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Reading notes. From: Quelques éléments d’histoire des nombres négatifs (Elements of a history of negative numbers) by Anne Boyé, Proyecto Pénélope, 2002, revision available here; On Solving Equations, Negative Numbers, and Other Absurdities: Part II by Ralph Raimi, available  here; Note sur l’histoire des nombres entiers négatifs (Note on the History of Negative Numbers) by Rémi Lajugie, 2016, here;  The History of Negative Numbers by Leo Rogers, here; Historical Objections against the Number Line, by Albrecht Heeffer, here; Making Sense of Negative Numbers by Cecilia Kilhamn, 2011 PhD thesis at the University of Gothenburg, here.  Also the extensive book by Gert Schubring on Number Concepts Underlying the Development of Analysis in 17-19th Century France and Germany, here. Translations are mine (including from Maclaurin and De Morgan, retranslated from Lajugie’s and Boyé’s French citations). This excursion was spurred by a side remark in the article How to Take Advantage of the Blur Between the Finite and the Infinite by the recently deceased mathematician Pierre Cartier, available here.

At dinner recently, with non-scientists, discussion revolved about ages and a very young child, not even able to read yet, volunteered about his forthcoming little brother that “when he comes out his age will be zero”. An adult remarked “indeed, and right now his age is minus five months”, which everyone young and old seemingly found self-evident. How remarkable!

From a elite concept to grade school topic

It is a characteristic of potent advances in human understanding that for a while they are understandable to a few geniuses only, or, if not geniuses, to a handful of forward-thinking luminaries, and a generation later, sometimes less, they are taught in grade school. When I came across object-oriented programming, those of us who had seen the light, so to speak, were very few. Feeling very much like plotting Carbonari, we would excitedly meet once in a while in exotic locations (for my Simula-fueled band usually in Scandinavia, although for the Smalltalk crowd it must have been California) to share our shared passion and commiserate about the decades it would take for the rest of humankind to see the truth. Then at some point, almost overnight, without any noticeable harbinger, the whole thing exploded and from then on it was object-oriented everything. Nowadays every beginning programmer talks objects — I did not write “understands”, they do not, but that will be for another article.

Zero too was a major invention. Its first recorded use as a number (not just a marker for absent entities) was in India in the first centuries of our era. It is not hard to imagine the mockeries. “Manish here has twenty sheep, Rahul has twelve sheep, and look at that nitwit Shankar, he sold all his sheep and still claims he has some, zero of them he says! Can you believe the absurdity? Ha ha ha.”

That dialog is imaginary, but for another momentous concept, negative numbers, we have written evidence of the resistance. From the best quarters!

The greatest minds on the attack

The great Italian mathematician Cardan (Gerolamo Cardano), in his Ars Magna from 1545, was among the skeptics. As told in a 1758 French History of Mathematics by Montucla (this quote and the next few ones are from Boyé):

In his article 7 Cardan proposes an equation which in our language would be x² + 4 x = 21 and observes that the value of x can equally be +3 or -7, and that by changing the sign of the second term it becomes -3 or +7. The name he gives to such values is “fake”.

The words I am translating here as “fake values” are, in Montucla, valeurs feintes, where feint in French means feigned, or pretended (“pretend values”). Although I have not seen the text of Ars Magna, which is in Latin anyway, I like to think that Cardan was thinking of the Italian word finto. (Used for example  in the title of an opera composed by Mozart at the age of 19, La Finta Giardinera, the fake girl gardener — English has no feminine for “gardener”. The false gardenerette in question is a disguised marchioness.) It is fun to think of negative roots as feigned.

Cardan also uses terms like “abundant” versus “failing” quantities (abondantes and défaillantes in French texts) for positive and negative:

Simple advice: do not confuse failing quantities with abundant quantities. One must add the abundant quantities between themselves, also subtract failing quantities between themselves, and subtract failing quantities from abundant quantities but only by taking species into account, that is to say, only operate same with same […]

There is a recognition of negative values, but with a lot of apprehension. Something strange, the author seems to feel, is at play here. Boyé cites the precedent of Chinese accountants who could manipulate positive values through black sticks and negative ones through red sticks and notes that it resembles what Cardan seems to be thinking here. In the fifteenth century, Nicolas Chuquet “used negative numbers as exponents but referred to them as `absurd numbers’”.

For all his precautions, Cardan did consider negative quantities. No lesser mind as Descartes, a century later (La Géométrie, 1637), is more circumspect. In discussing roots of equations he writes:

Often it turns out that some of those roots are false, or less than nothing [“moindres que rien”] as if one supposes that x can also denote the lack of a quantity, for example 5, in which case we have x + 5 = 0, which, if we multiply it by x³ − 9 x²  + 26 x − 24 = 0 yields  x⁴ − 4 x³ − 19 x² + 106 x − 120 = 0, an equation for which there are four roots, as follows: three true ones, namely 2, 3, 4, and a false one, namely 5.

Note the last value: “5”. Not a -5, but a 5 dismissed as “false”. The list of exorcising adjectives continues to grow: negative values are no longer “failing”, or “fake”, or “absurd”, now for Descartes they are “false”!  To the modern mind they are neither more nor less true than the “true” ones, but to him they are still hot potatoes, to be handled with great suspicion.

Carnot cannot take the heat

One more century later we are actually taking a step back with Lazare Carnot. Not the one of the thermodynamic cycle — that would be his son, as both were remarkable mathematicians and statesmen. Lazare in 1803 cannot hide his fear of negative numbers:

If we really were to obtain a negative quantity by itself, we would have to deduct an effective quantity from zero, that is to say, remove something from nothing : an impossible operation. How then can one conceived a negative quantity by itself?.

(Une quantité négative isolée : an isolated negative quantity, meaning a negative quantity considered in isolation). How indeed! What a scary thought!

The authors of all these statements, even when they consider negative values, cannot bring themselves to talk of negative numbers, only of negative quantities. Numbers, of course, are positive: who has ever heard of a shepherd who is guarding a herd of minus 7 lambs? Negative quantities are a slightly crazy concoction to be used only reluctantly as a kind of kludge.

Lajugie mentions another example, mental arithmetic: to compute 19 x 31  in your head, it is clever to multiply (20 -1) by (30 + 1), but then as you expand the product by applying the laws of distributivity you get negative values.

De Morgan too

We move on by three decades to England and Augustus De Morgan, yes, the one who came up with the two famous laws of logic duality. De Morgan in 1803, as cited by Raimi:

8-3 is easily understood; 3 can be taken from 8 and the remainder is 5; but 3-8 is an impossibility; it requires you to take from 3 more than there is in 3, which is absurd. If such an expression as 3-8 should be the answer to a problem, it would denote either that there was some absurdity inherent in the problem itself, or in the manner of putting it into an equation.

Raimi points out that “De Morgan is not naïve” but wants to caution students about possible errors. Maybe, but we are back to fear and to words such as “absurd”, as used by Chuquet three centuries before. De Morgan (cited by Boyé) doubles down in his reluctance to accept negatives as numbers:

0 − a is just as inconceivable as -a.

Here is an example. A father is 56 years old and his [son] is 29 years old. In how many years will the father’s age be twice his son’s age? Let x be that number of years; x satisfies 56 +x = 2 (29 + x). We find x = -2.

Great, we say, he got it! This simple result is screaming at De Morgan but he has to reject it:

This result is absurd. However if we change x into -x and correspondingly resolve 56−x = 2 (29−x), we find x = -2. The [previous] negative answer shows that we had made an error in the initial phrasing of the equation.

In other words, if you do not like the solution, change the problem! I too can remember a few exam situations in which I would have loved to make an equation more sympathetic by replacing a plus sign with a minus. Too bad no one told me I could.

De Morgan’s comment is remarkable as the “phrasing of  the equation” contained no “error” whatsoever.   The equation correctly reflected the problem as posed. One could find the statement of the problem mischievous (“in how many years” suggests a solution in the future whereas there is only one in the past), but the equation is meaningful and  has a solution — one, however, that horrifies De Morgan. As a result, when discussing the quadratic (second-degree) equation ax² + bx + c = 0, instead of accepting that a, b and c can be negative, he distinguishes no fewer than 6 cases, such as ax² – bx + c = 0, ax² + bx – c = 0 etc. The coefficients are always non-negative, it is the operators that change between + and  -. As a consequence, the determinant actually has two possible values, the one familiar to us, b² – 4ac, but also b² + 4ac for some of the cases. According to Raimi, many American textbooks of the 19th century taught that approach, forcing students to remember all six cases. (For a report about a current teaching distortion of the same topic, see a recent article on the present blog, “Mathematics Is Not a Game of Hit and Miss”, here.)

De Morgan (cited here by Boyé) feels the need to turn this reluctance to use negative numbers into a general rule:

When the answer to a problem is negative, by changing the sign of x in the equation that produced the result, we can discover that an error was made in the method that served to form this equation, or show that the question asked by the problem is too limited.

Sure! It is no longer “if the facts do not fit the theory, change the facts” (a sarcastic definition of bad science), but also “if you do not like the solution, change the problem”. All the more unnecessary (to a modern reader, who thanks to the work of countless mathematicians over centuries learned negative numbers in grade school, and does not spend time wondering whether they mean something) that if we keep the original problem the computed solution, x = -2, makes perfect sense: the father was twice his son’s age two years ago. The past is a negative future. But to see things this way, and to accept that there is nothing fishy here, requires a mindset for which an early 19-th century mathematician was obviously not ready.

And Pascal, and Maclaurin

Not just a mathematician but a great mathematical innovator. What is remarkable in all such statements against negative numbers is that they do not emanate from little minds, unable to grasp abstractions. Quite the contrary! These negative-number-skeptics are outstanding mathematicians. Lajugie gives more examples from the very top. Blaise Pascal in 1670:

Too much truth surprises; I know people who cannot understand that when you deduct 4 from zero, what remains is zero.

(Oh yes?, one is tempted to tell the originator of probability theory, who was fascinated by betting and games of chance: then I put the 4 back and get 4? Quick way to get rich. Give me the address of that casino please.) A friend of Pascal, skeptical about the equality -1 / 1 = 1 / -1: “How could a smaller number be to a larger one as a larger one to a smaller one?”. An English contemporary, John Wallis, one of the creators of infinitesimal calculus — again, not a nitwit! — complains that a / 0 is infinity, but since in a / -1 the denominator is lesser than zero it must follow that a / -1, which is less than zero (since it is negative by the rule of signs), must also be greater than infinity! Nice one actually.

This apparent paradox also bothered the great scientist D’Alembert, the 18-th century co-editor of the Encyclopédie, who resolves it, so to speak, by stating (as cited by Heeffer) that “One can only go from positive to negative through either zero or through infinity”; so unlike Wallis he accepts that 1 / -a is negative, but only because it becomes negative when it passes through infinity. D’Alembert concludes (I am again going after Heeffer) that it is wrong to say that negative numbers are always smaller than zero. Euler was similarly bothered and similarly looking for explanations through infinity: what does Leibniz’s expansion of 1 / (1 – x)  into 1 + x + x² + x³ + … become for x = 2? Well, the sum 1 + 2 + 4 + 8 + … diverges, so 1 / -1 is infinity!

We all know the name “Maclaurin” from the eponymous series. Colin Maclaurin  wrote in 1742, decades after Pascal (Boyé):

The use of the negative sign in algebra leads to several consequences that one initially has trouble accepting and has led to ideas that seem not to have any real foundation.

Again the supposed trouble is the absence of an immediately visible connection to everyday reality (a “real foundation”). And again Maclaurin accepts that quantities can be negative, but numbers cannot:

While abstract quantities can be both negative and positive, concrete quantities are not always capable of being the opposite of each other.

(cited by Kilhamn). Apparently Colin’s wife Anne never thought of buying him a Réaumur thermometer (see below) for his birthday.

Yes, two negatives make a positive

We may note that the authors cited above, and many of their contemporaries, had no issue manipulating negative quantities in some contexts, and to accept the law of signs, brilliantly expressed by the Indian mathematician Brahmagupta  in the early 7th century (not a typo); as cited by Rogers:

A debt minus zero is a debt.

A fortune minus zero is a fortune.

Zero minus zero is a zero.

A debt subtracted from zero is a fortune.

A fortune subtracted from zero is a debt.

The product of zero multiplied by a debt or fortune is zero.

The product of zero multiplied by zero is zero.

The product or quotient of two fortunes is one fortune.

The product or quotient of two debts is one fortune.

The product or quotient of a debt and a fortune is a debt.

The product or quotient of a fortune and a debt is a debt.

That view must have been clear to accountants. Whatever Pascal may have thought, 4 francs removed from nothing do not vanish; they become a debt. What the great mathematicians cited above could not fathom was that there is such a thing as a negative number. You can count up as far as your patience will let you; you can then count down, but you will inevitably stop. Everyone knows that, and even Pascal or Euler have trouble going beyond. (Old mathematical joke: “Do you know about the mathematician who was afraid of negative numbers? He will stop at nothing to avoid them”.)

The conceptual jump that took centuries to achieve was to accept that there are not only negative quantities, but negative numbers: numbers in their own right, not just temporarily  negated positive numbers (that is, the only ones to which we commonly rely in everyday life), prefaced with a minus sign because we want to use them as “debts”, but with the firm intention to move them back to the other side so as to restore their positivity  — their supposed naturalness —  at the end of the computation. We have seen superior minds “stopping at nothing” to avoid that step.

Others were bolder; Schubring has a long presentation of how Fontenelle, an 18-th century French scientist and philosopher who contributed to many fields of knowledge,  made the leap.

