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The Birkana hexadecimal number symbols

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Re: The Birkana hexadecimal number symbols

#51

Post by thaumasiotes »

ptaipale wrote: post #32
david-given wrote: post #25

Fun fact: you can count to hexadecimal on the fingers of one hand. The way it works is that each of your four fingers has four well-defined places on them: the three joints, plus the tip. You use your thumb to point at one of these. The first finger represents 1-4, the second 5-8, the third 9-12, the fourth 13-16. You count up and down by moving your thumb. Also, because you use the thumb of the same hand for pointin…

Or if you point just the joints, not the tips, you get base 12. If you count multiples of 12 with the five fingers in the other hand, you get to 60. And this is the reason we have the 12-hour, 60-minute system, and other sexagesimal systems, ever since ancient Babylonia. https://en.wikipedia.org/wiki/Sexagesimal

> And this is the reason we have the 12-hour, 60-minute system, and other sexagesimal systems, ever since ancient Babylonia.

> https://en.wikipedia.org/wiki/Sexagesimal

Your phrasing is quite a bit stronger than your source's:

> It is possible for people to count on their fingers to 12 using one hand only, with the thumb pointing to each finger bone on the four fingers in turn. A traditional counting system still in use in many regions of Asia works in this way, and could help to explain the occurrence of numeral systems based on 12 and 60

It was a long time ago; we don't actually know why the Mesopotamians liked cycles of 60, and it's unlikely that we ever will. But the argument "it's easy to divide 60 by 2, 3, 4, 5, and 6" is a lot more parsimonious. We do know that the Romans, despite using a base-10 number system, had money which divided into 12, not 10, subunits, precisely to make money easier to divide. 12 and 60 are technologically superior to 10, and this can explain their use even in societies which we know used base-10 numbers. (Such as... the Mesopotamians, who, as shown in your link, represented the value 47 as 4*10+7.)

Re: The Birkana hexadecimal number symbols

#52

Post by thaumasiotes »

hackuser wrote: post #35
ptaipale wrote: post #32

Earlier quoted context omitted.

Or if you point just the joints, not the tips, you get base 12. If you count multiples of 12 with the five fingers in the other hand, you get to 60. And this is the reason we have the 12-hour, 60-minute system, and other sexagesimal systems, ever since ancient Babylonia. https://en.wikipedia.org/wiki/Sexagesimal

Coincidentally, I am reading a leading history of mathematics, and just read the section on Mesopotamian math (the source of our base 60 customs, such as time, degrees in circle, etc.). The Sumerians (of Mesopotamia, as was Babylon) not only used base 60, but also were the first known to use position or place value to indicate power of 60 the same way we do in base 10, a significant invention. For contrast, the Roman…

> Other societies commonly have used base 20

I've seen this claim several times about French. Apparently it's a standard description of the French number system, but it is totally and obviously wrong on the facts.

Here are the characteristics you'd see in a base-20 number system: special words for 0/1/2/3/4/5/6/.../19 (the digits); special words for 20/400/8000/maybe 160000/... (the place values). No special word for 100, which is the not-obviously-significant value "50". No special word for 1000, which is the even-less-significant value "2A0".

Here are the characteristics you'd see in a base-10 number system: special words for 0/1/2/3/.../9; special words for 10/100/1000/maybe 10000/... .

Here's what French has: special words for 0/1/2/.../16; special words for 10/20/30/40/50/60/80/100/1000/... .

It's quite plain that French uses a base-10 number system with some irregular number names. Is there a society that actually used base 20 numbers?

I also note, in https://en.wikipedia.org/wiki/Sexagesimal#Usage , that the Sumerians didn't have symbols for 0..59 . They represent large numbers as a series of coefficients of powers of 60, but their "digits" have a base-10 internal structure, precisely as we represent minutes taking one of 60 values today ("6:32"). That suggests to me that the language, as opposed to the number writing system, was probably base 10.

Re: The Birkana hexadecimal number symbols

#53

Post by hackuser »

thaumasiotes wrote: post #52
hackuser wrote: post #35

Earlier quoted context omitted.

Coincidentally, I am reading a leading history of mathematics, and just read the section on Mesopotamian math (the source of our base 60 customs, such as time, degrees in circle, etc.). The Sumerians (of Mesopotamia, as was Babylon) not only used base 60, but also were the first known to use position or place value to indicate power of 60 the same way we do in base 10, a significant invention. For contrast, the Roman…

> Other societies commonly have used base 20 I've seen this claim several times about French. Apparently it's a standard description of the French number system, but it is totally and obviously wrong on the facts. Here are the characteristics you'd see in a base-20 number system: special words for 0/1/2/3/4/5/6/.../19 (the digits); special words for 20/400/8000/maybe 160000/... (the place values). No special word for…

Note that I didn't say anything about France. You seem very doubtful that any society would use something besides base 10; why?

