Martin Tangora will know that many people have worried about the implicit division by zero involved in the traditional derivation of the differential calculus. 

What he may not know -- but Alain Alcouffe certainly does! -- is that among the worried was no less a figure than Karl Marx, who left a substantial set of manuscripts dealing with the problem.

Assessments of Marx's efforts have varied (he was apparently unaware of contemporary work on limits), but Joseph Dauben has suggested that it contributed to interest in non-standard analysis among Chinese mathematicians.

Arcane as the topic may be, from the point of view of Marx's main work, his mathematical manuscripts have been translated into a number of languages, including one in French by our colleague Alain. 

Julian

-----Original Message-----

>> 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)
>>>>


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