Not everyone may yet get it

While I implied above that today even small children understand the concept, we may note in passing that there may still be people for whom it remains a challenge. Lajugie notes that the Fahrenheit temperature scale frees people from having to think about negative temperatures in ordinary circumstances, but since the 18-th century the (much more reasonable) Réaumur thermometer and Celsius scale goes under as well as above zero, helping people get familiar with negative values as something quite normal and not scary. (Will the US ever switch?)

Maybe the battle is not entirely won.  Thanks to Rogers I learned about the 2018 Lottery Incident in the United Kingdom of Great Britain and Northern Ireland, where players could win by scratching away, on a card, a temperature lower than the displayed figure. Some temperatures were below freezing. The game had to be pulled after less than a week as a result of player confusion. Example complaints included this one from a  23-year-old who was adamant she should have won:

“On one of my cards it said I had to find temperatures lower than -8. The numbers I uncovered were -6 and -7 so I thought I had won, and so did the woman in the shop. But when she scanned the card the machine said I hadn’t. I phoned Camelot [the lottery office] and they fobbed me off with some story that -6 is higher – not lower – than -8 but I’m not having it. I think Camelot are giving people the wrong impression – the card doesn’t say to look for a colder or warmer temperature, it says to look for a higher or lower number. Six is a lower number than 8. Imagine how many people have been misled.“

Again, quantities versus numbers. As we have seen, she could claim solid precedent for this reasoning. Most people, of course, have figured out that while 8 is greater than 6 (actually, because of that), -6 is greater than -8. But as Lajugie points out the modern, rigorous definition of negative numbers is (in the standard approach) far from the physical intuition (which typically looks like the two-directional line pictured at the beginning of this article, with numbers spreading away from zero towards both the right and the left). The picture helps, but it is only a picture.

Away from the perceptible world

If we ignore the intuition coming from observing a Réaumur or Celsius thermometer (which does provide a “real world” guide), the early deniers of negative numbers were right that this concept does not directly reflect the experiential understanding of numbers, readily accessible to everyone. The general progress of science, however, has involved moving away from such immediate intuition. Everyday adventures (such as falling on the floor) absolutely do not suggest to us that matter is made of sparse atoms interacting through electrical and magnetic phenomena. This march towards abstraction has guided the evolution of modern science — most strikingly, the evolution of modern mathematics.

Some lament this trend; think of the negative reactions to the so-called “new math”. (Not from me. I was caught by the  breaking of the wave and loved every minute of it.) But there is no going back; in addition, it is well known that some of the initially most abstract mathematical development, initially pursued without any perceived connection with reality, found momentous unexpected applications later on; two famous examples are Minkowski’s space-time formalism, which provided the mathematical framework for specifying relativity, and number-theoretical research about factoring large numbers into primes, which made modern cryptography (and hence e-commerce) possible.

Negative numbers too required abstraction to acquire mathematical activity. That step required setting aside the appeal to intuition and considering the purely concepts solely through its posited properties. We computer scientists would say “applying the abstract data type approach”. The switch took place sometime in the middle of the 19th century, spurred among others by Évariste Galois. The German mathematician Hermann Hankel — who lived only a little longer than Galois — explained clearly how this transition occurred for negative numbers (cited by Boyé among others):

The [concept of] number is no longer today a thing, a substance that is supposed to exist outside of the thinking subject or the objects that lead to it being considered; it is no longer an independent principle, as the Pythagoreans thought. […] The mathematician considers as impossible only that which is logically impossible, in the sense of implying a contradiction. […] But if the numbers under study are logically possible, if the underlying concept is defined clearly and distinctly, the question can no longer be whether a substrate exists in the world of reality.

A very modern view: if you can dream it, and you can make it free of contradiction (well, Hankel lived in the blissful times before Gödel), then you can consider it exists. An engineer might replace the second of these conditions by: if you can build it. And a software engineer, by: if you can compile and run it. In the end it is all the same idea.

Formally: a general integer is an equivalence class

In modern mathematics, while no one forbids you from clinging for help to some concrete intuition such as the Celsius scale, it is not part of the definition. Negative numbers are formally defined members of the zoo.

For those interested (and not remembering the details), the rigorous definition goes like this. We start from zero-or-positive integers (the set N of “natural” numbers) and consider pairs [a, b] of numbers (as we would do to define rationals, but the sequel quickly diverges). We define an equivalence relation which holds with another pair [a’, b’] if a + b’ = a’ + b. Then we can define the set Z of all integers (positive, zero, negative) as the quotient of N x N by that relation. The intuition if that the characteristic property of an equivalence class, such as [1, 4], [2, 5],  [3, 6]… , is that b – a, the difference between the second and first values, is the same for all pairs: 3 in this example (4 – 1, 5 – 2, 6 – 3 etc.). At least that property holds for b >= a; since we are starting from N, subtraction is defined only in that case. But then if we take that quotient as the definition of Z, we call members of that set “negative”, by pure convention, whenever b < a (if this property holds for one of the pairs in an equivalence class it holds for all of them), and positive if b > a. Zero is obtained for a = b.

We reestablish the connection with our good old natural integers by identifying N with the subset of Z for which b >= a. (This is an informal statement; the correct technical phrasing is that there is a “bijection” — a one-to-one correspondence, in fact an isomorphism — between that subset and N.) So we have plunged, or “embedded”, N into something bigger, to which most of its treasured properties (associativity and commutativity of addition etc.) immediately spread, while some limitations disappear; in particular, unlike in N, we can now subtract any Z integer from any other.

We also get the opposites of numbers as a result: for any m in Z, we can easily prove that there is another one n such that m + n = 0. That n can be written -m. The property is true for both positive and negative numbers, concepts that are also easy to define: we show that “>” is one of those operations that extend from N to Z, and the positive numbers are those m such that m > 0. Then if m is positive -m is negative, and conversely; 0 is the only number for which m = -m.

Remarkably, Z too is in one-to-one correspondence with N. (It is one of the definitions of an infinite set that it can be in one-to-one correspondence with one of its strict subsets, something that is obviously not possible for a finite set. To shine in cocktail parties you can refer to this property as “Dedekind-infinite”.) In other words, we have uncovered yet a new attraction of Hilbert’s Grand Hotel: the hotel has an annex, ready for the case of a guest coming with an unannounced companion. The companion will be hosted in the annex, in a room uniquely paired with the original guest’s room. The annex is a second hotel, but it is not exactly like the first: it does not have an annex of its own in the form of yet another hotel. It does have an annex, but that is the original hotel (the hotel of which it itself is the annex).

If you were not aware of the construction through equivalence classes of pairs and your reaction is “so much ado about so little! I do not need any of this to understand negative numbers and to know that m + -m = 0”, well, maybe, but you are missing part of the story: the observation that even the “natural” numbers are not that natural. Those we can readily apprehend as part of “natural” reality are the ones from 1 to something like 1000,  denoting quantities that we can reasonably count. If you really have extraordinary patience and time make this 1000,000 or even 1 million, that does not change the argument.

Even zero, as noted, took millennia to be recognized as a number. Beyond the numbers that we can readily fathom in relation to our experience at human scale, the set of natural integers is also an intellectual fiction. (Its official construction in the modern mathematical canon is seemingly even more contorted than the extension to Z sketched above: N, in the so-called Zermelo-Fraenkel theory (more pickup lines for cocktail parties!) contains the empty set for 0, and then sets each containing the previous one and a set made of that previous one. It is clearer with symbols: ø, {ø}, {ø, {ø}}, {ø, {ø}, {ø, {ø}}}, ….)

Coming back to negative numbers, Riemann (1861, cited by Schubring) held their construction as a fundamental step in the generalization process that characterizes mathematics, beautifully explaining the process:

The original object of mathematics is the integer number; the field of study increases only gradually. This extension does not happen arbitrarily, however; it is always motivated by the fact that the initially restricted view leads toward a need for such an extension. Thus the task of subtraction requires us to seek such quantities, or to extend our concept of quantity in such a way that its execution is always possible, thus guiding us to the concept of the negative.

Nature and nurture

The generalization process is also a process of abstraction. The move away from the “natural” and “intuitive” is inevitable to understand negative numbers. All the misunderstandings and fears by great minds, reviewed above, were precisely caused by an exaggerated, desperate attempt to cling to supposedly natural concepts. And we only talked about negative numbers! Similar or worse resistance met the introduction of imaginary and complex numbers (the names themselves reflect the trepidation!), quaternions and other fruitful but artificial creation of mathematics. Millenia before, the Greeks experienced shock when they realized that numbers such as π and the square root of 2 could not be expressed as ratios of integers.

Innovation occurs when someone sets out to disprove a statement of impossibility. (This technique also lies behind one approach to solving puzzles and riddles: you despair that there is no way out; then try to prove that there is no solution. Failing to complete that proof might end up opening for you the path to one.)

Parallels exist between innovators and children. Children do not know yet that some things are impossible; they make up ways. Right now I am sitting next to the Rhine and I would gladly take a short walk on the other bank, but I do not want to go all the way to the bridge and back. If I were 4 years old, I would dream up some magic carpet or other fancy device, inferred from bedtime stories, that would instantly transport me there. We grow up and learn that there are no magic carpets, but true innovators who see an unsolved problem refuse to accept that state of affairs.

In their games, children often use the conditional: “I would be a princess, and you would be a magician!”. Innovators do this too when they refuse to be stopped by conventional-wisdom statements of impossibility. They set out to disprove the statements. The French expression “prouver le mouvement en marchant”, prove movement by walking, refers to the Greek philosophers Diogenes of Sinope and  Zeno of Elea. Zeno, the story goes, used the paradox of Achilles and the tortoise to claim he had proved that movement is impossible. Diogenes proved the reverse by starting to walk.

In mathematics and in computer science, we are even more like children because we can in fact summon our magic carpets — build anything we dream of, provided we can define it properly. Mathematics and computer science are among the best illustrations of Yuval Noah Harari’s thesis that a defining characteristic of the human race is our ability to tell ourselves stories, including very large and complex stories. A mathematical theory is a story that we tell ourselves and to which we can convert other mathematicians (plus, if the theory is really successful, generations of future students). Computer programs are the same with the somewhat lateral extra condition that we must also enable some computing system to execute it, although that system is itself a powerful story that has undergone the same process. You can find variants of these observations in such famous pronouncements as Butler Lampson’s “in computer science, we can solve any problem by introducing an extra level of indirection” and Alan Kay‘s  “the best way to predict the future is to invent it”.

There is a difference, however, with children’s role-playing; and it can have dramatic effects. Children can indulge in make-believe for quite some time, continuing to live their illusions until they grow up and become reasonable. Normally they will not experience bad consequences (well, apart from the child who believes a little too hard, or from a window little too high, that his arms really are wings.) In adult innovation, sooner or later you have to reconcile the products of your imagination with the world. It may be the physical world (your autonomous robot was fantastic in the lab but it requires heavy batteries making it impractical), but things are just as bad with the virtual world of mathematics or software. It is great to define and extend your own freaky artificial worlds, but at some point you have to make sure they are consistent not just with already defined worlds but with themselves. As noted earlier, a mathematical concoction, however audacious, should be free of contradictions; and a software concept, however powerful, should be implementable. (Efficiently implementable.)

By any measure the most breathtaking virtual construction of modern mathematics is Cantor’s set theory, which scared many mathematicians,  the way negative numbers had terrified their predecessors. (Case in point: the editor of a journal to which Cantor had submitted a paper wrote that it was “a hundred years too soon”.  Cantor did not want to wait until 1984. The great mathematician Kronecker described him as “a corrupter of youth”. And so on.) More enlightened colleagues, however, soon recognized the work as ushering in a new era. Hilbert, in particular, was a great supporter, as were many of the top names in several countries. Then intellectual disaster struck.

Cantor himself and others, most famously Russell in a remark included in a letter of Frege, noticed a problem. If sets can contain other sets, and even contain themselves (the set of infinite sets must be infinite), what do we make of the set of all sets that do not contain themselves? Variants of this simple question so shook the mathematical edifice that it took a half-century to put things back in order.

Dream, check, build

Cantor, for his part, went into depression and illness. He died destitute and desperate. There may not have been a direct cause-to-effect relationship, but certainly the intellectual rejection and crisis did not help.

All the sadder that in the end set theory, after significant cleanup, turned out to be one of the biggest successes of history. We still discuss the paradoxes, but it is unlikely that today they prevent anyone from sleeping soundly at night.

Unlike those genuinely disturbing paradoxes of set theory, the paradoxes that led mathematicians of previous centuries to reject negative numbers were apparent only. They were not paradoxes but tokens of intellectual timidity.

The sole reason for fearing and skirting negative numbers was an inability to accept a construction that contradicted a simplistic view of physical reality. Like object-oriented programming and many other bold advances, all that was required was the audacity to take imagined abstractions seriously.

Dream it; check it; build it.

[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.

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.)

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.

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 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.

August of last year brought the sad news of Barry Boehm’s passing away on August 20. If software engineering deserves at all to be called engineering today, it is in no small part thanks to him.

“Engineer” is what Boehm was, even though his doctorate and other degrees were all in mathematics. He looked the part (you might almost expect him to carry a slide rule in his shirt pocket, until you realized that as a software engineer he did not need one) and more importantly he exuded the seriousness, dedication, precision, respect for numbers, no-nonsense attitude and practical mindset of outstanding engineers. He was employed as an engineer or engineering manager in the first part of his career, most notably at TRW, a large aerospace company (later purchased by Northrop Grumman), turning to academia (USC) afterwards, but even as a professor he retained that fundamental engineering ethos.

