Skip to content | Skip to menu | Skip to search

Banbury Cross

a pillow for lost thoughts...

Archives for: January 2012

Red Herring Issues

Ever since denizens of the Neanderthal valley acquired enough vocabulary to trash their fellow cavemen for wearing out of style loincloths, gossip has been an integral part of our evolution into higher forms of life. Considering the lack of electronic gadgets available to humanity up until recently, man's fixation on the fortunes of other men is understandable. In the absence of a boob tube, peeping into dimly lit windows of your neighbors must have been the best value in medieval entertainment. Who could blame the poor unwashed peasants for sitting under a linden tree and passing judgment on their peers. In the era of Facebook, our passion for sticking noses gently into other people's affairs has been coddled on a global scale. And there is nothing wrong with that - nobody is perfect, right? But a line should be drawn when this ancient human proclivity gets hijacked for political purposes.

The magical rise of Rick Santorum in the Republican primaries and his holy obsession with what happens in private bedrooms of private citizens is an indicator that the party of Abraham Lincoln knows quite well how to play the ball in the political arena. Economic issues? Nah, too complicated. State of education - we don't need that. Wobbly financial system? Oh, still plenty of blind eyes to turn in that general direction. Immigration, health care, runaway income inequality? Oh, quit bothering me. Why don't we just play into centuries old peeping reflexes and start commandeering personal lives of the electorate.

Not so long ago, Michele Bachmann (a serious presidential contender at that time) opined with an absolutely straight and well made up face: "Gay marriage is probably the biggest issue that will impact our state and our nation in the last, at least, thirty years. I am not understating that." Really, Michele? We are running record levels of federal deficit, millions of families are struggling with the aftermath of the economic crisis, our military is stretched thin and tired, and yet somehow you think that the average citizen should worry about some gay couple getting married on the other side of the town?

Social issues make for a great political chewing gum - they set your jaws in motion, but provide no nutrition to the body. They certainly won't help laid off Americans achieve their dreams. Neither will they stop the wealth flow into the upper strata of the society. But maybe that is exactly their purpose. It's all just a clever distraction for the population at large. There is a well connected group of people who profit from the status quo tremendously and they have absolutely no real interests in bringing the jobs back or lifting the working classes out of their poverty. From the point of view of this class, the ability to convince masses to vote against their own economic interest is priceless. That's why the social issues appear to be such a godsend. They are a masterfully placed red herring. A powerful wedge hammered into the popular opinion alongside an artificially created cleft. Divide and conquer at its best.

When it comes to massaging the minds of general public, social issues are second to only one other agent: fear. Nothing will hold restive mood of the populace at bay like a little dose of trepidation. I know this first hand. Communists in the old Soviet bloc used this tactic day in and day out. They figured out pretty quickly that people who are afraid are much easier to control than free and confident individuals. And contemporary right wing media took this doctrine to new heights. From Good Morning to the Evening News, we are bombarded with new evidence that some tent dwellers growing poppy plants in a desert on the other side of the globe pose existential threat to our way of living. Or that the latest labor friendly bill passing through Congress is a thinly veiled attempt to establish a socialistic dictatorship of the USSR. In the 21th century there is no shortage of things to be afraid of.

Under normal circumstances people like Bachmann or Santorum would be great fodder for Jay Leno. Unfortunately, we gave up normal circumstances around the time George Bush rolled into the office. In the era when American Idol contestants have better public recognition scores than recent presidents and news cycle is driven by Lindsey Lohan's court appearances normality is a rare flower. The sad truth is that people have always found it easier to be passionate about something they understand. It is hard to be furious about the credit default swaps or central bank's inflationary policy when you have only a vague idea of how it affects your life. And politicians just love that kind of setup. After all, waltzing with a Styrofoam mannequin in front of the TV cameras is so much more pleasant than having your toes stepped on by fickle reality when you try to tango with thornier issues.

Watching the seemingly never-ending marathon of Republican debates has been a surreal experience. Hours of prime time programming wasted on debating what form of entertainment corrupts our population most or which Middle East country we should be invading next. Nary a peep about the real problems. That Ben Bernanke's printing press is killing middle class America. That Congress, well supported by generous donations from the financial sector, spares no effort in shifting private debts onto the backs of US taxpayers. That good manufacturing jobs are being exported to cheap Asian countries with poor environmental controls and virtually no labor protection rights. But why worry about our country's future, when we can worry about details of our neighbor's sex life?

In the old days GOP stood for the Grand Old Party. It appears that these days that very same acronym merely reflects on the pragmatic menu of choices their loyal followers are being offered:

Gossip or Phobia?

And would you like Freedom Fries with that?


Rational points on the unit circle

Unit circle is a very simple object. It is just a set of all points in the plane which happen to be exactly one unit away from the center which you can think of as the usual origin in the coordinate plane. Like everything living in the coordinate plane, every single point of it corresponds to a pair of numbers, expressing its location with respect to the x and y axes. If you are of curious nature, as some mathematicians are, you may start wondering if there are any rational points on this circle? That means points whose both coordinates are common fractions.

Knowing how ubiquitous common fractions are, your gut instinct would advise that there must be tons of them. But if you start looking for examples you realize the answer is not as obvious as it seemed. Let us pick a common fraction for one coordinate - say x=1/2. Since any point on the circle satisfies the equation x^2+y^2=1 you can calculate the other one easily: y=Sqrt(3)/2. And there is the rub - square root of three is not a common fraction. So let's take another well known fractions for the first coordinate: x=1/3 or and x=2/3 and see if we get luckier. We won't. The corresponding y-coordinate turns out to contain those pesky square roots again. At this point you may think that situation is becoming hopeless and if there are any rational points on the circle at all, they are extremely rare. Indeed, unless you have a perfect square to begin with - and perfect squares are few and far between - taking a square root of a whole number happens to be profoundly irrational and thus not eligible to pose as a common fraction.

