Mathematics is not a game of hit and miss

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I was recently looking at the math exercises of a 14-year-old, having to do with quadratic (second-degree) equations.

The first thing that caught my eye is not a surprise: the difference between school and life. The quadratic polynomials appearing in the exercises, such as x2 – x – 6, all happen to have integer roots (3 and -2 in this case). Also, they all have 1 as the second-degree coefficient (the `a’ in a x2 + b x + c). There are good pedagogical reasons for these choices: with more general parameters, solving the equation becomes a task of numerical computation, which has no connection to the topic. But in any real-life application (say, the computation of where a ball thrown into the air will hit the ground) the solution will not come ready-made as in these school exercises.

I found one of the exercises very good. It reads this way (this is a Zurich school, I am translating from the German): A pencil factory has two machines. To produce 100 pencils, the older machine would take 10 minutes more than both machines running together. If in a minute the newer machine produces 32 pencils, how many does the older one produce in the same time? It provides a good opportunity to practice how to model a problem by defining the appropriate mathematical parameters. Then  — surprise  — you get a quadratic equation whose  solutions  — surprise  — are integers (only one of which makes sense). Useful gymnastics.

Another interesting example is the  equation

equation1

Interesting because if you do not use a bit of insight you will not get anywhere; after all, there is a range of 4 for the exponents (from -1 for the square root  to  0 for the constants, 1 for the terms in x, and 2 for the terms in x2), so squaring both sides to get rid of the square root, for example, would be hopeless. Now if you remember that this exercise goes with a lecture about 2nd-degree equations and apply what you have learned about them, you get the roots of the polynomial in the denominator on the left, x2 – x – 6, and can rewrite it as (x – 3) (x + 2). Then you notice that x – 3 also appears, multiplied by 5, in the right-side denominator; so you remove it on both sides, and from then it is all downhill: you get another quadratic equation which  — surprise  — has simple roots.

Throughout these exercises I see, introduced from the start, an idea that not all people having learned quadratic equations remember: the rule that any second-degree polynomial a x2 + b x + c can be written a (x – x0) (x – x1) where x0 and  x1 are the roots (including when they are the same). It is often useful to turn such a polynomial into this form (particularly simple when a = 1).

Then I probed  further and asked the student what he would do if the roots were not such simple integers. It turns out that he had no idea since that is not something they are taught at that level! They have not heard about the notion of determinant (b2 – 4 a c), and how it gives the solutions, through the standard formula: (-b ± d) / 2 a where d is the square root of the determinant.

I realized that the way they are taught to “solve” the equation (I have to put the word in quotes) is to try to guess some integer values that will make x2 + b x + c (good thing that a = 1 for all the examples!) zero. Specifically, you try out values u and v whose product is c and check whether (x – u) (x – v) works out to the given polynomial. If not, you continue guessing values until you find a pair that works. Mathematics as a game of hit-and-miss.

In the x2 – x – 6 example, let’s see… -3 and +2? Oh no, they do not fit. 1 and -6? Bummer. 6 and -1?  Also not. Maybe -2 and +3? Bingo!

This method of poking around until you find something that clicks seems to me a strange thing to teach. I should include a caveat here: I am not an expert in mathematical pedagogy (and not even a mathematician). So I am asking questions, not passing judgment. Also, the place being Switzerland, where processes are usually thought out carefully, especially in education, I have to assume that whoever designed this curriculum had some hunch of what he was doing. But the result is puzzling. The kind of mathematics that helps people (and on which today’s world rests, whether directly or through physics and computer science) is not about guessing results. It is about establishing rules, in the form of axioms and theorems, proving the latter (from the former), and then relying on them to derive whatever specific results you need. The edifice of rules has a deep and elaborate structure, devised over centuries by giants standing on the shoulders of giants standing on the shoulders of other giants. But once you have a rule you no longer have to go to the underlying layers; you directly use the result of the combined work of countless smart people. It does not matter how many times they tried to derive them and how many mistakes they made along the way: their work has been vetted many times, and you can use its outcome in full confidence.

If I use my guessing powers to try values that might make a x2 + b x + c zero, I will succeed once in a while, particularly for schoolbook exercises. When I do not succeed, I have no clue whether the reason is my insufficient intellectual agility, the absence of simple solutions (integers or simple fractions), or the absence of any solution (students at the level under consideration have not heard of imaginary numbers yet). If I learn the formula  (meaning, with a good teacher, not only learning it as a recipe but discovering why the recipe works), I am equipped to solve any quadratic equation, with or without  simple integer solutions. When solving such equations I do not need to apply ingenuity to guess solutions, a remarkably pointless exercise (except maybe the first few times). I can reserve my ingenuity to more interesting pursuits.

Indeed there would be so much more to teach. I looked at the textbook with its many pages of examples of quadratic equation to solve; more accurately, to guess. All piecemeal, example by example; no attempt at generality (isn’t the quest for general results one of the prime characteristics of the mathematical spirit?) They are not even taught that sometimes there are no solutions among the numbers they know; good luck to the enterprising student who, having found the roots of x2 – x – 6 through the recommended approach of trial and error, confidently embarks on solving x2 – x + 6 = 0 (it is almost the same and so cannot be much harder, right?).

All that space and student attention are wasted at the expense of the theoretical and practical properties of quadratic equations, second-degree polynomials and parabolas. We could direct students to web sites such as this one where they can play with parabolas, try different parameters and animate the results. We could explain how quadratic equations serve as a fundamental tool for computing trajectories of projectiles. We could even introduce the notion of parabolic mirror and its very practical benefit following from a basic geometrical property. And we could put all this into a form that a 14-year-old will readily understand.

Mathematics is not just about applications. I also feel sorry that these children, by just being shown haphazard tricks, miss the sheer beauty of the underlying ideas, which struck many of us when we learned them at the same age. What a pity.

