Ancient Numbers: Expressing Values, Devision & Subtraction

[Mol_Bolom]

I believe this is the forum to ask this question...

What, English translated, words were used to express values less than 1 and greater than 0 when they were first used? Also, how was devision and subtraction first expressed?

Also, were there any languages in Europe, Africa, or Persia/India that expressed numbers backwards compared to how the Germanic languages speak? An example of this is the Tzotzil Mayan language which the number 479 would be spoken as balunlajuneb schanvinik sjunbok', which translates to 19, 60, 400, completely backwards to how the Aztecs would have said it, centzontli ihuan yeipoalli ihuan caxtolli ihuan nahui which would be 400, 60, 19...


Thanks...

 

[CRGreathouse]

The ancient Egyptians had a special symbol for 2/3. Any fraction 1/n they expressed as n with a symbol over the top (shaped like an eye or pointed oval, re or er I think).

So 1/3 would be something like $$\stackrel{\prec\!\succ}{\mid\mid\mid}$$ and 0.15 as $$\stackrel{\prec\!\succ}{\cap}\; \stackrel{\prec\!\succ}{\cap\cap}$$ (1/10 + 1/20).

 

[Mol_Bolom]

What about the language though? Does anything still exist as to how they spoke something like that?

Oh, by the way, is it possible to use Mayan numerals here? And how?

 

[CRGreathouse]

What about the language though? Does anything still exist as to how they spoke something like that?

We do have a good idea of how ancient Egyptian was spoken, thanks to its similarity to Coptic. It's an Afro-Asiatic language, closely related to (but not a member of) the Semitic languages like Arabic and Hebrew.

 

[Mol_Bolom]

We use point and 'and' to dicern between the decimal. 3.5 would be spoken as either three point five, or three and five, as well as three and five tenths. When speaking of it in fractions we say three and a half, or three and one over two...And so on so forth...

So what would one say, about 1000 years ago, when speaking of these numbers in their language? (Translated in English)...

I am curious to know how the language evolved around the use of these ideas...

I'm looking for a literal translation...Such as 'baluneb schiuk vaklajuneb spas vo'ob scha'vinik' (9 + 16 = 25), which literally translates to "9 with 16 makes/does 5 20".

 

[CRGreathouse]

For Egyptian, 23.3 would be written as 'ten ten one one one (part) five ten', representing 23.3 = 10 + 10 + 1 + 1 + 1 + 1/5 + 1/10. Spoken, the integer part would translate more like ours: 'twenty three'. I have no idea how fractional parts would be pronounced.

You could search for pronunciations on the terms online, but I don't know them.

Babylonian used base-60 for both integer parts and fractions; 23.3 would be said something like '(twenty three) & (ten eight) sixtieths' = 20 + 3 + (10 + 8)/60.But this is perhaps three thousand years ago. A thousand years ago there were decimal fractions in Islamic Africa and the Indus, which would soon be introduced to Italy via Leonardo of Pisa (Fibonacci).

 

[DeaconJohn]

For Egyptian, 23.3 would be written as 'ten ten one one one (part) five ten', representing 23.3 = 10 + 10 + 1 + 1 + 1 + 1/5 + 1/10. Spoken, the integer part would translate more like ours: 'twenty three'. I have no idea how fractional parts would be pronounced.

You could search for pronunciations on the terms online, but I don't know them.

Babylonian used base-60 for both integer parts and fractions; 23.3 would be said something like '(twenty three) & (ten eight) sixtieths' = 20 + 3 + (10 + 8)/60.


But this is perhaps three thousand years ago. A thousand years ago there were decimal fractions in Islamic Africa and the Indus, which would soon be introduced to Italy via Leonardo of Pisa (Fibonacci).

That's really impressive, Greathouse. If you did that off the top of your head, that's impressive. If you took the time to look it up, that's impressive. In either case, the clarity, brevity, and easy flow of your use of language is impressive. Much better quality than I've seen in the references that explain the material you are covering.

Really impressive, Greathouse,

DJ

 

[CRGreathouse]

That's really impressive, Greathouse. If you did that off the top of your head, that's impressive. If you took the time to look it up, that's impressive. In either case, the clarity, brevity, and easy flow of your use of language is impressive. Much better quality than I've seen in the references that explain the material you are covering.

I'll assume for a moment that you're serious -- I hope you're not cruel enough to post that in jest.

Heh, I guess the thousands of pages of linguistics I devoured over the past two years payed off. The only reference I used was a quick Wikipedia check to see if Egyptian was closely related enough to be a Semetic language, or if it was its own branch of Afro-Asiatic. The rest I learned either from my readings in linguistics, or my excellent history of mathematics class I took as an undergrad.

There are still some points left unaddressed, though. I don't know if there's a word to separate the integer part from the whole part ("and" in English); I don't know the pronunciation of the numbers; I'm not sure if the languages had coded numbers like "thirty", though I believe they did.

Also, more systems would be useful here. I do recall that Greek had two systems, one additive (resembling Roman numerals) and one coded (alpha = 1, beta = 2, ... __ = 10, __ = 20, etc.; this included several obsolete letters like digamma) but I think it was said much like our number system, at least for whole numbers. Both Greeks and Romans preferred to use smaller units than fractions; I know the Roman used uncia "twelfth" for money, weight, and length; it's the ancestor of our "inch" and "ounce". But beyond that I can't call much to mind.

 

[DeaconJohn]

I'll assume for a moment that you're serious -- I hope you're not cruel enough to post that in jest.

Heh, I guess the thousands of pages of linguistics I devoured over the past two years payed off.

I was completely serious. And, I'm not the cruel type. I'm much more the "marshmellow" type. Hence the icon I chose.

I really like linguistics, but, I have not studied it extensively. Certainly nowhere near thousands of pages. Maybe hundreds.

DJ

 

[CRGreathouse]

Yeah, around the time my friend got a degree in Linguistics I decided it was cool so I got some recommendations from him. I try to read at least a little every now and then; right now I'm reading a book on typology.