LASER Summer School, Elba Island (Italy), September 2010
From left: Walter Tichy, Barry Boehm, Vic Basili (photograph by Bertrand Meyer)

Boehm’s passion was to turn the study of software away from intuition and over to empirical enquiry, rooted in systematic objective studies of actual projects. He was not the only one advocating empirical methods (others from the late seventies on included Basili, Zelkowitz, Tichy, Gilb, Rombach, McConnell…) but he had an enormous asset: access to mines of significant data—not student experiments, as most researchers were using!—from numerous projects at TRW. (Basili and Zelkowitz had similar sources at NASA.) He patiently collected huge amounts of project information, analyzed them systematically, and started publishing paper after paper about what works for software development; not what we wish would work, but what actually does on the basis of project results.

Then in 1981 came his magnum opus, Software Engineering Economics (Prentice Hall), still useful reading today (many people inquired over the years about projects for a second edition, but I guess he felt it was not warranted). Full of facts and figures, the book also popularized the Cocomo model for cost prediction, still in use nowadays in a revised version developed at USC (Cocomo II, 1995, directly usable through a simple Web interface at softwarecost.org/tools/COCOMO/

Cocomo provides a way to estimate both the cost and the duration of a project from the estimated number of lines of code (alternatively, in Cocomo II, from the estimated number of function points), and some auxiliary parameters to account for each project’s specifics. Boehm derived the formula by fitting from thousands of projects.

When people first encounter the idea of Cocomo (even in a less-rudimentary form than the simplified one I just gave), their first reaction is often negative: how can one use a single formula to derive an estimate for any project? Isn’t the very concept ludicrous anyway since by definition we do not know the number of lines of code (or even of function points) before we have developed the project? With lines of code, how do we distinguish between different languages? There are answers to all of these questions (the formula is ponderated by a whole set of criteria capturing project specifics, lines of code calibrated by programming language level do correlate better than most other measures with actual development effort, a good project manager will know in advance the order of magnitude of the code size etc.). Cocomo II is not a panacea and only gives a rough order of magnitude, but remains one of the best available estimation tools.

Software Engineering Economics and the discussion of Cocomo also introduced important laws of software engineering, not folk wisdom as was too often (and sometimes remains) prevalent, but firm results. I covered one in an article in this blog some time ago, calling it the “Shortest Possible Schedule Theorem”: if a serious estimation method, for example Cocomo, has determined an optimal cost and time for a project, you can reduce the time by devoting more resources to the project, but only down to a certain limit, which is about 75% of the original. In other words, you can throw money at a project to make things happen faster, but the highest time reduction you will ever be able to gain is by a quarter. Such a result, confirmed by many studies (by Boehm and many others after him), is typical of the kind of strong empirical work that Boehm favored.

The CMM and CMMI models  of technical management are examples of important developments that clearly reflect Boehm’s influence. I am not aware that he played any direct role (the leader was Watts Humphrey, about whom I wrote a few years ago), but the models’ constant emphasis on measurement, feedback and assessment are in line with the principles  so persuasively argued in his articles and books.

Another of his famous contributions is the Spiral model of the software lifecycle. His early work and Software Engineering Economics had made Boehm a celebrity in the field, one of its titans in fact, but also gave him the reputation, deserved or not, of representing what may be called big software engineering, typified by the TRW projects from which he drew his initial results: large projects with large budgets, armies of programmers of variable levels of competence, strong quality requirements (often because of the mission- and life-critical nature of the projects) leading to heavy quality assurance processes, active regulatory bodies, and a general waterfall-like structure (analyze, then specify, then design, then implement, then verify). Starting in the eighties other kinds of software engineering blossomed, pioneered by the personal computer revolution and Unix, and often typified by projects, large or small but with high added value, carried out iteratively by highly innovative teams and sometimes by just one brilliant programmer. The spiral model is a clear move towards flexible modes of software development. I must say I was never a great fan (for reasons not appropriate for discussion here) of taking the Spiral literally, but the model was highly influential and made Boehm a star again for a whole new generation of programmers in the nineties. It also had a major effect on agile methods, whose notion of  “sprint ” can be traced directly the spiral. It is a rare distinction to have influenced both the CMM and agile camps of software engineering with all their differences.

This effort not to remain wrongly identified with the old-style massive-project software culture, together with his natural openness to new ideas and his intellectual curiosity, led Boehm to take an early interest in agile methods; he was obviously intrigued by the iconoclasm of the first agile publications and eager to understand how they could be combined with timeless laws of software engineering. The result of this enquiry was his 2004 book (with Richard Turner) Balancing Agility and Discipline: A Guide for the Perplexed, which must have been the first non-hagiographic presentation (still measured, may be a bit too respectful out of a fear of being considered old-guard) of agile approaches.

Barry Boehm was an icon of the software engineering movement, with the unique position of having been in essence present at creation (from the predecessor conference of ICSE in 1975) and accompanying, as an active participant, the stupendous growth and change of the field over half a century.

Barry Boehm at a dinner at ICSE 2006, Shanghai (photograph by Bertrand Meyer)

I was privileged to meet Barry very early, as we were preparing a summer school in 1978 on Programming Methodology where the other star was Tony Hoare. It was not clear how the mix of such different personalities, the statistics-oriented UCLA-graduate American engineer and the logic-driven classically-trained (at Oxford) British professor would turn out.

Boehm could be impatient with cryptic academic pursuits; one exercise in Software Engineering Economics (I know only a few other cases of sarcasm finding its refuge in exercises from textbooks) presents a problem in software project management and asks for an answer in multiple-choice form. All the proposed choices are sensible management decisions, except for one which goes something like this: “Remember that Bob Floyd [Turing-Awarded pioneer of algorithms and formal verification] published in Communications of the ACM vol. X no. Y pages 658-670 that scheduling of the kind required can be performed in O (n³ log log n) instead of O (n³ log n) as previously known; take advantage of this result to spend 6 months writing an undecipherable algorithm, then discover that customers do not care a bit about the speed.” (Approximate paraphrase from memory [1].)

He could indeed be quite scathing of what he viewed as purely academic pursuits removed from the reality of practical projects. Anyone who attended ICSE 1979 a few months later in Munich will remember the clash between him and Dijkstra; the organizers had probably engineered it (if I can use that term), having assigned them the topics  “Software Engineering As It Is” and “Software Engineering as It Should Be”, but it certainly was spectacular. There had been other such displays of the divide before. Would we experience something of the kind at the summer school?

No clash happened; rather, the reverse, a meeting of minds. The two sets of lectures (such summer schools lasted three weeks at that time!) complemented each other marvelously, participants were delighted, and the two lecturers also got along very well. They were, I think, the only native English speakers in that group, they turned out to have many things in common (such as spouses who were also brilliant software engineers on their own), and I believe they remained in contact for many years. (I wish I had a photo from that school—if anyone reading this has one, please contact me!)

Barry was indeed a friendly, approachable, open person, aware of his contributions but deeply modest.

Few people leave a profound personal mark on a field. A significant part of software engineering as it is today is a direct consequence of Barry’s foresight.

Note

[1] The full text of the exercise will appear shortly as a separate article on this blog.

A version of this article appeared previously in the Communications of the ACM blog.

… is to have a top scientist spot your talent and encourage you, however humble your status may be then.

Wikipedia has a terse entry about Dirk Rembrandtsz (with “sz” at the end), presented as a “seventeenth-century Dutch cartographer, mathematician, surveyor, astronomer, teacher and [religious dignitary]” with “more than thirty scientific publications to his name” and various inventions. Seems just like another early scientific career, but digging a bit deeper reveals that the story goes beyond the ordinary.

The reason I looked up Rembrandtsz is that I ran into the following mention in a seminal book about Descartes, by Geneviève Rodis-Lewis (Calmann-Lévy, 1995). I did not know about Rodis-Lewis herself even though I now realize she was an impressive personality with a remarkable if difficult career (there is an entry about her in French Wikipedia). Here is the relevant extract from her book (pages 255-256), part of the story of Descartes’s years in the Netherlands. The translation is mine, as well as comments in brackets.

During the last years of his life in the Netherlands, Descartes had several opportunities to show [his] interest in people of very modest means. Baillet [Descartes’s first biographer, in the 17-th century] did not give the exact date of the first visit of a “peasant from Holland”, a “shoemaker” by trade, who was studying mathematics in books in vulgar language. [That is to say, not in Latin, presumably in Dutch or French.] When he came for the first time to Egmond [Descartes’s residence] and asked to see Descartes, the servants sent him away. Dirk Rembrandtsz “came back two or three months later”, insisting on being brought in. “His external appearance did nothing to help him get a better reception than before.” Descartes was told, however, of the return of this “annoying beggar” who obviously “wanted to talk philosophy with the purpose of getting some alms”. “Descartes sent him some money, which he refused, saying that he hoped that a third journey would be more productive than the first two.” When Descartes heard about this answer, he gave orders to receive him. “Rembrandtsz came back a few months later” and Descartes was able to appreciate “his skill and merit”. He helped him overcome difficulties and shared his method with him. “He added him to the circle of his friends.” Rembrandtsz “became, through studying with Descartes, one of the premier astronomers of this century”.

I find this story moving. The passionate, stubborn autodidact, determined to reach the highest steps in science in spite of miserable circumstances. The rejection by the servants, from instinctive class-based prejudices. The great scientist’s ability to overcome such prejudice and recognize a kindred, noble spirit and his devotion to the pursuit of knowledge. His generosity, his openness, his availability in spite of the many demands on his time. His encouragement to a young, unknown disciple. The numerous encounters which begin as lessons from a master and evolve towards a relationship of peers. And the later success of the aspiring scientist.

It is customary for an article to carry some kind of lesson or moral. This one does not. Or to be more exact it does have a lesson, several perhaps, but they are left to the reader to draw.

It is also customary, for an article that is written as a tribute to deceased people, that the writer would have known them. I never knew the protagonists of my chronicle. But my sister and I — along with a dear cousin, and I hope her children and grandchildren — are among the few people who still know they existed. Hence the need for a tribute lest the last traces of their stay on earth vanish forever.

They were German: Louis Bernheimer, born on 5 December 1875 in Issenhausen in Alsace, then part of Germany, and his wife Paola, born in Bayreuth on 12 February 1879, yes, that same Bayreuth where Wagner had premièred his quintessential German opera, Das Rheingold, three years before. They were German and seemingly, as we shall see, very German.

I know little about them, nothing else in fact than reported in this little note. One thing I do know is the nickname by which people in Paris called them behind their backs: “Mr. and Mrs. Bei Uns”. I know it because my father mentioned it to me. Just once, a long time ago, but I remember.

We need a bit of context. Herr und Frau Bernheimer flew Nazi Germany in the thirties with their son Fred, a young professional photographer, and settled to a safe place, or a place they thought was safe: Paris. There Fred met my father’s sister Éliane and married her; they had two children, my cousins. Now we are talking about the only people in this story whom I did know. Éliane was a strong personality, a dedicated feminist and activist. When her husband was hit with cancer and she abruptly found herself a widow with two young children and no resources, she took over his photography studio, learned the trade — about which she had known nothing — and made the business prosper. After the war, Studio Bernheim (the name shortened so that it would sound less German) became one of the fashionable addresses in Paris, thanks to both Éliane and her son Marc who trained himself to become its chief photographer while still a teenager.

Bei uns in German means the same as “chez nous” in French and translates as “at our home”, although that is not a good translation because English lacks a preposition that would accurately reflect the French “chez” or (in that sense) the German “bei”, which mean something like “in the home of”.  “Home” in a very intense and cozy sense, not just the physical house, but encompassing culture, country, community. Russians similarly say “U Nas”, literally “at ours” and, when talking about people, “Nashi”, literally “ours”, our people that is. In a Chekhov novella entitled  A boring story (full text available online here), when the antisemitic narrator wants to mention that at the theater last night the person seated in front of him was a Jew, he says that he was sitting behind an “iz nasikh”, a deformation with a fake Jewish accent of “iz nashikh”, one from our own, to suggest — ironically in light of the rest of my own boring story — a member of a tightly knit community.

It seems that the Bernheimers (to come back to them) were seen by their new extended family as stuffy Germans fitting the stereotypes. Not just stuffy: critical. Apparently, they went around commenting that whatever was being done in their new French surroundings was not being done right, and explaining the way it was done back home, “bei uns”. If so, it was perhaps not the best way to ingratiate themselves with their hosts, and it is not surprising that people in the family started referring to them acerbically, according to my father, as Mr. and Mrs. Bei Uns.

As noted, I never knew the Bernheimers, although in a different turn of the story I would — I should — have known them as a child. Therefore I cannot guess whether I would have yielded to family opinions and found them insufferable, or liked them as delightful, exotic older relatives having gone through hard times and now doting on their children, grandchildren, nephews and nieces. Maybe both. I feel a certain remote sympathy for them in any case, having probably been resented, like anyone who has lived in countries where people insist on the “korrekt” way of doing things and comes back to more lackadaisical cultures, as a bit of a Mr. Bei Uns myself.

The irony is that in the eyes of many people, including many who would never consider themselves antisemites, Jews still have the reputation of harboring a feeling of  solidarity with their own kin that transcends borders and trumps national allegiance. Here we have the reverse. Highly assimilated families on both sides, French Jews and German Jews, getting into a cultural conflict because some were French and some were German. Ever since the revolution emancipated French Jews, they have been passionately French. German Jews were just as passionately German (in the style of Heinrich Heine’s I think of Germany in the night, the poem entitled Nachtgedanken, written in exile in Paris, see its text here).  French Jews do not ask themselves how French their are, since their Frenchness is as obvious to them as the air they breathe; it’s others who want them to prove it again and again — something that no one ever seems to require of people from certain regions of France such as Brittany whose inhabitants have a loudly proclaimed attachment to their terroir of origin. Unbelievably, the question still resurfaces regularly; it is even a theme in the current presidential campaign.