There may be a grand plan behind the way these topics get taught, but I do not see it. I only see an approach that seems poised to drill into young minds the conviction that mathematics is but a sad, boring and pointless game of tricks.

 

Thanks to Manuel Oriol for useful observati9ns.

 

 

A new scientific index

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The CF-Index, or Conference Frustration index, is an integer n (n ≥ 1) defined as follows. You are at a conference where your paper submission was rejected, and sitting in the session devoted to that paper’s very topic. You think for yourself  “My paper was at least n times better than the average here”. That n is your CF-index.

It is a law of nature (like speed never exceeding that of light, or temperature never going below absolute zero) that n < 1 is impossible. (The reason is obvious: if you were not the kind to believe your work is at least as good as anyone else’s, you would have gone for another profession, one calling for modesty, realism and timidity — such as, say, politician.)  Values of n = 3 or 4 are normal. Beyond 10 you might consider seeking professional advice. (These observations have nothing to do with my being at ICSE right now.)

A remarkable group photo

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On 13-15 September 1999 a symposium took place in St Catherine College in Oxford,  in honor of Tony Hoare’s “retirement” from Oxford (the word is in quotes because he has had several further productive careers since). The organizers were Jim Woodcock, Bill Roscoe and Jim Davies. The proceedings are available as Millenial Perspectives in Computer Science, MacMillan Education UK, edited by Davies, Roscoe and Woodcock. The Symposium was a milestone event.

As part of a recent conversation on something else, YuQian Zhou(who was also there) sent me a group photo from the event, which I did not know even existed. I am including it below; it is actually a photo of a paper photo but the resolution is good. It is a fascinating gallery of outstanding people in programming and verification. (How many Turing award winners can you spot? I see 7.)

Many thanks to YuQian Zhou, Jim Woodcock and Bill Roscoe for insights into the picture in discussions of the past two weeks.

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Niklaus Wirth and the Importance of Being Simple

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[This is a verbatim copy of a post in the Communications of the ACM blog, 9 January 2024.]

I am still in shock from the unexpected death of Niklaus Wirth eight days ago. If you allow a personal note (not the last one in this article): January 11, two days from now, was inscribed in my mind as the date of the next time he was coming to my home for dinner. Now it is the date set for his funeral.

standing

Niklaus Wirth at the ACM Turing centenary celebration
San Francisco, 16 June 2012
(all photographs in this article are by B. Meyer)

A more composed person would wait before jotting down thoughts about Wirth’s contributions but I feel I should do it right now, even at the risk of being biased by fresh emotions.

Maybe I should first say why I have found myself, involuntarily, writing obituaries of computer scientists: Kristen Nygaard and Ole-Johan Dahl, Andrey Ershov, Jean Ichbiah, Watts Humphrey, John McCarthy, and most recently Barry Boehm (the last three in this very blog). You can find the list with comments and links to the eulogy texts on the corresponding section of my publication page. The reason is simple: I have had the privilege of frequenting giants of the discipline, tempered by the sadness of seeing some of them go away. (Fortunately many others are still around and kicking!) Such a circumstance is almost unbelievable: imagine someone who, as a student and young professional, discovered the works of Galileo, Descartes, Newton, Ampère, Faraday, Einstein, Planck and so on, devouring their writings and admiring their insights — and later on in his career got to meet all his heroes and conduct long conversations with them, for example in week-long workshops, or driving from a village deep in Bavaria (Marktoberdorf) to Munich airport. Not possible for a physicist, of course, but exactly the computer science equivalent of what happened to me. It was possible for someone of my generation to get to know some of the giants in the field, the founding fathers and mothers. In my case they included some of the heroes of programming languages and programming methodology (Wirth, Hoare, Dijkstra, Liskov, Parnas, McCarthy, Dahl, Nygaard, Knuth, Floyd, Gries, …) whom I idolized as a student without every dreaming that I would one day meet them. It is natural then to should share some of my appreciation for them.

My obituaries are neither formal, nor complete, nor objective; they are colored by my own experience and views. Perhaps you object to an author inserting himself into an obituary; if so, I sympathize, but then you should probably skip this article and its companions and go instead to Wikipedia and official biographies. (In the same vein, spurred at some point by Paul Halmos’s photographic record of mathematicians, I started my own picture gallery. I haven’t updated it recently, and the formatting shows the limits of my JavaScript skills, but it does provide some fresh, spontaneous and authentic snapshots of famous people and a few less famous but no less interesting ones. You can find it here. The pictures of Wirth accompanying this article are taken from it.)

liskov

Niklaus Wirth, Barbara Liskov, Donald Knuth
(ETH Zurich, 2005, on the occasion of conferring honorary doctorates to Liskov and Knuth)

A peculiarity of my knowledge of Wirth is that unlike his actual collaborators, who are better qualified to talk about his years of full activity, I never met him during that time. I was keenly aware of his work, avidly getting hold of anything he published, but from a distance. I only got to know him personally after his retirement from ETH Zurich (not surprisingly, since I joined ETH because of that retirement). In the more than twenty years that followed I learned immeasurably from conversations with him. He helped me in many ways to settle into the world of ETH, without ever imposing or interfering.

I also had the privilege of organizing in 2014, together with his longtime colleague Walter Gander, a symposium in honor of his 80th birthday, which featured a roster of prestigious speakers including some of the most famous of his former students (Martin Oderski, Clemens Szyperski, Michael Franz…) as well as Vint Cerf. Like all participants in this memorable event (see here for the program, slides, videos, pictures…) I learned more about his intellectual rigor and dedication, his passion for doing things right, and his fascinating personality.

