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CADFEM GmbH INFOPLANER 2/2005
Gottfried Wilhelm Leibniz:
philosopher, mathematician, physicist engineer, ...
Plenary lecture at the CADFEM Anniversary Conference
on 9th of November 2005 at the Bundeshaus
in Bonn, Germany
Gottfried Wilhelm Leibniz, born on 1st of July 1646 in Leipzig, a
lawyer by education, lived – with interruptions – for 40 years in
Hannover until his death on 14th of November 1716.
He was one of the leading intellectual fi gures of the 17th century
– the cradle of modern times – in all fi elds of knowledge of that
time, named as the last universal scholar. Far ahead of his time,
he was a universal inventor of many new subjects which are outlined
in the lecture as a synopsis of the Leibniz exhibition of the
author:
(I) in mathematics the infi nitesimal calculus (congenial with
Isaac Newton but much deeper and more extensive) and the
calculus of determinants;
(II) in mathematical and linguistic logic the “characteristica
universalis” as a universal language of science, combined with
the “ars inveniendi” and the “calculus logicus”;
(III) in the design and construction of new type and future-oriented
calculating machines, the famous four-function decimal
calculating machine and the (not constructed) “machina
arithmeticae dyadicae” (a binary calculating machine as the
logical anticipation of electronic computers), both reconstructed
by the author in a team for the Leibniz-exhibition with
eliminating construction faults;
Original Four-Function Decimal Calculating Machine with stepped
drums after 1693, Leibniz Library of Lower Saxony
Applications and Technology
(IV) in physics the formula for the kinetic
energy of a moving body in conjunction
with the fi rst formulation of the
Oil painting by
Andreas Scheits, 1704,
Firence, Uffi cies-Pitti
principle of extremal total energy in classical mechanics, and
– as a famous application of this – the geometric step-by-step
solution of the Brachistochrone problem, posed by Johann
Bernoulli and fi rst described and approximately solved by
Galileo Galilei. Leibniz’ discrete solution – besides four other
analytical solutions of this variational problem – is to be seen
as the precursor of the fi nite element method in time and
space.
(V) in technical improvements for mining in the Harz mountains
by inventing force- and energy-saving new devices and
machines.
Also Leibniz’ scientifi c achievements as a historian, lawyer and
librarian are very notable.
As a sixfold counsellor of electors, dukes and emperors in Europe
he acted as a lawyer, diplomat and politician with the goal of
creating peace between the absolutistic states as well as between
the split christian churches as a “pacidius”, a peacemaker, but he
failed in most cases. His main ambition can be seen in the foundation
of academies of science with the guiding postulates “theoria
cum praxis” and “commune bonum”, in order to develop and
increase pure and applied sciences with the goal of improving
the material and mental conditions of life for both, societies and
individuals in the beginning age of enlightenment.
The multiple activities and projects of Leibniz can only be understood
by his philosophical and theological thinking, trying to
integrate “ratio et religio”, published in his “Théodicée” and the
“Monodolgy”. He tried to bring together matter, mind and soul
in his “Leibniz worlds”, guided by his rational laws of thinking,
especially “nihil sine ratione”.
Today a growing interest in Leibniz’ work can be observed again
world wide, especially his philosophy and his fundamental inputs
into science and technology. We can still benefi t from his ingenious
contributions to network-thinking in all aspects of life.
Erwin Stein
Univ.Prof.em.Dr.-Ing.habil.Dr.-Ing.E.h.Dr.h.c.mult.,
Institute of Mechanics and Computational Mechanics,
University of Hannover, Hannover, Germany
E-Mail: stein@ibnm.uni-hannover.de