> Is there a society that actually used base 20 numbers?

From Struik, the book mentioned above, here is what I could find quickly:

Of 307 number systems of primitive American peoples investigated by W.C. Eels, 146 were decimal, 106 quinary [base 5] and quinary decimal, vigesimal [base 20] and quinary vigesimal. The vigesimal system in its most characteristic form occurred among the Mayans of Mexico and the Celts in Europe.

Give the book a try if you are interested in these things; he writes clearly and engagingly, with a personality and sophistication; the short factual passage above isn't representative. With due respect, I'm going to rely on the highly-regarded writing of arguably the leading historian in the field over Wikipedia. None of these number systems map directly to ours; I've omitted plenty of complexity (and Struik probably omitted more).

Re: The Birkana hexadecimal number symbols

#54

Post by thaumasiotes »

hackuser wrote: post #53
thaumasiotes wrote: post #52

Earlier quoted context omitted.

> Other societies commonly have used base 20 I've seen this claim several times about French. Apparently it's a standard description of the French number system, but it is totally and obviously wrong on the facts. Here are the characteristics you'd see in a base-20 number system: special words for 0/1/2/3/4/5/6/.../19 (the digits); special words for 20/400/8000/maybe 160000/... (the place values). No special word for…

Note that I didn't say anything about France. You seem very doubtful that any society would use something besides base 10; why? > Is there a society that actually used base 20 numbers? From Struik, the book mentioned above, here is what I could find quickly: Of 307 number systems of primitive American peoples investigated by W.C. Eels, 146 were decimal, 106 quinary [base 5] and quinary decimal, vigesimal [base 20] an…

> Note that I didn't say anything about France. You seem very doubtful that any society would use something besides base 10; why?

That's all you. I'm not doubtful that a society would use something besides base 10, but when you make the same claim that a lot of other people make, you risk being perceived as similar to those other people. The form of my comment is "I hear this same claim a lot from people who clearly don't know what they're talking about. Do you have something better than they have?"

I bought the book. Struik doesn't bother to expand on the selection you quoted at all. His citation, however, does have a bit more ( https://archive.org/stream/jstor-2972526/2972526_djvu.txt ):

> The vigesimal system usually occurs in connection with some other system.

> Quinary-vigesimal. This is most frequent. The Greenland Eskimo says "other hand two" for 7, "first foot two" for 12, "other foot two" for 17 and similar combinations to 20, "man ended." The Unalit is also quinary to twenty which is "man completed." But 40 is "two sets of animals' paws," 60 "three sets of animals' paws" and so on regularly to 400 where there is an interesting change in the formation of this primary base (20 X 20) from animals back to man, for 400 is "20 sets of man's paws."

A list of nahuatl numbers can be found here ( http://www.omniglot.com/language/numbers/nahuatl.htm ), and it is quinary-vigesimal. Maya numerals, in their symbolic written form, are also quinary-vigesimal (in the same sense that written Sumerian numerals are decimal-sexagesimal -- that is to say, they are purely quinary, but the forms 20 to 24 aren't used), and Celtic numerals (the words) seem to be a weird quinary-decimal-vigesimal hybrid. This doesn't fill me with confidence in Struik. But Celtic aside, I am satisfied that several American number systems were vigesimal and not decimal.

>> I also note, in https://en.wikipedia.org/wiki/Sexagesimal#Usage , that the Sumerians didn't have symbols for 0..59 . They represent large numbers as a series of coefficients of powers of 60, but their "digits" have a base-10 internal structure

> With due respect, I'm going to rely on the highly-regarded writing of arguably the leading historian in the field over Wikipedia

If you looked at the link, you might notice that all I was relying on was pictures of the cuneiform glyphs. But hey, why read when you can just generally slam wikipedia?

Re: The Birkana hexadecimal number symbols

#55

Post by glandium »

thaumasiotes wrote: post #52
hackuser wrote: post #35

Earlier quoted context omitted.

Coincidentally, I am reading a leading history of mathematics, and just read the section on Mesopotamian math (the source of our base 60 customs, such as time, degrees in circle, etc.). The Sumerians (of Mesopotamia, as was Babylon) not only used base 60, but also were the first known to use position or place value to indicate power of 60 the same way we do in base 10, a significant invention. For contrast, the Roman…

> Other societies commonly have used base 20 I've seen this claim several times about French. Apparently it's a standard description of the French number system, but it is totally and obviously wrong on the facts. Here are the characteristics you'd see in a base-20 number system: special words for 0/1/2/3/4/5/6/.../19 (the digits); special words for 20/400/8000/maybe 160000/... (the place values). No special word for…

> It's quite plain that French uses a base-10 number system with some irregular number names

Well, it has two interesting irregularities on two of the multiples of 10 that are the origin of the base-20 theory: 80 and 90. They are "quatre vingt" and "quatre vingt dix", literally "four twenty" and "four twenty ten". 70 is also "soixante dix", literally "sixty ten".