Why did I never get to decide by myself who Mr. and Mrs. Bei Uns really were: chauvinistic scolds, or a charming old-world couple? If they thought of themselves as German, as part of “uns”, the “uns” ruling Germany had a different understanding. When Germany invaded France in 1940, the Bernheimers flew, like many others, to the South of France, which until 1942 remained a supposedly “free” zone. Then the Germans invaded the “free” zone too. In August of 1943 Mr. and Mrs Bei Uns were rounded up near Bayonne. The town is close to the Spanish border; I do not know if they had hoped to cross over, as others managed to do. They were interned in the Mérignac camp, where Bordeaux airport lies today. From Bordeaux they were transferred to the infamous camp at Drancy, near Paris. From there they were put on convoy number 26 to Auschwitz, where they were murdered.

Science progresses through people taking advantage of others’ insights and inventions. One of the conditions that makes the game possible is that you acknowledge what you take. For the originator, it is rewarding to see one’s ideas reused, but frustrating when that happens without acknowledgment, especially when you are yourself punctilious about citing your own sources of inspiration.

I have started to record some concepts that are widely known and applied today and which I believe I originated in whole or in part, whether or not their origin is cited by those who took them. The list below is not complete and I may update it in the future. It is not a list of ideas I contributed, only of those fulfilling two criteria:

• Others have built upon them.  (If there is an idea that I think is great but no one paid attention to it, the list does not include it.)
• They have gained wide visibility.

There is a narcissistic aspect to this exercise and if people want to dismiss it as just showing I am full of myself so be it. I am just a little tired of being given papers to referee that state that genericity was invented by Java, that no one ever thought of refactoring before agile methods, and so on. It is finally time to state some facts.

Facts indeed: I back every assertion by precise references. So if I am wrong — i.e. someone preceded me — the claims of precedence can be refuted; if so I will update or remove them. All articles by me cited in this note are available (as downloadable PDFs) on my publication page. (The page is up to date until 2018; I am in the process of adding newer publications.)

Post-publication note: I have started to receive some comments and added them in a Notes section at the end; references to those notes are in the format [A].

Final disclaimer (about the narcissistic aspect): the exercise of collecting such of that information was new for me, as I do not usually spend time reflecting on the past. I am much more interested in the future and definitely hope that my next contributions will eclipse any of the ones listed below.

Programming concepts: substitution principle

Far from me any wish to under-represent the seminal contributions of Barbara Liskov, particularly her invention of the concept of abstract data type on which so much relies. As far as I can tell, however, what has come to be known as the “Liskov Substitution Principle” is essentially contained in the discussion of polymorphism in section 10.1 of in the first edition (Prentice Hall, 1988) of my book Object-Oriented Software Construction (hereafter OOSC1); for example, “the type compatibility rule implies that the dynamic type is always a descendant of the static type” (10.1.7) and “if B inherits from A, the set of objects that can be associated at run time with an entity [generalization of variable] includes instances of B and its descendants”.

Perhaps most tellingly, a key aspect of the substitution principle, as listed for example in the Wikipedia entry, is the rule on assertions: in a proper descendant, keep the invariant, keep or weaken the precondition, keep or strengthen the postcondition. This rule was introduced in OOSC1, over several pages in section 11.1. There is also an extensive discussion in the article Eiffel: Applying the Principles of Object-Oriented Design published in the Journal of Systems and Software, May 1986.

The original 1988 Liskov article cited (for example) in the Wikipedia entry on the substitution principle says nothing about this and does not in fact include any of the terms “assertion”, “precondition”, “postcondition” or “invariant”. To me this absence means that the article misses a key property of substitution: that the abstract semantics remain the same. (Also cited is a 1994 Liskov article in TOPLAS, but that was many years after OOSC1 and other articles explaining substitution and the assertion rules.)

Liskov’s original paper states that “if for each object o1 of type S there is an object o2 of type T such that for all programs P defined in terms of T, the behavior of P is unchanged when o1 is substituted for oz, then S is a subtype of T.” As stated, this property is impossible to satisfy: if the behavior is identical, then the implementations are the same, and the two types are identical (or differ only by name). Of course the concrete behaviors are different: applying the operation rotate to two different figures o1 and o2, whose types are subtypes of FIGURE and in some cases of each other, will trigger different algorithms — different behaviors. Only with assertions (contracts) does the substitution idea make sense: the abstract behavior, as characterized by preconditions, postconditions and the class invariants, is the same (modulo respective weakening and strengthening to preserve the flexibility of the different version). Realizing this was a major step in understanding inheritance and typing.

I do not know of any earlier (or contemporary) exposition of this principle and it would be normal to get the appropriate recognition.

Software design: design patterns

Two of the important patterns in the “Gang of Four” Design Patterns book (GoF) by Gamma et al. (1995) are the Command Pattern and the Bridge Pattern. I introduced them (under different names) in the following publications:

• The command pattern appears in OOSC1 under the name “Undo-Redo” in section 12.2. The solution is essentially the same as in GoF. I do not know of any earlier exposition of the technique. See also notes [B] and [C].

• The bridge pattern appears under the name “handle technique” in my book Reusable Software: The Base Component Libraries (Prentice Hall, 1994). It had been described several years earlier in manuals for Eiffel libraries. I do not know of an earlier reference. (The second edition of Object-Oriented Software Construction — Prentice Hall, 1997, “OOSC2” –, which also describes it, states that a similar technique is described in an article by Josef Gil and Ricardo Szmit at the TOOLS USA conference in the summer of 1994, i.e. after the publication of Reusable Software.)

Note that it is pointless to claim precedence over GoF since that book explicitly states that it is collecting known “best practices”, not introducing new ones. The relevant questions are: who, pre-GoF, introduced each of these techniques first; and which publications does the GoF cites as “prior art”  for each pattern. In the cases at hand, Command and Bridge, it does not cite OOSC1.

To be concrete: unless someone can point to an earlier reference, then anytime anyone anywhere using an interactive system enters a few “CTRL-Z” to undo commands, possibly followed by some “CTRL-Y” to redo them (or uses other UI conventions to achieve these goals), the software most likely relying on a technique that I first described in the place mentioned above.

Software design: Open-Closed Principle

Another contribution of OOSC1 (1988), section 2.3, reinforced in OOSC2 (1997) is the Open-Closed principle, which explained one of the key aspects of inheritance: the ability to keep a module both closed (immediately usable as is) and open to extension (through inheritance, preserving the basic semantics. I am mentioning this idea only in passing since in this case my contribution is usually recognized, for example in the Wikipedia entry.

Software design: OO for reuse

Reusability: the Case for Object-Oriented Design (1987) is, I believe, the first publication that clearly explained why object-oriented concepts were (and still are today — in Grady Booch’s words, “there is no other game in town”) the best answer to realize the goal of software construction from software components. In particular, the article:

• Explains the relationship between abstract data types and OO programming, showing the former as the theoretical basis for the latter. (The CLU language at MIT originated from Liskov’s pioneering work on abstract data types, but was not OO in the full sense of the term, missing in particular a concept of inheritance.)
• Shows that reusability implies bottom-up development. (Top-down refinement was the mantra at the time, and promoting bottom-up was quite a shock for many people.)
• Explains the role of inheritance for reuse, as a complement to Parnas’s interface-based modular construction with information hiding.

Software design: Design by Contract

The contribution of Design by Contract is one that is widely acknowledged so I don’t have any point to establish here — I will just recall the essentials. The notion of assertion goes back to the work of Floyd, Hoare and Dijkstra in the sixties and seventies, and correctness-by-construction to Dijktra, Gries and Wirth, but Design by Contract is a comprehensive framework providing:

• The use of assertions in an object-oriented context. (The notion of class invariant was mentioned in a paper by Tony Hoare published back in 1972.)
• The connection of inheritance with assertions (as sketched above). That part as far as I know was entirely new.
• A design methodology for quality software: the core of DbC.
• Language constructs carefully seamed into the fabric of the language. (There were precedents there, but in the form of research languages such as Alphard, a paper design only, not implemented, and Euclid.)
• A documentation methodology.
• Support for testing.
• Support for a consistent theory of exception handling (see next).

Design by Contract is sometimes taken to mean simply the addition of a few assertions here and there. What the term actually denotes is a comprehensive methodology with all the above components, tightly integrated into the programming language. Note in particular that preconditions and postconditions are not sufficient; in an OO context class invariants are essential.

Software design: exceptions

Prior to the Design by Contract work, exceptions were defined very vaguely, as something special you do outside of “normal” cases, but without defining “normal”. Design by Contract brings a proper perspective by defining these concepts precisely. This was explained in a 1987 article, Disciplined Exceptions ([86] in the list), rejected by ECOOP but circulated as a technical report; they appear again in detail in OOSC1 (sections 7.10.3 to 7.10.5).

Other important foundational work on exceptions, to which I know no real precursor (as usual I would be happy to correct any omission), addressed what happens to the outcome of an exception in a concurrent or distributed context. This work was done at ETH, in particular in the PhD theses  of B. Morandi and A. Kolesnichenko, co-supervised with S. Nanz. See the co-authored papers [345] and [363].

On the verification aspect of exceptions, see below.

Software design: refactoring

I have never seen a discussion of refactoring that refers to the detailed discussion of generalization in both of the books Reusable Software (1994, chapter 3) and Object Success (Prentice Hall, 1995, from page 122 to the end of chapter 6). These discussions describe in detail how, once a program has been shown to work, it should be subject to a posteriori design improvements. It presents several of the refactoring techniques (as they were called when the idea gained traction several years later), such as moving common elements up in the class hierarchy, and adding an abstract class as parent to concrete classes ex post facto.

These ideas are an integral part of the design methodology presented in these books (and again in OOSC2 a few later). It is beyond me why people would present refactoring (or its history, as in the Wikipedia entry on the topic) without referring to these publications, which were widely circulated and are available for anyone to inspect.

Software design: built-in documentation and Single-Product principle

Another original contribution was the idea of including documentation in the code itself and relying on tools to extract the documentation-only information (leaving implementation elements aside). The idea, described in detail in OOSC1 in 1988 (sections 9.4 and 9.5) and already mentioned in the earlier Eiffel papers, is that code should be self-complete, containing elements of various levels of abstraction; some of them describe implementation, but the higher-level elements describe specification, and are distinguished syntactically in such a way that tools can extract them to produce documentation at any desired level of abstraction.

The ideas were later applied through such mechanisms as JavaDoc (with no credit as far as I know). They were present in Eiffel from the start and the underlying principles, in particular the “Single Product principle” (sometimes “Self-Documentation principle”, and also generalized by J. Ostroff and R. Paige as “Single-Model principle”). Eiffel is the best realization of these principles thanks to:

• Contracts (as mentioned above): the “contract view” of a class (called “short form” in earlier descriptions) removes the implementations but shows the relevant preconditions, postconditions and class invariants, given a precise and abstract specification of the class.
• Eiffel syntax has a special place for “header comments”, which describe high-level properties and remain in the contract view.
• Eiffel library class documentation has always been based on specifications automatically extracted from the actual text of the classes, guaranteeing adequacy of the documentation. Several formats are supported (including, from 1995 on, HTML, so that documentation can be automatically deployed on the Web).
• Starting with the EiffelCase tool in the early 90s, and today with the Diagram Tool of EiffelStudio, class structures (inheritance and client relationships) are displayed graphically, again in an automatically extracted form, using either the BON or UML conventions.

One of the core benefits of the Single-Product principle is to guard against what some of my publications called the “Dorian Gray” syndrome: divergence of an implementation from its description, a critical problem in software because of the ease of modifying stuff. Having the documentation as an integral part of the code helps ensure that when information at some level of abstraction (specification, design, implementation) changes, the other levels will be updated as well.

Crucial in the approach is the “roundtripping” requirement: specifiers or implementers can make changes in any of the views, and have them reflected automatically in the other views. For example, you can graphically draw an arrow between two bubbles representing classes B and A in the Diagram Tool, and the code of B will be updated with “inherit A”; or you can add this Inheritance clause textually in the code of class B, and the diagram will be automatically updated with an arrow.

It is important to note how contrarian and subversive these ideas were at the time of their introduction (and still to some extent today). The wisdom was that you do requirements then design then implementation, and that code is a lowly product entirely separate from specification and documentation. Model-Driven Development perpetuates this idea (you are not supposed to modify the code, and if you do there is generally no easy way to propagate the change to the model.) Rehabilitating the code (a precursor idea to agile methods, see below) was a complete change of perspective.

I am aware of no precedent for this Single Product approach. The closest earlier ideas I can think of are in Knuth’s introduction of Literate Programming in the early eighties (with a book in 1984). As in the Single-product approach, documentation is interspersed with code. But the literate programming approach is (as presented) top-down, with English-like explanations progressively being extended with implementation elements. The Single Product approach emphasizes the primacy of code and, in terms of the design process, is very much yoyo, alternating top-down (from the specification to the implementation) and bottom-up (from the implementation to the abstraction) steps. In addition, a large part of the documentation, and often the most important one, is not informal English but formal assertions. I knew about Literate Programming, of course, and learned from it, but Single-Product is something else.

Software design: from patterns to components

Karine Arnout’s thesis at ETH Zurich, resulting in two co-authored articles ([255] and [257], showed that contrary to conventional wisdom a good proportion of the classical design patterns, including some of the most sophisticated, can be transformed into reusable components (indeed part of an Eiffel library). The agent mechanism (see below) was instrumental in achieving that result.

