to the nth degree

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to the nth degree

Post by Archived Topic » Tue Dec 14, 2004 12:47 am

Hello all,

I have often heard the phrase "to the Nth degree" but have been unable to find any indication of its origin. I assume it comes from mathematics, with "N" being a variable, but why "N"? Why not "X"? Can anyone shed any light on this subject?

Thanks,
Submitted by Jeff Freeman (Orlando - U.S.A.)
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to the nth degree

Post by Archived Reply » Tue Dec 14, 2004 1:01 am

As I recall my schoolboy math(s),algebraic equations expressed a number "to the power of"...whatever.
10 to the power of 2 = ten squared. To the power of three = 10x10x10 = 10 cubed...and so on.
The squiggly thing on its side (KEN, HELP)was to the power of infinity, but 10 to the power of "n" stood for "any number...anything you want to use".
In other words.. an unknown.
So, to the "nth degree" means to a degree beyond the known, beyond the imaginable; as in taking to every possibility, eveny infinity, but who knows.
The factors x, y, z, etc are always known or described quantities, thus to the "power of x" is tangible and exact, and does not evoke the "who can tell" associations.
"To the nth degree" is Cosmic, man!
R

Reply from Robert Masters (Asia - Thailand)
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to the nth degree

Post by Archived Reply » Tue Dec 14, 2004 1:14 am

Thanks for clearing that up for me, Robert. Much obliged.

JF
Reply from Jeff Freeman (Orlando, FL - U.S.A.)
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to the nth degree

Post by Archived Reply » Tue Dec 14, 2004 1:27 am

Not to mention . . . have you ever tried to SAY "to the xth degree"? It just doesn't roll trippingly off the tongue the way "nth degree" does! *G*
Reply from K. Allen Griffy (Springfield, IL - U.S.A.)
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to the nth degree

Post by Archived Reply » Tue Dec 14, 2004 1:41 am

I pondered long to what degree
A number should I take and see
A sign that alle would know to be
the cloak for alle posbility.
I tried a one, a two, a three,
Alas alack! t'was not 2 B.
3B I thought, and then 4C,
And then the answer came to me.
N o number was the one to be,
And N it was! Posterity!

R
Reply from Robert Masters (Asia - Thailand)
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to the nth degree

Post by Archived Reply » Tue Dec 14, 2004 1:54 am

Jeff, TO THE Nth DEGREE means to the utmost extent or highest degree possible, ‘to the max.’ <“He tried to be polite to the nth degree with his girlfriend’s parents”>. It comes from the field of mathematics where ‘degree’ means the power or exponent to which a number or symbol for a number is raised. ‘X squared’ means X to the second power or ‘second degree.’ A polynomial function, for example, in which the highest power of X that appears is the second, is referred to as a ‘second degree’ equation. (hmm! Where from ‘give someone the 3rd degree’?). Taking something to the nth degree came to denote figuratively taking something to an extreme degree, although in math it really just means taking it to whatever degree ‘n’ symbolizes – to the required power.

The use of the word ‘degree’ for ‘power’ in mathematics first appeared in print in 1796 in a math dictionary (see below). The first appearance in print of ‘nth was in 1755 and was also in reference to math (see below).’The first appearance of ‘nth’ not in reference to mathematics, and in the sense of ‘utmost’ was in 1827 (but accompanied by the word ‘power’ and not ‘degree’: <“My notions about it have been . . . very fuddled and bewildered; and, I suppose, if I were to attempt to analyse and explain them, I might raise my fuddle TO THE Nth POWER”—‘Remains’ (1838) by R. H. Forude, I. page 219>.

The first appearance of the full expression ‘to the nth degree’ was in 1897 <“The Neapolitan . . . is an Italian TO THE Nth DEGREE.”—‘Edinburgh Review,’ 4 July>
______________________________
<1755 “If the given series . . . be raised TO THE Nth POWER, the terms of the series will truly exhibit all the different chances in all the proposed (n) observations.”—‘Philosophical Transactions of the Royal Society,’ 49, page 84>

<1796 “Equations . . . are said to be of such a DEGREE according to the highest power of the unknown quantity.”—‘A Mathematical and Philosophical Dictionary’ by Hutton>

<1852 “Minerva was great upon the occasion; starched TO THE Nth.”— ‘Lewis Arundel or the Railroad of Life’ by F. E. Smedley, xxiii> [[mistakenly given by Barnhart as 1st appearance in print of ‘nth’]]

<1863 “To determine the number of umbilici on a surface of THE Nth DEGREE.”—‘Solid Geometry’ by P. Frost & Wolstenholme, page 418> [[1st appearance in print in the mathematical sense]]

<1928 “In America the film-cutter is a man with a sub-editorial mind developed TO THE Nth DEGREE.”—‘Sunday Express,’ 18 March>

<1948 “You're as right as the nightingale's song. You're the Nth of perfection.”—‘Lyrics’ (1983) by Cole Porter, page 271/3> [[with word ‘degree’ dropped]]

<1956 “None of the words which Ned Sheldon . . . found so obnoxious seems to me acutely distasteful, with the exception of ‘funeral parlor’, which carries nice-nellieism TO THE Nth DEGREE.”—‘N.Y. Book Review,’ 30 September, page 2/2>