Some of his distinctive qualities are embodied in a book published on the occasion of an earlier event, School of Niklaus Wirth: The Art of Simplicity (put together by his close collaborator Jürg Gutknecht together with Laszlo Boszormenyi and Gustav Pomberger; see the Amazon page). The book, with its stunning white cover, is itself a model of beautiful design achieved through simplicity. It contains numerous reports and testimonials from his former students and colleagues about the various epochs of Wirth’s work.

bauer

Niklaus Wirth (right)
with F.L. Bauer, one of the founders of German computer science
Zurich,22 June 2005

Various epochs and many different topics. Like a Renaissance man, or one of those 18-th century “philosophers” who knew no discipline boundaries, Wirth straddled many subjects. It was in particular still possible (and perhaps necessary) in his generation to pay attention to both hardware and software. Wirth is most remembered for his software work but he was also a hardware builder. The influence of his PhD supervisor, computer design pioneer and UC Berkeley professor Harry Huskey, certainly played a role.

Stirred by the discovery of a new world through two sabbaticals at Xerox PARC (Palo Alto Research Center, the mother lode of invention for many of today’s computer techniques) but unable to bring the innovative Xerox machines to Europe, Wirth developed his own modern workstations, Ceres and Lilith. (Apart from the Xerox stays, Wirth spent significant time in the US and Canada: University of Laval for his master degree, UC Berkeley for his PhD, then Stanford, but only as an assistant professor, which turned out to be Switzerland’s and ETH’s gain, as he returned in 1968,)

 

lilith

Lilith workstation and its mouse
(Public display in the CAB computer science building at ETH Zurich)

One of the Xerox contributions was the generalized use of the mouse (the invention of Doug Englebart at the nearby SRI, then the Stanford Research Institute). Wirth immediately seized on the idea and helped found the Logitech company, which soon became, and remains today, a world leader in mouse technology.
Wirth returned to hardware-software codesign late in his career, in his last years at ETH and beyond, to work on self-driving model helicopters (one might say to big drones) with a Strong-ARM-based hardware core. He was fascinated by the goal of maintaining stability, a challenge involving physics, mechanical engineering, electronic engineering in addition to software engineering.
These developments showed that Wirth was as talented as an electronics engineer and designer as he was in software. He retained his interest in hardware throughout his career; one of his maxims was indeed that the field remains driven by hardware advances, which make software progress possible. For all my pride as a software guy, I must admit that he was largely right: object-oriented programming, for example, became realistic once we had faster machines and more memory.

Software is of course what brought him the most fame. I struggle not to forget any key element of his list of major contributions. (I will come back to this article when emotions abate, and will add a proper bibliography of the corresponding Wirth publications.) He showed that it was possible to bring order to the world of machine-level programming through his introduction of the PL/360 structured assembly language for the IBM 360 architecture. He explained top-down design (“stepwise refinement“), as no one had done before, in a beautiful article that forever made the eight-queens problem famous. While David Gries had in his milestone book Compiler Construction for Digital Computers established compiler design as a systematic discipline, Wirth showed that compilers could be built simply and elegantly through recursive descent. That approach had a strong influence on language design, as will be discussed below in relation to Pascal.

The emphasis simplicity and elegance carried over to his book on compiler construction. Another book with the stunning title Algorithms + Data Structures = Programs presented a clear and readable compendium of programming and algorithmic wisdom, collecting the essentials of what was known at the time.

And then, of course, the programming languages. Wirth’s name will forever remained tied to Pascal, a worldwide success thanks in particular to its early implementations (UCSD Pascal, as well as Borland Pascal by his former student Philippe Kahn) on microcomputers, a market that was exploding at just that time. Pascal’s dazzling spread was also helped by another of Wirth’s trademark concise and clear texts, the Pascal User Manual and Report, written with Kathleen Jensen. Another key component of Pascal’s success was the implementation technique, using a specially designed intermediate language, P-Code, the ancestor of today’s virtual machines. Back then the diversity of hardware architectures was a major obstacle to the spread of any programming language; Wirth’s ETH compiler produced P-Code, enabling anyone to port Pascal to a new computer type by writing a translator from P-Code to the appropriate machine code, a relatively simple task.

Here I have a confession to make: other than the clear and simple keyword-based syntax, I never liked Pascal much. I even have a snide comment in my PhD thesis about Pascal being as small, tidy and exciting as a Swiss chalet. In some respects, cheekiness aside, I was wrong, in the sense that the limitations and exclusions of the language design were precisely what made compact implementations possible and widely successful. But the deeper reason for my lack of enthusiasm was that I had fallen in love with earlier designs from Wirth himself, who for several years, pre-Pascal, had been regularly churning out new language proposals, some academic, some (like PL/360) practical. One of the academic designs I liked was Euler, but I was particularly keen about Algol W, an extension and simplification of Algol 60 (designed by Wirth with the collaboration of Tony Hoare, and implemented in PL/360). I got to know it as a student at Stanford, which used it to teach programming. Algol W was a model of clarity and elegance. It is through Algol W that I started to understand what programming really is about; it had the right combination of freedom and limits. To me, Pascal, with all its strictures, was a step backward. As an Algol W devotee, I felt let down.
Algol W played, or more precisely almost played, a historical role. Once the world realized that Algol 60, a breakthrough in language design, was too ethereal to achieve practical success, experts started to work on a replacement. Wirth proposed Algol W, which the relevant committee at IFIP (International Federation for Information Processing) rejected in favor of a competing proposal by a group headed by the Dutch computer scientist (and somewhat unrequited Ph.D. supervisor of Edsger Dijkstra) Aad van Wijngaarden.

Wirth recognized Algol 68 for what it was, a catastrophe. (An example of how misguided the design was: Algol 68 promoted the concept of orthogonality, roughly stating that any two language mechanisms could be combined. Very elegant in principle, and perhaps appealing to some mathematicians, but suicidal: to make everything work with everything, you have to complicate the compiler to unbelievable extremes, whereas many of these combinations are of no use whatsoever to any programmer!) Wirth was vocal in his criticism and the community split for good. Algol W was a casualty of the conflict, as Wirth seems to have decided in reaction to the enormity of Algol 68 that simplicity and small size were the cardinal virtues of a language design, leading to Pascal, and then to its modular successors Modula and Oberon.

