Base 36

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Base 36

Post by dalehileman » Wed May 18, 2005 9:44 pm

A base-16 system, where A through F represent 10 through 15, where "10" means 16, is called hexidecimal; in a base-36 system, where A through Z might represent 10 through 35, "10" means 36

There ought to be an application for a system where the base no. is divisible by so many others, ie, 1,2,3,4,6,9,12,18. However, the mult tables would be hellaciously hard to learn. Anyhow, what would you call it
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Base 36

Post by Nahani » Wed May 18, 2005 11:40 pm

...something terribly impolite, I'm afraid...
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Base 36

Post by spiritus » Wed May 18, 2005 11:50 pm

Dale,
If I told you, I would have to kill myself.
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Base 36

Post by Ken Greenwald » Thu May 19, 2005 2:56 am

Dale,

For the record the base systems with names that I am aware of are: 2 - binary, 3 - ternary, 4 - quaternary, 5 - quinary, 6 - senary, 7- septenary, 8 - octal, 9 - nonary (as in ‘get thee to a nonary’), 10 -decimal, 11 - undenary, 12- duodecimal, 16 - hexadecimal, 20 - vigesimal, 60 - sexagesimal

The ancient Mayan numeral system was 'vegesimal' (base 20) and the Babylonian system (based on the Sumerian system) was 'sexagesimal' (base 60). The base 60 system is preserved in modern measurement of time (hours, minutes, and seconds) and angles (60 minutes per degree, 60 seconds per minute). They possibly chose 360 degrees as the central angle of a full circle from the Babylonian year, which was composed of 360 days (12 months of 30 days each) – consistent with their interest in multiples and divisors of 60. I don’t ever recall hearing a convincing explanation for why there are 24 hours in a day and I don’t know when the ‘hour’ was first used. One guess would be that 12 held significance because there were 12 full moons in a year and so day and night were divided into 12 parts each, and Romans did use (for some purposes) the duodecimal system, based on the number 12.

So if you are into having a base with a lot of divisors, try base 60, which has 11 proper divisors (whole numbers that divide in evenly, not including the base number itself) whereas base 36 has only 8. Having a lot of divisors was critical in ancient monetary, weight systems, etc. because that meant that that various fractions would turn out to be whole numbers. For example, an ancient Babylonian unit of weight (of varying value) was the ‘mina’ which was equal to 60 ‘shekels.’ So by the common way that things were divided (e.g. halves, thirds, quarters, fifths, sixths, tenths, etc.) the result would be whole numbers of shekels.

As far as applications, I’m not up on what exotica folks are using for computational base systems lately, but last I heard it was hexadecimal (base 16), and I really don’t know if there is now a need in computing for anything higher. The only area that I can think of where a higher base system might possibly be advantageous is in the area of encryption, but I know nothing about that.

Since there is no official name that I know of for a base 36 system, my vote would be for:

HEXATRIGESIMAL
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Ken G – May 18, 2005
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Post by Erik_Kowal » Thu May 19, 2005 4:11 am

I would go for 'tridecimosenary'.
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Base 36

Post by Ken Greenwald » Thu May 19, 2005 5:27 am

Erik, TRIDECIMOSENARY trips lightly off the tongue and does have a nice ring to it. And, in fact, it is probably closer to how the Greeks and Romans would have written it, since both wrote their numbers from left to right with the units digit on the right. But taking as a model the way the other base systems have been named (for whatever reason), it looks like they are tacking the units place onto the front rather than the back, with the tens place written as multiples of ten and with the particular multiple tacked on in front as prefix of ‘gesimal.’ Thus we have ‘duodecimal’ means 12 = 2 + 10 and ‘hexadecimal’ means 16 = 6 + 10. Since 20 is vigesimal and 60 is sexagesimal, then thirty is probably ‘triagesimal’ or more simply ‘trigesimal,’ and this would give 36 = 6 + 30 and HEXATRIGESIMAL.