Re: The Birkana hexadecimal number symbols

#56

Post by FoeNyx »

thaumasiotes wrote: post #52
hackuser wrote: post #35

Earlier quoted context omitted.

Coincidentally, I am reading a leading history of mathematics, and just read the section on Mesopotamian math (the source of our base 60 customs, such as time, degrees in circle, etc.). The Sumerians (of Mesopotamia, as was Babylon) not only used base 60, but also were the first known to use position or place value to indicate power of 60 the same way we do in base 10, a significant invention. For contrast, the Roman…

> Other societies commonly have used base 20 I've seen this claim several times about French. Apparently it's a standard description of the French number system, but it is totally and obviously wrong on the facts. Here are the characteristics you'd see in a base-20 number system: special words for 0/1/2/3/4/5/6/.../19 (the digits); special words for 20/400/8000/maybe 160000/... (the place values). No special word for…

> I've seen this claim several times about French.

Who said it was about modern French?

French has been heavily influenced by different cultures. Some apparently used full or partial vigesimal systems such as in Basque, Breton, Normans, maybe Gaulish too. And some others like the Roman, Saxon were mostly decimal systems.

There are examples in French literature of the Middle Ages of numerals based on twenty (30 was (20+10) "vingt et dix", 40 was (2×20) "deux vingt", 50 was ((2×20)+10) "deux vingt et dix", 60 was (3×20) "trois vingt", etc).

One of the most famous vestigial example is the "Hospice des Quinze-Vingts" (15×20) founded in 1260 in Paris and was intended to house 300 patients.

That system was progressively replaced by decimal system at the end of Middle Ages, and most of the etymology can be now related to latin and a bit of greek.

Still currently in France numbers from 80 to 99 seems to follow the old system : 80 is (4×20) "quatre-vingt", and 90 is (4×20)+10 "quatre-vingt dix".

Re: The Birkana hexadecimal number symbols

#57

Post by lern_too_spel »

yorwba wrote: post #46
lern_too_spel wrote: post #45

Earlier quoted context omitted.

This method is impractical to use due to the way the human hand works. Representing numbers where the middle and ring fingers are in different positions is tricky, and using this method for counting quickly is nearly impossible because it requires the simultaneous movement of multiple fingers up and down. The method of counting on finger creases, on the other hand, is entirely practical, and I've known people who hav…

There is quite some variation in the way the human hand works. I can move my middle and ring fingers completely independently, but when I stretch my left middle finger, my left pinky tries to extend, too. I can prevent this by pressing its tip against my palm. Except for this difficulty, simultaneously moving multiple fingers is no problem for me. For binary counting you just need to flip a group of fingers inward an…

Now try counting to 32 using the creases method. You'll beat that time without any practice. I can count on my creases faster than I can count in my head, and it requires little mental effort, which is why you would use an external counter in the first place.

Re: The Birkana hexadecimal number symbols

#58

Post by hackuser »

thaumasiotes wrote: post #54
hackuser wrote: post #53

Earlier quoted context omitted.

Note that I didn't say anything about France. You seem very doubtful that any society would use something besides base 10; why? > Is there a society that actually used base 20 numbers? From Struik, the book mentioned above, here is what I could find quickly: Of 307 number systems of primitive American peoples investigated by W.C. Eels, 146 were decimal, 106 quinary [base 5] and quinary decimal, vigesimal [base 20] an…

> Note that I didn't say anything about France. You seem very doubtful that any society would use something besides base 10; why? That's all you. I'm not doubtful that a society would use something besides base 10, but when you make the same claim that a lot of other people make, you risk being perceived as similar to those other people. The form of my comment is "I hear this same claim a lot from people who clearly…

I'm not sure what inspired these somewhat angry responses. I'm just discussing ancient mathematics, which is not a hot button issue. Sorry if I offended you somehow.

Re: The Birkana hexadecimal number symbols

#59

Post by hnsummarizer »

grzm wrote: post #26
andars wrote: post #21

Earlier quoted context omitted.

Is this a bot? This summary is nearly the length of the article, just lacking the actual images of Birkana symbols.

I believe so, looking at the other comments it's posted in the hour it's been on the site: https://news.ycombinator.com/threads?id=hnsummarizer

Hello! I'm a human with a bot friend-- I read up on the debates about HN summaries and so I'll be making a chrome extension so that I don't provide previews to anyone that doesn't want one.
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