that the metric system does have an appeal in the simplicity of multiplying by ten, but you get so used to the 16 tablespoons to a cup and 16 cups to a gallon conversion that it isn't hard at all. But while the metric system offers some initial ease of conversion, it comes at a price of rarely getting to measure anything in small whole numbers or even one and half of anything.

Take the following bread recipe in imperial units:

imperial units
4 cups unbleached all-purpose flour
1 tablespoon light brown sugar
1 1/3 cups warm water (110 degrees F/45 degrees C)
1 1/2 teaspoons salt
1 1/2 teaspoons olive oil
1 (.25 ounce) package active dry yeast

1 egg
1 tablespoon water
2 tablespoons cornmeal


Convert this to metric units:
946.35295 ml unbleached all-purpose flour
14.7867648 ml light brown sugar
315.450904 ml warm water (110 degrees F/45 degrees C)
7.39338242 ml salt
7.39338242 ml olive oil
1 package active dry yeast

1 egg (no conversion necessary but the egg should come from a French hen)
14.7867648 ml water
29.5735297 ml cornmeal

Now of course you'd round the metric units up to some reasonable integers so you weren't squinting at the decimal points all day, but since we're going to try to make this recipe even more convenient by using 1 of something, let's do our rounding at the end.

So let's say we're going to slightly enlarge the recipe to use exactly one liter of flour for ease of execution. That isn't such an increase that our dough will be too big for the pan. Since we increased our flour from 0.946 liters to 1.0 liters, we'll increase everything in the recipe by 1/0.946 or 1.057:

1 liter of flour…
1 liter of flour
16.5 ml light brown sugar
333.3 ml water
7.8 ml salt
7.8 ml olive oil
1 package active dry yeast

1 egg
15.625 ml water
31.250 ml cornmeal

Now let's round those numbers to some reasonable integer values since noone wants to measure 7.8 ml:

1 liter of flour
16.5 ml light brown sugar (or round it down to 15)
333.3 ml water
8 ml salt (or round it down to 7.5)
8 ml olive oil (or round it down to 7.5)

1 egg
16 ml water (maybe round this down to 15)
31 ml cornmeal (maybe round this down to 30)

Now here's my point: measuring 8 ml of salt or olive oil is a pain in the arse. Now I expect that what's used is a 5 ml measuring spoon and a 2.5 measuring spoon to get 7.5 ml and call it done. But who's doing more math in the execution phase: the person whose recipe called for 1.5 somethings and they used a 1 something measure and a 0.5 something measure, or the person whose recipe calls for 7.8 or 7.5 ml and they said to themselves, well, that's 2.5 + 5 ml, so I'll use a 5 and a 2.5 measuring spoon. The metric person ends up measuring more stuff in odd little numbers -- no wonder it's called the metric system. A good recipes sees a lot more execution than it does conversion, and I appreciate the simplicity of measuring 1 of this or 2 of those. It's as if someone assigned names to the frequently-used quantities from the metric system: 250 ml, let's call it a cup. 5 ml, let's call it a teaspoon. 2.5 ml, call it half a teaspoon.

Then again, 1 and a third cups is about pi deciliters, so maybe you're onto something there.

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bad example alex--any baker (as opposed to a cook or chef) will tell you
1--its much more accurate to measure flour for bread by weight, (rather than volume)

2--since flour can absorb moisture, (and the moisture make the flour heavier) you get better results if you make bread by weight (metric) than if you do it by volume.(cups or liters!)

i have (and have had for more than 20 years) a kitchen scale.

there are times when i cook by volume (imperial) but other times i cook (bake mostly) by weights-(mostly metric nowdays since my current kitchen scale has metric and imperial measures)

(there are other time, muffins, and quick breads, when i just wing it..and just add flour (till there is enough, and sugar, and fat the same way) and the results, after years of cooking are fine!)

its easier for me to work in imperial measurement, (i know them so well) but for baked goods, the results are more consistant if i work with metrics (and weigh out the flour rather than measuring out the flour!)

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Well if any baker can tell me, then this baker just asks himself: how exactly is it more accurate to weigh the flour?

I've never understood this. Flour will gain weight when it has absorbed moisture, which means that your x grams of flour on the scale is really slightly LESS flour than you think. Or to put it another way, the total water content of your recipe has already been partially supplied by the atmosphere. Unless your weighing operation tells you how much water to withold or how much flour to add I honestly don't see how it helps to weigh it. Perhaps you know exactly how much additional weight you need for a given hygrometer reading?

Conversely, unless you know how much the volume changes between 1 dry cup and 1 slightly damp cup of flour, you can't do much with the volume measure method to account for moisture either. But I suspect that the changes in weight are greater than the changes in volume for a given rise in humidity, which means that weighing would be less accurate than measuring. Maybe I'm missing something, though. Is it that by also weighing the salt, you can be sure that the proportion of salt to flour is constant? Seems like salt would absorb a greater proportion of water per gram than flour though...

In practice, when I bake bread at home I know that I will use roughly three parts flour for every 1 part water, but I mix it in gradually and add or subtract according to texture. I previously worked as a baker both in a restaurant and in a small bread bakery. In the latter, bread was made by dumping an entire x lb bag into Hobart floor mixer, then adding y gallons of water, using a gallon pitcher. For quantities that large the effect of the atmosphere was negligible.

