“I don’t have time for administration”

Academic life includes self-governance and require people to sit in committees, take on various duties, serve as director of studies, graduate program director, chair of PhD chair of external relations, department vice chair or chair, dean…

Not everyone wants to play. It is not rare to encounter faculty members who tell you bluntly that as researchers they are too good to waste their time on boring organizational tasks that any mere mortal, or at least any mere academic, can fulfill.

This common situation came to my mind, as I was reading an outstanding new (2022) biography of Louis Pasteur by Michel Morange [1], when I came across the chapter on Pasteur’s return to the École Normale Supérieure in 1857. Excerpting and translating:

He was given two titles: administrator, and director of studies. The function of administrator consisted of supervising the life of students living on campus and to oversee the canteen as well as the dormitory rooms. It was part of his duties to check the correct operation of doors and windows, and to commission any necessary paintwork. He was more generally responsible for maintaining order inside the school and to monitor the student’s attire as well as their behavior.

Impressive! That was a time of highest scientific productivity for Pasteur (in spite of major personal tragedies), with one breathtaking discovery after the other, including anaerobiosis (life without air), pioneering studies of fermentation, preparing and performing numerous experiments, carefully refuting spontaneous generation… He was also a dedicated teacher, giving numerous lectures and exposing students to his research.

Remember Pasteur the next time a colleague tells you that his research is too indispensable to the progress of humankind to allow him to take on organizational tasks. If Pasteur could find time for his evening round of checking the dorm doors, for telling the students to dress better, and for overseeing new paint jobs, maybe you can be director of studies for the department for a couple of years.

Such willingness to take on management duties is part of the price academics pay for the many benefits of academic self-governance. The alternative is to be managed by bean-counting manager types who do not understand academia. Or, perhaps a more immediate risk, to let the bad scientists (who will find the time) take on these tasks. A look at thriving top universities usually reveals that, at the helm, there is a top scientist. Someone who succeeded in education and research and is devoting a few years to moving the institution forward. Lesser universities are managed by lesser academics. If the good people shirk their responsibilities, the bad ones will take over. Or is your research more important than Louis Pasteur’s?

 

References

[1] Michel Morange, Pasteur, Payot, 2022. In French. (Other books by Morange have been translated into English, particularly his History of Biology by Princeton University Press, but I do not know about this one.)

The path wrongly taken

The dominant discourse right now is “Calm down, this is just the normal game of democracy”. Actually, “this” is not the normal course of democracy. Everyone has experienced the disappointment of a favored candidate losing. The result of Tuesday is something else, not seen before in our lifetime: the triumph of indecency and the rout of decency.

There is in the world a general category of decent people, who as one of their characteristics seek out the company of other decent people. (“Elective affinities”.) They have been massively and perhaps decisively defeated.

What makes people decent is not that they never do bad things (although they perhaps strive not to do more of them than necessary), but that as much as possible they prefer certain things over their obverses. For example, they prefer:

  • Telling  the truth over lying.
  • Elegance over vulgarity.
  • Education over arrogant ignorance.
  • Arguments over insults.
  • Beauty over ugliness.
  • Joy over gloom.
  • Progress over regress.
  • Health over disease.
  • Financial well-being over widespread poverty.
  • Reason over mania.
  • Science over fables.
  • Helping others over hurting them.
  • Encouraging others over denigrating them.
  • Peace over war.
  • Respect over contempt.
  • Calm over violence.
  • Tolerance over intolerance.
  • Honesty over dishonesty.
  • Democracy over totalitarianism.
  • Freedom over slavery.
  • As an example of the last pair, women’s freedom over their submission to hateful men.
  • Kindness over cruelty.
  • Fairness over injustice.
  • Sanity over insanity.

(Again) those preferences do not mean that decent people never indulge in any of the second terms of these pairs, but that given a choice they will lean towards the first terms,  that they prefer the world to evolve in the direction of these first terms, and that they naturally associate with other people with similar preferences. The first terms all go well with each other (after all, what is science if not the dogged pursuit of truth? What is democracy if not the reign of tolerance?), and all the second terms go well with each other too, but until now it was exceedingly rare to see a  widely popular leader in a civilized country, and his zealots, deliberately embrace everything indecent and reject everything decent. At worst they would on the sly adopt a few indecencies here and there.

The pair elected yesterday is unique in the history of the United States by having deliberately, ostensibly and proudly chosen every second term. Every single one, many times, in the public’s full view, and under the cheers of their supporters.

That is why all decent people are desperate today. The desperation has nothing to do with matters of left versus right, or democrat versus republican, or higher taxes versus tax cuts, or the price of eggs, or any other political issue of substance.  It has everything to do with decency over indecency.

