D iscussion 81
arithm étiques, m ais il n e m e sem ble pas que cette invention tech n iq u e ait in flué s u r le développem ent des m athém atiques.
La véritable application des m athém atiques aux problèm es1 concrets posés p a r la physique e t la techn iqu e nécessite la résolution d’équations différentielles, et d’équations aux dérivées partielles, ainsi que le recours aux principes du calcul infinitésim al, du calcul des variations et des a u tres branches de l’analyse m athém atique. Ce n ’est donc q u ’à p a rtir de la fin du XVIIe siècle, lorsque les élém ents de ces disciplines a u ro n t été progressivem ent découverts que l’on p o u rra envisager u n e applica tion des m athém atiques aux problèm es généraux les plus élém entaires posés par la physique e t p ar le développem ent des techniques et ce n ’est guère q u ’a u X IX e siècle que les m athém atiques d eviendront l’u n des principaux o utils du progrès technique, la technique é ta n t elle-m êm e pour les m athém atiques u n e incom parable source d’inspiration.
— - \
• \
J. R. R a vetz
I w ish to concentrate m y rem ark s on th e m iddle period discussed by Professor Daumas. F rom th e list of sciences p en etratin g techniques th a t he gives, one can see a series: M athem atics, A stronom y, Physics, C hem istry, Biology. It is in such a n o rd e r th a t sciences achieve advance to a new stag e of development, o r in th is case, p en etrate technique.
We can learn some things from a stu d y of th is list. F irst, th is is th e series of effective penetration, an d it is1 n o t th e sam e a s th e series of attem p ts a t applying science to practical m atters. C hem istry and Geology are tw o good exam ples o f w here th e atte m p t was made, a n d failed. O ther exam ples a re in th e dream s a n d program m es o f th e Royal Society of London. N apoleon once said th a t defeats a re m ore instru ctiv e th an victories, w e should le a rn how to use this m axim fo r o u r ow n w ork.
It seem ed to m e on reading th e paper of P rofessor D aum as th a t he stressed, p erhaps too much', th e lim ited ex ten t of th e p en etratio n of science in th is m iddle period. To be sure, m ost o f techniques continued to be unaffected b y science. B ut th e few successful applications of science w ere o f th e g reatest im portance. N avigation is a n obvious exam ple. A nother exam ple is th e steam engine. It h as been said for m any y ears th a t science owes m o re to th e steam engine th a n th e steam engine to science. This is tru e w ith one exception. The idea of th e poissibility of vacuum engine such as th a t of Newcomen a n d W att, comes from th e studies of n a tu ra l philosophy of th e X V IIth cen tu ry .
One final point on th e series. A t th e en d is Biology, and th ere science has n ot y et conquered. Even in th e technology of te x tile m anufacture,
82 L e progrès des sciences e t celu i des tech n iqu es
m y colleagues at th e U niversity of Leeds are freq u en tly in th e position of try in g to' explain w h y th e draftsm en succeed w ith th e ir techniques. A nd in th e bionsiocial sphere, such a s in agricultu re, th e 'difficulties are even greater.
M y last com m ent concerns th e effect of technology on science in th e m iddle period. To (be su re technology provided problem s a n d in stru m en ts to science, b u t th ere w as something even m ore im portant: a basic com ponent of th e new idea of “science” w hich w as advanced by th e founders of the “mechanical philosophy”. The case of Bacon is well known. I w ould rem in d th a t Descartes used Dioptics as a n illu stratio n of his M ethod; th ere h e sta rte d w ith physical theories of light and vision, proceeded to th e m athem atical problem s of th e shape of lenses, a n d con cluded w ith specifications' for a lens-grinding m achine.
D. J. de Solla Price
I should like to ad d a footnote to th e w ords of- Professor Daumas on th e problem of technology (French technique). It seems to me most useful and im p o rtan t to 'distinguish betw een tw o dimes, practically distinct a n d different in th e ir historical character. It is a m a tter of Low Technology a n d High Technology. As fo r th e Low Technology, it is an uncom fortable fact for th e historian th a t w ritin g an d th e w ritte n language are com paratively la te pieces of technology.
By th e tim e of this developm ent and, b y definition, th e end of p re historic tim es, m an h ad alread y acquired q u ite com plex techniques for housing, agriculture, w aterw orks, le a th e r tanning, dyeing, m etal w ork, weapons a n d all sorts of tools. S tarting on th e m ost e a rly tim es at such a high level, subsequent change w as quite gradual a n d slow until th e In du strial Revolution. W ith High Technology it is a qu ite different m atter. Beginning q u ite early, b u t flow ering in Hell'enistic times, th e re grew up a special devices technology of scientific in stru m en ts — astro nom ical devices, p la n e ta ry a n d other autom ata, astrolabes and geared m achines for calculation a n d dem onstration. I t is specially interesting th a t m uch of th is history is attested no t from te x ts b u t ra th e r from ex tan t artifacts in o u r m useum s. W hat is im p o rtan t about th is artisan trad itio n is th a t it gives ris e d irec tly to th e m edieval a n d renaissance schools of clockm akers and o th er m athem atical practitioners. These are most im portant, n o t o n ly because th ey dom inated th e experim ental philosophy of the X V IIth a n d la te r centuries, b u t also because they are th e trad itio n from w hich sp rin g th e m echam cdl techniques of th e in d u stria l revolution.
