Dear Martin

Your daughter's professor was and is surely correct. Indeed, it is
probably not an exaggeration to argue that a mathematics undergraduate has
an easier time of it at economics graduate level than their economics
counterpart. This is why we need more history of thought - and I don't
mean history of mathematics!

As ever

Bob



On Tue, July 29, 2014 20:13, Martin Tangora wrote:
> 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
>