Continuing with my own perspective, I admired these designs, but when I saw Simula 67 and object-oriented programming I felt that I had come across a whole new level of expressive power, with the notion of class unifying types and modules, and stopped caring much for purely modular languages, including Ada as it was then. A particularly ill-considered feature of all these languages always irked me: the requirement that every module should be declared in two parts, interface and implementation. An example, in my view, of a good intention poorly realized and leading to nasty consequences. One of these consequences is that the information in the interface part inevitably gets repeated in the implementation part. Repetition, as David Parnas has taught us, is (particularly in the form of copy-paste) the programmer’s scary enemy. Any change needs to be checked and repeated in both the original and the duplicate. Any bug needs to be fixed in both. The better solution, instead of the interface-implementation separation, is to write everything in one place (the class of object-oriented programming) and then rely on tools to extract, from the text, the interface view but also many other interesting views abstracted from the text.

In addition, modular languages offer one implementation for each interface. How limiting! With object-oriented programming, you use inheritance to provide a general version of an abstraction and then as many variants as you like, adding them as you see fit (Open-Closed Principle) and not repeating the common information. These ideas took me towards a direction of language design completely different from Wirth’s.

One of his principles in language design was that it should be easy to write a compiler — an approach that paid off magnificently for Pascal. I mentioned above the beauty of recursive-descent parsing (an approach which means roughly that you parse a text by seeing how it starts, deducing the structure that you expect to follow, then applying the same technique recursively to the successive components of the expected structure). Recursive descent will only work well if the language is LL (1) or very close to it. (LL (1) means, again roughly, that the first element of a textual component unambiguously determines the syntactic type of that component. For example the instruction part of a language is LL (1) if an instruction is a conditional whenever it starts with the keyword if, a loop whenever it starts with the keyword while, and an assignment variable := expression whenever it starts with a variable name. Only with a near-LL (1) structure is recursive descent recursive-decent.) Pascal was designed that way.

A less felicitous application of this principle was Wirth’s insistence on one-pass compilation, which resulted in Pascal requiring any use of indirect recursion to include an early announcement of the element — procedure or data type — being used recursively. That is the kind of thing I disliked in Pascal: transferring (in my opinion) some of the responsibilities of the compiler designer onto the programmer. Some of those constraints remained long after advances in hardware and software made the insistence on one-pass compilation seem obsolete.

What most characterized Wirth’s approach to design — of languages, of machines, of software, of articles, of books, of curricula — was his love of simplicity and dislike of gratuitous featurism. He most famously expressed this view in his Plea for Lean Software article. Even if hardware progress drives software progress, he could not accept what he viewed as the lazy approach of using hardware power as an excuse for sloppy design. I suspect that was the reasoning behind the one-compilation-pass stance: sure, our computers now enable us to use several passes, but if we can do the compilation in one pass we should since it is simpler and leaner.
As in the case of Pascal, this relentless focus could be limiting at times; it also led him to distrust artificial intelligence, partly because of the grandiose promises its proponents were making at the time. For many years indeed, AI never made it into ETH computer science. I am talking here of the classical, logic-based form of AI; I had not yet had the opportunity to ask Niklaus what he thought of the modern, statistics-based form. Perhaps the engineer in him would have mollified his attitude, attracted by the practicality and well-defined scope of today’s AI methods. I will never know.

As to languages, I was looking forward to more discussions; while I wholeheartedly support his quest for simplicity, size to me is less important than simplicity of the structure and reliance on a small number of fundamental concepts (such as data abstraction for object-oriented programming), taken to their full power, permeating every facet of the language, and bringing consistency to a powerful construction.

Disagreements on specifics of language design are normal. Design — of anything — is largely characterized by decisions of where to be dogmatic and where to be permissive. You cannot be dogmatic all over, or will end with a stranglehold. You cannot be permissive all around, or will end with a mess. I am not dogmatic about things like the number of compiler passes: why care about having one, two, five or ten passes if they are fast anyway? I care about other things, such as the small number of basic concepts. There should be, for example, only one conceptual kind of loop, accommodating variants. I also don’t mind adding various forms of syntax for the same thing (such as, in object-oriented programming, x.a := v as an abbreviation for the conceptually sound x.set_a (v)). Wirth probably would have balked at such diversity.

In the end Pascal largely lost to its design opposite, C, the epitome of permissiveness, where you can (for example) add anything to almost anything. Recent languages went even further, discarding notions such as static types as dispensable and obsolete burdens. (In truth C is more a competitor to P-Code, since provides a good target for compilers: its abstraction level is close to that of the computer and operating system, humans can still with some effort decipher C code, and a C implementation is available by default on most platforms. A kind of universal assembly language. Somehow, somewhere, the strange idea creeped into people’s minds that it could also be used as a notation for human programmers.)

In any case I do not think Niklaus followed closely the evolution of the programming language field in recent years, away from principles of simplicity and consistency; sometimes, it seems, away from any principles at all. The game today is mostly “see this cute little feature in my language, I bet you cannot do as well in yours!” “Oh yes I can, see how cool my next construct is!“, with little attention being paid to the programming language as a coherent engineering construction, and even less to its ability to produce correct, robust, reusable and extendible software.

I know Wirth was horrified by the repulsive syntax choices of today’s dominant languages; he could never accept that a = b should mean something different from b = a, or that a = a + 1 should even be considered meaningful. The folly of straying away from conventions of mathematics carefully refined over several centuries (for example by distorting “=” to mean assignment and resorting to a special symbol for equality, rather than the obviously better reverse) depressed him. I remain convinced that the community will eventually come back to its senses and start treating language design seriously again.

