Talk:Decimal
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I've made tow changes. First, there was a statement that "It is the most widely used numeral system, perhaps because a human usually has four fingers and a thumb on each hand, giving a total of ten digits on both hands." The proper preposition is "over", not "on". "On" creates an ambiguity as to whether it means that each hand has a total of 10 fingers, or together have 10 fingers.
Also, there was a statement that + means plus and - means minus. When it comes to sign, that is WRONG. The signs are positive and negative, not plus and minus.
Decimal is the number system humans use because of the fact that we have ten fingers.
I heard that some cultures prefered to use the hexadecimal system because they didn't count their fingers on their hands. But instead, they counted with one hand using one thumb to touch on the finger tips and the bends at their finger joints. (There are 16 points on each human hand, hence a hexidecimal system.) However, the decimal system became so wide spread internationally that it dominates now.
I heard about this over twenty years ago from my high school teacher. I don't know his source of this information. I am wondering if any wikipedians out there can confirm this.
If the counting finger-joints technique were more prevailing than counting fingers, human society could have adopted the hexadecimal system which is much better compatible with binary computers nowadays.
The ancient Mayan civilization used base 20 in their numbering system. Their numeric symbols denote values from 0 to 19. (source: http://www.eecis.udel.edu/~mills/maya.htm)
Avoid fallacies in arguments. Just because the people that use decimal do so because they have 10 fingers doesn't mean that all humans use decimal. Nor does it invalidate any of these base 16 or base 20 systems. The article should point out that not all people use decimal (and I will edit it). --drj
I don't think there are any societies that used base 16 though. The highschool teachers story seems suspect. Base 20 is of course fingers and toes. But where does base 12 come from? --AxelBoldt
12 presumably comes from months of the year. Many calendars have 12 months in a year (not just because it is nearly the number of lunar months in a year). Imagine you are an early geek into factors and astronomy. Observe: 360 days in a year, aha! that factorises easily with nice factors like 12, 60, 24, etc. The base 16 claim seems very dubious to me. Fingers and toes didn't occur to me though it is plausible. --drj.
I think the 12, 24, 60 business came from the Babylonians/Persians? Somewhere that direction and long before Greece. --rmhermen I said "geek" not "greek"! Bablylonians/Mesopotamia is the generally agreed source I believe. --drj
Are roman numerals a number system? What is the base?
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- In Wikipedia, this is now called a numeral system -R. S. Shaw.
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- It's a number system, but not a positional one, so it doesn't have a base. --AxelBoldt
So perhaps the article on number systems should mention it?
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- In Wikipedia, this is now called a numeral system -R. S. Shaw.
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- Yes it should. --AxelBoldt
In the US weighing system, one pound = 16 ounces. In Chinese weighing system, one catty = 16 taels. Though they are not number systems, but at least it give some hints why the number 16 is involved in measurements universally. In any systems that use division, any power of 2 is a good candidate for convenience sake. For example, a gallon = 4 quarts = 8 pints = 128 fluid ounces = 1024 fluid drams etc.
Looks like human are attracted to the power of 2 and astronmonical periods and our fingers and toes.
A old British pound = 20 shillings
one old shilling = 12 pences
20 and 12 can still be explained, but 1 mile = 1760 yards??? how did they come up with that number?
Have you heard the story about how the butt size of the Roman horses decided the rail guage in the current US railroad system?
In decimal counting, the Fibonacci numbers repeat the sequence of the last digit over a period of 60. Every other numeral system with base less than 14, repeats in less than half of this (often 24).
Base Period of last digit of Fibonnacci Numbers 2 3 3 8 4 6 5 20 6 24 (last two digits too) 7 16 8 12 9 24 10 60 (unusually big) 11 10 12 24 (last two digits too) 13 28 14 48
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[edit] 12 and 60
I think it is quite established that the use of 12 and 60 in many cultures on several continents comes from the fact that 12 and 60 have 'relatively' many divisors, {1,2,3,4,6,12} for 12, and {5,10,15,20,30} in addition for 60. This is very useful when it comes to fractional quantities etc, especially before the introduction of p-adic numeral systems with fractional part.
