Tuesday, January 09, 2007

Ordinal Numbers Revisited




Q. My apologies for bothering you, but I came across your blog 'All in Order' dated 20 Dec 06, as I've been trying to ascertain at least 2nd and 3rd order equivalents for both the noun 'primacy' and the adjective 'primal'.

In terms of 'primal' I uncovered 'tertial', but this only seems to relate to a bird's feathers; and 'tertian', but whilst this has several definitions, none of them signify 'being third in order'. I also came across 'secundal', but again this only seems to relate to musical chords involving the interval of 2.

I'm somewhat stumped, especially in terms of 'primacy', for which I haven't been able to find any 2nd, 3rd order, etc. equivalents at all. Any help appreciated.
Thanks,
Luke (London, UK)

…………………………………………………………………………………..

A. No problem at all, Luke; thanks for writing. Many elements intersect here: science, Latin, English, etc. Given my scientific illiteracy, I probably can’t give a definitive answer. But that's never stopped me from trying.

Before tackling primacy and primal, let me review two other sets. The ordinal numbers are the numbers that show sequence or rank; they give the order in which items are arrayed.

There are two such ordinal lists that I deal with on a regular basis: the set beginning with first, and the set beginning with primary. I’m not in touch with the subset names (help, readers!), but as I see it, the first set shows spatial or chronological order, and the second set shows order of precedence or effect:

Spatial/Chronological..............Precedence/Effect*

first..............................................primary
second.........................................secondary
third............................................tertiary
fourth.........................................quaternary
fifth.............................................quinary
sixth............................................senary
seventh.......................................septenary
eighth.........................................octonary
ninth...........................................novenary
tenth...........................................decenary

*spelling confirmed in the online Oxford English Dictionary

So the second day of an experiment (chronological order) or the second mouse injected with a serum is a much different ordering than a secondary effect that results while experimenting (e.g., dehydration). Hence, the existence of two lists of ordinal numbers to represent two different focuses (foci to the traditional).

Note: first and primary in the lists above can be synonyms, but exact synonymity ends when you get to number 2 and beyond.

Now, back to primacy and primal. The ordinal numbers--the ones that show sequence or ranking--are adjectives. So you put your finger on the problem with the word primacy, Luke, when you identified it as a noun. The noun to follow primacy would be something like subordination or inferiority or dependence. There won’t be a cascading list of adjectives as with first or primary.

Primal is more complicated. Its strongest or most common meanings are original/primitive or something in the range of fundamental/deep-seated. In a less-used meaning, it becomes a synonym for primary. So I would suggest that we would normally slide from primal to secondary and then continue down that already-established list.

Musicology from centuries back brings up yet another list, but they are nouns (clusters of intervals), not adjectives, and they are only of historical interest. They include secundal, quartal (also spelled, on some sites, as quatral), quintal, sextal, septal, and octal, but a chord composed of thirds is called tertian instead of tertial. (When we check out tertial, we run across the third row of bird feathers, as you discovered.) So we don’t have a third column for ordinal adjectives here.

In computer science, there does seem to be another stream of adjectives: unary, binary, and ternary. These are the three operators, operator defined as a symbol or sign used in javascript to identify a specific operation.


Finally, there is also a (mostly obsolete) series that ran this way:

unal (1893) Single; that is one only; based on unity.
binal (1806) Twin, double, twofold.
trinal (1907) Composed or consisting of three parts; threefold.
ternal (1680) Consisting of three; threefold, triple.
quaternal (1813) cross-referenced to quaternary.
quintal (not listed in OED)
sextal (1971) Pertaining to a system of numerical notation with 6 as base.
septal (not listed as a numerical term in OED)
octal (1991) Relating to or designating a system of numerical notation that employs 8 rather than 10 as base.
nonal (not listed in OED)
noval (not listed in OED)
decimal (2007) Relating to tenth parts, or to the number ten; proceeding by tens.



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2 Comments:

Blogger TomRScott said...

Great article.

Regarding usage in computer science:

"In computer science, there does seem to be another stream of adjectives: unary, binary, and ternary. These are the three operators, operator defined as a symbol or sign used in javascript to identify a specific operation.
"

There are two such lists, the one you refer to above (operators) and one for different base numeric or numeral systems which you reference elsewhere.

Operators:
The class and name of operators relates to the number of operands. The expression "2+2" has two operands and one operator. In this case, "+" is acting or being utilized as a binary operator and the two 2's are the two operands. Binary operations are more fully defined at http://en.wikipedia.org/wiki/Binary_operator.

The "+" was acting as a binary operator. However, it can also be a unary operator with only one operand just as the minus (-) sign is used when it indicates something less than zero such as in the expression "-1 + 44 = 43".

Functions such as used in the expression "Sqrt(4) = 2" are essentially operators and are often referenced with the same terminology. This is especially true when used (such as I did here for the square root function) to replace an operator symbol that can be "hand written" but for which no key or character is available on a computer.

With regard to Java, like the creators of any computer programming language, Java's creators used terms from mathematics not only in describing math operations but also used them for analogous situations such as when describing how many arguments (the operands of a function) a function or procedure is capable of utilizing or requires.

Base Systems Nomenclature:
Numeric or numeral base systems are named in a similar manner. Computers utilize more than one base system in their programming and usage. The terminology for the numberic or numeral base systems comes from the number of symbols used by a given base system to represent numeric values. Thus, binary is based on two symbols, "0" and "1". One would count in binary as 0, 1, 10, 11, 100... We humans commonly use ten symbols and work in base ten or decimal.

One good reference is: http://en.wikipedia.org/wiki/Numeral_system

Common Base Systems Used with Computers:
Binary - Base 2 (0, 1, 10, 11, ...)
Octal - Base 8 (0, ..., 7, 10)
Decimal - Base 10 (0, ..., 9, 10)
Hexadecimal - Base 16 (0, ..., 9, A, ..., F, 10)

If you have ever read a MAC address on computer equipment you have read "hex".

- Tom

4:51 PM  
Blogger Michael J. Sheehan said...

Tom:

Thanks for filling in an area foreign to me. You have increased the value of the article.

7:41 AM  

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