And particularly with truth over falsehood. The first of the above pairs largely subsumes the others: when society starts tolerating constant, blatant, enormous lies as if they were part of expected discourse, everything else falls out. Dictators understand this process well.

We hear that “no one knows what is going to happen”. Not so. We know something with certainty: catastrophes are coming our way. The only unknown is how many of them will hit us. For one thing the fight against climate change is doomed: all experts tell us that the change is not linear and that we have (we had) at best a few years to avoid the worst. As the US, the biggest  source of warming and emissions (although by no means the only large one), turns away from climate action, everyone else, beginning with China, will have an excellent excuse to do nothing. The consequences are horrendous to contemplate, and will be with us soon.  Another certain catastrophe is chaos in the US, merrily encouraged by its enemies. The part of the country that voted for sanity is defeated and despondent but not gone; come the first round of anti-constitutional measures, we may expect no end to clashes. Tens of millions of Americans are almost certainly going to lose their health insurance, going back to a situation unique in developed countries.  Women, denied abortion and resorting to back-alley substitutes, will die by the thousands. It is better not to think too much of what will happen to Ukraine now (and through a possible ricochet effect to Poland and the Baltic states).  Or of what would ensue in the case of a new health crisis, with loony anti-vaccine, anti-mask activists at the helm. Of what will take place at all levels of governments, with none of the “adults in the room” around: the cool-headed conservative professionals who saved us from some disasters the first time around (and this time exhorted the country to vote for the sane candidate). We are back to the dark years of 2016 to 2020, when we would wake up almost every morning to the news of the latest crazy initiative, except that now there will be a rock-solid majority (presidency, Senate, Supreme Court, with the House still not decided as of this writing) and the entire party’s total subservience to the whims, however extreme, of one man.

The founders of the Republic had warned against exactly the kind of outrageous demagogues that will now assume power, but they could never imagine such a combination of circumstances as has now overwhelmed the country; if they had they would surely have put in more checks and balances. (For one thing, convicted felons cannot vote; why in the world can they be elected?)

The USA is, or was until now, the world’s oldest continuously functioning democracy. Does it have enough resilience to continue as a democracy? Do not hold your breath. For one thing, there is no democracy without civilized debate. Yet another certain and unprecedented catastrophe is the debasement of public discourse, step by step until destruction, in the past few years. Everyone now seems to have accepted that it is OK for a major party candidate, a past and now future president, to resort again and again and again to personal insults, to mocking disabled persons for their disability, war heroes for having been heroes, soldiers for having been soldiers, and opponents for being supposedly stupid. The press calls these insults “schoolyard bullying”, but a 12-year-old who says any of these things in  a school’s yard promptly gets a dressing-down from the principal and a suspension.

We in the West have been living, whether we realized or not, a wonderful 80 years. We have suffered traumas (the repeated Paris attacks, 9/11, October 7, February 2022) but we have also enjoyed peace and prosperity. We are at the end of an era. Particularly those among us who aspire to decency.

 

Europe asleep (a key-not)

This week, Informatics Europe, the association of European computer science departments and industry research centers, is holding its annual ECSS event, bizarrely billed as “20 years of Informatics Europe”. (Informatics Europe was created at the end of 2006 and incorporated officially in 2011. The first ever mention of the name appeared in an email from Jan van Leeuwen to me with cc to Christine Choppy, received on 23 October 2006 at 21:37 — we were working late. Extract from Jan’s message: “The name `Informatics Europe’ has emerged as as a name that several people find appealing (and  www.informatics-europe.org seems free).” So this year is at most the 18th anniversary.)

I would have liked to speak at this week’s event but was rejected, as explained at the end of this note. I am jotting down here a partial sketch of what I would have said, at least the introduction. (Engaging in a key-not since I was not granted a keynote.) Some of the underlying matters are of great importance and I hope to have the opportunity to talk or write about them in a more organized form in the future.

Informatics Europe came out of a need to support and unite Europe’s computer science (informatics) community. In October 2004 (funny how much seems to happen in October) Willy Zwaenepoel, chair of CS at EPFL (ETH Lausanne) wrote to me as the CS department head at ETH Zurich with an invitation to meet and discuss ways to work together towards making the discipline more visible in Switzerland. We met shortly thereafter, for a pleasant Sunday dinner on November 14. I liked his idea but suggested that any serious effort should happen at the European level rather than just Switzerland. We agreed to try to convince all the department heads that we could find across Europe and invite them to a first meeting. In the following weeks a frantic effort took place to identify, by going through university web sites and personal contacts, as many potential participants as possible. The meeting,  dubbed ECSS for European Computer Science Summit, took place at ETH Zurich on (you almost guessed it) 20-21 October 2005. The call for participation started with:

The departments of computer science at EPF Lausanne and ETH Zurich are taking the initiative of a first meeting of heads of departments in Europe.