I think the number of months is rather a consequence than a reason for the choice of 12: observe that a (natural, i.e. lunar) month is rather 4 weeks than 30 days, and 52 / 4 = 13, and not 12, (a (solar) year having 52 weeks plus about 1.25 days.) MFH 12:52, 8 Apr 2005 (UTC)
- A base other than 10 and 20 may be used in a measurement system for the division's sake, but it is rare to use such a base for a language's counting system. Duodecimal systems are used only in several North Nigerian languages and in the Chepang language of Nepal. The latter seems to be from the Nepalese way of counting using fingers (see the figure).
- The Babylonian sexagesimal system clearly had an internal decimal system, and 60 was used instead of 100 for ease of division. It is more appropriate to call it a mixed-radix system of bases 10 and 6.
- By the way, a year has about 12.368 months, not 13 — divide the solar year (365.2422 days) by the lunar month (29.53059 days). - TAKASUGI Shinji 10:42, 2005 Apr 12 (UTC)
[edit] synonym for decimal
I think we should start using the unambiguous word aal instead of decimal, because every base is decimal in its own base. Actually every time we say "base 10" we should say "base A" instead.
In this way we would always represent the base with the first digit that is not used for that base eg.:
base 2 ( = 10 in base 2) -> digits 0,1
base 3 ( = 10 in base 3) -> digits 0,1,2
base 9 ( = 10 in base 9) -> digits 0,1,2,3,4,5,6,7,8
base A ( = 10 in base A) -> digits 0,1,2,3,4,5,6,7,8,9
base B ( = 10 in base B) -> digits 0,1,2,3,4,5,6,7,8,9,A
I've been thinking about this for years, so I hope you all will agree with me on this.
--Ortonormale 00:47, 2005 May 11 (UTC)
It may be good to remember that the root "deci" means ten and "a" is a letter that is not associated with the base ten number system (why add another thing to confuse people?). Besides, saying "aal" would be more ambiguous than saying "Decimal". It sounds the same as "all" -Michael
- very funny. but
Yes, you would be right. I mean that since the discovery of base conversion, numerals have acquired new meanings while losing the direct link to their etymology. We could say that a new abstract level has been introduced between the original etymological meaning and the new virtual meaning. For example: 11 in base 2 represents the same quantity represented by 3 in base 8. Luckily or unluckily (according to your point of view) we have not a different set of names for each numeral in each base, therefore we have two possibilities:
- we can spell each numeral in every base but the base A (really sad)
- we can extend the same language structure we already use for base A to all bases up to Z.
In this latter case, we could simply say "eleven" to read the numeral 11 in whichever base. The same concept would apply to "ten", "decimal" and "digit".
Obviously, we would have ambiguities when not specifying the actual base, but this already happens when writing.
Nothing really fun so far. The funny part comes when we want to read numbers like
- APPLE that is: "aytypee thousand pee hundred eltyee"
- CRAZY that is: "ceetyar thousand ay hundred zeewy"
- SPELLING that is: "espee million ee hundred eltyel thousand i hundred entyjee"
- DECIMAL that is: "dee million ee hundred ceetyi thousand em hundred aytyel"
Again: obviously (as you have noticed) we would have an obstacle to complexity increase trying to use bases that are greater than Z, but this already happens when writing. It is a common problem for non positional numbering systems, but a simple solution consists in grouping. So for example we could use the base 2xG (or simply 2G) in which each digit is represented by a group of 2 digits in base G, like
- 20 08,
- simply spelled "two zero blank zero eight" or
- spelled-read "twenty zerotyeight" or
- read "twentytyzerotyeight"
- A5 47 FF 00,
- simply spelled "ay five blank four seven blank ef ef blank zero zero"
- spelled-read "aytyfive fourtyseven eftyef zerotyzero"
- read "aytyfive thousandty fourtyseven hundredty eftyeftyzeroty"
--Ortonormale 00:22, 2005 May 19 (UTC)
- I find it totally meaningless. Don't confuse numbers and notations. Ten is ten, the number of circles in oooooooooo whichever base you use. Likewise, decimal always means base ten. What 10 means depends on the base, but decimal is default. No one would call (10)2 ten. It's two. - TAKASUGI Shinji 06:25, 2005 May 19 (UTC)
[edit] Finger and base 10
The article claims that we use decimal numbering because humans have 10 fingers. I find this claim highly suspect: 10 fingers is sufficent to count in base 11 (just as one finger is sufficent to count in base 2). Does someone have a good citation for this? --Gmaxwell 20:33, 22 May 2005 (UTC)
- I don't have the citation you request, but I think it's a very sensible claim even without documentation. A few things I find relevant:
- Base 10 in number words is older than base 10 in a positional number system.
