John von Neumann, aka "Johnny" was more likely than not the greatest mathematician of the last century, making contributions to a wide range of fields including set theory, functional analysis, quantum mechanics, ergodic theory, continuous geometry, economics, game theory, computer science, numerical analysis, hydrodynamics (as it relates to explosions) etc. etc. as well as many other mathematical fields.

He first came to my attention because of his work on a subject that has always fascinated me... the Manhattan Project. In the earliest days of development, the majority of those working on the actual process by which the fissionable material would reach super criticality believed that the only reliable method was what was referred to as a "Gun Assembly", where one sub critical mass would be fired into another to achieve super criticality. While this was reliable, it was grossly inefficient, and also not scalable.

Von Neumann was one of the mathematicians who worked on the explosive lens process, an elegant and complex solution which is more widely known as an implosion style device. This process is the one that was tested at Trinity, the worlds first man made atomic detonation, and has been at the core of every nuclear and thermo-nuclear device since. In any case, tales of von Neumann's prowess abound, and there was one that always appealed to me.

Von Neumann was once asked to solve a classic "fly puzzle"...

Two bicyclists start twenty miles apart and head toward each other, each going at a steady rate of 10 Mph. At the same time, a fly that travels at a steady 15 Mph starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and the flies to the front wheel of the southbound one again, and continues in this manner till he is crushed between the two front wheels. Question: what total distance did the fly cover?

There are two ways to answer the problem. One is to calculate the distance the fly covers on each leg of its trips between the two bicycles and finally sum the infinite series so obtained. The quick way is to observe that the bicycles meet exactly an hour after they start so that the fly had just an hour for his travels; the answer must therefore be 15 miles. When the question was put to von Neumann, he solved it in an instant, and thereby disappointed the questioner...

"Oh, you mush have heard the trick before!"

"What trick" asked von Neumann, "all I did was sum the infinite series."

## Comments