But overly pessimistic viewpoint is misleading as well. Despite the slim odds of hitting a perfect square, there are in fact infinitely many rational points on the unit circle. If you want to see that without breaking too much algebraic sweat, you can connect the point (-1,0) with any rational point on the y-axis (and of those there are plenty because there you do NOT have to worry about that other coordinate) and then see where the resulting line intersects the circle. It is a fun calculation and it leads to points like (3/5,4/5) or (5/13,12/13) or (20/29,21/29) which are clearly rational and (slightly less clearly) lying on the unit circle. In fact, if you paid attention in high school algebra classes, you may recognize them as sides of Pythagorean triangles. They are among the most amazing objects of all mathematics.

For lay people this is one the most puzzling paradoxes in elementary mathematics. On the one hand these points are rare and difficult to calculate, but on the other there are infinitely many of them and they fill the circle densely to boot. That means no matter how tiny arc of the circle you consider, there will always be infinitely many points on it whose coordinates are common fractions. In other words, no part of the circle is fraction free. I sometimes imagine myself as a tiny ant standing in the center of that circle and watching all those rational points on it as if they were stars on a night sky.

Now if you moved that little ant to one such point on the circle, it would see the coordinate cross from a point which is algebraically simple (a pair of fractions) and unlike any other. In a certain sense these points are like people. They see the Cartesian geometry of the circle from their very unique and rational view point. Just like every person sees the circumstances of their lives from a very special, and hopefully rational, vantage point.

2012 will be a tough year and many important decisions will have to be made. Let's hope they will stay rational - like those Pythagorean points on the circle. They may be hard to find, but hey - there are infinitely many to choose from.

Pearls of Wisdom

George Santayana, a Spanish philosopher and novelist once said: "Those who do not learn from history are bound to repeat it". And that is the deep truth about the plight of the human race on this planet, although Mark Twain would probably temper our expectations with his famous disctum "History does not repeat itself, but it does rhyme".

This Christmas I finally found some time to put together a collection of quotes that had caught my attention over the past year. They show nicely how mankind continues to struggle with a fairly limited but recurring set of problems. We just don't seem to be able to learn from our past mistakes.


A democracy is always temporary in nature; it simply cannot exist as a permanent form of government. A democracy will continue to exist up until the time that voters discover that they can vote themselves generous gifts from the public treasury. From that moment on, the majority always votes for the candidates who promise the most benefits from the public treasury, with the result that every democracy will finally collapse due to loose fiscal policy, which is always followed by a dictatorship.

This piece of wisdom is usually attributed to Alexander Frasier Tytler. He may not be the original author, but the quote captures the primary weakness of democracy quite fittingly.


The budget should be balanced, the treasury should be refilled, public debt should be reduced, the arrogance of officialdom should be tempered and controlled, and the assistance to foreign lands should be curtailed lest Rome become bankrupt. People must again learn to work, instead of living on public assistance.

This is an old one - usually attributed to Marcus Tullius Cicero (most likely an embellished version of one of his actual speeches). But this piece again neatly summarizes the timeless problem of human governance. Living beyond one's means seems to be the end game of all complex societies. Too bad there was no Twitterus in those days, otherwise this Roman philosopher and statesman could have started "Occupy Circus Maximus" - a new and revolutionary movement that might have saved the already crumbling empire and put the whole civilization on a fast track into modern times.


In the absence of the gold standard, there is no way to protect savings from confiscation through inflation. There is no safe store of value. If there were, the government would have to make its holding illegal, as was done in the case of gold [...]
This is the shabby secret of the welfare statists' tirades against gold. Deficit spending is simply a scheme for the confiscation of wealth. Gold stands in the way of this insidious process. It stands as a protector of property rights.

This is Alan Greenspan in one of his early objectivist essays. It shows how far way he strayed away from his youthful ideals but it also shows the true dilemma of monetary policy. However imperfect the gold standard may be, the moment our money acquires arbitrary value it becomes an object of manipulation.


Lenin is said to have declared that the best way to destroy the capitalist system was to debauch the currency. By a continuing process of inflation, governments can confiscate, secretly and unobserved, an important part of the wealth of their citizens. By this method they not only confiscate, but they confiscate arbitrarily; and, while the process impoverishes many, it actually enriches some [...] As the inflation proceeds and the real value of the currency fluctuates wildly from month to month, all permanent relations between debtors and creditors, which form the ultimate foundation of capitalism, become so utterly disordered as to be almost meaningless; and the process of wealth-getting degenerates into a gamble and a lottery.

This is an actual quotation from John Maynard Keynes ("The Economic Consequences of the Peace"). This quote points in the same direction as young Greenspan. The manipulation of currency (which almost always means its debasement) is not a sound and fair economic policy. Although it may be politically the most convenient one.


And that's it for now. Close the textbook. However familiar our problems may seem, they will always need to be rehashed in terms of a new context. While we can learn a lot from the past, we should keep our eyes on the ultimate prize: the future. Or as one Johann Wolfgang von Goethe once put it - All theory, dear friend, is gray, but the golden tree of life springs ever green.


This site works better with web standards! Original skin design courtesy of Tristan NITOT.