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Although percentage bands are useful and many trading systems have been created using them, they have a number of problems Bollinger explains: By addressing those problems, I was led to create Bollinger Bands The first problem was that you needed different width bands from stock to stock Some stocks need bands that are 2 to 3 percent wide, and some stocks need bands that are 7 to 10 percent wide Because the bands varied, depending on the stock and time period, Bollinger said using them was very time consuming, primarily because you had to draw them by hand Perhaps the worst problem with percentage bands, he says, was they allowed your emotions to enter the trading process, which is a disaster, as we all know He says that percentage bands were designed based on data the trader wanted to include, a very subjective process I was looking for a system that could set the bands automatically, Bollinger says At the time, he was an options trader and was very concerned with how options were priced, which was based on calculating volatility: In those days, we believed that volatility was a fixed number We thought it was part of the property of a security In other words, once volatility was calculated for a security, it wouldn t be revised No one bothered to calculate it more than once a year, because it was believed that volatility didn t change, he says Fortunately, Bollinger had access to an early version of a spreadsheet called SuperCalc using the old CP/M [Control Program for Microcomputers] operating system One day I copied the volatility formula on the spreadsheet and saw for the first time that volatility was actually a dynamic number, he explains It was changing all the time And I said, That s interesting! That s when he realized he could use the volatility calculation to make the percentage bands more adaptive to real-life market conditions Over the course of a few months, with trial and error and different forms of volatility calculations, I came up with Bollinger Bands, notes Bollinger At the time, he knew he had a valuable tool, but he didn t think others would recognize it The way it was introduced to the public was through a television interview I did on the Financial News Network in the early 1980s, he says I showed a chart that had my indicator on it I said we are projecting that the market will rally from the lower band to the upper band in a relatively short.

Here s a challenge!

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In 1963, during a meeting of President Kennedy s scienti c advisors, John Tukey, a mathematician from Princeton, explained to IBM s Dick Garwin a fast method for computing Fourier transforms Garwin listened carefully, because he was at the time working on ways to detect nuclear explosions from seismographic data, and Fourier transforms were the bottleneck of his method When he went back to IBM, he asked John Cooley to implement Tukey s algorithm; they decided that a paper should be published so that the idea could not be patented Tukey was not very keen to write a paper on the subject, so Cooley took the initiative And this is how one of the most famous and most cited scienti c papers was published in 1965, co-authored by Cooley and Tukey The reason Tukey was reluctant to publish the FFT was not secretiveness or pursuit of pro t via patents He just felt that this was a simple observation that was probably already known This was typical of the period: back then (and for some time later) algorithms were considered second-class mathematical objects, devoid of depth and elegance, and unworthy of serious attention But Tukey was right about one thing: it was later discovered that British engineers had used the FFT for hand calculations during the late 1930s And to end this chapter with the same great mathematician who started it a paper by Gauss in the early 1800s on (what else ) interpolation contained essentially the same idea in it! Gauss s paper had remained a secret for so long because it was protected by an old-fashioned cryptographic technique: like most scienti c papers of its era, it was written in Latin

Here is a riddle that ought to get your brain running at full speed Consider this infinite product: 1 ( 1) 1 ( 1) 1 ( 1) 1 ( 1) If we start multiplying from left to right, we get a sequence of products that come out like this, in order: 1, 1, 1, 1, 1, 1, 1, 1, The products switch back and forth between 1 and 1, endlessly The final product therefore cannot be defined No integer can have two values at the same time But suppose we try to apply the commutative law to the original expression infinitely many times! We can then rearrange the factors to get this: ( 1) ( 1) 1 1 ( 1) ( 1) 1 1 Now imagine that we try to group the integers in pairs, infinitely many times, like this: [( 1) ( 1)] [1 1] [( 1) ( 1)] [1 1] That gives us 1 1 1 1 The sequence of products in this case is 1, 1, 1, 1, Now it seems as if the product of the whole thing is equal to 1! What s going on

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