But since we are the coiners of the name of this new base system, we are free to do whatever the hell we choose and I’ll go for ‘consistency before beauty’ – although any mathematician worth their salt would probably say ‘beauty before consistency’ as they held open the door for their victim to pass through. (<:)

Ken – May 18, 2005
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Base 36

Post by Erik_Kowal » Thu May 19, 2005 6:46 am

Ken, I agree with your logic. After some further investigation (which I ought to have done before posting the above) it is clear to me that 'tridecimo-' would refer to thirteen, not thirty, and hence 'tridecimosenary' would mean 'relating to thirteen plus six', which would be a nonsensical way of saying 'relating to nineteen'.
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Base 36

Post by haro » Thu May 19, 2005 11:14 am

Some confusion may be caused by the simple fact that those names are all based on Latin except 'hexadecimal,' which is a mongrel: 'Hexa' is Greek and 'decimal' is Latin. I suppose the word 'hexadecimal' was made up by computer geeks without a linguistic background. I don't know if it had a history before the advent of binary logic. There it came in handy because 4 bits can respresent the range of integers between 0 and 15.
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Base 36

Post by dalehileman » Fri May 20, 2005 2:12 pm

Thanks guys
It might be interesting to speculate what sort of application might use base-19
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Base 36

Post by kagriffy » Fri May 20, 2005 5:58 pm

Knowledge of different base systems can come in handy. I remember as a kid, when we'd play hide-and-seek, I'd count to 100 using a base 5 system: 1, 2, 3, 4, 10, 11, 12, 13, 14, 20, . . . 43, 44, 100! Ready or not, here I come! Of course, I could have saved even MORE time by using the binary system: 1, 10, 11, 100! *G*
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Base 36

Post by Ken Greenwald » Sat May 21, 2005 12:31 am

Allen, I can’t say that your assertion is is baseless! (&lt)

Ken – May 20, 2005
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Base 36

Post by haro » Sat May 21, 2005 6:47 pm

Allen, I hope you are not a bank employee and count bills the same way....

Ken, I think the correct term for a base 36 numeral system ought to be 'trigentasenary.' In Latin, '36' is 'trigenta sex' (sounds kinky, doesn't it?). 'Sex' is 'six,' and 'senarius' is 'consisting of six,' hence 'senary.' 'Hexa,' as used in your suggestion, is Greek and would make the term a strange mixture just like 'hexadecimal,' which is sort of a foreign body among all the purely Latin-based terms.
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Base 36

Post by Ken Greenwald » Sun May 22, 2005 2:11 am

Hans Joerg, I think that, technically, you are right. However, in reading through several discussions on base system naming, there seems to be a tendency to want them to end in ‘esimal,’ perhaps to reinforce that we are talking about a base system. There is also an argument for not ending them in ‘nary’ so as to reserve that ending for the adjective describing the base systems above base 11. For example ‘vigenary,’ ‘tricenary,’ ‘sexagenary,’etc. (see OED and Dr. Math) are already in use to mean pertaining to 20, 30, 60, etc. (for base systems and groupings). However, it is too late for base names below 11, for some are already set in concrete as both the base name and the adjective. Also, note in my second quote below, how Dr. Math’s first thought for a base 21 system is ‘univesimal’ and not ‘vigentiunary.’ For interesting thoughts on the naming of base systems and some attempts at providing some that are more logical see Dr. Math at The Math Forum. Also see Numerical Prefixes for info on Latin and Greek math prefixes at the fairly interesting word website Phrontistery

<"'hexadecimal' is the common computer-science terminology, but it is unsatisfactory because it is a combination of the Greek 'hexa' and the Latin 'decim.' The proper Latin should be 'sedecim' or 'sexdecim,' yielding either 'sedecimal' or 'sexadecimal.' Schwartzman writes: 'Since hexadecimal is a rather long word, it is sometimes abbreviated hex. The word hexadecimal is unusual because Greek and Latin elements are combined; the expected purely Latin form would be sexadecimal, but then computer hackers would be tempted to shorten the word to SEX.'"—‘Dr. Math>

<I've found no references to names like "unvigesimal," so you are free
to invent your own combinations for 21, 22, and so on.—‘Dr. Math'>
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Ken – May 21, 2005
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Base 36

Post by Phil White » Sun May 22, 2005 9:48 am

The correct term describing base 16 in German is in fact "sedezimal", although in programming manuals, you often see simply "hex", presumably from the influence of English.

There's a general tendency in German to be a little more "careful" with Latin- and Greek-derived words than we are in English, even to the extent of fully declining the proper name "Jesus" when used in normal speech.
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Base 36

Post by haro » Sun May 22, 2005 11:55 am

Phil, what you said about declining 'Jesus' in German is correct, but otherwise I think mixing Greek and Latin components is about as frequent in German as it is in English. 'Hexadezimal' including 'hex' is used in German too, and 'Automobil,' 'Implantologie,' 'Telefax' and hundreds, maybe thousands, of other Greek-Latin hybrids are exactly the same as in English.
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