From electronics to maths and money madness

November 23, 2015 // By Dennis Feucht
Dennis Feucht discusses different infinities, the madness of George Cantor and what can be learned about the irrational exuberance of the financial markets.

In electronics, we are familiar with bounded ranges on circuit variables, yet the idea of infinity is also common in electronics theory and does not seem to invoke insanity among engineers. This is not the case, however, in other endeavors, and can be found in such varied places as mathematics and global finance.

 

Chief Agoran, Addison Wiggin, wrote in his Halloween 2014 article in The Daily Reckoning, a money-oriented website that has a readership exceeding the New York Times and Wall Street Journal, that Agora is interested in human emotion including insanity, a state of mind coming into fashion not only in the financial world but in the whole social order. Yet mathematicians, those quiet scholars who contemplate abstract notions, have been there and done that already.

In the late 1800s, a German mathematician, Georg Cantor, studied infinity. He spent a large fraction of his life in the mental institution in Halle, Germany. Then in the early twentieth century, his successor, Kurt Goedel, came to America, made important math contributions, and spent time in and out of a mental institution in Maine. Goedel was a good friend of Einstein who was Goedel’s opposite: humorous, gregarious, outgoing. Einstein liked Goedel for his far-reaching ideas.

Infinity is common in electronics engineering. Op-amps ideally have infinite gain, and at infinite frequency, reactances are zero or infinite. Infinite time is required for circuits to reach a complete steady state. The idea of infinity pushes the human mind and our ability to contemplate abstractions to its limits, yet in electronics, infinity has more of a practical role as a limiting consequence of what is finite and does not invoke much irrationality.

Perhaps the madness infinity causes among mathematicians is linked to madness in finance. Before we take that on, what exactly drove Cantor and Goedel mad? Perhaps the answer can give us some insight into money madness. Cantor started with the simple fact that there are an infinite number of counting numbers. If you don’t believe this, just add one to the largest number and you have an even larger number. They go on without end. The counting numbers can be plotted on a number line, and in between 1, 2, 3, etc. are fractions - lots of them.

Next: Orders of infinity