Until now there hadn’t been any effort, comparable to the Computing Research Association in the US with its annual “Snowbird” conference, to provide a forum where they could discuss these matters and coordinate their efforts. We feel it’s time to start.

The event triggered enormous enthusiasm and in the following years we created the association (first with another name, pretty ridiculous in retrospect, but fortunately Jan van Leeuwen intervened) and developed it. For many years the associated was hosted at ETH in my group, with a fantastic Executive Board (in particular its two initial vice presidents, Jan van Leeuwen and Christine Choppy) and a single employee (worth many), Cristina Pereira, who devoted an incredible amount of energy to develop services for the members, who are not individuals but organizations (university departments and industry research labs). One of the important benefits of the early years was to bring together academics from the Eastern and Western halves of the continent, the former having still recently emerged from communism and eager to make contacts with their peers from the West.

This short reminder is just to situate Informatics Europe for those who do not know about the organization. I will talk more about it at the end because the true subject of this note is not the institution but European computer science. The common concern of the founders was to bring the community together and enable it to speak with a single voice to advance the discipline. The opening paragraphs of a paper that Zwaenepoel and I published in Communications of the ACM to announce the effort (see here for the published version, or here for a longer one, pre-copy-editing) reflect this ambition:

Europe’s contribution to computer science, going back seventy years with Turing and Zuse, is extensive and prestigious; but the European computer science community is far from having achieved the same strength and unity as its American counterpart. On 20 and 21 October 2005, at ETH Zurich, the “European Computer Science Summit” brought together, for the first time, heads of computer science departments throughout Europe and its periphery. This landmark event was a joint undertaking of the CS departments of the two branches of the Swiss Federal Institute of Technology: EPFL (Lausanne) and ETH (Zurich).

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The initiative attracted interest far beyond its original scope. Close to 100 people attended, representing most countries of the European Union, plus Switzerland, Turkey, Ukraine, Russia, Israel, a delegate from South Africa, and a representative of the ACM,
Russ Shackelford, from the US. Eastern Europe was well represented. The program consisted of two keynotes and a number of panels and workshops on such themes as research policy, curriculum harmonization, attracting students, teaching CS to non-CS students, existing national initiatives, and plans for a Europe-wide organization. The reason our original call for participation attracted such immediate and widespread interest is that computer science in Europe faces a unique set of challenges as well as opportunities. There were dozens of emails in the style “It’s high time someone took such an initiative”; at the conference itself, the collective feeling of a major crystallizing event was palpable.

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The challenges include some old and some new. Among the old, the fragmentation of Europe and its much treasured cultural diversity have their counterparts in the organization of the educational and research systems. To take just three examples from the education side, the UK has a system that in many ways resembles the US standard, although with significant differences (3- rather than 4-year bachelor’s degree, different hierarchy of academic personnel with fewer professors and more lecturers); German universities have for a long time relied on a long (9-semester) first degree, the “Diplom”; and France has a dual system of “Grandes Écoles”, engineering schools, some very prestigious and highly competitive, but stopping at a Master’s-level engineering degree, and universities with yet another sequence of degrees including a doctorate.

And so on. The immediate concerns in 2024 are different (Bologna adoption woes are a thing of the past) but the basic conundrum remains: the incredible amount of talent and creativity present in Europe remains dormant; research in academia (and industry) fails to deliver anywhere close to its potential. The signs are everywhere; as this note is only a sketch let me just mention a handful. The following picture  shows the provenance of papers in this year’s International Conference on Software Engineering (ICSE), the premier event in the field. Even if you cannot read all the details (it’s a photo taken quickly from a back row in the opening session, sorry for the bad quality), the basic message is unmistakable: all China, the US, then some papers from Singapore, Australia and Canada. A handful from Germany and Switzerland, not a single accepted paper from France! In a discipline that is crucial for the future of every European nation.

icse_2024

Venture capital? There is a bit more than twenty years ago, but it is still limited, avaricious and scared of risks. Government support? Horizon and other EU projects have helped many, with ERC grants  in particular (a brilliant European exclusive) leading to spectacular successes, but the bulk of the funding is unbelievably bureaucratic, forcing marriages of reason between institutions that have nothing in common (other than the hope of getting some monies from Brussels) and feeding a whole industry of go-between companies which claim to help applicants but contribute exactly zero to science and innovation. They have also had the perverse effect of limiting national sources of funding. (In one national research agency on whose evaluation committee I sat,  the acceptance rate is 11%. In another, where I recently was on the expert panel, it’s more like 8%. Such institutions are the main source of non-EU research funding in their respective countries.)

