From Electronics to Math and Money Madness

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.

Cantor proved that the number of fractions, which is also infinite, is of the same “size” of infinity as the counting numbers. With both, however, there are still huge empty spaces on the number line, filled by what are called irrational numbers, and there are even more of them than the rational numbers – the counting numbers and fractions. It was mathematicians who gave these names to these numbers; were they already thinking about sanity? One German mathematician, Leopold Kronecker, did not believe any numbers actually existed except the counting numbers. He avoided madness by denial.

The number of irrational numbers brought in the idea that there are different sizes, or orders , of infinity. And what drove Cantor mad was that he could not tell whether there was an intermediate order of infinity between that of the rational and irrational numbers – or whether there were infinite orders of infinity. Goedel later proved that it is logically impossible to tell. Then he too went bonkers. (If you want to know why, read The Mystery of the Aleph by Amir D. Aczel, Four Walls Eight Windows, 2000 – a readable book about mathematicians and infinity.)

Mathematics is a demanding mental activity but Goedel proved that even math has fundamental logical limits. This for a while was itself maddening to some mathematicians. The madness of the financial world is of a less mentally demanding nature, though it is related to mathematical madness. One connection is found in a false assumption about reality and infinity. It relates to government debt or how high the stock market will go. When the quantities that describe financial behavior – the variables of finance – are assumed to have an infinite range without causing major changes in the world, financial infinity madness is active.

In other areas of life – certainly in electronics – we know that quantities run out of operating range; a car runs out of gas, then behaves differently. An op-amp runs of out of input or output voltage range and saturates. A sound system distorts when the volume is turned up too high. A politician in charge of the military pushes the button when taunted to geopolitical excess. Some of these variables can be measured, such as gas or voltage or distortion, and others, like political behavior, are hard to quantify.

Economists, and especially those in econometrics , have tried to do with social behavior involving wealth what engineers do with circuits. They define quantities, measure them, develop theories, and then try to predict their values. Yet every physical or social variable has a limited range before it becomes nonlinear and some qualitatively different behavior occurs. The financial world is now showing significant symptoms of nonlinearity, as trade imbalances, institutional debt, and the issuance of money created by merely willing it into existence increase without precedent. If these social variables are like voltage or current in circuits, then something different happens when they approach their limits.

As engineers, we consider that our skills pertain to the subject-matter of engineering, yet reality has a consistency and similar character throughout. What we know of the behavior of electrons under the conditions we place upon them also has some broader relevance to the social world and the behavior of us humans, at least in statistically large groups under various conditions. Many who participate in the dynamics of the financial world seem to suppose, in practice at least, that its variables have infinite ranges. Will the stock market really go up forever? What limits it? And what limit is there on the expansion of the money supply in economies with finite growth rates? Is there any limit to how far one can go into debt before something different happens?

Those who tend to deny the finiteness of ranges of physical or even social variables join eminent mathematicians of the past and suffer from infinity madness. In engineering, we are not afforded that mental “luxury”. From the way our circuits work, we can well surmise that when even social variables extend too far, social behavior will change in some significant way. Hopefully, farsighted thinking of a kind that is familiar to us as engineers can apprise us of what generally to expect might happen outside our world of electronics – or at least give us sufficient insight into its behavior to avoid infinity madness.

8 comments on “From Electronics to Math and Money Madness

  1. jimfordbroadcom
    November 4, 2015

    Thanks, Dennis, for this excellent post!  Reminded me of George Gamov's One, Two, Three, Infinity , which I read in high school in the early 1980's, nerd that I was (and still am).  Gamov discusses the various types of infinities, symbolized by the Hebrew letter aleph with different subscripts.  Also there is Douglas Hofstadter's Goedel, Escher, Bach: an Eternal Golden Braid , which I have not gotten around to reading, but I understand that it brings together those 3 geniuses' work in mathematics, art, and music, while having a great sense of humor, a feat definitely not to be sneezed at.

