An Engineer's View

In the following my opinion is given on different topics at irregular times.

13. November 2016:

I am user of programming languages. My observation:

More than 200 years ago Gauss put complex numbers on a firm and solid basis such that any scientifically educated person nowadays finds the application of complex numbers a very natural thing.

Nevertheless there continue to appear new and "improved" programming languages which do not contain the elementary data type complex.

Clearly, I know how to get around the problem if no complex numbers are available. Nevertheless, having no complex numbers is inconvenient and can cost quite some time and energy.

Therefore dear programming language developers: If you design new or improved languages please do incorporate complex numbers as basic types for the benefit of engineers, mathematicians, physicists, and all other scientifically oriented people who, I think, would appreciate this very much and be very grateful to you.

P.S.: In addition, my preference would be to have integers, floating point-, and complex numbers where the user can select the number of bits at the outset, e.g. float.prec(256), if a user wants 256 bit sized floating point numbers. (By the way: IBM's REXX Programming language had this feature already thirty years ago!).

22. November 2016:

Let me talk about the different culture of scientists and engineers on the one hand and musicians on the other. If you talk to musicians you will easily find out that they have quite a different culture concerning the knowledge of their subject. Mention the well-tempered clavier or talk about the nineth symphony to any musician and you will realise that all musicians know these works of Bach and Beethoven, you don't even have to mention the name of the composers. Furthermore, the musicians all have the original literature if not personally, then easily disposable. You will find lots of editions of the well-tempered clavier in almost any country of the world.
Now mention the title Disquisitiones Arithmeticae (or in German Arithmetische Untersuchungen) or a similar engineering calibre to a scientist or engineer and not many will know about what you are going to talk in spite of the fact that the importance of Gauss's Disquisitiones Arithmeticae can not be overestimated (it is still current research literature!). Before the internet made it possible to download the collected works of Gauss, it also was quite a problem to get the works of Gauss. In the town I lived in the nineties of the last century, there was a big library which had it. But it was not possible to take it out of the library because as a rule, works which were older than 100 years could not be taken out of the library. If one wanted to buy the collected works of Gauss one had to realise that this was possible, but one had to buy all the volumes, and the price was quite high (about two and a half thousand Deutsche Mark, which nowadays would be about the same in Euro or Dollars).
So you probably will admit that there is a cultural difference: Musicians care much more about their musical heritage than do scientists with their scientific legacy. This is quite beneficial for the musicians, scientists should learn from them.
As a result of this attitude, i.e. neglecting a bit their heritage, scientists and engineers very often compensate this (and hope for advances), by going to conferences on new research subjects. This attitude, of course, is good, but not so much as most people think. It clearly is very advantageous to get to know fellow researchers all over the world. But, in my opinion, often it would be more beneficial to study the works of old masters.
That is what musicians do. They also have their conferences about new music, but on a level which is several orders of magnitudes lower. Critics may add, that musicians had their peak in the 18th and 19th century and have long ago seen their best times but that's not what I'm concerned about. My point here is that sometimes to study the old masters helps more for current research than does a big conference (I am not against conferences).
I will give two examples in my next sciblogs. A comparatively old one and an up to now apparently not known example.

13. December 2016:

Let's consider one of two examples I announced where studying the old masters would have been very beneficial. It is well-known, but apparently still not widely-known, that the Fast Fourier Transform (FFT) is such a case. The FFT was an essential algorithm in offshore detection of nuclear tests in the Soviet Union (see D.K.Maslen, D.N.Rockmore, The Cooley-Tukey FFT and Group Theory, Notices of the AMS, November 2001, pp.1151-1160) which was important for ratification of a nuclear test ban between the United States and the Soviet Union in the Kennedy-time. R.Garwin of IBM and J.W.Cooley at a meeting of President Kennedy's Science Advisory committee found it essential to program this algorithm. As the FFT algorithm is a key-algorithm in signal processing they could convince Tukey to program this algorithm, who apparently did not know that the original purpose was for nuclear test verification. The collaboration of Cooley and Tukey resulted in the paper J.W.Cooley, J.W. Tukey, An algorithm for the machine calculation of complex Fourier series, Math. Comp. 19, (1965), 297-301.
The important thing about the FFT is that it enables the computation of the Discrete Fourier Transform (DFT) with complexity O(n log n) instead of O(n2) for a sequence of n numbers, an essential algorithmic reduction. The remarkable point is that Gauss investigated and used this algorithm at least in 1805 if not earlier, it probably saved him laborious computations when he computed the orbits of celestial bodies. What also should be noted is that he treated the most general case for arbitrary composite length n. For further details on the historic development of the FFT see M.T.Heidemann, D.H.Johnson, C.S.Burrus, Gauss and the History of the Fast Fourier Transform, IEEE ASSP Magazine, October 1984, pp.15-21. Gauss' work containing the FFT was published posthumously and is contained in the third volume of his collected works (Gauss, Theoria interpolationis Methodo Nova Tractata, pp.265-330).

