What is the origin of the analogy between numbers less than zero and bad things? This question just occurred to me. I have been using this analogy without thinking about its history.
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I can only think it has something to do with Puritan theology, since it is far more prevalent in America than it is in Europe.– WS2Commented Nov 16, 2014 at 18:07
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4Do you have any examples?– nohatCommented Nov 16, 2014 at 18:36
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Profit and loss statements.– JenSCDCCommented Nov 17, 2014 at 13:17
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This is pretty weak stuff, but it is true that negative numbers are < positive numbers, and so inferior.– OldcatCommented Dec 16, 2014 at 19:18
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The term :"negative" has other applications besides mathematics and numbers. If you say something derogatory people might say you're "being negative" -- nothing at all to do with numbers.– Hot LicksCommented Mar 16, 2015 at 22:16
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3 Answers
A mathematician would point out that 'Negative' numbers have nothing to do with 'moral negatives'; rather, they simply 'negate' their 'natural number' counterpart.
Remember, subtraction can sometimes be considered not to exist: the act of subtraction is actually the addition of a 'negative' number.
Remember also that 'natural' numbers are those we now call 'positive integers'.
A 'natural' number, negated, is simply removed and leaves nothing. How does one express that on paper, mathematically? By positing a number ("Posit" in this sense, is the philosophical meaning of declaring or making a statement), such as 'five (+5)'. Then, we negate it, by positing (same sense) some value that results in zero when combined or otherwise taken as a whole. We posit this 'negating value' by using the mark/glyph we now associate with subtraction -- in this case ("negating five" (-5)).
The upshot is that we can write: " + 5 + (-5) = 0 ", where every 'plus sign' is a posit (or declaration) of a new value. The 'minus sign' simply denotes a 'negating' value of the original.
Notwithstanding what I said in my comment above it would appear from the OED long to predate Puritanism.
And it predates the mathematical sense, the earliest reference to which is in the 17th century (around the time of Newton).
There are several references from the 15th century, and Shakespeare uses it in A Winter's Tale (1623)
If thou wilt confesse, or else be impudently negatiue, To haue nor Eyes nor Eares nor Thought.
However that particular reference - of actually denying something- is said by the OED to be obsolete.
There seems little doubt however, that my first instinct concerning Puritanism, may not have been far off the mark, with this diatribe against Catholics:
1600 J. Hamilton Facile Traictise in T. G. Law Catholic Tractates (1901) 235 Thay mon also renunce ane vther article of thair negatiue faith detest and indulgencis.
I still adhere to the view that in today's world the notion is employed far more by Americans than it is elsewhere. Somebody will now produce a lot of Ngrams to prove me wrong. But beware, I take a negative view of Ngrams!
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1All of your quotes use the “damaging; undesirable; unfavourable” sense of negative and have nothing to do with negative numbers like -1. Your answer doesn't address the question's claims. Commented Nov 16, 2014 at 18:51
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@jwpat7 But I thought that was what the question was about. 'Damaging, undesirable, unfavourable, negative' predates the use of negative for numbers less than nought.– WS2Commented Nov 16, 2014 at 18:55
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Negation is often used to express fault or poor esteem of some sort. That has nothing to do with negative numbers, which didn't become common in mathematics until the 16th century or so, and weren't fully integrated into theory until the mid-19th. Who knows what associations the OP has between them? Not me, for sure. Commented Nov 16, 2014 at 19:17
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@WS2, The question posits an “analogy between numbers less than zero and bad things”. I don't know whether such an analogy exists in general. Of course it is valid or not in specific cases; eg, a negative bank balance is undesirable, while a negative statement balance usually is a good thing. But as a general rule, I don't look at number like -47431 and think “How Awful! How Unfortunate!”. Commented Nov 16, 2014 at 19:18
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@jwpat7 Got any evidence? Yes. It is clear from the entries in the OED that the use of 'negative' to describe 'bad utterances' begin as early as 1460. 'Impudently negative' says Shakespeare in 1623. But it is also clear from the OED that 'negative numbers' do not enter the mathematical lexicon until the 17th century. John Lawler says perhaps 16th.– WS2Commented Nov 16, 2014 at 19:26
From Merriam-Webster Online:
Negative -- adjective
a: marked by denial, prohibition, or refusal ; also : marked by absence, withholding, or removal of something positive b (1) : denying a predicate of a subject or a part of a subject <“no A is B” is a negative proposition> (2) : denoting the absence or the contradictory of something (3) : expressing negation c : adverse, unfavorable
a : lacking positive qualities; especially : disagreeable b : marked by features of hostility, withdrawal, or pessimism that hinder or oppose constructive treatment or development c : promoting a person or cause by criticizing or attacking the competition
a (1) : less than zero and opposite in sign to a positive number that when added to the given number yields zero <−2 is a negative number> (2) : having more outgo than income : constituting a loss b : extending or generated in a direction opposite to an arbitrarily chosen regular direction or position
a : being, relating to, or charged with electricity of which the electron is the elementary unit b : having more electrons than protons c (1) : having lower electric potential and constituting the part toward which the current flows from the external circuit (2) : being the electron-emitting electrode of an electron tube
a : not affirming the presence of a condition, substance, or organism suspected to be present; also : having a test result indicating the absence especially of a condition, substance, or organism b : directed or moving away from a source of stimulation c : less than the pressure of the atmosphere
: having the light and dark parts in approximately inverse relation to those of the original photographic subject
of a lens : diverging light rays and forming a virtual inverted image
Now, only two of the 7 definitions have any, er, "negative connotation". And if you examine definition 1.a closely you will see that it says "marked by absence". A negative number is an "absence" of the corresponding positive value, just as a photographic negative is an image where the light regions are "absent" (dark) and the dark regions are "present" (light).
The meaning of "negative" as "disagreeable" or "unfavorable" is only a small corner of the word's full use.
answered Mar 16, 2015 at 22:37