    And your mention of the insanity of the financial and political communities reminded me of how politicians' math is so different from most other people's math!  Hence the joke about the banker, the electrical engineer, and the politician taking a test.  One question says, “Name the problem when expected output exceeds input.”  The banker says, “That's easy; overdraft.”  The EE says, “That's easy; overload.”  The politician says, “Aha, a trick question; there's no problem!”

    One thing that keeps bothering me about government is that there doesn't seem to be enough negative feedback; that is, government seems to continue to grow without bound.  For example, one person gets elected to office and he/she brings in his/her supporters/cronies who decide to build up departments under them, and so on and so on.  In business, in contrast, there is the need to make a profit, and so there is at least some negative feedback as to how many people can be hired and paid.

    Another big irritation is the U.S. debt ceiling.  It seems very simple to me; if I were to do as Congress has done and spend more than I bring in, my bank would definitely not increase my credit limit!  But that is exactly what Congress and the President are asking for!  NO, I say, we should decrease the debt ceiling, not increase it!  Duh!  Talk about financial insanity!

  2. D Feucht
    November 4, 2015


    “One thing that keeps bothering me about government is that there doesn't seem to be enough negative feedback;”

    I wish it were that simple. Actually, the root of the problem does not lie with govt as such but with those who control it: the Money Power, the Establishment, the Insiders, the Power Elite, the Ruling class, what-have-you. Remember President Jimmy Who?, the peanut farmer from Georgia? Nobody heard of him before, and he ends up in the White House. Why? The Trilateralists, Zbigniew Brzezinsky, leading back to David Rockefeller. Obama is a repeat, only George Soros is involved this time.

    Political power is “the ability to influence” and the means of that power is money. Presidents execute the agendas of those who put them there. The two political parties were infiltrated and subverted by the Rulers well over a century ago. Now, they are in the late stages of consolidating their control, the end game …. It can be maddening but the good news is that this game is finite.

  3. Navelpluis
    November 5, 2015

    Great article, Dennis, thanks for writing this.

    I know that you are into analogue electronics design: Does choosing the right opamp for your application not drive you mad? Hahaha And how about critical applications that really can go wrong? For example: A control circuit driving a 40kW motor on a crane. This -for me- always give thoughts. 

    There are examples of civil engineers who went completely bunkers due to the fact that they had doubt about 'will the bridge hold'? Will the building stand?? This effect must certainly be the case with electrical and electronic engineers who are doing 'the heavier' things, like electricity nets and extremely large and dangerous electric constructions.

    I think to get mad is all about balance. Sitting in a mad house can also be the reason to be able to do your thing without disturbance. Managers around us are very good in disturbing that: They kill our enviroment to do our work, so driving us mad. On the other hand, we learn skills like communication to the right guys to be able to buy that Oscilloscope. So, building up our enviroment again. I think this stupid example tells us about balance. Our enviroment around us forces us to do so, otherwise I think we all already were extremely mad 😉

  4. vbiancomano
    November 7, 2015

    It appears to me from the literature that both Cantor and Goedel long suffered from extreme depression with significant OCD, which is a madness unto itself; thus their histories are not surprising.

    Economic madness is a different horse, however, not in the same class. It results from a lack of understanding by even experts that the various economic debt numbers, whatever the amounts, have no real meaning in a system based on fiat currencies. That is, such economies are based on a test of faith. So as long as the rest of the world believes in the full faith and trust of the US, for instance, to pay its debts with tangible products if need be, there's sufficient confidence in the markets and the US can continue to print money indefinitely. Indeed, the country has yet to collapse from a long-building $18T debt and it's because of an act of worldwide faith.

    As for engineers, they get around the issue of infinity (and possible insanity) often because they have feedback loops and control theory to fall back on, as implied in one comment.

  5. D Feucht
    November 8, 2015

    Well summarized! Trust is the intangible key element in the dynamics. The whole financial house of cards depends on maintaining the mass delusion that paper or digital accounting-entry money have value in themselves.

    One of the great amazements of the 20th century to me is that it is possible to go into a supermarket, load a shopping cart full of real wealth, and at the checkout counter, they will let you leave that store with all that wealth merely by giving them a few pieces of worthless paper!