Programming, design and specification concepts: abstract data types

Liskov’s and Zilles’s ground-breaking 1974 abstract data types paper presented the concepts without a mathematical specification, using programming language constructs instead. A 1976 paper (number [3] in my publication list, La Description des Structures de Données, i.e. the description of data structures) was as far as I know one of the first to present a mathematical formalism, as  used today in presentations of ADTs. John Guttag was taking a similar approach in his PhD thesis at about the same time, and went further in providing a sound mathematical foundation, introducing in particular (in a 1978 paper with Jim Horning) the notion of sufficient completeness, to which I devoted a full article in this blog  (Are My Requirements Complete?) about a year ago. My own article was published in a not very well known journal and in French, so I don’t think it had much direct influence. (My later books reused some of the material.)

The three-level description approach of that article (later presented in English for an ACM workshop in the US in 1981, Pingree Park, reference [28]) is not well known but still applicable, and would be useful to avoid frequent confusions between ADT specifications and more explicit descriptions.

When I wrote my 1976 paper, I was not aware of Guttag’s ongoing work (only of the Liskov and Zilles paper), so the use of a mathematical framework with functions and predicates on them was devised independently. (I remember being quite happy when I saw what the axioms should be for a queue.) Guttag and I both gave talks at a workshop organized by the French programming language interest group in 1977 and it was fun to see that our presentations were almost identical. I think my paper still reads well today (well, if you read French). Whether or not it exerted direct influence, I am proud that it independently introduced the modern way of thinking of abstract data types as characterized by mathematical functions and their formal (predicate calculus) properties.

Language mechanisms: genericity with inheritance

Every once in a while I get to referee a paper that starts “Generics, as introduced in Java…” Well, let’s get some perspective here. Eiffel from its introduction in 1985 combined genericity and inheritance. Initially, C++ users and designers claimed that genericity was not needed in an OO context and the language did not have it; then they introduced template. Initially, the designers of Java claimed (around 1995) that genericity was not needed, and the language did not have it; a few years later Java got generics. Initially, the designers of C# (around 1999) claimed that genericity was not needed, and the language did not have it; a few years later C# and .NET got generics.

Genericity existed before Eiffel of course; what was new was the combination with inheritance. I had been influenced by work on generic modules by a French researcher, Didier Bert, which I believe influenced the design of Ada as well; Ada was the language that brought genericity to a much broader audience than the somewhat confidential languages that had such a mechanism before. But Ada was not object-oriented (it only had modules, not classes). I was passionate about object-oriented programming (at a time when it was generally considered, by the few people who had heard of it as an esoteric, academic pursuit). I started — in the context of an advanced course I was teaching at UC Santa Barbara — an investigation of how the two mechanisms relate to each other. The results were a paper at the first OOPSLA in 1986, Genericity versus Inheritance, and the design of the Eiffel type system, with a class mechanism, inheritance (single and multiple), and genericity, carefully crafted to complement each other.

With the exception of a Trellis-Owl, a  design from Digital Equipment Corporation also presented at the same OOPSLA (which never gained significant usage), there were no other OO languages with both mechanisms for several years after the Genericity versus Inheritance paper and the implementation of genericity with inheritance in Eiffel available from 1986 on. Eiffel also introduced, as far as I know, the concept of constrained genericity, the second basic mechanism for combining genericity with inheritance, described in Eiffel: The Language (Prentice Hall, 1992, section 10.8) and discussed again in OOSC2 (section 16.4 and throughout). Similar mechanisms are present in many languages today.

It was not always so. I distinctly remember people bringing their friends to our booth at some conference in the early nineties, for the sole purpose of having a good laugh with them at our poster advertising genericity with inheritance. (“What is this thing they have and no one else does? Generi-sissy-tee? Hahaha.”). A few years later, proponents of Java were pontificating that no serious language needs generics.

It is undoubtedly part of of the cycle of invention (there is a Schopenhauer citation on this, actually the only thing from Schopenhauer’s philosophy that I ever understood [D]) that people at some point will laugh at you; if it did brighten their day, why would the inventor deny them one of the little pleasures of life? But in terms of who laughs last, along the way C++ got templates, Java got generics, C# finally did too, and nowadays all typed OO languages have something of the sort.

Language mechanisms: multiple inheritance

Some readers will probably have been told that multiple inheritance is a bad thing, and hence will not count it as a contribution, but if done properly it provides a major abstraction mechanism, useful in many circumstances. Eiffel showed how to do multiple inheritance right by clearly distinguishing between features (operations) and their names, defining a class as a finite mapping between names and features, and using renaming to resolve any name clashes.

Multiple inheritance was made possible by an implementation innovation: discovering a technique (widely imitated since, including in single-inheritance contexts) to implement dynamic binding in constant time. It was universally believed at the time that multiple inheritance had a strong impact on performance, because dynamic binding implied a run-time traversal of the class inheritance structure, already bad enough for single inheritance where the structure is a tree, but prohibitive with multiple inheritance for which it is a directed acyclic graph. From its very first implementation in 1986 Eiffel used what is today known as a virtual table technique which guarantees constant-time execution of routine (method) calls with dynamic binding.

Language mechanisms: safe GC through strong static typing

Simula 67 implementations did not have automatic garbage collection, and neither had implementations of C++. The official excuse in the C++ case was methodological: C programmers are used to exerting manual control of memory usage. But the real reason was a technical impossibility resulting from the design of the language: compatibility with C precludes the provision of a good GC.

More precisely, of a sound and complete GC. A GC is sound if it will only reclaim unreachable objects; it is complete if it will reclaim all unreachable objects. With a C-based language supporting casts (e.g. between integers and pointers) and pointer arithmetic, it is impossible to achieve soundness if we aim at a reasonable level of completeness: a pointer can masquerade as an integer, only to be cast back into a pointer later on, but in the meantime the garbage collector, not recognizing it as a pointer, may have wrongly reclaimed the corresponding object. Catastrophe.

It is only possible in such a language to have a conservative GC, meaning that it renounces completeness. A conservative GC will treat as a pointer any integer whose value could possibly be a pointer (because it lies between the bounds of the program’s data addresses in memory). Then, out of precaution, the GC will refrain from reclaiming the objects at these addresses even if they appear unreachable.

This approach makes the GC sound but it is only a heuristics, and it inevitably loses completeness: every once in a while it will fail to reclaim some dead (unreachable) objects around. The result is a program with memory leaks — usually unacceptable in practice, particularly for long-running or continuously running programs where the leaks inexorably accumulate until the program starts thrashing then runs out of memory.

Smalltalk, like Lisp, made garbage collection possible, but was not a typed language and missed on the performance benefits of treating simple values like integers as a non-OO language would. Although in this case I do not at the moment have a specific bibliographic reference, I believe that it is in the context of Eiffel that the close connection between strong static typing (avoiding mechanisms such as casts and pointer arithmetic) and the possibility of sound and complete garbage collection was first clearly explained. Explained in particular around 1990 in a meeting with some of the future designers of Java, which uses a similar approach, also taken over later on by C#.

By the way, no one will laugh at you today for considering garbage collection as a kind of basic human right for programmers, but for a long time the very idea was quite sulfurous, and advocating it subjected you to a lot of scorn. Here is an extract of the review I got when I submitted the first Eiffel paper to IEEE Transactions on Software Engineering:

Systems that do automatic garbage collection and prevent the designer from doing his own memory management are not good systems for industrial-strength software engineering.

Famous last words. Another gem from another reviewer of the same paper:

I think time will show that inheritance (section 1.5.3) is a terrible idea.

Wow! I wish the anonymous reviewers would tell us what they think today. Needless to say, the paper was summarily rejected. (It later appeared in the Journal of Systems and Software — as [82] in the publication list — thanks to the enlightened views of Robert Glass, the founding editor.)

Language mechanisms: void safety

Void safety is a property of a language design that guarantees the absence of the plague of null pointer dereferencing.

The original idea came (as far as I know) from work at Microsoft Research that led to the design of a research language called C-omega; the techniques were not transferred to a full-fledged programming language. Benefiting from the existence of this proof of concept, the Eiffel design was reworked to guarantee void safety, starting from my 2005 ECOOP keynote paper (Attached Types) and reaching full type safety a few years later. This property of the language was mechanically proved in a 2016 ETH thesis by A. Kogtenkov.

Today all significant Eiffel development produces void-safe code. As far as I know this was a first among production programming languages and Eiffel remains the only production language to provide a guarantee of full void-safety.

This mechanism, carefully crafted (hint: the difficult part is initialization), is among those of which I am proudest, because in the rest of the programming world null pointer dereferencing is a major plague, threatening at any moment to crash the execution of any program that uses pointers of references. For Eiffel users it is gone.

Language mechanisms: agents/delegates/lambdas

For a long time, OO programming languages did not have a mechanism for defining objects wrapping individual operations. Eiffel’s agent facility was the first such mechanism or among the very first together the roughly contemporaneous but initially much more limited delegates of C#. The 1999 paper From calls to agents (with P. Dubois, M. Howard, M. Schweitzer and E. Stapf, [196] in the list) was as far as I know the first description of such a construct in the scientific literature.

Language mechanisms: concurrency

The 1993 Communications of the ACM paper on Systematic Concurrent Object-Oriented Programming [136] was certainly not the first concurrency proposal for OO programming (there had been pioneering work reported in particular in the 1987 book edited by Tokoro and Yonezawa), but it innovated in offering a completely data-race-free model, still a rarity today (think for example of the multi-threading mechanisms of dominant OO languages).

SCOOP, as it came to be called, was implemented a few years later and is today a standard part of Eiffel.

Language mechanisms: selective exports

Information hiding, as introduced by Parnas in his two seminal 1972 articles, distinguishes between public and secret features of a module. The first OO programming language, Simula 67, had only these two possibilities for classes and so did Ada for modules.

In building libraries of reusable components I realized early on that we need a more fine-grained mechanism. For example if class LINKED_LIST uses an auxiliary class LINKABLE to represent individual cells of a linked list (each with a value field and a “right” field containing a reference to another LINKABLE), the features of LINKABLE (such as the operation to reattach the “right” field) should not be secret, since LINKED_LIST needs them; but they should also not be generally public, since we do not want arbitrary client objects to mess around with the internal structure of the list. They should be exported selectively to LINKED_LIST only. The Eiffel syntax is simple: declare these operations in a clause of the class labeled “feature {LINKED_LIST}”.

This mechanism, known as selective exports, was introduced around 1989 (it is specified in full in Eiffel: The Language, from 1992, but was in the Eiffel manuals earlier). I think it predated the C++ “friends” mechanism which serves a similar purpose (maybe someone with knowledge of the history of C++ has the exact date). Selective exports are more general than the friends facility and similar ones in other OO languages: specifying a class as a friend means it has access to all your internals. This solution is too coarse-grained. Eiffel’s selective exports make it possible to define the specific export rights of individual operations (including attributes/fields) individually.

Language mechanisms and implementation: serialization and schema evolution

I did not invent serialization. As a student at Stanford in 1974 I had the privilege, at the AI lab, of using SAIL (Stanford Artificial Intelligence Language). SAIL was not object-oriented but included many innovative ideas; it was far ahead of its time, especially in terms of the integration of the language with (what was not yet called) its IDE. One feature of SAIL with which one could fall in love at first sight was the possibility of selecting an object and having its full dependent data structure (the entire subgraph of the object graph reached by following references from the object, recursively) stored into a file, for retrieval at the next section. After that, I never wanted again to live without such a facility, but no other language and environment had it.

Serialization was almost the first thing we implemented for Eiffel: the ability to write object.store (file) to have the entire structure from object stored into file, and the corresponding retrieval operation. OOSC1 (section 15.5) presents these mechanisms. Simula and (I think) C++ did not have anything of the sort; I am not sure about Smalltalk. Later on, of course, serialization mechanisms became a frequent component of OO environments.

Eiffel remained innovative by tackling the difficult problems: what happens when you try to retrieve an object structure and some classes have changed? Only with a coherent theoretical framework as provided in Eiffel by Design by Contract can one devise a meaningful solution. The problem and our solutions are described in detail in OOSC2 (the whole of chapter 31, particularly the section entitled “Schema evolution”). Further advances were made by Marco Piccioni in his PhD thesis at ETH and published in joint papers with him and M. Oriol, particularly [352].

Language mechanisms and implementation: safe GC through strong static typing

Simula 67 (if I remember right) did not have automatic garbage collection, and neither had C++ implementations. The official justification in the case of C++ was methodological: C programmers are used to exerting manual control of memory usage. But the real obstacle was technical: compatibility with C makes it impossible to have a good GC. More precisely, to have a sound and complete GC. A GC is sound if it will only reclaim unreachable objects; it is complete if it will reclaim all unreachable objects. With a C-based language supporting casts (e.g. between integers and pointers) and pointer arithmetic, it is impossible to achieve soundness if we aim at a reasonable level of completeness: a pointer can masquerade as an integer, only to be cast back into a pointer later on, but in the meantime the garbage collector, not recognizing it as a pointer, may have wrongly reclaimed the corresponding object. Catastrophe. It is only possible in such a language to have a conservative GC, which will treat as a pointer any integer whose value could possibly be a pointer (because its value lies between the bounds of the program’s data addresses in memory). Then, out of precaution, it will not reclaim the objects at the corresponding address. This approach makes the GC sound but it is only a heuristics, and it may be over-conservative at times, wrongly leaving dead (i.e. unreachable) objects around. The result is, inevitably, a program with memory leaks — usually unacceptable in practice.