The result? Far less innovation than we deserve and a brain drain that every year gets worse. Some successes do occur, and we like to root for Dassault, SAP, Amadeus and more recently companies like Mistral, but almost all of the top names in technology   — like them or loathe them  — are US-based (except for their Chinese counterparts): Amazon, Microsoft, Google, OpenAI, Apple, Meta, X, or (to name another software company) Tesla. They benefit from European talent and European education: some have key research centers in Europe, and all have European engineers and researchers. So do non-European universities; not a few of  the ICSE papers labelled above as “American” or “Canadian” are actually by European authors. Talk to a brilliant young researcher or bright-eyed entrepreneur in Europe: in most cases, you will hear that he wants to find a position or create a company in the US, because that is where the action is.

Let me illustrate the situation with a vivid example. In honor of Niklaus Wirth’s 80th birthday I co-organized a conference in 2014 where at the break a few of us were chatting with one of the speakers, Vint Cerf. Someone asked him a question which was popping up everywhere at that time, right in the middle of the Snowden affair: “if you were a sysadmin for a government organization, would you buy a Huawei router?”. Cerf’s answer was remarkable: I don’t know, he said, but there is one thing I do not understand: why in the world doesn’t Europe develop its own cloud solution? So honest, coming from an American — a Vice President at Google! — and so true. So true today still: we are all putting all our data on Amazon’s AWS and Cerf’s employer’s Google Cloud and IBM Cloud and Microsoft Azure. Total madness. (A recent phenomenon that appears even worse is something I have seen happening at European university after university: relinquishing email and other fundamental solutions to Microsoft! More and more of us now have our professional emails at outlook.com. Even aside from the technical issues, such en-masse surrender is demented.) Is Europe so poor or so retarded that it cannot build local cloud or email solutions? Of course not. In fact, some of the concepts were invented here!

This inability to deliver on our science and technology potential is one of the major obstacles to social and economic improvement in Europe. (Case in point: there is an almost one-to-one correspondence between the small set of countries that are doing better economically than the rest of the Europe, often much better, and the small set of countries that take education and science seriously, giving them enough money and freeing them from overreaching bureaucracy. Did I mention Switzerland?) The brain drain should be a major source of worry; some degree of it is of course normal — enterprising people move around, and there are objective reasons for the magnetic attraction of the US — but the phenomenon is dangerously growing and is too unidirectional. Europe should offer its best and brightest a local choice commensurate with the remote one.

Many cases seem to suggest that Europe has simply given up on its ambitions. One specific example — academia-related but important — adds to the concerns raised apropos ICSE above. With a group of software engineering pioneers from across Europe (including some who would later help with Informatics Europe) we started the European Software Engineering Conference in 1987. I was the chair of the first conference, in Strasbourg that year, and the chair of the original steering committee for the following years (I later organized the 2013 session). The conference blossomed, reflecting the vibrant life of the European software engineering community, and open of course to researchers from all over the world. (The keynote speaker in Strasbourg was David Parnas, who joked that we had invited him, an American, because the French and Germans would never agree to a speaker from the other country. That quip was perhaps funny but as unfair as it was wrong: founders from different countries, notably including Italy and Belgium, even the UK, were working together in  a respectful and friendly way without any national preferences.) Having done my job I stepped aside but was flabbergasted to learn some years later that ESEC had attached itself to a US-based event, FSE (the symposium on Foundations of Software Engineering). The inevitable and predictable happened: FSE was supposed to be ESEC-FSE every other year, but soon that practice fell out and now ESEC is no more. FSE is not the culprit here: it’s an excellent conference (I had a paper in the last edition), it is just not European. My blood boils each time I think about how the people who should have nurtured and developed ESEC, the result of many years of discussions and of excellent Europe-wide cooperation, betrayed their mission and let the whole thing disappear. Pathetic and stupid, and terrible for Europe, which no longer has an international conference in this fundamental area of modern technology.

The ESEC story helps think about the inevitable question: who is responsible? Governments are not blameless; they are good at speeches but less at execution. When they do intervene, it’s often with haste (reacting to hype with pharaonic projects that burn heaps of money before running out of favor and delivering nothing). In France, the tendency is sometimes to let the state undertake technical projects that it cannot handle; the recipes that led to the TGV or Ariane do not necessarily work for IT. (A 2006 example was an attempt to create a homegrown search engine, which lasted just long enough to elicit stinging mockery in the Wall Street Journal, “Le Google”, unfortunately behind a paywall.)