14. December 2016:

This sciblog is about the Berlekamp-Massey algorithm. For people not familiar with algebraic coding I will give a short overview on this algorithm (for the motivation of algebraic coding also have a look here ). After transmission of a codeword vector through a channel the receiver gets a possibly erroneous vector. From this the so-called syndromes are computed. In algebraic coding this means usually the syndrome polynomial S(z). Then the final task is to find the closest codeword of the received vector. To do this one must solve the so-called key-equation of coding. It reads σ(z) S(z) = ω(z) mod zL. Solving this means finding the lowest degree polynomials σ(z) and ω(z) from the syndrome polynomial. From the roots of the polynomial σ(z) one gets the positions of the errors and (in the non-binary case) with the additional help of ω(z) one finds the values of the errors. Thus one obtains the codeword sent (if not too many errors occured).
For almost ten years in the history of coding-theory, the main-bottleneck of decoding was solving the key-equation. Then this problem was essentially solved by Berlekamp with his algorithm (see Elwyn R. Berlekamp, Algebraic Coding Theory, 1968). It found widespread dissemination in particular when James Massey gave a version of this algorithm in terms of shift registers. This algorithm now has the name Berlekamp-Massey algorithm.

I can't remember exactly when I stumbled across an algorithm which I found quite remarkable. It was probably sometime between 2006 and 2008. For general interest and with some applications in filter theory in mind I was studying (or better looking through) the two volumes of the nestor of continued fractions. Some mathematicians and specialists in the field will know that I am talking about Oskar Perron. In the second volume Perron considers so-called C-type continued fractions and explains an algorithm due to Frank. Later I was looking up Frank's original paper and found that the treatment of Perron is much more elegant than Frank's. This is often the case. The first who develops a new result usually does not have the most brilliant presentation. In any case Perron's presentation is brilliant. I was reading the description of this algorithm conveniently lying on a comfortable sofa and understood this algorithm immediately. Now what is the point you will ask. Well the point is, if you replace finite field for the usual field you find out that the Frank-Perron algorithm (my suggestion, it stems from Frank and the lucid description is due to Perron) is essentially the Berlekamp-Massey algorithm. For sceptics here is the essential page (Satz 3.8). Hence another case where looking at classics could have saved much time and effort (Frank's paper is from 1946 and Perrons book, i.e. the third edition where he considered this, is from 1957).

By the way, when I found this, I first thought that I should write a nice exposition. But soon I dropped this idea. Mainly for two reasons. First writing well-written expositions takes quite some time and effort and as long as I can work on new subjects my choice favors working on new subjects. The second reason is that such an exposition will probably not make friends. Nobody likes wisenheimers who tell everybody how ignorant they are. Therefore this sciblog is probably the right place. My point is that continued fractions have a lot of potential in coding theory (and many other fields). Also I do not argue that the Berlekamp-Massey algorithm should be renamed. I think, this not appropriate. There are plenty of cases where results have been rediscovered in different fields under different names. The exact references for the Frank-Perron algorithm: O. Perron, Die Lehre von den Kettenbrüchen, B.G.Teubner, Band 2, Stuttgart, 1957, 3.verbesserte und erweiterte Auflage. The copy I used is the 1977 reprographic reprint of the third edition. The original paper of Frank is: E.Frank, Corresponding type continued fractions. American Journal of Mathematics 68, 1946.

31st May 2017:

A famous mathematician as cadger of the Diabetes Society?

The grave of the famous composer Mozart does not exist anymore. I guess that most people of Vienna would appreciate having Mozart’s grave preserved, not only for touristic purposes but as a place to honour this great musician. This error (i.e. the disappearance of his grave) occured immediately after his death.

