Perhaps one of our more numerate colleagues will check me on this, but
calculus books used to give at least a footnote to "l'Hospital's Rule"
giving a determinate value to a ratio that appears to collapse into 0/0 when
one of its arguments falls to 0. (It was the work of one of the Bernoulli's,
who named it for his rich patron.) It is useful in the math of finance.
Thus the problem of "ghostly fingers" was dispelled, at least in this case.
Is this analogy acceptable math? Will it let Newton and Berkeley rest easier
in their graves?
Mason Gaffney
-----Original Message-----
From: Societies for the History of Economics [mailto:[log in to unmask]] On
Behalf Of Robert Cord
Sent: Wednesday, July 30, 2014 7:47 AM
To: [log in to unmask]
Subject: Re: [SHOE] ghostly fingers
Thanks, Joe. Birkbeck College in London has a Department of Economics,
Mathematics and Statistics.
I suppose I was thinking more along the lines of when and if an economics
department is subsumed into a maths faculty, i.e. without the word
'economics' even making an appearance in the faculty title. But I think I
was getting ahead of myself.
As ever
Bob
On Wed, July 30, 2014 14:54, Joe Horton wrote:
> Yes, it has happened. Until recently Chicago State University had a
> Department of Mathematics, Computer Science, and Economics. I believe
> Economics has now been moved out of that department.
>
>
> Joe Horton
>
>
>>>> Robert Cord <[log in to unmask]> 7/29/2014 5:22 PM >>>
>>>>
> Indeed.
>
>
> I wonder how long it will be before economics 'departments' are housed
> in the mathematics faculty. Perhaps it has already happened somewhere.
>
> As ever
>
>
> Bob
>
>
>
>
> On Tue, July 29, 2014 21:07, Lawrence Boland wrote:
>
>> Bob, I would go further:
>>
>>
>>
>> Some argue that the culture of mathematics departments has
>> overtaken graduate economics to the extent that realism is of lesser
>> concern than elegance. I saw this culture first hand and when I took
>> graduate mathematics classes as part of my graduate education.
>>
>> LB
>>
>>
>>
>> On 29-Jul-14 12:48 PM, Robert Cord wrote:
>>
>>
>>> 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]
>
>
>>>>>> r>> 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
>>>>
>>>
>>
>>
>> --
>> Lawrence A. Boland, FRSC
>> Department of Economics, Simon Fraser University
>> Burnaby BC Canada V5A-1S6
>> phone: 778-782-4487, web: http://www.sfu.ca/~boland
>>
>>
>>
>
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