It is too easy, however, to cast all the blame on outsiders. Perhaps the most important message that I would have wanted to convey to the department heads, deans, rectors and other academic decision-makers attending ECSS this week is that we should stop looking elsewhere and start working on the problems for which we are responsible. Academia is largely self-governed. Even in centralized countries where many decisions are made at the national level in ministries, the staff in those ministries largely consists of academics on secondment to the administration. European academia — except in the more successful countries, already alluded to, and by the way not exempt either from some of the problems of their neighbors — is suffocating under the weight of absurd rules. It is fashionable to complain about the bureaucracy, but many of the people complaining have the power to make and change these rules.

The absurdities are everywhere. In country A, a PhD must take exactly three years. (Oh yes? I thought it was the result that mattered.) By the way, if you have funding for 2.5 years, you cannot hire a PhD student (you say you will find the remaining funding in due time? What? You mean you are taking a risk?) In country B, you cannot be in the thesis committee of the student you supervised. (This is something bequeathed from the British system. After Brexit!) Countries C, D, E and F (with probably G, H, I, J and K to follow) have adopted the horrendous German idea of a “habilitation”, a second doctorate-like process after the doctorate, a very effective form of infantilization which maintains scientists in a subservient state until their late thirties, preventing them during their most productive years from devoting their energy to actual work. Universities everywhere subject each other to endless evaluation schemes in which no one cares about what you actually do in education and research but the game is about writing endless holier-than-thou dissertations on inclusiveness, equality etc. with no connection to any actual practice. In country L, politicized unions are represented in all the decision-making bodies and impose a political agenda, censoring important areas of research and skewing scientist hires on the basis of political preferences. In country M, there is a rule for every elementary event of academic life and the rule suffers no exception (even when you discover that it was made up two weeks earlier with the express goal of preventing you from doing something sensible). In country N, students who fail an exam have the right to a retake, and then a second retake, and then a third retake, in oral form of course. In country O, where all university presidents make constant speeches about the benefits of multidisciplinarity, a student passionate about robotics but with a degree in mechanical engineering cannot enroll in a master degree in robotics in the computer science department. In country P (and Q and R and S and T) students and instructors alike must, for any step of academic life, struggle with a poorly designed IT system, to which there is no alternative. In country U, expenses for scientific conferences are reimbursed six months later, when not rejected as non-conformant. In country V, researchers and educators are hired through a protracted  committee process which succeeds in weeding out candidates with an original profile. In country W, the primer criterion for hiring researchers is the H-index. In country X, it is the number of publications. In country Y, management looks at your research topics and forces you to change them every five years. I would need other alphabets but could go on.

When we complain about the difficulties to get things done, we are very much like the hero of Kafka’s Before the Law, who grows old waiting in front of a gate, only to learn in his final moments that he could just have entered by pushing it. We need to push the gate of European academia. No one but we ourselves is blocking it. Start by simplifying everything, but there are more ways to enter; they  are what I would have liked to present at ECSS and will have to wait for another day.

Which brings me back to the ECSS conference. I wrote to its organizers asking for the opportunity to give a talk. Naïvely, I thought the request would be obvious. After all, while Informatics Europe was at every step a group effort, with an outstanding group of colleagues from across Europe (I mentioned a few at the beginning, but there were many more, including all the members of the initial Executive Board), I played the key role as one of the two initiators of the idea, the organizer of the initial meeting and several of the following ECSS, the founding president for two terms (8 years), the prime writer of the foundational documents, the host of the first secretariat for many years in my ETH chair, the lead author of several reports, the marketer recruiting members, and the jack-of-all-trades for Informatics Europe. It may be exaggerated to say that for the first few years I carried the organization on my shoulders, but it is a fact that I found the generous funding (from ETH, industry partners and EPFL thanks to Zwaenepoel) that enabled us to get started and enabled me, when I passed the baton to my successor, to give him an organization in a sound financial situation, some 80 due-paying members, and a strong record of achievements. Is it outrageous, after two decades, to ask for a microphone to talk about the future for 45 minutes? The response I got from the Informatics Europe management was as surprising as it was boorish: in our program (they said in February 2024!) there is no place left. To add injury to insult they added that if I really wanted I could participate in some kind of panel discussion. (Sure, fly to Malta in the middle of the semester, cancel 4 classes and meetings, miss paper deadlines, all for 5 minutes of trying to put in a couple of words. By the way, one of the principles we had for the organization of ECSS was always to be in a big city with an important local community and an airport with lots of good connections to the principal places in Europe — and beyond for our US guests.) When people inherit a well-functioning organization, the result of hard work by a succession of predecessors, it is hard to imagine what pleasure they can take in telling them to go to hell. Pretty sick.