One of the interesting features of meeting Niklaus Wirth the man, after decades of studying from the works of Professor Wirth the scientist, was to discover an unexpected personality. Niklaus was an affable and friendly companion, and most strikingly an extremely down-to-earth person. On the occasion of the 2014 symposium we were privileged to meet some of his children, all successful in various walks of life: well-known musician in the Zurich scene, specialty shop owner… I do not quite know how to characterize in words his way of speaking (excellent) English, but it is definitely impossible to forget its special character, with its slight but unmistakable Swiss-German accent (also perceptible in German). To get an idea, just watch one of the many lecture videos available on the Web. See for example the videos from the 2014 symposium mentioned above, or this full-length interview recorded in 2018 as part of an ACM series on Turing Award winners.

On the “down-to-earth” part: computer scientists, especially of the first few generations, tend to split into the mathematician types and the engineer types. He was definitely the engineer kind, as illustrated by his hardware work. One of his maxims for a successful career was that there are a few things that you don’t want to do because they are boring or feel useless, but if you don’t take care of them right away they will come back and take even more of your time, so you should devote 10% of that time to discharge them promptly. (I wish I could limit that part to 10%.)

He had a witty, subtle — sometimes caustic — humor. Here is a Niklaus Wirth story. On the seventh day of creation God looked at the result. (Side note: Wirth was an atheist, which adds spice to the choice of setting for the story.) He (God) was pretty happy about it. He started looking at the list of professions and felt good: all — policeman, minister, nurse, street sweeper, interior designer, opera singer, personal trainer, supermarket cashier, tax collector… — had some advantages and some disadvantages. But then He got to the University Professor row. The Advantages entry was impressive: long holidays, decent salary, you basically get to do what you want, and so on; but the Disadvantages entry was empty! Such a scandalous discrepancy could not be tolerated. For a moment, a cloud obscured His face. He thought and thought and finally His smile came back. At that point, He had created colleagues.

When the computing world finally realizes that design needs simplicity, it will do well to go back to Niklaus Wirth’s articles, books and languages. I can think of only a handful of people who have shaped the global hardware and software industry in a comparable way. Niklaus Wirth is, sadly, sadly gone — and I still have trouble accepting that he will not show up for dinner, on Thursday or ever again — but his legacy is everywhere.

AI will move mountains

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In August I was planning for my participation in the ICTSS conference in Bergamo, Italy, and wanted to find some accommodation within walking distance of the conference place. Bergamo has a medieval “città alta”, high city, at the top of a hill, and a “città bassa”, low city, down in the valley, where modern expansion happens. I had only passed through Bergamo once before but enough to know that it is not that easy or fast to commute between the two parts, so it is better to plan your accommodation properly.

It was not immediately clear from the online map where the conference venue belonged, so I thought that maybe this was an opportunity to find some actual use for ChatGPT. (So far I am not a great fan, see here, but one has to keep one’s mind open.) I asked my question:

 

question_bergamo

and received an answer (here is the first part):

answer_bergamo

Good that I did not stop here because the answer is plain wrong; the Piazzale in question (the main site of the university, and a former convent, as I later found out) is in the high city. Even more interesting was the second part of the answer:

changed_bergamo

Now this is really good. With my Southern California experience I am not that easily surprised: it is a common joke in Santa Barbara (an area prone to mudslides, particularly when it rains after a fire) that you might go to bed in your house at the top of a hill and wake up the next morning in the same house but with a whole new set of neighbors at the bottom of a valley. The other way around, though, is quite new for me.

AI-induced levitation! Of an entire city area! Since September 2021, the Piazzale San Agostino and its historic university buildings might have moved up 250 meters from low to high city. Artificial Intelligence is so amazing.

As a codicil to this little report: at that point I had decided to drop this absurd tool and look for a reliable source, but noticed that I had made a mistake in the Italian phrase: the name of high city is “città alta”, whereas I had put the words in the reverse order (as shown above). Since I like to do things right I asked the question again with the proper order, not changing anything else, not questioning the previous results, just repeating the question with a correct phrasing:

 

question2

and got this:

answer2_bergamo

The amazement continues. I had not complained, not questioned the answer, not emitted any doubt or criticism, and here is this tool apologizing again. And leaving me with two exactly contradictory answers. Which one am I supposed to believe? If I ask again, am I going to get a new set of excuses and a reversal to the original answer? (I did not try.)

I will continue my quest to find out whatever this thing might be good for.

A writing exercise

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I recently wrote a working paper (on academic careers) and since it was urgently needed I did not want to spend time on style issues but instead to keep things simple. So I preceded it with the comment “Using he’ as an abbreviation for `he or she’.”  I received the helpful suggestion that I could have used “they” ‘instead.

I have a great style exercise for you. Rewrite the following text (a fictitious description of a fictitious interview session) using the “they” style. Keep the rest of the content as it is of course.

All the candidates are in the room. Each in turn gives his presentation to the committee, in the presence of the other candidates, who may use the opportunity to revise their own presentations. It can make for an awkward situation because they are actually competing with him and with each other for the position. At the end of his presentation, the committee members ask him the questions that they have prepared during his talk; he engages in a free discussion with them. He then steps outside so that they can discuss his performance in his absence; when they are done, they call him back into the room and they tell him the result of their assessment of him, giving him the opportunity to prompt them for more detailed comments about his presentation and more generally about what they think of his profile. Afterwards, he will in turn listen to the other candidates’ presentations, which in spite of the competitive situation give him an opportunity to learn from them and network with them for his own benefit.

 

 

The “NATO expansion” canard

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Are you not tired, too, of those endlessly repeated arguments that, sure, it was not very polite of Putin to invade Ukraine, but you have to understand the situation, it’s all the fault of NATO’s aggressive westward expansion which, you know, was provoking the Russians!