Smalltalk, like Lisp, made garbage collection possible, but was not a typed language and missed on the performance benefits of treating simple values like integers as a non-OO language would. Although in this case I do not at the moment have a specific bibliographic reference, I believe that it is in the context of Eiffel that the close connection between strong static typing (avoiding mechanisms such as casts and pointer arithmetic) and the possibility of sound and complete garbage collection was first clearly explained. Explained in particular to some of the future designers of Java, which uses a similar approach, also taken over later on by C#.

By the way, no one will laugh at you today for considering garbage collection as a kind of basic human right for programmers, but for a long time it was quite sulfurous. Here is an extract of the review I got when I submitted the first Eiffel paper to IEEE <em>Transactions on Software Engineering:

Software engineering: primacy of code

Agile methods are widely and properly lauded for emphasizing the central role of code, against designs and other non-executable artifacts. By reading the agile literature you might be forgiven for believing that no one brought up that point before.

Object Success (1995) makes the argument very clearly. For example, chapter 3, page 43:

Code is to our industry what bread is to a baker and books to a writer. But with the waterfall code only appears late in the process; for a manager this is an unacceptable risk factor. Anyone with practical experience in software development knows how many things can go wrong once you get down to code: a brilliant design idea whose implementation turns out to require tens of megabytes of space or minutes of response time; beautiful bubbles and arrows that cannot be implemented; an operating system update, crucial to the project which comes five weeks late; an obscure bug that takes ages to be fixed. Unless you start coding early in the process, you will not be able to control your project.

Such discourse was subversive at the time; the wisdom in software engineering was that you need to specify and design a system to death before you even start coding (otherwise you are just a messy “hacker” in the sense this word had at the time). No one else in respectable software engineering circles was, as far as I know, pushing for putting code at the center, the way the above extract does.

Several years later, agile authors started making similar arguments, but I don’t know why they never referenced this earlier exposition, which still today I find not too bad. (Maybe they decided it was more effective to have a foil, the scorned Waterfall, and to claim that everyone else before was downplaying the importance of code, but that was not in fact everyone.)

Just to be clear, Agile brought many important ideas that my publications did not anticipate; but this particular one I did.

Software engineering: the roles of managers

Extreme Programming and Scrum have brought new light on the role of managers in software development. Their contributions have been important and influential, but here too they were for a significant part prefigured by a long discussion, altogether two chapters, in Object Success (1995).

To realize this, it is enough to read the titles of some of the sections in those chapters, describing roles for managers (some universal, some for a technical manager): “risk manager”, “interface with the rest of the world” (very scrummy!), “protector of the team’s sanity”, “method enforcer” (think Scrum Master), “mentor and critic”. Again, as far as I know, these were original thoughts at the time; the software engineering literature for the most part did not talk about these issues.

Software engineering: outsourcing

As far as I know the 2006 paper Offshore Development: The Unspoken Revolution in Software Engineering was the first to draw attention, in the software engineering community, to the peculiar software engineering challenges of distributed and outsourced development.

Software engineering: automatic testing

The AutoTest project (with many publications, involving I. Ciupa, A. Leitner, Y. Wei, M. Oriol, Y. Pei, M. Nordio and others) was not the first to generate tests automatically by creating numerous instances of objects and calling applicable operations (it was preceded by Korat at MIT), but it was the first one to apply this concept with Design by Contract mechanisms (without which it is of little practical value, since one must still produce test oracles manually) and the first to be integrated in a production environment (EiffelStudio).

Software engineering: make-less system building

One of the very first decisions in the design of Eiffel was to get rid of Make files.

Feldman’s Make had of course been a great innovation. Before Make, programmers had to produce executable systems manually by executing sequences of commands to compile and link the various source components. Make enabled them to instead  to define dependencies between components in a declarative way, resulting in a partial order, and then performed a topological sort to produce the sequence of comments. But preparing the list of dependencies remains a tedious task, particularly error-prone for large systems.

I decided right away in the design of Eiffel that we would never force programmers to write such dependencies: they would be automatically extracted from the code, through an exhaustive analysis of the dependencies between modules. This idea was present from the very the first Eiffel report in 1985 (reference [55] in the publication list): Eiffel programmers never need to write a Make file or equivalent (other than for non-Eiffel code, e.g. C or C++, that they want to integrate); they just click a Compile button and the compiler figures out the steps.

Behind this approach was a detailed theoretical analysis of possible relations between modules in software development (in many programming languages), published as the “Software Knowledge Base” at ICSE in 1985. That analysis was also quite instructive and I would like to return to this work and expand it.

Educational techniques: objects first

Towards an Object-Oriented Curriculum ( TOOLS conference, August 1993, see also the shorter JOOP paper in May of the same year) makes a carefully argued case for what was later called the Objects First approach to teaching programming. I would be interested to know if there are earlier publications advocating starting programming education with an OO language.

The article also advocated for the “inverted curriculum”, a term borrowed from work by Bernie Cohen about teaching electrical engineering. It was the first transposition of this concept to software education. In the article’s approach, students are given program components to use, then little by little discover how they are made. This technique met with some skepticism and resistance since the standard approach was to start from the very basics (write trivial programs), then move up. Today, of course, many introductory programming courses similarly provide students from day one with a full-fledged set of components enabling them to produce significant programs.

More recent articles on similar topics, taking advantage of actual teaching experience, are The Outside-In Method of Teaching Programming (2003) and The Inverted Curriculum in Practice (at ICSE 2006, with Michela Pedroni). The culmination of that experience is the textbook Touch of Class from 2009.

Educational techniques: Distributed Software Projects

I believe our team at ETH Zurich (including among others M. Nordio, J. Tschannen, P. Kolb and C. Estler and in collaboration with C. Ghezzi, E. Di Nitto and G. Tamburrelli at Politecnico di Milano, N. Aguirre at Rio Cuarto and many others in various universities) was the first to devise,  practice and document on a large scale (see publications and other details here) the idea of an educational software project conducted in common by student groups from different universities. It yielded a wealth of information on distributed software development and educational issues.

Educational techniques: Web-based programming exercises

There are today a number of cloud-based environments supporting the teaching of programming by enabling students to compile and test their programs on the Web, benefiting from a prepared environment (so that they don’t have to download any tools or prepare control files) and providing feedback. One of the first — I am not sure about absolute precedence — and still a leading one, used by many universities and applicable to many programming languages, is Codeboard.

The main developer, in my chair at ETH Zurich, was Christian Estler, supported in particular by M. Nordio and M. Piccioni, so I am only claiming a supporting role here.

Educational techniques: key CS/SE concepts

The 2001 paper Software Engineering in the Academy did a good job, I think, of defining the essential concepts to teach in a proper curriculum (part of what Jeannette Wing’s 2006 paper called Computational Thinking).

Program verification: agents (delegates etc.)

Reasoning about Function Objects (ICSE 2010, with M. Nordio, P. Müller and J. Tschannen) introduced verification techniques for objects representing functions (such as agents, delegates etc., see above) in an OO language. Not sure whether there were any such techniques before.

Specification languages: Z

The Z specification language has been widely used for formal development, particularly in the UK. It is the design of J-R Abrial. I may point out that I was a coauthor of the first publication on Z in English (1980),  describing a version that preceded the adaptation to a more graphical-style notation done later at Oxford. The first ever published description of Z, pertaining to an even earlier version, was in French, in my book Méthodes de Programmation (with C. Baudoin), Eyrolles, 1978, running over 15 pages (526-541), with the precise description of a refinement process.

Program verification: exceptions

Largely coming out of the PhD thesis of Martin Nordio, A Sound and Complete Program Logic for Eiffel (TOOLS 2009) introduces rules for dealing with exceptions in a Hoare-style verification framework.

Program verification: full library, and AutoProof

Nadia Polikarpova’s thesis at ETH, aided by the work of Carlo Furia and Julian Tschannen (they were the major contributors and my participation was less important), was as far as I know the first to produce a full functional verification of an actual production-quality reusable library. The library is EiffelBase 2, covering fundamental data structures.

AutoProof — available today, as a still experimental tool, through its Web interface, see here — relied on the AutoProof prover, built by the same team, and itself based on Microsoft Research’s Boogie and Z3 engines.

More

There are more concepts worthy of being included here, but for today I will stop here.

Notes

[A] One point of divergence between usual presentations of the substitution principle and the view in OOSC and my other publications is the covariance versus contravariance of routine argument types. It reflects a difference of views as to what the proper policy (both mathematically sound and practically usable) should be.

[B]  The GoF book does not cite OOSC for the command or bridge patterns. For the command pattern it cites (thanks to Adam Kosmaczewski for digging up the GoF text!) a 1985 SIGGRAPH paper by Henry Lieberman (There’s More to Menu Systems than Meets the Screen). Lieberman’s paper describes the notion of command object and mentions undoing in passing, but does not include the key elements of the command pattern (as explained in full in OOSC1), i.e. an abstract (deferred) command class with deferred procedures called (say) do_it and undo_it, then specific classes for each kind of command, each providing a specific implementation of those procedures, then a history list of commands supporting multiple-level undo and redo as explained in OOSC1. (Reading Lieberman’s paper with a 2021 perspective shows that it came tantalizingly close to the command pattern, but doesn’t get to it. The paper does talk about inheritance between command classes, but only to “define new commands as extensions to old commands”, not in the sense of a general template that can be implemented in many specific ways. And it does mention a list of objects kept around to enable recovery from accidental deletions, and states that the application can control its length, as is the case with a history list; but the objects in the list are not command objects, they are graphical and other objects that have been deleted.)

[C] Additional note on the command pattern: I vaguely remember seeing something similar to the OOSC1 technique in an article from a supplementary volume of the OOPSLA proceedings in the late eighties or early nineties, i.e. at the same time or slightly later, possibly from authors from Xerox PARC, but I have lost the reference.

[D] Correction: I just checked the source and learned that the actual Schopenhauer quote (as opposed to the one that is usually quoted) is different; it does not include the part about laughing. So much for my attempts at understanding philosophy.

What can you do to or with an algorithm? In other words, what is a good verb to substitute for the hyphen in   “— the algorithm”?

You can learn an algorithm. Discovering classical algorithms is a large part of the Bildungsroman of a computer scientist. Sorting algorithms, graph algorithms, parsing algorithms, numerical algorithms, matrix algorithms, graphical algorithms…

You can teach an algorithm. Whether a professor or just a team leader, you explain to others why the obvious solution is not always the right one. As when  I saw that someone had implemented the traversal part of a garbage collection scheme (the “mark” of mark-and-sweep) using a recursive algorithm. Recursion is a great tool, but not here: it needs a stack of unpredictable size, and garbage collection, which you trigger when you run out of space, is not precisely the moment to start wildly allocating memory. In comes the Deutsch-Schorr-Waite algorithm, which improbably (as if tightrope-walking) subverts the structure itself to find its way forth and back.

To teach it, you can dance an algorithm. Sounds strange, but Informatics Europe gave its 2013 education award to the “AlgoRhythmics” group from at Sapientia University in Romania, which  demonstrates algorithms using central-European dances; see their rendering of Merge Sort:

(Their page has more examples. I see that recently they expanded to other kinds of dance and will let you discover binary search as flamenco and backtracking as classical ballet.) More generally you can simulate or animate an algorithm.

You can admire an algorithm. Many indeed are a source of wonder. The inner beauty of topological sort, Levenshtein or AVL can leave no one indifferent.

You can improve an algorithm. At least you can try.

You can invent an algorithm. Small or large, ambitious or mundane, but not imagined yet by anyone. Devising a new algorithm is a sort of rite of passage in our profession. If it does prove elegant, useful and elegant, you’ll get a real kick (trust me). Then you can publish the algorithm.

You can prove an algorithm, that is to say, mathematically establish its correctness. It is indeed increasingly unreasonable to publish an algorithm without correctness arguments. Maybe I have an excuse here to advertize for an an article that examines important algorithms across a wide variety of fields and showcases their main claim to correctness: their loop invariants.

You can implement an algorithm. That is much of what we do in software engineering, even if as an OO guy I would immediately add “as part of the associated data structure”.

Of late, algorithms have come to be associated with yet another verb; one that I would definitely not have envisioned when first learning about algorithms in Knuth (the book) and from Knuth (the man — who most certainly does not use foul language).

You can fuck an algorithm.

Thousands of British students marched recently to that slogan:

chants of “fuck the algorithm” as a speaker talks of losing her place at medical school because she was downgraded. pic.twitter.com/P15jpuBscB

— huck (@HUCKmagazine) August 16, 2020

They were demonstrating against a formula (the Guardian gives the details) that decided on university admissions. The starting point for these events was a ministerial decision to select students not from their grades at exams (“A-level”), which could not take place because of Covid, but instead from their assessed performance in their schools. So far so good but the authorities decided to calibrate these results with parameters deduced from each school’s past performance. Your grade is no longer your grade: if Jill and Joan both got a B, but Jill’s school has been better at getting students into (say) Oxford in the past, then Jill’s B is worth more than Joan’s B.

The outcry was easy to predict, or should have been for a more savvy government. Students want to be judged by their own performance, not by the results of some other students they do not even know. Arguments that the sole concern was a legimitate one (an effort to compensate for possible grade inflation in some schools) ceased to be credible when it came out that on average the algorithm boosted grades from private schools by 4.7. No theoretical justification was going to be of much comfort anyway to the many students who had been admitted to the universities of their dreams on the basis of their raw grades, and after the adjustment found themselves rejected.

In the end, “Fuck the Algorithm!” worked. The government withdrew the whole scheme; it tried to lay the blame for the fiasco on the regulatory authority (Ofqual), fooling no one.