Disagreements among cooks aside, my main point is that cooking with the metric system on a small scale requires one to operate between the main units. The imperial system on the other hand, directly correlates between units and actions. 1 teaspoon means that the cook takes the teaspoon and fills it up once. The analogous measure by the metric cook is either to take a 1 ml spoon five times (hardly likely), or a 5 ml spoon once, which strikes me as a surrogate for a teaspoon. If they called 5 ml a metric teaspoon I'd be fine with that. Likewise if you're constantly referring to a 200 ml or a 240 ml measuring cup, you're using a surrogate for an imperial cup rather than making optimal use of a ten-based system. But measuring everything out in odd amounts nearly equal to imperial units seems to be using the metric system with a wink.

The ideal kitchen measuring system would be ten-based like the metric system but would have units that agreed with the impositions of nature (e.g. the size of an egg) and the practicalities of living. For example the basic unit for a small spoon-like measure would ideally be the amount of salt you'd use in a common dish, something like that. The unit of liquid measure should be the amount of liquid most commonly used such as the amount of water in a loaf. And the conversion of units should be in an easy-to-calculate system such as tens. IMO the imperial system satisfies the practical criteria better than metric, and the metric satisfies the conversion criteria better.

For other purposes the elegance of the metric system is undeniable. e.g. 1 mL of water at STP has a mass of 1 gram. 1 cubic meter of water is one metric ton. And the fundamental unit of lenth, the meter, while officially described as the wavelength of a a certain color of light (sadly, not Kentucky blue), is about the length of a person's stride.

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>the meter, while officially described as the wavelength of a a certain color of light (sadly, not Kentucky blue), is about the length of a person's stride.

Not if you're born Toulouse.


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True, if you're born Toulouse, you have to make many more strides with your short legs to make le trek.

/Really, I got nuthin'

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Poor Toulouse. While a starving young artist living in a Paris atelier, he was the victim of a quick-moving fire in the middle of the night. He grabbed his Levis and headed out, but was overcome by the smoke. Luckily for him and for the world, a firefighter pulled him to safety and resuscitated him. His first words on regaining consciousness were, "Did you save my artwork?" The firefighter shook his head and replied, "I am sorry. You have nothing, Toulouse, but your jeans."


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Poor Toulouse indeed. Speaking of fire, I used to make fluxes for fire assay, a type of refining technique. This was not cooking, although a 900 C furnace was used, and at this temperature, small amounts of moisture are inconsequential (large amounts were!). It was important to weigh the ingredients (components) rather than measure them volumetrically. The correct ratios could be assured this way. Significant density variation could occur amongst the batches, due to the measuring-container packing techniques used by different technicians.

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packing techniques used by different technicians. Mm--as in, a cloud of flour will explode, but a cup of it won't?
Good to see you, my friend! [hug]

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Quote:

Exactly what tricky parts have I ignored? I don't think I've ignored the tricky parts at all. I've presented them in a working context that makes them seem less tricky in the first place.




Well, to start with - you left out teaspoons entirely. 48 teaspoons in a cup. 1/3 of a cup is also a very common measurement but no even number of tablespoons or ounces, but it's 16 teaspoons.

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How convenient then that you can use the 1/3 measuring cup included in your set, instead of spooning out 5 tablespoons and 1 teaspoon, which would be tiresome and ridiculous.

Honestly, my point was that there was some logic to the system, not that it's perfect. I think it is quirky that the system uses a multiple of 3 to go from tsp to tablespoon, when almost everything else is based on multiples of 4. But I never found it that hard on a mathematical basis to work with the 3 tsp/TB ratio. For one thing, I don't convert little units like teaspoons into big units like cups. If I were multiplying a recipe that originally called for 2 tsp of salt, it would have to be one hell of big dinner party before I was expressing the salt in cups. And even if I were making an 8 x recipe, it wouldn't be the end of the world to convert 2 tsp x 8 = 16 tsp = 1/3 cup. (If I'm throwing a dinner party for 32 people, then spending 3 minutes to enlarge the recipe is the least of my worries.)

With regular use I find the imperial system to be no more difficult than the U.S. currency, like when you're due $0.83 in change and it takes you no time at all to think, well that's three quarters, a nickel, and three pennies. You don't fret about the fact that a quarter is 1/4 of a dollar but 2.5 times a dime. You already know the coins as familiar objects so there's no stress. It's the same way for me with imperial system in the kitchen. YMMV.

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That's all fine. What I wondered about was problems converting imperial to metric, which is a different matter entirely.

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converting imperial to metric is not hard--provide you have 1 extra tool, and some newer (than 20 years old) measuring cups.

all my measuring cups have both cups and liters (or ml) marked on them--and have had since the early 1970's.

the extra tool? a kitchen scale. my current scale is electronic, (Under $25 at ikea) weighs things in lbs/oz (down to a quarter ounce!) and in kilo's. its good for up to over 3 kilo's. its about the size of saucer, and a set up for tare (so you don't weight the bowl with the flour)

1 liter is close to 1 quart--(as a rough measure) so reading and understanding a recipe isn't hard 250 ml of liquid is about 1 cup. (and the smaller the quanity of liquid required, the less precise one needs to be!
for many recipes, the slight difference between a quart and liter won't matter at all!

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