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Forum » SpaceEngine » Off-topic Discussions » Number bases: history and possible future. (History in detail. Discuss usage of other bases.)
Number bases: history and possible future.
Gondor2222Date: Wednesday, 14.08.2013, 00:49 | Message # 1
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Warning: this post is VERY long so I've condensed it into a series of spoilers. There's a lot of history in here so if you want to just get to the debate without taking into account ancient linguistic theory feel free to skip to sections relevant to your interests.

Basic explanation if you're not aware of how a positional number system works:


Prehistory of the development of base ::::: and why we call it "ten":



The earlier nonpositional systems:

Latin: the long story with the history of each symbol:


Latin: the short story:


Arabic numerals: origins:



The language of numbers and its relevance to the base-debate:


The possible proposals and their merits. In this section, I have expressed those numbers for which base-::::: and the given-base representation refer to different quantities using dots. For example, decimal 6 is represented as ::: in base 4 but 6 in base 7.


So, reading what you guys have from this, what do you guys think? Questions and discussions on the language of numbers and the theoretical adoption of other bases is welcome in this thread.


Edited by Gondor2222 - Wednesday, 14.08.2013, 00:51
 
midtskogenDate: Wednesday, 14.08.2013, 17:37 | Message # 2
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Quote (Gondor2222)
descendents also include Hittite

Some have argued that Hittite is a sister language of IE, that IE and Hittite share a common ancestor. This to explain some features in Hittite that IE lacks, such as the three genders. It's a finer point of classification in my opinion, and the gender system in Hittite just serves as an excellent explanation for how genders arose in IE.

Quote (Gondor2222)
reconstructions indicate that the name for "five" was probably the word for "fist"

I don't think that is well supported. I think it's lost to obscurity. It has been proposed that IE penkʷe is the postfix "and" (-kʷe) and a word for thumb, then meaning "and the thumb". A colourful explanation, suggesting that counting arose from naming the individual fingers and last and fifth the thumb. But I doubt it.

Quote (Gondor2222)
the name for "ten" was probably the two words for "two hands"

dekṃ(t) = de-kṃt ("two hands")? It's really tempting to read the de- as "two". And "kṃt" looks very similar to Germanic "hand" which is otherwise unexplained. But this I think belongs to pure speculation. It looks more likely that dekṃt "ten" and kṃtom "hundred" are related (not necessarily excluding the "two hands" hypothesis), but how or even which way doesn't seem entirely clear.

What is pretty certain is that our counting system arose from the number of fingers (otherwise a more practical base would have been chosen), and that the names for the numbers are very, very old and have changed relatively little. They're certainly recognisable if we go back more than 5000 years.

Note that there is another non-IE language in Europe not related to anything else, Basque. It's probably the last surviving remnant of a language group that was widespread in Europe before the IE invasion. It uses a vigesimal counting system, and it has been suggested that Basque has influenced French, Danish and Celtic languages which have a semi-vigesimal system.

Quote (Gondor2222)
its daughter language Proto-Germanic began calling ten tens "kmtom count" in their own language, indicating that the original kmtom was not a definite count to begin with.

I'm not sure what you're saying here, but it's worth noting that "hundred" in Germanic languages meant "120" well into the middle ages. It may be an early Germanic invention.

Quote (Gondor2222)
then M. Larger numbers didn't become necessary until after the fall of the western Roman Empire, and so are less important here.

There was a need for larger numerals (than 1000) even during the republic. Such as in economy. There exist a couple of notations: adding lines around the letters or stacking up like this: CCCCIƆƆƆƆ (deciens centena milia, 1,000,000), but I don't have my books here to check what was used in the different periods. I think, though, such extra notation frequently was omitted, assuming it was understood whether the counting was in singles, thousands or 100,000's.

A discussion of the Babylonian numerals would fit in here as well, which was sexagesimal (well, more precisely decimal-sexagesimal perhaps). The system survives in our minutes, seconds and angles.

Added (14.08.2013, 20:37)
---------------------------------------------
In my copy of my favourite encyclopedia, Natural history by Pliny, there are many big numbers, which are either written in full (such as "ā turbidō ad lūnam uīciēns centum mīlia stadiōrum" "from the windy air to the moon two million stades (=370,000 km)). Other places regular numerals with strokes above and/or to the sides to multiply with 1000 and 100,000. But the manuscript has been copied many times at the notation could have been updated in medieval times. So we must look at inscriptions to find certain examples of ancient use. In republic inscriptions I find symbols for 5000, 10,000 and 100,000. 5000 and 10,000 look like an extra D or M stacked outside an inner one, not unlike CCIƆƆ which I already mentioned. So such symbols did exist. The 100,000 symbol (circle with a vertical bar and to V's inside) was on an inscription dated as early as c. 260 BC.





NIL DIFFICILE VOLENTI


Edited by midtskogen - Wednesday, 14.08.2013, 19:44
 
Forum » SpaceEngine » Off-topic Discussions » Number bases: history and possible future. (History in detail. Discuss usage of other bases.)
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