Later on, people got smarter. In Berlin famous people are lying in so-called Ehrengräbern (graves of honour) to prevent that such graves disappear. A photograph of the Ehrengrab of Hermann and Oskar Minkowski is displayed here . This photograph was taken around 2013. The brown brick indicates the Ehrengrab. Scientifically oriented people know that Hermann Minkowski is a very famous mathematician and physist (he essentially completed the theory of special relativity by introducing the Minkowskian spacetime). His brother Oskar was a famous diabetes researcher.
Around 2014 and finally 2015 local politicians in Berlin decided to repeat the errors of the people of Vienna. For financial reasons they reduced the number of honour graves. The status Ehrengrab for Hermann und Oskar Minkowski was revoked.

At the end of 2015 I used a suitable event to ask a Kulturstaatsminister of Berlin about this decision. He was not aware of this and asked for some information. I sent him an email which was answered in January 2016 (see here in German). The answer essentially confirmed my opinion that an honorary grave nowadays depends on the popularity of a certain person. To put it more drastically: The future honorary graves will be mainly for actors and politicians.

I then wrote some emails to responsible persons of the university and the town Göttingen to inform them about this decision (Hermann Minkowski was a professor at Göttingen). As Göttingen, a comparably small town, has an incredibly high number of very famous scientists (among them more than 40 nobel laureates) and money is scarce everywhere, they are of course not particulary keen on getting additional celebrities from Berlin.

But finally, I received a nice email from a mathematics professor who informed me that the grave of the Minkowskis will not disappear. The reason for this is that the Diabetes Society will pay for it.

So everything seems fine and I was quite satisfied with the information that the grave of Hermann and Oskar Minkowski will not disappear.

Unfortunately, this comes at a price. I realised this when a couple of months ago I went to the cemetery with some friends (it is located quite nicely not far from the huge Olympic Stadion). At the grave of Hermann and Oskar Minkowski there are now given weather-proof information sheets (a good idea) which inform about the famous diabetes researcher Oskar Minkowski. Alas, the information about Hermann Minkowski: Nothing.

Addendum: Currently (as of 15th may 2018) the information on Oskar Minkowski has also disappeared.

5-th August 2018:

Ideology and Opportunism in scientific textbooks?

In general in scientific books the probability is not very high that you will find much ideology and opportunism. You will find such things mainly in the so-called cargo sciences (that is the word of the famous physicist Feynman). Each time seems to have its cargo-sciences. I am certainly not keen on discussing the current state of cargo-sciences. Most scientists today will have no problem to identify them. (Just a small example from the past decades, where I had a very strong feeling of cargo-science are my dim remembrances of many ‚spectacular‘ results reported in newspapers of a certain Professor Bender from the notorious institute of parapsychology in Freiburg.)

But that is not what I want to talk about. My focus is more on exact sciences like Mathematics and Physics. Do you think for example that all good physics books are free from ideology and opportunism?

Well, I suppose that most people would say that good physics books are to a great extent free from ideology and opportunism. For example most people would not expect in a book on the subject of Relativity Theory to find some sentences about Lenin. Or would you?

Well then consider this sentence from a well-known physics book:

It is astonishing how fast — already 1908 in his work ‚Materialism and Empirocriticism‘ - W.I.Lenin in his discussion about Positivism reacted on the development of Einsteins predecessors and how he generalized the notion of matter used by Engels which was based on Newtons state of knowledge, such that it satisfied the new insights of Relativity Theory.

(My translation, the original text is in German.)

This sentence is from the book: Ernst Schmutzer, Relativitätstheorie aktuell. I have scanned the page on which this sentence occurs here . The scan is from the second edition 1981. The book first appeared at the occasion of the Einstein Centenary in the year 1979. Up to now there are five editions. I also checked the fourth edition which appeared in 1989. The sentence is contained there, so it probably is also contained in the third edition. Now the interesting thing: The fifth edition appeared in 1996 and as you can see here the same text of the fourth edition is contained with a slight change. Namely the sentence about Lenin dissappeared.

As you all probably know the East German real existing socialism collapsed in 1989. Well, Ernst Schmutzer is a renowned East German physicist and in my opinion this book is a very good introduction to Relativity Theory.

But concerning the sentence on Lenin, in my opinion, one can clearly call opportunism either that he plugged in the sentence into the first four editions or that he deleted the sentence in the fifth edition.

© 2016-2018 Klaus Huber