You see this argument everywhere on social networks and also from people such as the former French prime minister Jospin (in March of 2022!). Plus of course Noam Chomsky, for whom there is no atrocity committed by a dictator anywhere that cannot be justified by some real or imagined American turpitude. (Evidence that (1) a great scientist is not immune to shameful delusions and (2) Chomsky, the kind of person who would not last two weeks in one of the regimes he praises, is really fortunate that his family landed in a country where he can safely spew out whatever theory he likes, however outrageous.) Most recently in an opinion piece of the New York Times.

Come on. NATO is a defensive alliance. It has no offensive designs on any part of the world. It does not gobble up any countries: its members all decided to join NATO for their own security.

As to the supposed provocation: if I have an aggressive neighbor with attack dogs and my other neighbors have built a fence to shield themselves from him, am I “provoking” him if I ask them to extend the fence to encompass my house?

It is obvious to all who is aggressive and who is aggressed. Shame on those who insinuate otherwise.

New article: scenarios versus OO requirements

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Maria Naumcheva, Sophie Ebersold, Alexandr Naumchev, Jean-Michel Bruel, Florian Galinier and Bertrand Meyer: Object-Oriented Requirements: a Unified Framework for Specifications, Scenarios and Tests, in JOT (Journal of Object Technology), vol. 22, no. 1, pages 1:1-19, 2023. Available here with link to PDF  (the journal is open-access).

From the abstract:

A paradox of requirements specifications as dominantly practiced in the industry is that they often claim to be object-oriented (OO) but largely rely on procedural (non-OO) techniques. Use cases and user stories describe functional flows, not object types.

To gain the benefits provided by object technology (such as extendibility, reusability, and reliability), requirements should instead take advantage of the same data abstraction concepts – classes, inheritance, information hiding – as OO design and OO programs.

Many people find use cases and user stories appealing because of the simplicity and practicality of the concepts. Can we reconcile requirements with object-oriented principles and get the best of both worlds?

This article proposes a unified framework. It shows that the concept of class is general enough to describe not only “object” in a narrow sense but also scenarios such as use cases and user stories and other important artifacts such as test cases and oracles. Having a single framework opens the way to requirements that enjoy the benefits of both approaches: like use cases and user stories, they reflect the practical views of stakeholders; like object-oriented requirements, they lend themselves to evolution and reuse.

The article builds in part on material from chapter 7 of my requirements book (Handbook of Requirements and Business Analysis, Springer).

Statement Considered Harmful

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I harbor no illusion about the effectiveness of airing this particular pet peeve; complaining about it has about the same chance of success as protesting against split infinitives or music in restaurants. Still, it is worth mentioning that the widespread use of the word “statement” to denote a programming language element, such as an assignment, that directs a computer to perform some change, is misleading. “Instruction” is the better term.

A “statement” is “something stated, such as a single declaration or remark, or a report of fact or opinions” (Merriam-Webster).

Why does it matter? The use of “statement” to mean “instruction” obscures a fundamental distinction of software engineering: the duality between specification and implementation. Programming produces a solution to a problem; success requires expressing both the problem, in the form of a specification, and the devised solution, in the form of an implementation. It is important at every stage to know exactly where we stand: on the problem side (the “what”) or the solution side (the “how”). In his famous Goto Statement Considered Harmful of 1968, Dijkstra beautifully characterized this distinction as the central issue of programming:

Our intellectual powers are rather geared to master static relations and our powers to visualize processes evolving in time are relatively poorly developed. For that reason we should do (as wise programmers aware of our limitations) our utmost to shorten the conceptual gap between the static program and the dynamic process, to make the correspondence between the program (spread out in text space) and the process (spread out in time) as trivial as possible.

Software verification, whether conducted through dynamic means (testing) or static techniques (static analysis, proofs of correctness), relies on having separately expressed both a specification of the intent and a proposed implementation intended to realize that intent. They have to remain distinct; otherwise we cannot even define what it means that the program should be correct (correct with respect to what?), and even less what it means to validate the program (validate it against what?).

In many approaches to verification, the properties against which we validate programs are called assertions. An assertion expresses a property that should hold at some point of program execution. For example, after the assignment instruction a := b + 1, the assertion a ≠ b will hold. This notion of assertion is used both in testing frameworks, such as JUnit for Java or PyUnit for Python, and in program proving frameworks; see, for example, the interactive Web-based version of the AutoProof program-proving framework for Eiffel at autoproof.sit.org, and of course the entire literature on axiomatic (Floyd-Hoare-Dijkstra-style) verification.

The difference between the instruction and the assertion is critical: a := b + 1 tells the computer to do something (change the value of a), as emphasized here by the “:=” notation for assignment; a ≠ b does not direct the computer or the computation to do anything, but simply states a property that should hold at a certain stage of the computation if everything went fine so far.

In the second case, the word “states” is indeed appropriate: an assertion states a certain property. The expression of that property, a ≠ b, is a “statement” in the ordinary English sense of the term. The command to the computer, a := b + 1, is an instruction whose effect is to ensure the satisfaction of the statement a ≠ b. So if we use the word “statement” at all, we should use it to mean an assertion, not an instruction.

If we start calling instructions “statements” (a usage that Merriam-Webster grudgingly accepts in its last entry for the term, although it takes care to define it as “an instruction in a computer program,” emphasis added), we lose this key distinction.

There is no reason for this usage, however, since the word “instruction” is available, and entirely appropriate.

So, please stop saying “an assignment statement” or “a print statement“; say “an assignment instruction” and so on.

Maybe you won’t, but at least you have been warned.

Recycled This article was first published in the “Communications of the ACM” blog.

