Disclosure:  I am a (retired) mathematician, and in particular a 
(retired) teacher of calculus.

In my line of work we have all heard of Berkeley's "ghosts of departed 
quantities," but most of us would probably not know that this witty 
criticism was published in 1734.  There is a very satisfactory article 
in Wikipedia on the Berkeley book, The Analyst, that gives plenty of 
context for the jibe:

> http://en.wikipedia.org/wiki/The_Analyst

I don't think that "ghostly fingers" has any connection to this.  As I 
think some of you already have done, I checked the Google Ngram Viewer 
for "ghostly fingers" and it does not appear until the 1830s.  There is 
nothing about "fingers" in the Berkeley discussion.

An economics professor told my daughter, whose B.A. was in economics, 
that grad school in economics was essentially mathematics.  Whether or 
not that is true, I would have thought that all of you would know the 
correct definition of the slope of a curve, which involves forming a 
quotient, and then finding the limit as both members of that fraction 
tend to zero.  One must strictly avoid actually setting the members to 
zero, but the limit makes sense anyway.  And Berkeley is witty about it, 
and can be said to be correct (see the Wiki referenced above), but 
Berkeley is long gone, and the calculus is still very much with us.

On 7/28/2014 10:30 AM, Alain Alcouffe wrote:
> Thanks for the tips
> I believed that it was a reference to Berkeley and his "ghosts of 
> departed quantities" but by this sentence, Berkeley targeted the 
> infinitesimals (or the calculus) not the law of motion. Besides, I 
> could not find the expression or an approaching one in Berkeley..
> Then I searched in the 4 letters of Isaac Newton to Bentley - in the 
> third one, Newton came very close to the idea.. describing a “divine 
> arm” placing planets ...
> Anyway I continue to suspect that despite google search the expression 
> could be found during the 18th century - (possibly as a joke about the 
> Holy Ghost)
> During the 20th century, the expression in relation to Newton appears 
> in A. Koestler, The Sleepwalkers. A History of Man’s Changing Vision 
> of the Universe, London, Penguin Books, 1959, p. 511. (and also 
> ghost-fingers)
>
> On 28/07/2014 14:35, Scot Stradley wrote:
>> I don't have the quotes at fingertip, but the phrase probably refers 
>> to Berkeley's critique of the metaphysics of calculus.
>> Newton's method of determining the limit involved the use of 
>> triangles whose side adjacent to the curve was gradually
>> reduced so that the known properties of geometry could explain the 
>> slope of the curve.  Newton lays this out in Book
>> I of the Principia.  Obviously the size of the side facing the curve 
>> and the area of the triangle were gradually reduced--
>> hence the reference to vanishing quantities.
>>
>> Scot A. Stradley, Ph.D.
>> Professor of Finance
>> Offutt School of Business
>> Concordia College
>> Moorhead, MN 56562
>>
>> ________________________________________
>> From: Societies for the History of Economics [[log in to unmask]] on 
>> behalf of Nicholas Theocarakis [[log in to unmask]]
>> Sent: Sunday, July 27, 2014 6:44 PM
>> To: [log in to unmask]
>> Subject: Re: [SHOE] ghostly fingers
>>
>> Dear Alain
>> I did a check on Google Books setting time parameters. The phrase 
>> "ghostly fingers" does not appear before the 19th century.
>> This might help.
>> Nikos
>>
>>
>> On Sat, Jul 26, 2014 at 9:58 AM, Alain Alcouffe 
>> <[log in to unmask]<mailto:[log in to unmask]>> 
>> wrote:
>> Dear Colleagues,
>> In the Methodology of economics, Mark Blaug wrote :
>> he was unable to meet the objection of many of his contemporaries 
>> that the very notion of gravity
>> acting instantaneously at a distance without any material medium to 
>> carry the force - ghostly fingers clutching through the void! - is 
>> utterly metaphysical. (cf. snd edition, p. 6).
>> Actually Blaug has added several references in footnote 2:
>> Toulmin, S., and J. Goodfield. 1963. The Fabric of the Heavens. 
>> London: Penguin Books., pp. 281-2;
>> Toulmin and Goodfield, 11965. The Architecture of Matter. London: 
>> Penguin Books, pp. 217-20;
>> Hanson, N. R. 1965. Patterns of Discovery. Cambridge: Cambridge 
>> University Press. pp. 90-1;
>> Losee, J. 1972. A Historical Introduction to the Philosophy of 
>> Science. London: Oxford University
>> Press., pp. 90-3
>> But I could not check any (except Losee). When I read this sentence 
>> three decades ago, I took  "ghostly fingers" for an allusion to 
>> Berkeley's Analyst (Criticising "fluxions", Berkeley wrote: May we 
>> not call them the ghosts of departed quantities?). But working on 
>> Smith's History of Astronomy, I am afraid I was wrong and Mark Blaug 
>> did not quote Berkeley at all and could have another author or 
>> passage in mind. Has anybody a suggestion? (I cannot check Blaug's 
>> references myself except Losee)
>> best regards


-- 
Martin C. Tangora
tangora (at) uic.edu