Gymnosophists etc.

[Girish Beeharry]

Hi,

I have sent a rather detailed private note to Lars Fosse about Newton &
Leibnitz; unfortunately, I no longer have a copy of it. I was trying to
make the point that they discovered two rather different approaches to two
different kinds of problems. Newton asked himself the question:' Knowing
how a particle moves now, in terms of its speed and acceleration, how to
predict how it evolves in the future (or how was it in the past)?'; this
is differential calculus in a nutshell! Leibnitz said: 'Of all the
possible routes a particle can take, how should I choos the one in which
it spends less time for going from one fixed point to another (say)'; this
is  variational calculus highly simplified. All this is usually bundled
together as infinitesimal calculus.

On Tue, 7 May 1996, L.S.Cousins wrote:

> Lars Martin Fosse writes re Leibnitz-Newton:
> 
> >According to my encyclopedia, the two discovered infinitesimal calculations
> >independently of each other. If more recent theories say otherwise, I would
> >like to know about them.
> 
> Probably the issue as to whether there was communication between the two is
> not very relevant to this list. What is relevant is that they were both
> highly versed in very closely related systems of mathematical and
> scientific knowledge. In other words they are in no way valid as examples
> of totally independent simultaneous invention of knowledge.
> 
Given the above, I disagree with your two last sentences.

> If we had only the information that Newton in England and Leibnitz in
> Europe both invented calculus in the seventeenth century, we might infer
> the existence of influences between British and Continental cultures at
> that time and we would be right to do so; for the invention of calculus was
> a development from and on the basis of the pre-existing mathematical
> knowledge which was largely a common heritage.
> 
We might infer many things and most of our inferences would be invalid.
Newton was the student of Barrow, here, and that influenced him to go into
the type of problems I mentioned above whereas Leibnitz was more
'philosophical' and sought questions about 'le meilleur des mondes' (as
Voltaire put it in his satirical portrayal of Leibnitz as Maitre Pangloss
in 'Candide'). Your statement above is too general. Both really INVENTED
quite new stuff!! The mathematical knowledge was not that 'common' as
Newton was at one of the best places to be for mathematics and Leibnitz
was not (which gives an indication of his towering mathematical
abilities). Circulation of ideas took a lot of time; they had no
preprints, no WWW, not even email! :-)

I wish to apologize for the lack of Indological content of the above.

bye,

Girish Beeharry