    Why do they do it? Because they believe (trust) that they too can pass it on to their suppliers in exchange for wealth. It is a game of musical chairs in that whoever is holding the bag of Green Paper when the music stops loses.

    The evolving state of global finance shows me (increasingly clearly) that we are on the cusp of a catastrophe. It would not take a single EMP bomb over Kansas to destroy the USA, only a major instability in the dynamics of the financial system. If any of the half-dozen or more credit (trust, again) links that moves food from field to fork (or plow to pot) fails, the trucks will no longer back up to the unloading docks at the supermarkets, which ordinarily carry about a three-day (just-in-time!) supply of items.

    The prepper movement is not misguided in this regard. At the least, as engineers it would be easy for us to buy some 500 gallon plastic water tanks, direct the spigots on our house roofs into them, and maintain a water reserve. (I have mine, but they are my water supply here in the Belize jungle.) The remaining financial and social sanity also maintains the high-tech social system. Without electricity, we are back in the horse-and-buggy days. This advanced technological society we have participated in creating is … vulnerable!

  6. vbiancomano
    November 9, 2015

    Indeed, too much technology is not a good thing for many reasons, particularly when it involves excessive interplay with the dark intangibles of the human mind. If I were heading an engineering program, I'd require that all students view “Forbidden Planet” (1956) to serve as the indelible example of how super technology and intellect can lead to catastrophe. The film's underlying theme is basically consistent with a fundamental rule of engineering: Be smart enough to know when to stop designing.

  7. jimfordbroadcom
    November 11, 2015

    True, it all comes down to trust.  Even beyond the worthless paper in the supermarket are of course the numbers in accounts accessed by magnetic stripes on plastic cards or other even more esoteric means.  I think holding a piece of paper or a plastic card makes sense to most people, but the next evolution of money, such as bitcoin, in which “wealth” is generated by solving equations, is beyond most people's understanding, mine included.  Feel free to educate me about this new mining via computer because I don't quite get it.

    Something else I find interesting about fiat monetary systems is the adage that “bad money drives out the good”.  That is, suppose we were on a gold standard, and the good money is backed by gold.  One tends to hold onto the good money rather than use it for trade, while trading with the bad fiat money.  After all, it's just worthless paper, and sure, I'll trade this worthless paper to you for hard goods!  Soon enough, no good money is left in circulation.  Next step after that is a cashless society, where all monetary wealth is numbers stored on computers.  I'm not smart enough to figure out what the next step after that is.

  8. D Feucht
    November 11, 2015

    Bitcoin is a way (perhaps) of avoiding third-party side-effects in transactions (which potentially could drive sales-tax bodies crazy), yet it does not have any worth in itself. The obvious problem addressed by Bitcoin is how to make payments in a global market. What is being bought is shipped by parcel delivery. Material money, such as metal coins, can be shipped too (though governments try to discourage it). The key element is trust by whoever ships first.

    An example of a global financial network that works and is based on trust between people who know each other is the Mideastern hawala network. So was earlier America. A trust-based community is founded on personal knowledge of the character of persons and not on impersonal and increasingly desperate methods of impersonal identification, classification, proceduralization, numbering, etc. As Secret Agent (Danger Man in Britain) said in the '60s TV show: “I will not be stamped, indexed, filed, briefed, debriefed or numbered!”

    Your succinct explanation of Gresham's Law was well put. The Trilateral world is now at the point where the good money is considered (in the USA mostly) a “barbaric relic” which has been all but driven out of the marketplace. The next step is to introduce a form of money where every transaction is known and permitted or not by the Money Power. If I were British I would say “mark of the beast and all that, you know.” A few regional currencies will be used (such as the proposed Amero) backed by a different money for the central banks, the Special Drawing Rights (SDR) of the central bank of the central banks, the BIS in Basel, Switzerland. This is yet another good reason for developing an alternative hawala economy among the Secret-Agent-minded of the world – assuming the communication and transportation infrastructure can continue to be freely used.

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.