Analogue computers in the future Aer these two simple examples, a question arises: “What does the future hold for analogue computers? Aren’t they beasts of the past?” Far from it! Even—and especially—today there is a plethora of applications for analogue computers where their particular strengths can be of great benefit. For example, electronic analogue computers yield more instructions per second per wa than most other devices and hence are ideally suited for low power applications, such as in medicine. They also oﬀer an extremely high degree of parallelisation, with all of the computing elements working in parallel with no need for explicit synchronisation or critical code sections. The speed at which computations are run can be changed by changing the capacitance of the capacitors that perform the integration (indeed, many classical analogue computers even had a buon labelled “10×”, which switched all integration capacitors to a second set that had a tenth of the original capacity, yielding a computation speed that was ten times higher). On top of this, and especially important today, they are more or less impossible to hack as they have no stored programs. A modern incarnation of an analogue computer still under development is shown in the header of the article. In contrast to historic machines it is highly modular and can be expanded from a minimal system with two chassis to several racks full of computing elements. When Lord Kelvin first came up with analogue computing, lile did he know the incredible amount of progress in science and technology that his idea would make possible, nor the longevity of his idea even today in an era of supercomputers and vast numerical computations. Bernd Ulmann is professor for Business Informatics at the FOM University of Applied Sciences for Economics and Management in Frankfurt-am-Main, Germany. His primary interest is analogue computing in the 21st century. If you would like to know more about analogue computing, visit analogmuseum.org and have fun with diﬀerential equations.
My favourite shape
Heptadecagon Sebastiano Ferraris
My favourite geometrical figure is the heptadecagon, a regular polygon with 17 sides. It comes with the history of a great challenge that required the eﬀorts of almost eighty generations of mathematicians to solve. Ancient Greeks knew how to construct polygons with 3, 4, 5, 6, 8, 10, 12, 15, 16, and 20 edges using only a straightedge and compass, while 18th century algebraists knew that it was impossible to use the same tools to construct polygons with 7, 9, 11, 13, 14, 18 and 19 sides. Gauss, at 19, was the first to prove that the heptadecagon was constructible. 59