- Try teaching a child (age 4-7) to count-in-11's using the fingers of two hands; then (when you have despaired) try teaching counting-in-10's instead. Or try teaching counting-in 6'5 and counting-in-5's using one hand only.
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- Right. 10 fingers. 0 (no fingers) 1,2,3,4,5,6,7,8,9,10 ... Which is all of the single digit symbols in base 11. Really. Base-11 is more obvious for hand counting than base-10, as long as you have a concept of zero. --Gmaxwell 22:35, 23 May 2005 (UTC)
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- The chinese abacus has 5 beads on each wire to represent values 0-4 (the 5th being used only temporarily in calculations). The japanese abacus is similar but has done away with the extra beads, at the expense of making its use slightly harder to learn.
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- Right, I know how to use a chinese abacus. I'm not following how it helps this argument. ... Thanks for replying though... I honestly didn't expect a reply anytime soon! --Gmaxwell 22:35, 23 May 2005 (UTC)
Zero is an artificial mathematical symbol, unnatural for human perception. "Decimal" does not *necesarily* imply that 10 is spelled using two symbols. When you start counting fingers, 10 ranks the same as each of the 1 to 9 numerals. So, why ten and not eleven? Try to quickly show the number 30 by flashing your fingers. It's as natural as... 123. Now, try with 33. Still think that base eleven suits your fingers? Luciand 15:50, 29 December 2005 (UTC)
[edit] This article may need work
I am not really happy with the current TOC:
Contents
* 1 Decimal notation
o 1.1 Alternative notations
o 1.2 Decimal fractions
o 1.3 Other rational numbers
o 1.4 Real numbers
* 2 History
o 2.1 Decimal writers
* 3 See also
* 4 External links
The article is about decimal notation, so it does not make sense (to me) to have a section titled "decimal notation". And even if it is there, I don't see why one should have a subsection called "Alternative notation". That should be its own section, preferably at the bottom, as it is a related topic to decimal notation, but not the focus of the article. Comments? Oleg Alexandrov (talk) 00:54, 22 February 2006 (UTC)
[edit] "perhaps" because of ten fingers?
Is there any other theory at all for explaining the decimal system?
From a mathematical point of view, I see no argument that could be made for ten - two (or powers of two) is special, of course, since it's the smallest possible base (powers of two are just a neat way of cramming several binary digits into one handy symbol), three would give you balanced ternary, and I believe you can formalise the fact that 12 has a large number of factors.
Of course, it's possible that there might be a psychological aspect that makes 10 a natural choice, or that it was just an accident of history, but in the absence of support for either of those theories, maybe we should state this a bit more strongly?
RandomP 18:51, 13 May 2006 (UTC)
- The words for five and hand are related in many languages, especially in New Guinean languages. And ten or twenty is called as a person in some languages. That strongly suggests our ancestors counted their fingers. How easy division will be is pointless - counting is much older than division. Languages of base-6 (Ndom), base-8 (Yuki), base-15 (Huli), and base-24 (Kakoli) have been reported.
- Source:
- - TAKASUGI Shinji 14:33, 15 May 2006 (UTC)
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- Thanks. Certainly interesting to know, but note that my question was whether there is any other theory for the use of ten, other than that that happens to be the number of non-thumb fingers.
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- RandomP 15:21, 15 May 2006 (UTC)
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- Gee, counting "non-thumb fingers" would lead us to use base 8 among most members of my species. Anyway, the mention of bases 6, 15, and 24 suggest the human predisposition to finger use is not absolutely overwhelming. -R. S. Shaw 18:55, 15 May 2006 (UTC)
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- Oops, sorry. I meant to say "fingers including thumbs", but got confused. Nothing to do with my extra pinkies, I assure you. RandomP 23:03, 15 May 2006 (UTC)
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- New Guinea, the most linguistically diverse area in the world, have various bases such as 4, 5, 6, 10, 15, 20, and 24. Body-part tally systems are also common. Eurasia is almost unified under decimal, with scattered vigesimal systems in its outer rim - Celtic languages, Basque, Caucasian languages, Dravidian languages, Burushaski, Ainu, etc. That suggests decimal spread and overwhelmed other bases in Eurasia. It seems to me China was the origin of decimal, because it has had a strict decimal system from the beginning while many other languages have special words for teens and decades. - TAKASUGI Shinji 00:18, 16 May 2006 (UTC)
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