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October 17

"The" calculus

I remember that decades ago some people or books referred to "the calculus" rather than simply "calculus". That always struck me as strange because we don't say "I'm studying the geometry" or the like.

Is "the calculus" still in current use?
What was the origin of the "the" in the phrase "the calculus"? Was it something like referring to "the method", with the word "method" then falling out of use in any other context? Duoduoduo (talk) 17:50, 17 October 2012 (UTC)[reply]

The OED notes that The differential calculus is often spoken of as ‘the calculus’ (as opposed, for example, to the relational calculus or any other calculus). Unhelpfully its citations stop in 1878, so I can't use this to answer your second question, but this is in accord with my own impressions. (A citation I know of: When you start mathematics you do not begin with the calculus. in Mere Christianity, 1948.)Marnanel (talk) 19:10, 17 October 2012 (UTC)[reply]

"The calculus" likely means "the calculation", as opposed to the branch of mathematics. StuRat (talk) 19:30, 17 October 2012 (UTC)[reply]

No, it does mean exactly the branch of mathematics. See my OED reference above. Marnanel (talk) 20:08, 17 October 2012 (UTC)[reply]

Here are examples where it means "the calculation":[1],[2], [3]. StuRat (talk) 20:18, 17 October 2012 (UTC)[reply]

It's true, it is certainly possible to use calculus as a count noun and put the in front of it, and then the the has no special significance. However, the fixed phrase the calculus refers specifically to integral and differential calculus, as distinct from, say, thepropositional calculus. --Trovatore (talk) 20:28, 17 October 2012 (UTC)[reply]

This actually looks like a question for the Language Desk. Roger (talk) 20:31, 17 October 2012 (UTC)[reply]

I took a look at propositional calculus, the article consistently uses the construction "a calculus". I'm posting a "cross-refdesk" note about this question to the Language desk. Roger (talk) 20:38, 17 October 2012 (UTC)[reply]

I'm not sure what your point is, with regard to a calculus. As I said, calculus can be used as a count noun, and then it works grammatically like any other count noun, with a and the. However, the fixed phrase the calculus always means integral/differential calculus and extensions thereof. --Trovatore (talk) 21:19, 17 October 2012 (UTC)[reply]

StuRat has the right answer above, originally it meant "the method of calculating/reckoning" integrals and differentials. It was discussedhere briefly. From the OED:

3. Math. A system or method of calculation, ‘a certain way of performing mathematical investigations and resolutions’ (Hutton); a branch of mathematics involving or leading to calculations, as the differential adj. and n., integral adj. and n. calculus, etc. The differential calculus is often spoken of as ‘the calculus’.

1672 Philos. Trans. (Royal Soc.) 7 4017, I cannot yet reduce my Observations to a calculus.

1753 Philos. Trans. 1751–2 (Royal Soc.) 47 62 Mr. Clairant..kept his calculus a profound secret.

1796 C. Hutton Math. & Philos. Dict. I. 234 We say the Arithmetical or Numeral Calculus, the Algebraical Calculus, the Differential Calculus, the Exponential Calculus, the Fluxional Calculus, the Integral Calculus, the Literal or Symbolical Calculus, etc...Algebraical, Literal or Symbolical Calculus is..the same with algebra.

1804 Philos. Trans. (Royal Soc.) 94 219 If the introduction of the new calculi, as they have been called, has extended the bounds of science.

1837 T. Carlyle French Revol. III. ii. i. 95 Science, which cannot, with all its calculuses, differential, integral, and of variations, calculate the Problem of Three gravitating Bodies.

1846 J. S. Mill Syst. Logic iii. xxiv. §6 The general problem of the algebraical calculus.

1854 G. Boole Investig. Laws Thought i, The exhibition of logic in the form of a calculus.

1878 ‘G. Eliot’ College Breakfast Party in Macmillan's Mag. July 167 Fount of spirit force Beyond the calculus.

μηδείς (talk) 20:58, 17 October 2012 (UTC)[reply]

Further, remember that Geometry was named in classical times by the Greeks and referred to in Latin which does not use a definite article. Calculus was invented during the Modern English period and, since it meant "the (method of) reckoning" was naturally referred to as "the calculus" when discussed in English. μηδείς (talk) 21:04, 17 October 2012 (UTC)[reply]

That's not quite what the OED entry you just quoted says. It says that a calculus is a method of reckoning (and not "a calculation"). And this is still true: there are plenty of calculi which are not the differential or the integral calculus. But it goes on to say that one particular calculus, namely differential calculus, is often known simply as the calculus. Marnanel (talk) 21:45, 17 October 2012 (UTC)[reply]

I think OED is a little off here — it's not differential calculus to the exclusion of integral calculus. My definition would be "those parts of real analysis (well, including complex analysis) that are directly relevant to scientists and engineers". It's not really a "branch of mathematics", per se, but a collection of tools from mathematics (although there was a time, before Weierstrass et al, when it could have been called a branch of mathematics in its own right).

But still, however it came about, StuRat's finds of the calculus in other contexts don't change the central point that the calculus as a fixed phrase means specifically that collection of tools and methods. --Trovatore (talk) 21:54, 17 October 2012 (UTC)[reply]

If you can refer to "a calculus", you can refer to "the calculus", Marnanel. That's the way count nouns work. It is not my place to give pride of place to one calculus over another. μηδείς (talk) 21:59, 17 October 2012 (UTC)[reply]

I don't give a damn what your place is. The OED, in the entry you quoted, does find it appropriate to note that the language gives pride of place to one calculus over another, in that the phrase "the calculus" has a particular meaning of "the differential calculus" separate from its ordinary interpretation as a count noun preceded by the definite article. Marnanel (talk) 22:19, 17 October 2012 (UTC)[reply]

You so crazeh. μηδείς (talk) 23:01, 17 October 2012 (UTC)[reply]

Answering my own first question, as to whether "the calculus" referring to calculus is still in use:this 1997 book uses it in its title and intro. Duoduoduo(talk) 22:37, 17 October 2012 (UTC)[reply]

This thread has been moved to Wikipedia:Reference desk/Language#Language issue on the Mathematics Refdesk. Please make all further comments there. Duoduoduo (talk) 14:48, 18 October 2012 (UTC)[reply]