These U.K. events of August 2020 will mark a turning point in the relationship between computer science and society. Not for the revelation that our technical choices have human consequences; that is old news, even if we often pretend to ignore it. Not for the use of Information Technology as an excuse; it is as old (“Sorry, the computer does not allow that!”) as IT itself. What “Fuck the Algorithm!” highlights is the massive danger of the current rush to apply machine learning to everything.

As long as we are talking marketing campaigns (“customers who bought the product you just ordered also bought …”) or image recognition, the admiring mood remains appropriate. But now, ever more often, machine learning (usually presented as “Artificial Intelligence” to sound more impressive) gets applied to decisions affecting human lives. In the US, for example, machine-learning algorithms increasingly help judges make decisions, or make the decisions themselves. Following this slippery path is crazy and unethical. It is also dangerous, as the U.K. students’ reaction indicates.

Machine learning does what the name indicates: it reproduces and generalizes the dominant behaviors of the past. The algorithms have no notion of right and wrong; they just learn. When they affect societal issues, the potential for societal disaster is everywhere.

Amid all the enthusiasm generated by the elegant techniques invented by machine-learning pioneers over the last two decades, one barely encounters any serious reservation. Codes of ethics (from ACM and others) have little to contribute.

We should be careful, though. Either we get our act together and define exacting controls on the use of machine learning for matters affecting people’s fates, or we will see a massive rejection of algorithmic technology, the right parts along with the wrong ones.

The British students of the year 2020’s weird summer will not be the last ones to tell us to fuck the algorithm.

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

Another completely unexpected gem from the Viaje de Turquia (see the previous article on this blog): a 16-th century statement of the Dunning-Kruger effect!

An effect, of course, which has never been more visible than today (just watch the news).

Against Pedro, who narrates his travels and travails, the dialog sets two other characters, friends from his youth. They serve both as foils for Pedro, enabling his cleverness to shine — they are themselves not the brightest candles on the cake —, and as the embodiment of conventional wisdom. He occasionally gets really impatient with them, although always friendly, and at some point cites this ditty that he remembers from his youth in Spain:

Blind people want to see,

The deaf man wants to hear,

The fat man wants to slim,

The lame man wants to run.

For the fool there is no remedy:

Since he fancies that he knows,

He does not care to learn more.

Wow!

At this gloomy moment it is good to find a gem in an unexpected place.

I am reading (in translation) the Viaje de Turquia, or Turkish Voyage — literaly, Voyage of Turkey — a 16th-century epic dialog, whose authorship is disputed. It is a precious source of information on the period and rings throughout like a true story. The hero, Pedro, tells of his time as a prisoner of war of the Turks and the ignominies he had to suffer for years. He is a doctor, if a self-taught one, and has cured many members of the Pasha’s entourage, but at some point the Pasha, out of spite, sends him back to the harshest form of manual labor. One of his former patients, rich and high-ranked, spots him, the intellectual struggling to move heavy materials in the dirt and under the whip, and mocks him:

Hey, all the philosophy of Aristotle and Plato, all the medical science of Galen, all the eloquence of Cicero and Demosthenes, how have they helped you?

To which Pedro, having put his sack on his shoulder and wiped the tears caused by this pique, answers, looking him straight in the eye:

They have helped me live through days like this one.

Pretty good, I thought. Not just the sense of repartee, but the sentiment itself (echoing by the comments of many a mistreated intellectual in later ages including ours).

Not only that, but it worked, at least for a while. So astounded was the persecutor by the retort, that he took Pedro’s sack to carry it himself, and convinced the Pasha to relieve Pedro from hard work and give him money.

Earlier this year I was in Sofia for a conference, at the main university (Saint Kliment) which in the entrance hall had an exhibition about its history. There was this student poster and song from I think around 1900:

I like the banner (what do you think?). It even has the correct Latin noun and verb plurals.

Anyone know where to find a university today with that kind of students, that kind of slogan, that kind of attitude and that kind of grammar? Please send me the links.

Imagine having had coffee, over the years, with each of Euclid, Galileo, Descartes, Marie Curie, Newton, Einstein, Lise Leitner, Planck and de Broglie. For a computer scientist, if we set aside the founding generation (the Turings and von Neumanns), the equivalent is possible. I have had the privilege of meeting and in some cases closely interacting with pioneer scientists, technologists and entrepreneurs, including Nobel, Fields and Turing winners, Silicon-Valley-type founders and such. It is only fair that I should share some of the traits I have observed in them.

Clarification and disclaimer:

• This discussion is abstract and as a result probably boring because I am not citing anyone by name (apart from a few famous figures, most of whom are dead and none of whom I have met). It would be more concrete and lively if I buttressed my generalities by actual examples, of which I have many. The absence of any name-dropping is a matter of courtesy and respect for people who have interacted with me unguardedly as a colleague, not a journalist preparing a tell-all book. I could of course cite the names for positive anecdotes only, but that would bias the story (see point 4). So, sorry, no names (and I won’t relent even if you ask me privately — mumm like a fish).
• I am looking at truly exceptional people. They are drawn from a more general pool of brilliant, successful scientists and technologists, of which they form only a small subset. Many of their traits also apply to this more general community and to highly successful people in any profession. What interests me is the extra step from brilliant to exceptional. It would not be that difficult to identify fifty outstanding mathematics researchers in, say, 1900, and analyze their psychological traits. The question is: why are some of them Hilbert and Poincaré, and others not?
• Of course I do not even begin to answer that question. I only offer a few personal remarks.
• More generally, cargo cult does not work. Emulating every one of the traits listed below will not get you a Nobel prize. You will not turn into a great composer by eating lots of Tournedos Rossini. (Well, you might start looking like the aging Rossini.) This note presents some evidence; it does not present any conclusion, let alone advice. Any consequence is for you to draw, or not.
• The traits obviously do not universally characterize the population observed. Not all of the people exhibit all of the traits. On the other hand, my impression is that most exhibit most.

1 Idiosyncratic

“Idiosyncratic” is a high-sounding synonym for “diverse,” used here to deflect the ridicule of starting a list of what is common to those people by stating that they are different from each other. The point is important, though, and reassuring. Those people come in all stripes, from the stuffy professor to the sandals-shorts-and-Hawaiian-shirt surfer.  Their ethnic backgrounds vary. And (glad you asked) some are men and some are women.

Consideration of many personality and lifestyle features yields no pattern at all. Some of the people observed are courteous, a delight to deal with, but there are a few jerks too. Some are voluble, some reserved. Some boastful, some modest. Some remain for their full life married to the same person, some have been divorced many times, some are single. Some become CEOs and university presidents, others prefer the quieter life of a pure researcher. Some covet honors, others are mostly driven by the pursuit of knowledge. Some wanted to become very rich and did, others care little about money.  It is amazing to see how many traits appear irrelevant, perhaps reinforcing the value of those that do make a difference.

2 Lucky

In trying to apply a cargo-cult-like recipe, this one would be the hardest to emulate. We all know that Fleming came across penicillin thanks to a petri dish left uncleaned on the window sill; we also know that luck favors only the well-prepared: someone other than Fleming would have grumbled at the dirtiness of the place and thrown the dish into the sink. But I am not just talking about that kind of luck. You have to be at the right place at the right time.

Read the biographies, and you will see that almost always the person happened to study with a professor who just then was struggling with a new problem, or did an internship in a group that had just invented a novel technique, or heard about recent results before everyone else did.

Part of what comes under “luck” is luck in obtaining the right education. Sure, there are a few autodidacts, but most of the top achievers studied in excellent institutions.

Success comes from a combination of nature and nurture. The perfect environment, such as a thriving laboratory or world-class research university, is not enough; but neither is individual brilliance. In most cases it is their combination that produces the catalysis.

3 Smart

Laugh again if you wish, but I do not just mean the obvious observation that those people were clever in what they did. In my experience they are extremely intelligent in other ways too. They often possess deep knowledge beyond their specialties and have interesting conversations.

You approach them because of the fame they gained in one domain, and learn from them about topics far beyond it.

4 Human

At first, the title of this section is another cause for ridicule: what did you expect, extraterrestrials? But “human” here means human in their foibles too. You might expect, if not an extraterrestrial, someone of the oracle-of-Delphi or wizard-on-a-mountain type, who after a half-hour of silence makes a single statement perfect in its concision and exactitude.

Well, no. They are smart, but they say foolish things too. And wrong things. Not only do they say them, they even publish them. (Newton wasted his brilliance on alchemy. Voltaire — who was not a scientist but helped promote science, translating Newton and supporting the work of Madame du Châtelet — wasted his powerful wit to mock the nascent study of paleontology: so-called fossils are just shells left over by picnicking tourists! More recently, a very famous computer scientist wrote a very silly book — of which I once wrote, fearlessly, a very short and very disparaging review.)

So what? It is the conclusion of the discussion that counts, not the meanderous path to it, or the occasional hapless excursion into a field where your wisdom fails you. Once you have succeeded, no one will care how many wrong comments you made in the process.

It is fair to note that the people under consideration probably say fewer stupid things than most. (The Erich Kästner ditty from an earlier article applies.) But no human, reassuringly perhaps, is right 100% of the time.

What does set them apart from many people, and takes us back to the previous trait (smart), is that even those who are otherwise vain have no qualms recognizing  mistakes in their previous thinking. They accept the evidence and move on.

5 Diligent

Of two people, one an excellent, top-ranked academic, the other a world-famous pioneer, who is the more likely to answer an email? In my experience, the latter.

Beyond the folk vision of the disheveled, disorganized, absent-minded professor lies the reality of a lifetime of rigor and discipline.

This should not be a surprise. There is inspiration, and there is perspiration.  Think of it as the dual of the  broken-windows theory, or of the judicial view that a defendant who lies in small things probably lies in big things: the other way around, if you do huge tasks well, you probably do small tasks well too.

6 Focused

Along with diligence comes focus, carried over from big matters to small matters. It is the lesser minds that pretend to multiplex. Great scientists, in my experience, do not hack away at their laptops during talks, and they turn off their cellphones. They choose carefully what they do (they are deluged with requests and learn early to say no), but what they accept to do they do. Seriously, attentively, with focus.

A fascinating spectacle is a world-famous guru sitting in the first row at a conference presentation by a beginning Ph.D. student, and taking detailed notes. Or visiting an industrial lab and quizzing a junior engineer about the details of the latest technology.

For someone who in spite of the cargo cult risk is looking for one behavior to clone, this would be it. Study after study has shown that we only delude ourselves in thinking we can multiplex. Top performers understand this. In the seminar room, they are not the ones doing email. If they are there at all, then watch and listen.

7 Eloquent

Top science and technology achievers are communicators. In writing, in speaking, often in both.

This quality is independent from their personal behavior, which can cover the full range from shy to boisterous.  It is the quality of being articulate. They know how to convey their results — and often do not mind crossing the line to self-advertising. It is not automatically the case that true value will out: even the most impressive advances need to be pushed to the world.

The alternative is to become Gregor Mendel: he single-handedly discovered the laws of genetics, and was so busy observing the beans in his garden that no one heard about his work until some twenty years after his death. Most of us prefer to get the recognition earlier. (Mendel was a monk, so maybe he believed in an afterlife; yet again maybe he, like everyone else, might have enjoyed attracting interest in this world first.)

In computer science it is not surprising that many of the names that stand out are of people who have written seminal books that are a pleasure to read. Many of them are outstanding teachers and speakers as well.

8 Open

Being an excellent communicator does not mean that you insist on talking. The great innovators are excellent listeners too.

Some people keep talking about themselves. They exist in all human groups, but this particular trait is common among scientists, particularly junior scientists, who corner you and cannot stop telling you about their ideas and accomplishments. That phenomenon is understandable, and in part justified by an urge to avoid the Mendel syndrome. But in a conversation involving some less and some more recognized professionals it is often the most accomplished members of the group who talk least. They are eager to learn. They never forget that the greatest insighs can start with a casual observation from an improbable source. They know when to talk, and when to shut up and listen.

Openness also means intellectual curiosity, willingness to have your intellectual certainties challenged, focus on the merit of a comment rather than the commenter’s social or academic status, and readiness to learn from disciplines other than your own.

9 Selfish

People having achieved exceptional results were generally obsessed with the chase and the prey. They are as driven as an icebreaker ship in the Sea of Barents. They have to get through; the end justifies the means; anything in the way is collateral damage.

So it is not surprising, in the case of academics, to hear colleagues from their institutions mumble that X never wanted to do his share, leaving it to others to sit in committees, teach C++ to biology majors and take their turn as department chair. There are notable exceptions, such as the computer architecture pioneer who became provost then president at Stanford before receiving the Turing Award. But  you do not achieve breakthroughs by doing what everything else is doing. When the rest of the crowd is being sociable and chatty at the conference party long into the night, they go back to their hotel to be alert for tomorrow’s session. A famous if extreme case is Andrew Wiles, whom colleagues in the department considered a has-been, while he was doing the minimum necessary to avoid trouble while working secretly and obsessively to prove Fermat’s last theorem.

This trait is interesting in light of the soothing discourse in vogue today. Nothing wrong with work-life balance, escaping the rat race, perhaps even changing your research topic every decade (apparently the rule in some research organizations). Sometimes a hands-off, zen-like attitude will succeed where too much obstination would get stuck. But let us not fool ourselves: the great innovators never let go of the target.

10. Generous

Yes, selfishness can go with generosity. You obsess over your goals, but it does not mean you forget other people.