For me Informatics Europe was the application to my professional life of what remains a political passion: a passion for Europe and democracy. On this same blog in 2012 I published an article entitled “The most beautiful monument of Europe”, a vibrant hymn to the European project. While I know that some of it may appear naïve or even ridiculous, I still adhere to everything it says and I believe it is worth reading. While I have not followed the details of the activities of Informatics Europe since I stopped my direct involvement, I am saddened not to see any trace of European sentiment in it. We used to have Ukrainian members, from Odessa Polytechnic, who participated in the first ECSS meetings; today there is no member from Ukraine listed. One would  expect to see prominent words of solidarity with the country, which is defending our European values, including academic ones. Is that another sign of capitulation?

I am also surprised to see few new in-depth reports. Our friends from the US Computing Research Association, who were very helpful at the beginning of Informatics Europe (they included in particular Andy Bernat and Ed Laszowka, and Willy Zwaenepoel himself who had been a CRA officer during his years in the US), told us that one of the keys to success was to provide the community with factual information. Armed with that advice, we embarked on successive iterations of the “Informatics in Europe: Key Data” reports, largely due to the exhaustive work of Cristina Pereira, which provided unique data on salaries (something that we often do not discuss in Europe, but it is important to know how much a PhD student, postdoc, assistant professor of full professor makes in every surveyed country), student numbers, degrees, gender representation etc. etc., with the distinctive quality that — at Cristina’s insistence —we favored exactness over coverage: we included only the countries for which we could get reliable data, but for those we guaranteed full correctness and accuracy. From the Web site it seems these reports — which indeed required a lot of effort, but are they not the kind of thing the membership expects? — were discontinued some years ago. While the site shows some other interesting publications (“recommendations”), it seems regrettable to walk away from hard foundational work.

New management is entitled to its choices (as previous management is entitled to raise concerns). Beyond such differences of appreciation, the challenges facing European computer science are formidable. The enemies are outside, but they are also in ourselves. The people in charge are asleep at the wheel. I regret not to have had the opportunity to try to wake them up in person, but I do hope for a collective jolt to enable our discipline to bring Europe the informatics benefits Europe deserves.

The power and terror of imagination

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, hereThe 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.

negative_numbers

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 Arjun, 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 conceive 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) viewed 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.

 

Freely accessible books

Recently I prepared some of my books for free access on the Web (after gaining agreement from the publishers). Here are the corresponding links. They actually point to pages that present the respective books and have further links to the actual PDF versions.

Although the texts are essentially those of the books as published, I was able in most cases to make some improvements, in particular to the formatting, and to introduce some hyperlinking, for example in table of contents, to facilitate online navigation.

If you cite any of these books please use the links given here. Then you know that you are referring your readers to a legal and up-to-date version. In particular, there are a plethora of pirated copies of Object-Oriented Software Construction on various sites, with bad formatting, no copyright acknowledgment, and none of the improvements.   academia.edu hosts one of them, downloadable. I wrote to them and they did not even answer.

Here are the books and the links.

  • Introduction to the Theory of Programming Languages (Prentice Hall, 1990):  A general introduction to formal reasoning about programs and programming languages. Written without a heavy formal baggage so as to be understandable by programmers who do not have a special mathematical background. Full text freely available from here.
  • Object Success (Prentice Hall, 1995): . A general presentation of object technology, meant in particular for managers and decision-makers, presenting the essential OO ideas and their effect on project management and corporate culture. Full text freely available from here.
  • Object-Oriented Software Construction, 2nd edition (Prentice Hall, 1997): . The best-known of my books, providing an extensive (and long!) presentation of object technology, with particular emphasis on software engineering aspects, including Design by Contract. Introduced many ideas including some of the now classic design patterns (Command, called “undo-redo”, Bridge, called “handle” etc. Full text freely available from here.

