Not an unreasonable question, given that most non-human mammals (including all the other primates) don’t grasp the concept of pointing.
And I do have some personal (though not quite hands-on) experience with another spacecraft that carried a disc. When some of my grad school classmates made a picosat, one of the things they included on it (in addition to the scientific payload) was a small-format CD, carrying the names and personal messages of a bunch of members of the public. Everyone knew that after that disc was put into the satellite chassis, it would never be put in any CD reader again, and that it would burn up in the atmosphere in a few months or years, but still, people liked the idea of putting their messages in space, even if they’d never be received by anyone.
Septante and nonante are indeed used in Swiss French (also Belgian), but very few people apparently say octante, even though there is a pervasive belief that they do. Swiss francophones (but not Belgian) tend to use huitante instead, as per this article.
However, I question whether this is in any way related to the influence of Gaulish or other Celtic languages. In most cases where French people use one word but Belgian and Swiss francophones (and sometimes Canadian) use another, what happened is that the “Belgian and Swiss” term used to be prevalent among the francophone world while the “French” one was limited to the Île-de-France, and the influence of Paris over France made it the common French term while the other one only persisted outside France.
Spoken numbers in Thai may be interesting. There are separate one-syllable words for ten, hundred, thousand, ten-thousand, hundred-thousand and million. Most numbers are quoted to two significant digits, so 270,000 would be “two hundred-thousand seven.” Technically trained people phrase this differently: “twenty-seven ten-thousand.”
The single-syllable powers-of-ten stop at million, so 10,000,000,000 would be spoken as “ten-thousand million.” Note that “thousand thousand” doesn’t mean million, it’s an idiom meaning “several thousand.” The utterance “million million” is ambiguous! It’s the technical phrase for trillion, but in rural Thai is more likely to mean “several million.”
“One” is handled variously. 1000 can be rendered as “one thousand,” “thousand one” or simply “thousand.” So “thousand two” means 1200 but “thousand one” means 1000 (at least in rural Central Thai)! To quote a price of 1100, a disambiguator must be appended: either “one thousand one” or “thousand one hundred.”
Thai has its own version of Hindu-Arabic numerals: ๐๑๒๓๔๕๖๗๘๙ instead of 0123456789. Thirty years ago prices in rural markets were often shown with Thai numerals, but they’re less common now except for formal documents (incl. wedding invitations). Banknotes show the note’s serial number with both Thai and Western numerals.
There is one context where Thai numerals can still be found in a thriving tourist resort like Pattaya. Venues that have separate admission prices for foreigners and for Thai nationals will often show the Thai price either spelled out in Thai, or with Thai numerals.
Northern French dialects used as the word for “yes” some variant of oïl, i.e. o-il, from Latin hoc ille meaning “this is it”, while Southern French dialects used oc from Latin hoc meaning “this”. Because of this they are respectively called the Oïl languages, meaning French and the other Northern French dialects such as Picard, Walloon, Poitevin, etc., and the Oc languages, also called Occitan: for example Gascon, Provençal, etc. (Some people also refer to the “Si languages”, coming from Latin sic meaning “this”, which can mean Italian dialects in this context.) See Wikipedia on Langues d’oïl.
Most of the languages formerly spoken in France have declined relative to French, so I guess it is in a way related, except that the Oïl languages were not restricted to the Paris region but covered a large part of northern France and Belgium.
Indeed. I used to know a conceptual artist who etched beautiful drawings on poetry on glass panes . . . and then buried them around the world at secret placezls that had some significance to her, never having exhibited them.
There are unique properties for our base, number 10, but also there are unique properties for any integer.
For example, square root of 10 is 3.162… which is closer to pi than square root of any other integer. But I doubt if there are any properties which imply base 10 more practical, elegant or superior to other bases (from purely mathematical standpoint of course, not counting cultural and anatomical ones).
As for the “best base” that would probably be some composite number which is smallish enough to be manageable, such is 12, as other noted.
On a side note, base 10 is not nearly unique base among the humans.
I love Toynbee tiles! I’ve actually been writing notes for a novel about a man who roams a city at night, leaving little designs/installations wherever he goes, and a woman who during the day becomes fascinated and then obsessed with them.
My wife and I still have our ancient (ca. 1982?) solar Casio CM-100 “computer math calc” handheld calculators, operating in binary, octal, decimal, and hex, with full arithmetical and logical functions. Those were useful at work on OS-370 systems, and with our first home computer, a Heathkit H8 with its octal front panel keypad and display. But manual octal math isn’t difficult - just ignore thumbs.
This is almost certainly false. Yes, you can count on your phalanges to make a duodecimal or sexagesimal system of dactylographic numeration, but it’s extremely unlikely any such practice inspired the Sumerian/Babylonian written base-60 positional numerals.
Rather, the use of base-60 place-value numbers was probably an outcome of administrative procedures in early urban civilizations to make it easier to deal with a huge variety of metrological systems that used different multiples including 10, 12, 6, 5, 3, etc. The Mesopotamian cuneiform numerals are mostly composed from signs for 1 and 10 (and in earlier forms, 6 as well), and the basic Sumerian and Akkadian numeral words are primarily decimal (not place-value). This suggests that their users naturally counted in groups of ten (as well as in smaller groups such as twos, fours, fives, etc.), just as most humans always have. The sexagesimal written number systems are relatively recent and sophisticated inventions, rather than a mere reflection of some pre-literate counting system.
A lot of people like to make up, and a lot of people readily believe, “just-so stories” about why some ancient phenomenon has some supposed easily-understood “natural” explanation instead of a rather arbitrary and complex historically contingent one. But such stories should always be regarded with skepticism until/unless solidly substantiated.
I was actually going to question jasb’s post. I was under the impression that, in addition to using base 10 like the rest of the planet, the Babylonians really, really liked the number 6. This is because (I’ve heard) 6 is the only number that is both the sum and the product of its factors [assuming we include 1 but not 6.] IOW, 1+2+3=6 and 123=6.
6 is a perfect number, but it’s not the only one. 28 = 1+2+4+7+14 is another one that was known to antiquity, as well as 496 and 8128, and we now know of several others (as well as knowing that they’re related to the Mersenne primes).
But it’s easy to come up with reasons why any given small number is “special”, and there’s nothing about a number being perfect that would make it well-suited as a base of a number system, so the fact that 6 is perfect is probably completely irrelevant.
Fun fact: While pi would, without doubt, be irrational as well as transcendent (and quite possibly even normal!) in all bases, the existence of the Bailey-Borwein-Plouffe formula for the n:th digit might make you think base 16 (actually, any power of 2 !) is somehow “special” with respect to pi!
(Of course, there *might *exist similar formulae in other bases; we just haven’t found them yet! :))
Nitpick: Every product of two distinct primes is the product of its factors. But yes; 6 is the unique number as claimed. (1 works in some phrasings.) (Though I doubt if this is the source of the Babylonian base-60.)
But yes; 6 is the unique number as claimed. (1 works in some phrasings.) (Though I doubt if this is the source of the Babylonian base-60.)