*"For it is unworthy of excellent
men to lose hours like slaves in the labour of calculation which could safely
be relegated to anyone else if machines were used." (G.W.Leibniz)*

Gottfried
Wilhelm von Leibniz (sometimes spelled as Leibnitz) was born on July 1, 1646 in Leipzig.
He was a son of Friedrich Leibniz, a professor in moral philosophy at the University of
Leipzig. Shortly before his death Friedrich is reported to have pointed towards his
library and instructed his 6-year old son "Take, read." This gave the young
Leibniz unlimited access to his father's large library and laid the foundation for him to
ultimately become one of the great philosophers, scientists, mathematicians of
the 17^{th} century.

At the young age of 15 he enrolled at the University of Leipzig to study Law, but when at the age of 20 he applied to be awarded his doctorate, it was refused as he was considered too young. He left Leipzig and went to the University of Altdorf in Nürnberg, which quickly recognised his genius, awarded him his degree and offered him a professorship, of which he accepted the first but turned down the latter.

In 1667 he accepted a position as advisor to the Elector of Mainz. This function enabled him to travel extensively across Europe and he regularly visited cities like Paris and London. During his travels he met many scientists and scholars of his time, incl. Huygens, Boyle, Armauld, Spinoza, etc. He stayed in contact with most of these scientists and philosophers to exchange ideas and to discuss developments, theories, religion and politics. This resulted in an extensive correspondence and more than 15,000 letters from Leibniz to about 1000 different people have been preserved.

In 1672 the Elector sent Leibniz to Paris on a diplomatic mission to King Louis XIV. He would stay in Paris till the Elector's death in 1676. It is during his stay in Paris that he learned of Pascal's calculator. Having noticed the Pascaline's limitations, Leibniz was convinced he could design a better machine and started to work on a device that not only could add and subtract but was also capable of doing multiplications, divisions and even evaluating square roots of numbers. He soon faced the same obstacles that Pascal had experienced – poor workmanship, unable to create the fine mechanics required for the machine. Leibniz solved this problem by engaging the services of local clockmaker Olivier who was a fine craftsman.

Local stamps issued by Citipost Hannover (2012) showing original
design drawing, final product and intricate detail of the *Stepped Reckoner*

**The Stepped Reckoner**

The Leibniz
calculator, which he called the *Stepped Reckoner*, was based on a new
mechanical feature, the stepped drum or *Leibniz Wheel*. It was a cylinder
with nine bar-shaped teeth of different lengths, which increased in equal steps
around the drum. This brilliant concept has been used in many later
calculators, for example the famous barrel-shaped C*urta* calculator. When
the first wooden prototype of the *Stepped Reckoner* was constructed
Leibniz was able to show it to the Royal Society in London. Although the model
did not work properly, the Society members were impressed and asked him to create a proper
working model. The final version was only completed in 1674.

Although it
is believed only two *Stepped Reckoners* have been constructed, the
machine itself was actually lost for more than 200 years. Apparently it was
stored in an attic of one of the buildings of the University of Göttingen
where a crew of workmen who came to fix a leaking roof accidentally found it in
1879. This model resides in the Hannover State Library. The other model is in
the Deutches Museum in München. In the 20^{th} century a number of replicas
of the Leibniz calculator have been built, one of them by IBM.

Although
quite a few stamps have been issued to commemorate this great scientist, only
one philatelic item, a Romanian Postal Card issued in 2004, pictures the *Stepped
Reckoner*.

**Maths & Logic**

Leibniz is
more widely known for his work in mathematics. Following his meetings with
Huygens in Paris he started studying geometry and in 1674 he invented differential and integral
calculus and designed a mathematical notation for it. In the later years of his
life he landed up in arguments with Isaac Newton, who was president of the
Royal Society in London, who claimed he had discovered it first. The mathematical community
was divided on who was first, but the Germans still claim it to be Leibniz. However, as
Leibniz' notation was better than Newton's, we still use the Leibniz notation today,
like his integral symbol ∫ which is
an elongated S from the Latin word *summa*.

The second
area where Leibniz had a significant influence on the development of the future
computer was the discipline of symbolic logic. He believed that the laws of thought or
human reasoning, i.e. logic,
could be described in a mathematical system and language, rather than the
normal spoken and written language which he found too ambiguous in its
description for that purpose. According to Leibniz' logic, man's ideas are
compounded of a small number of simple ideas which form the alphabet of human
thought. Complex ideas derive from these simple ideas by combining them in a
way analogous to arithmetical multiplication, hence the logical operators
addition, negation and multiplication. His ideas were largely ignored by the
scientific world at that time as they barely understood his concepts. This was
partially caused by the fact that his developments in this area were not
published as such but "hidden" in his correspondence. It would be
George Boole who used Leibniz' ideas to develop his *Boolean logic* about
125 years later. When Leibniz came upon the Chinese "I Ching" (Book
of Changes") he found his ideas confirmed as I Ching depicts the universe
as a series of on-off, yes-no, male-female, dark-light dualities. From this
Leibniz developed his binary system, consisting of ones and zeros. In his
beliefs the binary system had a semi-religious – philosophical meaning with one
representing God and zero being Void. When converting the decimal numbers to a
string of ones and zeros, the long strings of binary numbers must have
disheartened him as he never combined the concept of his binary system with his
mechanical calculator. It would be Atanasoff in the late 1930s who would
achieve that. Leibniz had never really found a use for his binary system.

**What is a binary system?**

Binary table in Leiniz’s own handwriting

Modern computers all use the binary system for which Leibniz had laid the foundation. Where in a decimal system (base 10) the digits 0 – 9 are used to represent a number, in a binary system (base 2) only the digits 0 and 1 are used. So the numbers 1 – 10 are represented as follows in a binary system:

decimal |
binary |
incl. Leading zeros |

0 |
0 |
0000 |

1 |
1 |
0001 |

2 |
10 |
0010 |

3 |
11 |
0011 |

4 |
100 |
0100 |

5 |
101 |
0101 |

6 |
110 |
0110 |

7 |
111 |
0111 |

8 |
1000 |
1000 |

9 |
1001 |
1001 |

10 |
1010 |
1010 |

Larger numbers
quickly result in very large strings of 0s and 1s, for example 2345 becomes 100100101001
in binary. Computer scientists in the 20^{th} century managed to harness these growing strings of
binary numbers and they would introduce the term *bit* (from * bi*nary
digi

With his many contacts all over Europe it is not surprising that Leibniz tried to bring some of these scientists in contact with each other. This finally resulted in his founding of the Berlin Academy of Science in 1700 where he also served as its first president.

Stamps and cancellation issued 1975 to commemorate Leibniz’ Acadamy of Science in Berlin

The last years of his life Leibniz lived in rather obscurity and when he died on November 14, 1716, in Hannover, his passing was not even acknowledged in his Academy of Science, nor in the Royal Society of London.

**
© Wobbe Vegter, 2005**