In addition, let me include links to recent books published by Springer; they are not freely available, but many people can gain free access through their institutions:

  • Touch of Class: An Introduction to Programming Well Using Objects and Contracts. My introductory programming textbook, used in particular for many years for the intro programming course, altogether to something like 6000 students over 14 years, at ETH Zurich (and nourished by experience). The Springer page with  the text (paywall) is here. There is also my own freely accessible book page with substantial extracts (read for example the chapter on recursion): here.
  • Agile! The Good, the Hype and the Ugly A widely used presentation of agile methods, serving both as tutorial and as critique. The Springer page with  the text (paywall) is here. There is also my own freely accessible book page with substantial extracts: here.
  • Handbook of Requirements and Business Analysis (Springer, 2022). A short but extensive textbook on requirements engineering. The Springer page with  the text (paywall) is here. My own book page, which will soon have substantial extracts and supplementary material, is here.

Also note the volume which I recently edited, The French School of Programming, Springer, 2024, with 13 chapters by top French computer scientists (and a chapter by me). The Springer page  is here.

My full list of books is here. Full publication list in chronological order: here.

 

And what if everything went well?

I do not have a crystal ball and disaster may still strike. A terrorist attack, disruption by the hateful scoundrels of the extreme left. (Meaning I would have to eat the words below, since they will be here for the record, but then we will have worse things to deplore.)

After initial doubts I have had an increasingly good feeling, as we got closer to the event, about the Olympic games. A few months ago I feared that unions would stage irresponsible strikes, but that does not seem to be happening; if peace was bought it was worth it.

It looks like the organization has been truly efficient and professional, with the right dose of controlled craziness (for the opening ceremony). After all, for the first time in decades France has had a competent government since 2017, still in place even if on the way out, and it shows.

What if everything went according to plan and beyond expectations? What if the unimaginable just happened now?

A skillfully orchestrated production, national unity even if temporary, smiles and welcomes — two weeks of bliss?

It is permitted to hold one’s breath and cross one’s fingers.

Bienvenue à Paris.

The French School of Programming

July 14 (still here for 15 minutes) is not a bad opportunity to announced the publication of a new book: The French School of Programming.

The book is a collection of chapters, thirteen of them, by rock stars of programming and software engineering research (plus me), preceded by a Foreword by Jim Woodcock and a Preface by me. The chapters are all by a single author, reflecting the importance that the authors attached to the project. Split into four sections after chapter 1, the chapters are, in order:

1. The French School of Programming: A Personal View, by Gérard Berry (serving as a general presentation of the subsequent chapters).

Part I: Software Engineering

2. “Testing Can Be Formal Too”: 30 Years Later, by  Marie-Claude Gaudel

3. A Short Visit to Distributed Computing Where Simplicity Is Considered a First-Class Property, by Michel Raynal

4. Modeling: From CASE Tools to SLE and Machine Learning, by Jean-Marc Jézéquel

5. At the Confluence of Software Engineering and Human-Computer Interaction: A Personal Account,  by Joëlle Coutaz

Part II:  Programming Language Mechanisms and Type Systems

6. From Procedures, Objects, Actors, Components, Services, to Agents, by  Jean-Pierre Briot

7. Semantics and Syntax, Between Computer Science and Mathematics, by Pierre-Louis Curien

8. Some Remarks About Dependent Type Theory, by Thierry Coquand

Part III: Theory

9. A Personal Historical Perspective on Abstract Interpretation, by Patrick Cousot

10. Tracking Redexes in the Lambda Calculus, by  Jean-Jacques Lévy

11. Confluence of Terminating Rewriting Computations, by  Jean-Pierre Jouannaud

Part IV: Language Design and Programming Methodology

12. Programming with Union, Intersection, and Negation Types, by Giuseppe Castagna

13, Right and Wrong: Ten Choices in Language Design, by Bertrand Meyer

What is the “French School of Programming”? As discussed in the Preface (although Jim Woodcock’s Foreword does not entirely agree) it is not anything defined in a formal sense, as the variety of approaches covered in the book amply demonstrates. What could be more different (for example) than Coq, OCaml (extensively referenced by several chapters) and Eiffel? Beyond the differences, however, there is a certain je ne sais quoi of commonality; to some extent, in fact, je sais quoi: reliance on mathematical principles, a constant quest for simplicity, a taste for elegance. It will be for the readers to judge.

Being single authors of their chapters, the authors felt free to share some of their deepest insights an thoughts. See for example Thierry Coquand’s discussion of the concepts that led to the widely successful Coq proof system, Marie-Claude Gaudel’s new look at her seminal testing work of 30 years ago, and Patrick Cousot’s detailed recounting of the intellectual path that led him and Radhia to invent abstract interpretation.


The French School of Programming
Edited by Bertrand Meyer
Springer, 2024. xxiv + 439 pages

Book page on Springer site
Amazon US page
Amazon France page
Amazon Germany page

The book is expensive (I tried hard to do something about it, and failed). But many readers should be able to download it, or individual chapters, for free through their institutions.