Toute la rage du Monde

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Un chef d’état donne une conférence de presse ; par exemple Emmanuel Macron, président de la république française, le 17 avril dernier. Les journaux publieront des commentaires louangeurs ou critiques, mais en premier lieu, si ce sont des journaux d’information, ils rendront compte de ce qui a été dit. Leur manchette sera du genre de celle du Guardian ce jour-là :

guardian

Dans ses autres articles et éditoriaux le Guardian, très à gauche et très remonté contre Macron, ne se gêne pas pour exprimer ses critiques. Mais il commence par faire son travail d’information : M. Macron a donné tel jour une conférence de presse sur tel thème, il a expliqué ceci et annoncé cela. Quelle différence avec le quotidien autrefois « de référence » dans le pays même de Macron, Le Monde. Inutile en « une » de chercher à s’informer sur l’exposé ; à la place, le lecteur a droit à l’opinion des journalistes, un arrêt définitif et cinglant :

engagées

Ce qu’il a dit ? Quels sont ces chantiers ? Mystère. Et aucune importance. Sans doute le lecteur serait incapable de former sa propre opinion sur la nouveauté, ou non, des annonces de Macron. Ou il y perdrait trop de temps. Les grands experts du Monde lui évitent cette fatigue en interprétant pour lui le discours, plutôt que de le décrire. Tout ce qui compte est leur jugement.

Jour après jour,  au lieu d’informer, Le Monde mène une campagne de démolition du gouvernement actuel qui n’a rien à envier aux plus beaux (ou mauvais) jours de l’Humanité d’antan. Cantonons-nous à quelques exemples pris au hasard dans le mois d’avril 2023, reflétant comment un quotidien autrefois sérieux compose aujourd’hui ses  Unes. Le 5 avril, le gouvernement ayant annoncé vouloir dissoudre un groupuscule violent, « Les Soulèvements de la Terre », responsable de millions d’euros de destructions et déprédations les mois précédents et cherchant en permanence l’affrontement avec les forces de l’ordre, voici ce que Le Monde trouve de mieux à titrer :

Pasted

Aucune nuance, aucun recul. Le terme « méga-bassine » est lui-même tendancieux. Il s’agit d’une réserve d’eau, destinée à préserver cette ressource pour faire face aux étés de plus en plus chauds que nous connaissons. On peut être pour ou contre mais force est de noter que dans aucun autre pays d’Europe occidentale ce genre de discussion ne passe par des émeutes d’une telle violence (47 gendarmes blessés ce jour-là). La « bataille » principale n’est pas celle des arguments mais une bataille au sens propre entre les forces de l’ordre et des extrémistes déchaînés. Rien de tout cela dans le titre et le résumé, seulement l’annonce que le mouvement a « réfuté point par point » — la cause est entendue et jugée ! — les raisons du gouvernement. Comme s’il s’agissait d’une aimable discussion d’idées (où l’un des partenaires a raison par définition) et non du contrôle d’une organisation subversive (contestable ou non, la décision de construire la réserve a été votée par les pouvoirs régionaux normalement élus).

Le titre publié deux jours avant est lui, plutôt amusant dans son obsession critique :

bourdieu

Populiste en plus de ses autres tares, il est le représentant de la Noblesse d’État ! Ah tiens, François Hollande, que Le Monde traita toujours avec de grands égards, n’en était pas, lui ? Fils de médecin, élevé à Neuilly, ancien élève de Saint-Jean Baptiste de la Salle puis HEC, Sciences Po et l’ENA, ayant commencé sa carrière à la Cour des Comptes, ensuite militant et responsable politique pendant toute sa carrière, oui, Hollande est de gauche, donc c’est le Peuple, le vrai ! Et Macron l’affreux représentant du Système.

Mais ne nous inquiétons pas trop, dans ce cas précis il s’agissait d’une « Tribune », présentée comme telle. Revenons à l’information, ou plutôt ce qui devrait en être. Le 10 avril Le Monde traite en Une d’écologie, sujet que vous croyez peut-être sérieux mais sur lequel votre quotidien préféré choisit son parti — comme Pierre Dac et Francis Blanche, le parti d’en rire :

parti

Absolument. Rien de sérieux dans ce gouvernement, tout ce qu’il fait, quand ce n’est pas scandaleux, doit être risible. Le lendemain on revient au scandaleux :

étouffer

Si Macron voulait vraiment « étouffer » quelque chose, bonne chance dans un pays où les moyens d’information de masse (Le Monde n’étant que l’un d’eux) sont ligués contre lui. (Note lexicale : « peuple » tel qu’employé ici est une abréviation pour « émeutiers et incendiaires ». Quant à la « légitimité » des syndicats, parlons-en : 10% des salariés français sont syndiqués, moins de 8% dans le privé et, même dans le secteur public, moins de 20%. En outre, de quels « syndicats» s’agit-il au juste ? Dans les autres pays, les salariés d’une entreprise ou d’une branche se groupent en un syndicat pour défendre leurs intérêts. Un seul syndicat, bien sûr. En France, il y a 4 ou 5 syndicats rivaux dans une même entreprise, petits partis politiques subventionnés se disputant les voix des quelques votants.)
Le 13 avril, un point vraiment lumineux sur la situation :

colère

Nulle trace de ce que le supposé sentiment d’injustice et de colère n’est le fait que d’une partie de la population, chauffée à blanc par les extrémistes de gauche et de droite. Quant au 49.3, il est difficile de voir en quoi ce mécanisme prévu par la Constitution —précisément pour les cas difficiles, comme celui-ci, où une partie de la droite classique a été intimidée voire terrorisée par les menaces reçues de toute part — est injuste ou prompt à susciter la colère. Il est après tout sujet à un vote de défiance (qui a eu lieu et a échoué). Du reste ce mécanisme a été surtout utilisé par la gauche sous Mitterrand: 3 fois par Pierre Bérégovoy, 8 fois par Édith Cresson et 28 fois par Michel Rocard (vingt-huit fois !). Je n’ai pas souvenir que lors de ses 6 utilisations par Manuel Valls, sous Hollande, Le Monde ait crié à l’injustice et compati à la légitime colère du Peuple. Ce qui frappe dans ce titre c’est une fois de plus le matraquage quotidien : le scandale et la malfaisance sont toujours du même côté, et l’injustice subie et la colère justifiée toujours de l’autre.

