The Best of all Possible Worlds: A Life of Leibniz in Seven Pivotal Days
Michael Kempe, Pushkin Press, £20

MICHAEL KEMPE, director of the Leibniz Archive in Hanover, has written an enthralling biography of Gottfried Wilhelm Leibniz. It is not a conventional biography. Instead Kempe presents a series of snapshots of significant days in Leibniz’s life, vivid pictures of how he lived and worked in Paris, Zellerfeld, Hanover, Berlin and Vienna.

Leibniz was one of the last representatives of a type of universal scientist, with the 17th century scientific revolution’s optimistic trust in progress, and also with the hope, dating back to the Renaissance, of being able to lay claim to all the world’s knowledge. In his amazingly productive life, Leibniz indeed made major contributions across a huge range of disciplines.

He invented a simple symbolic language that made it possible to add together the sums of infinitely small values. This made it possible to operate with infinite values, just as we do with finite values. His notational technique shortened the long route to calculating the mathematically infinite. Among other things, his calculus of infinitesimals provided the means to completely describe the science of mechanics.

He experimented with binary numbers. He was not the first to do so, but he continually promoted this numeral system, so much so that his name became inseparably linked with the development of binary arithmetic, out of which grew the digital code used in computer technology. In 1938, Konrad Ruse, who built one of the first functional computers, explicitly paid tribute to Leibniz’s work. 

Leibniz also used the binary calculation method to programme a machine. In 1679-80 he came up with ideas for two calculators that would use the binary system. 

And he worked out how this binary principle could be used in algebra as well. On this basis, George Boole, centuries later, developed the algebraic logic we use today in computer programming. 

Thus Leibniz contributed to three crucial components of modern digital technology: binary numbers, dyadic machines and binary algebra. 

He saw that simple substances, understood in their physical form as perceptible phenomena, guarantee that there is a difference between the real and the imagined. He rejected Bishop Berkeley’s idealism, the theory that only perceptions are real. To speak of something’s being imagined only makes sense if something exists that isn’t imagined.

Consider the current notion that we may be living in a computer-simulated world. Leibniz argued that to speculate in this way assumes that a real world must exist. If something is a simulation, then there is something being simulated, and there is someone doing the simulating.

He conceived of motion as the permanent condition of all mobile bodies and he saw everything as connected. Both these ideas foreshadow Marx’s materialism.

Leibniz used the presentation of evidence in a legal context to guide his research as a historian, distinguishing, like a good jurist, between levels of certainty: irrefutable proof, high-probability assumption (presumption), low-probability assumption (conjecture) and, finally, circumstantial evidence and speculation.

For Leibniz, the realisation of the best possible world was a task that challenges us all to help shape our environment and to work on our own self-optimisation, most importantly, morally. He saw the world as always already the best because it carries within itself the possibility of its optimisation.

What makes Leibniz’s optimism still attractive is the way that he thought in terms of possibilities, of choices, of freedom. The pessimist knows of only one direction that the world can move in. The optimist always sees alternatives and opportunities.