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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. edit: sp 
Last edited by maverick; 03/13/2006 4:10 PM.
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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
Last edited by maverick; 03/13/2006 4:42 PM.
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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.
TEd
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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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formerly known as etaoin...
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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
--
Alan Fitch
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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?
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.
TEd
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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=36However, 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
dalehileman
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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
Last edited by belMarduk; 03/14/2006 8:06 PM.
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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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Quote:
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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Quote:
... 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?
TEd
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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
Last edited by dalehileman; 03/14/2006 11:59 PM.
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Quote:
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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formerly known as etaoin...
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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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veteran
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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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Pooh-Bah
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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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Quote:
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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Quote:
... 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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