Le 13 avril, suite des grèves à répétition. Un journal même minimalement soucieux de la vie quotidienne de ses lecteurs parlerait des complications incessantes, des attentes interminables dans les gares et aéroports, des trésors d’invention auxquels sont réduits ceux qui doivent faire garder leurs enfants, des nouvelles pertes colossales pour l’économie du pays, de l’annulation de la première visite d’État que le nouveau roi britannique avait choisi de réserver à la France. (D’avoir peu d’admiration pour la monarchie actuelle et encore moins pour l’Angleterre du Brexit n’empêche pas de ressentir la gifle monumentale qu’a constituée cette annulation.) Non, il ne s’agit que des luttes glorieuses du Peuple en révolte :

intransigeance

Intransigeance ? Qu’attend-on au juste : qu’un gouvernement élu sur la promesse d’une réforme et l’ayant fait passer au Parlement décide tout à coup de l’annuler ? Peut-être pour rassurer les Libraires en Colère (si l’on devine correctement le mot tronqué sur la photo de banderole) ? Cette Une du Monde et des dizaines d’autres comme elles sont de purs appels à manifester ; jour après jour le journal explique aimablement à ses lecteurs quant et où participer. Comme s’ils n’avaient rien de mieux à faire.

Le même jour, un autre sommet de l’élite intellectuelle éclairant le monde :

veutpas

En d’autres temps Le Monde était attaché aux principes constitutionnels. Notez l’illustration menaçante. Côté constitution, avec sa sagacité habituelle le journal avait annoncé dès le 26 mars ce qui allait se passer :

rousseau-3

Les opposants à la réforme, ayant perdu à toutes les étapes, se rattachaient à l’espoir que le Conseil Constitutionnel annulât tout. Bien entendu il n’avait aucune raison de le faire. Son rôle n’est pas de substituer la volonté des manifestants du jour à celle du Parlement élu. Peut-être y jouait-il  « en quelque sorte son destin » mais aux dernières nouvelles il existe encore. Le 26 mars il pouvait encore y avoir débat, mais un journal objectif et sérieux aurait publié une analyse factuelle et prudente.

Tout cela n’empêche pas Le Monde de continuer de tirer sur tout ce qui bouge du côté du gouvernement. Le 21 avril, Macron ayant rencontré des enseignants :

crispe

Si quelqu’un crispe, il semblerait que ce soit plutôt Le Monde, mais bon. Ce qui compte, bien sûr, ce ne sont pas les avancées forcément viciées du gouvernement mais la réaction des 18,4%, les syndicats. Conjecture oiseuse : s’il n’y avait pas eu le  « pacte enseignant », est-ce que plus rien n’aurait « terni » la joie débordante desdits syndicats et leur soutien désormais enthousiaste aux projets éducatifs du gouvernement ?

Après le passage de la réforme des retraites (au grand soulagement de beaucoup), Macron et Borne ont annoncé vouloir continuer avec les réformes. Quel dommage, selon Le Monde, qu’ils soient en situation si difficile ! Le 24 avril, pauvre Macron :

doute

Pour Borne ce n’est pas mieux (26 avril) :

spectre

À ce point d’affaiblissement rien ne pourrait être pire, mais si, on peut s’affaiblir encore :

affaiblit

Le 1er mai, reportage sur les manifestations, dans le même genre que les précédents, par exemple :

violence

Le « mais » est vraiment adorable. Un« mais » dans le style bien connu de « je ne suis pas raciste, mais… ». En réalité, depuis des mois (et dès la crise des gilets jaunes) Le Monde affiche une attitude de compréhension presque affectueuse vis-à-vis des pires excès. Macron, pour qui l’écoute, n’est en rien méprisant et son attitude est le contraire de celle de quelqu’un qui prendrait les gens pour des imbéciles. Ses discours sont de très haute tenue (comme l’étaient, du reste, ceux de François Hollande) ; il explique et il justifie. Ne se sentent méprisés que ceux qui en réalité le méprisent, pour des raisons qu’on n’a pas de mal à imaginer (il est passé par la banque Rothschild , comme Pompidou du reste, il parle bien, il joue du piano, il n’a pas besoin de « prendre de haut » pour qu’on détecte en lui le premier de la classe). Et d’ailleurs s’il l’était, méprisant, en quoi cela justifierait-il de mettre le feu à la brasserie La Rotonde ? Dans les pays développés seule la France est en proie à ces manifestations régulièrement violentes qui dégénèrent. Les activistes du Monde n’ont rien à y redire ; il préfèrent réserver leur indignation pour ceux qui essayent de moderniser le pays.

La rage anti-Macron et anti-Borne se déchaîne jour après jour dans ce qui fut le quotidien respecté de Beuve-Méry et (malgré ses défauts) une source d’informations souvent fiables et de commentaires pondérés. Il semble avoir été pris en otage par une poignée de propagandistes peu soucieux de journalisme. On voit bien que les éléments les plus responsables en sont gênés ; Sylvie Kaufmann publie dans le New York Times des analyses raisonnées et raisonnables, Françoise Fressoz écrit des éditoriaux équilibrés. On se demande si c’est pour maintenir une façade respectable pour les lecteurs étrangers qui ne voient pas le déferlement quotidien de bile anti-Établissement remplaçant l’information de base.

Dommage vraiment qu’on en soit venu là. Je ne sais pas ce qu’on enseigne aujourd’hui dans les écoles de journalisme en France, mais tous les autre grands pays démocratiques ont leurs journaux de référence qui appliquent (ou essayent d’appliquer, avec d’inévitables ratés) la distinction fondamentale entre nouvelles et opinions. Que faudrait il pour que les lecteurs français aient à nouveau un journal sérieux, objectif et crédible ?