Indeed, while there are a few solo artists in the group under observation, a striking feature of the majority is that in addition to their own achievements they led to the creation of entire communities, which often look up to them as gurus. (When I took the comprehensive exam at Stanford, the first question was what the middle initial “E.” of a famous professor stood for. It was a joke question, counting for maybe one point out of a hundred, helpfully meant to defuse students’ tension in preparation for the hard questions that followed. But what I remember is that every fellow student whom I asked afterwards knew the answer. Me too. Such was the personality cult.) The guru effect can lead to funny consequences, as with the famous computer scientist whose disciples you could spot right away in conferences by their sandals and beards (I do not remember how the women coped), carefully patterned after the master’s.

The leader is often good at giving every member of that community flattering personal attention. In a retirement symposium for a famous professor, almost every person I talked too was proud of having developed a long-running, highly personal and of course unique relationship with the honoree. One prestigious computer scientist who died in the 80’s encouraged and supported countless young people in his country; 30 years later, you keep running into academics, engineers and managers who tell you that they owe their career to him.

Some of this community-building can be self-serving and part of a personal strategy for success. There has to be more to it, however. It is not just that community-building will occur naturally as people discover the new ideas: since these ideas are often controversial at first, those who understood their value early band together to defend them and support their inventor. But there is something else as well in my observation: the creators’ sheer, disinterested generosity.

These people are passionate in their quest for discovery and creation and genuinely want to help others. Driven and self-promoting they may be, but the very qualities that led to their achievements — insight, intellectual courage, ability to think beyond accepted ideas — are at the antipodes of pettiness and narrow-mindedness. A world leader cannot expect any significant personal gain from spotting and encouraging a promising undergraduate, telling a first-time conference presenter that her idea is great and worth pushing further, patiently explaining elementary issues to a beginning student, or responding to a unknown correspondent’s emails. And still, as I have observed many times, they do all of this and more, because they are in the business of advancing knowledge.

These are some of the traits I have observed. Maybe there are more but, sorry, I have to go now. The pan is sizzling and I don’t like my tournedos too well-done.

(Originally published on CACM blog.)

An article published here a few years ago, reproducing a note I wrote much earlier (1992), pointed out that conventional wisdom about the history of software engineering, cited in every textbook, is inaccurate: the term “software engineering” was in use before the famous 1968 Garmisch-Partenkichen conference. See that article for details.

Recently a colleague wanted to cite my observation but could not find my source, a 1966 Communications of the ACM article using the term. Indeed that text is not currently part of the digitalized ACM archive (Digital Library). But I knew it was not a figment of my imagination or of a bad memory.

The reference given in my note is indeed correct; with the help of the ETH library, I was able to get a scan of the original printed article. It is available here.

The text is not a regular CACM article but a president’s letter, part of the magazine’s front matter, which the digital record does not always include. In this case historical interest suggests it should; I have asked the ACM to add it. In the meantime, you can read the scanned version for  a nostalgic peek into what the profession found interesting half a century ago.

Note (12 November 2018): The ACM Digital Library responded (in a matter of hours!) and added the letter to the digital archive.

(Revised from an article originally published in the CACM blog. Part 2 of a two-part article.)

Part 1 of this article (to be found here, please read it first) made fun of authors who claim that software engineering is a total failure — and, like everyone else, benefit from powerful software at every step of their daily lives.

Catastrophism in talking about software has a long history. Software engineering started around 1966 [1] with the recognition of a “software crisis“. For many years it was customary to start any article on any software topic by a lament about the terrible situation of the field, leaving in your reader’s mind the implicit suggestion that the solution to the “crisis” lay in your article’s little language or tool.

After the field had matured, this lugubrious style went out of fashion. In fact, it is hard to sustain: in a world where every device we use, every move we make and every service we receive is powered by software, it seems a bit silly to claim that in software development everyone is wrong and everything is broken.

The apocalyptic mode has, however, made a comeback of late in the agile literature, which is fond in particular of citing the so-called “Chaos” reports. These reports, emanating from Standish, a consulting firm, purport to show that a large percentage of projects either do not produce anything or do not meet their objectives. It was fashionable to cite Standish (I even included a citation in a 2003 article), until the methodology and the results were thoroughly debunked starting in 2006 [2, 3, 4]. The Chaos findings are not replicated by other studies, and the data is not available to the public. Capers Jones, for one, publishes his sources and has much more credible results.

Yet the Chaos results continue to be reverently cited as justification for agile processes, including, at length, in the most recent book by the creators of Scrum [5].

Not long ago, I raised the issue with a well-known software engineering author who was using the Standish findings in a talk. Wasn’t he aware of the shakiness of these results? His answer was that we don’t have anything better. It did not sound like the kind of justification we should use in a mature discipline. Either the results are sound, or we should not rely on them.

Software engineering is hard enough and faces enough obstacles, so obvious to everyone in the industry and to every user of software products, that we do not need to conjure up imaginary scandals and paint a picture of general desolation and universal (except for us, that is) incompetence. Take Schwaber and Sutherland, in their introductory chapter:

You have been ill served by the software industry for 40 years—not purposely, but inextricably. We want to restore the partnership.

No less!

Pretending that the whole field is a disaster and no one else as a clue may be a good way to attract attention (for a while), but it is infantile as well as dishonest. Such gross exaggerations discredit their authors, and beyond them, the ideas they promote, good ones included.

As software engineers, we can in fact feel some pride when we look at the world around us and see how much our profession has contributed to it. Not just the profession as a whole, but, crucially, software engineering research: advances in programming methodology, software architecture, programming languages, specification techniques, software tools, user interfaces, formal modeling of software concepts, process management, empirical analysis and human aspects of computing have, step after step, belied the dismal picture that may have been painfully accurate in the early days.

Yes, challenges and unsolved problems face us at every corner of software engineering. Yes, we are still at the beginning, and on many topics we do not even know how to proceed. Yes, there are lots of things to criticize in current practices (and I am not the least vocal of the critics, including in this blog). But we need a sense of measure. Software engineering has made tremendous progress over the last five decades; neither the magnitude of the remaining problems nor the urge to sell one’s products and services justifies slandering the rest of the discipline.

Notes and references

[1] Not in 1968 with the NATO conference, as everyone seems to believe. See an earlier article in this blog.

[2] Robert L. Glass: The Standish report: does it really describe a software crisis?, in Communications of the ACM, vol. 49, no. 8, pages 15-16, August 2006; see here.

[3] J. Laurens Eveleens and Chris Verhoef: The Rise and Fall of the Chaos Report Figures, in IEEE Software, vol. 27, no. 1, Jan-Feb 2010, pages 30-36; see here.

[4] S. Aidane, The “Chaos Report” Myth Busters, 26 March 2010, see here.

[5] Ken Schwaber and Jeff Sutherland: Software in 30 Days: How Agile Managers Beat the Odds, Delight Their Customers, And Leave Competitors In the Dust, Wiley, 2012.

On April 11 I gave the “Ershov lecture” in Novosibirsk. I talked about concurrency; a video recording is available here.

The lecture is given annually in memory of Andrey P. Ershov, one of the founding fathers of Russian computer science and originator of many important concepts such as partial evaluation. According to Wikipedia, Knuth considers Ershov to be the inventor of hashing. I was fortunate to make Ershov’s acquaintance in the late seventies and to meet him regularly afterwards. He invited me to his institute in Novosibirsk for a two-month stay where I learned a lot. He had a warm, caring personality, and set many young computer scientists in their tracks. His premature death in 1988 was a shock to all and his memory continues to be revered; it was gratifying to be able to give the lecture named in his honor.

A few years back my mother started writing her memoirs. She only completed a few chapters, hand-written, and I offered to type them up. There was not enough material to approach a publisher (my fault, for not pushing her to write more); the text has remained unpublished. I am making it available now: see here.

It is in French; if there is enough interest I will translate it. (Although the text is not very long, it is well written so the translation should be done carefully.) For reference I have included below the entry about my mother in one of many books about the period.

Here as a taste of her text is a translation of a short extract from chapter 5 (Grenoble, 1942, where her mission in the resistance network was to find safe havens for Jewish children):

 Along with hosting families there were religious boarding schools, and I should pay homage to a young Mother Superior, whose name I unfortunately forgot, who accepted some of our little girls cordially and without any afterthoughts. From schools for boys, however, how many rejections we had to suffer!

I also have to evoke that other Mother Superior, stern and dry, who after making me languish for several days while asking for the approval of her supervisors finally consented to see four or five little girls. I arrived with five of my charges, whom my neighbor had brought to me after their parents were arrested on that very morning. I can still see the high-ceilinged parlor, the crucifix on the wall, the freshly waxed and shining floor, the carefully polished furniture and a tiny figure with curly brown hair, all trembling: the eldest girl, who at the point of entering stepped back and burst into tears.  “One does not enter crying the house of the Holy Virgin Mary”, pronounced the Mother Superior, who had me take my little flock back to Grenoble, without further concerning herself with its fate.

And this note from the final chapter about the days of the Liberation of France, when under a false name she was working as a nurse for the Red Cross in the Limoges area:

This time it was the collaborationists’ turn to flee. I almost became a victim in a tragicomic incident when once, doing my daily rounds, I had to show my papers to a young FFI [members of the internal resistance army], aged maybe eighteen, who claimed the papers were fakes. Indeed they were: I still had not been able to re-establish my true identity. I tried to explain that as a Jew I had had to live under a borrowed name. He answered that by now all the “collabos” claimed to be Jewish to escape the wrath of the people…

 To understand the note that follows it is necessary to know a bit about the history of the period: the Drancy camp, OSE (see the Wikipedia entry), the Garel network. For the 100-th anniversary of OSE a documentary film was produced, featuring my mother among the interviewees; see a short reference to the movie here.

Biographical entry

From: Organisation juive de combat — Résistance / Sauvetage (Jewish Combat Organization: Resistance and Rescue), France 1940-1945, under the direction of Jean Brauman, Georges Loinger and Frida Wattenberg, Éditions Autrement, Paris, 2002.
Comments in brackets […] are by me (BM).

Name: Meyer née Kahn, Madeleine
Born 22 May 1914 in Paris
Resistance networks: Garel
Resistance period: from 1941 to the Liberation: Rivesaltes (Pyrénées-Orientales), Font-Romeu (Pyrénées-Orientales), Masgelier (Creuse), Lyons, Grenoble, Limoges
Supervisors: Andrée Salomon, Georges Garel

In July of 1942, Madeleine Kahn was sent by Andrée Salomon and Georges Garel to work at Rivesaltes [a horrendous “transit camp”, see here] as a social worker. She worked there for several weeks and helped improve the life of people interned there; she managed to extricate from the camp a number of children that she took to Perpignan and moved to several hosting places such as Font-Romeu and Le Masgelier. In Le Masgelier [a center that hosted Jewish children], she was assigned the mission of convoying to Marseilles, for emigration to the United States, Jewish children who were of foreign origin and hence in a particularly dangerous situation. [These were children from Jewish families that had fled Germany and Austria after Hitler’s accession to power and were particular sought by the Nazis.] The local authorities had put them up in the castle of Montgrand, already used as a hosting camp for elderly Austrian refugees. The Germans’ arrival  into the Southern half of France [until 1942 they were only occupying the Northern half of the country] abruptly stopped the departures for the US, and the authorities changed the children’s status to prisoners, held in appalling conditions. Madeleine Kahn remained alone with the children. All escape attempts failed. They were only freed after a long time, and sent back in some cases to their families and in others to Le Masgelier.

In November of 1942, Georges Garel and Andrée Salomon put Madeleine Kahn in charge of organizing the reception and hiding of children in the Isère area [the region around Grenoble], which by then was still part of the Italian-occupied zone. [Italian occupation was generally felt much lighter than the German one, in particular regarding persecution of Jews.] The mission was to find hosting families or religious institutions, catholic or protestant, and in advance of such placement to prepare the children to their new [false] identities and help separate them from their parents [when still alive and not deported]. It was also necessary to obtain the support of some authorities, such as Mme Merceron-Vicat from the child support administration and Sister Joséphine of Our Lady of Sion. After a while Madeleine was joined by Dr. Selinger and Herta Hauben, both of whom were eventually deported. Later on she collaborated with Fanny Loinger [another key name in the Jewish resistance], who for safety reasons took over in Isère and particularly in the Drôme.

After the departure of the Italians [and their replacement by the Germans], the situation became extremely dangerous and she had constantly to move the children around.

Warned that she was being tracked, Madeleine Kahn hurried to reclaim two babies that had been left in the La Tronche nursery. The director refused to give her Corinne, aged one, as earlier on three Germans had come for her, wanting to take her to Drancy [the collection point in France for the train convoys en route for Auschwitz], where her parents were being held. Upon seeing the child’s age, the Germans had left, announcing they would come back with a nurse. Instantly, Madeleine summons her friends in various [resistance] organizations and the process sets into motion: produce a fake requisition order in German with a fake seal stenciled from a war prisoner’s package; hire a taxi; make up a nurse’s uniform for Renée Schutz, German-born in Berlin as Ruth Schütz. Equipped with the requisition order, the false German nurse arrives at the nursery while Madeleine acts as a sentry to stop the Germans if needed. Corinne, the baby, is saved. [I became friends with her in the nineteen-seventies.]

The duped Germans were enraged. From an employee of the nursery they obtained Madeleine’s address, but she had left. The landlady gave them the address of Simone, Madeleine’s sister. [Simone was not a member of the network but knew all about it.] Interrogated under torture, she gave nothing away. All attempts to free her failed. She was deported to Auschwitz from where [adopting along the way an 8-year-old girl whose parents had already been deported, who clung to her, causing her to be treated like mothers with children, i.e. gassed immediately] she never returned.