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Topic: [HM] Fourier and time-incrementation in system progamming
Replies: 3   Last Post: Jan 31, 2006 2:43 PM

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 Udai Venedem Posts: 19 Registered: 2/16/05
[HM] Fourier and time-incrementation in system progamming
Posted: Dec 17, 2005 4:47 PM

Dear all historians,
Fourier is, no possible contest, of unlimited richness. I came recently
on his last "great" Memoir:
- [1] Mémoire sur la théorie de la chaleur, p. 581-622 in MARS 1825 t.
8, Paris, Didot 1829.
of which very large extracts have been previously published in
Férussac's Bulletin, under the ref.:
- [2] Mémoire sur la théorie de la chaleur (Extrait du mémoire lu à
l'Académie des sciences le 1er décembre 1828). 1829, t. 11 p. 13-30.

In [2] p. 18-19, as ne varietur in [1] § VI. Principe dont on a déduit
la solution générale, Fourier displays words and method, which sound
absolutely like very modern system programming. The problem Fourier
analyses is to find the distribution of heat along a bar with variable
temperatures at the two extremities. First, he reaffirms his
"superposition" principle", which is to say linearity. Second, he
modelises the problem as an input-output process. And third, he
increments outputs as initial conditions reassignments.
For example, he writes (P is here for the Greek Pi) :
<< Supposons que le temps T soit partagé en une multitude
de parties t1, t2, t3, etc.; on assujettit d'abord l'extrémité O du
prisme à la température zéro, et l'extrémité P à une température fixe
b. On détermine l'état où le solide est parvenu après le temps t1; on
considère ensuite cet état que l'on vient de déterminer comme l'état
initial où se trouve le solide, lorsqu'on commence à assujettir la
seconde extrémité P à une autre température fixe b1 + b2 >>
and so on.
I have three question to you, professional historians:
1) Has all this been noticed before? May be by Pr. Kuhn?
2) Has Fourier been the first to analyse dynamic processes that way?
2) What especially about Fourier's wording of "state" (in French:
"état")? Is he the first to use this word and concept to describe a
process?

Udai Venedem
http://aaaa.fr.eu.org/alta.mathematica/

Date Subject Author
12/17/05 Udai Venedem
12/26/05 mmeo
1/31/06 Udai Venedem