<1974 “Ballynennan Moon was one of the tallest and slimmest of racing greyhounds. He was genuine TO THE Nth DEGREE. His consistent record bears this out.”—‘Win at Greyhound Racing’ by H. E. Clarke, xxii. page 139>

<2000 “Benetton takes this principle of ‘shock value’ TO THE Nth DEGREE.”—‘International Journal of Advertising,’ 19, page 16
>
(Oxford English Dictionary, Facts on File Dictionary of Clichés, Barnhart Concise Dictionary of Etymology, Word and Phrase Origins by Nigel Rees, American Heritage Dictionary of Idioms)
______________________

Ken G – December 3, 2004
Reply from Ken Greenwald (Fort Collins, CO - U.S.A.)
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to the nth degree

Post by Archived Reply » Tue Dec 14, 2004 2:21 am

Thanks for the detailed info, Ken. I knew the meaning of the phrase, and understood the mathematical meaning of degree, but was just unsure about the Nth part. I knew it represented a variable, but didn't know why "N". I think it's been pretty well cleared up for me now. I had no idea it went back so far in history!

You did arouse my curiosity about 3rd degree now, though, as in giving someone the 3rd degree. I always assumed that came from the 3rd degree being the most severe, as in burns. Although when dealing with crime, 1st degree is more severe...hmmm is right!

JF
Reply from Jeff Freeman (Orlando, FL - U.S.A.)
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to the nth degree

Post by Archived Reply » Tue Dec 14, 2004 2:34 am

So far the mathematical aspect of N or n hasn't really been cleared up. In math(s), N stands for the entire set of natural numbers or positive integers, i.e. the whole range of numbers from 1 (not including 0) to infinity. Maybe Ken can dig up something more conclusive, but I have always assumed that N stands for the Latin word 'numerus' = number. The ole Romans had neither zero nor negative numbers.
N is neither an unknown nor a "cosmic" number; it's just indeterminate. In Math(s) any number "to the Nth power / degree" means an integer equal to or bigger than that given number. Since 1 to the 1st power = 1, the result needn't even be a big number. It may be very big, but basically it's just equal to the number itself or higher.
How and why the term 'to the Nth degree' got to be used in the sense of something extremely big is beyond me. Maybe it was a mere misunderstanding of the mathematical background popularized by some half-educated hacks around the time Ken mentioned for the first appearance of "nth" outside of a mathematical context.
Reply from Hans Joerg Rothenberger (Walenstadt - Switzerland)
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to the nth degree

Post by Archived Reply » Tue Dec 14, 2004 2:47 am

Obviously we don't have any freemasons on the site, or there wouldn't be questions regarding the 3rd degree and its origins...
Reply from Leighton Harris (Cambridge - England)
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to the nth degree

Post by Archived Reply » Tue Dec 14, 2004 3:01 am

Hans...is there a difference between an "unknown" and being indeterminate? I'm not a mathamatician.
R
Reply from Robert Masters (Asia - Thailand)
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to the nth degree

Post by Archived Reply » Tue Dec 14, 2004 3:14 am

Hans, Here’s my guess, which is in agreement with your ‘half-educated hacks’ concept, although they may have been educated, but just not in math. If you notice, the first person to use ‘to the nth degree’ (in print) to mean ‘the utmost’ was not a mathematician but an English novelist. It’s my guess that early users of the expression ‘to the nth degree’ to mean ‘the utmost’ were talking off the tops of their heads and knew little of mathematics. Perhaps they had heard of ‘degree’ and ‘n’ in their schooldays (or elsewhere) and recalled something about ‘n’ often becoming very large, and simply put 2 and 2 together and got 3. The misuse of technical language is common in the non-technical community and one sees befuddlement over, and misuse of, such basic terms all the time (e.g. imaginary numbers, precision, accuracy, centrifugal force, mass, weight, . . . .

Ken – December 3, 2004
Reply from Ken Greenwald (Fort Collins, CO - U.S.A.)
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to the nth degree

Post by Archived Reply » Tue Dec 14, 2004 3:27 am

Robert, I'm not a methematician either. What I wrote above is what's left from high school. That was 40 years ago. Purists may find minor flaws, but I think basically it should still be valid.
In an equation, an unknown is a number that is not known yet but has to be found. An indeterminate number cannot be found, because it is - uh - indeterminate. It can be any number.
Let me give you two examples:
1) You have five apples. Jack says he has twice as many, but won't tell you how many he has. It's up to you. The number of Jack's apples is the unknown, and if he isn't lying, it's possible for you to solve the equation.
2) Jill's legs are shorter than yours. Her pace is 9/10 of yours. When you and Jill take the same number N of steps, she will always be your pace x N x 0.9 behind you. It doesn't matter how many steps you take, it may be one or gazillions, the formula always gives you her lag in relation to your pace. Here, N is not unknown, it's just indeterminate; you can take any number you like.
By the way, in math(s), the term 'indeterminate' can be used in yet another sense, but I think that would go beyond the scope of this discussion.
Ken, I agree with you. I wrote "half-educated hacks" after having googled "R. H. Forude" to no avail; "Forude" yielded many hits, most of them Scandinavian pages not dealing with English names, let alone writers. I eventually gave up without finding the guy you mentioned. So I concluded that he probably wasn't a very outstanding figure, which may be wrong. Sorry about my lack of knowledge in that field.
Reply from Hans Joerg Rothenberger (Walenstadt - Switzerland)
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