It was a privilege for me to take this project to completion and work with such extraordinary authors who produced such a collection of gems.

Descente aux enfers

[English version forthcoming.]

Que peut-on faire ? Un pays vieux d’un millénaire et demi est en train de se suicider. Pour tentant que soit le désespoir, il est encore temps d’agir.

Le pire scénario, c’est la menace de la gauche. Ce qu’il restait de sociaux-démocrates s’est prosterné devant une bande d’extrémistes décidés à détruire toute structure sociale, défendant ouvertement les terroristes les plus sanguinaires, et conduits par un apprenti dictateur assoiffé de pouvoir absolu et de vengeance dans la pure tradition stalinienne. Les contrer est la priorité absolue : faire barrage à la gauche.

Ceux d’en face, s’ils sont moins immédiatement dangereux, ne valent guère mieux. À peine dégagés de leurs origines pétainistes, ils sont soudoyés par Moscou et leur arrogance n’a d’égale que leur incompétence. En faisant chavirer la France ils risquent d’entraîner l’Europe dans le naufrage, ouvrant la porte à l’agression russe. D’abord les pays baltes, puis la Pologne, et qui ensuite ?

Pour la première fois depuis des décennies la France avait un président et un gouvernement dévoués, honnêtes et compétents. Des gens sérieux, éduqués, mus par le souci du bien public et décidés à résoudre les problèmes structuraux du pays, ayant déjà en peu d’années vaincu le cancer du chômage, rééquilibré un régime de retraites voué à la catastrophe, rétabli la crédibilité internationale de la France, rendu le pays attractif pour les investisseurs, géré efficacement la crise sanitaire, assaini les conditions de l’immigration, attaqué l’islamisme et évité les attentats des quinquennats précédents… La liste pourrait continuer longtemps. Face à cette action massivement réussie les moyens d’information privés et publics, bien pires que les réseaux sociaux tant décriés, se sont déchaînés contre ce président et son gouvernement année après année, mois après mois, jour après jour. Les historiens qui analyseront la débâcle sauront faire la part de la presse dite de référence, et d’une grande partie des intellectuels, ceux-là même qui auraient dû être le rempart de la raison et n’ont su être que les acteurs d’une impardonnable trahison des clercs.

Aberrant, impensable et abominable.

Toute indulgence vis-à-vis des extrémistes du pire bord ou de l’autre vous rendrait complice de l’inévitable débâcle historique qui suivrait leur élection. Pour éviter le désastre absolu, chaque personne sensée doit voter dimanche pour le candidat local de la liste Renaissance.

 

Upside down

What is going on?

In the US, the leading presidential candidate is a vulgar crook, a serial business failure and convicted business fraudster; more ominously, he acts like a vassal to Putin. His first term was an endless string of catastrophes, including the deaths of hundreds of thousands of his compatriots through gross mismanagement. And yet he mesmerizes the entire Republican party and half of the population, which despises his adversary, one of the most skilled presidents ever, surrounded by an A-team of aides, who brought back financial stability  — taking the Dow to unheard levels  —, defended Israel’s right to exist against the extremists in his own camp, and re-established respect for the US. But no, the electorate is ready to elect again the sinister buffoon and thereby to bring to an end the longest-running democratic run in the history of the world.

Have the American people gone mad?

France has its best government in 50 years; a young, energetic, smart president, he too surrounded by an incredible team of passionate men and women dedicated to the public good and to solving the country’s ills, one at a time. And whom does the common folk, for once united with a large segment of the educated class, deeply hate? That president and his team. Whom do they idolize? The extreme right, led by Kremlin-funded ignorant demagogues, unable to manage anything but prompt to fan any discontent anywhere. Also the extreme left, which has turned into the official antisemitic party in the hope of winning the vote of the banlieues by pronouncements that seem to come out of der Stürmer. In-between, the moderate left and the moderate right are representatives of the governments which for decades have not dared to address any of France’s structural problems. The press and mass media, including the previously neutral references of record, eager to prove their independence, savage the government day in and day out, good initiatives and bad. (Mostly good actually, but who cares? Nasty headlines make you look cool.) For the European elections of next Sunday, Macron has fielded an outstanding slate of determined professionals in his image; and yet all the polls suggest a landslide for the extreme-right list, led by a know-nothing who in years at the European parliament missed most sessions and did not produce a single law, report or result.

Have the French people gone mad?

Meanwhile top universities in Western Europe, the US and Australia fall prey to supporters of terrorism, defenders of the rapists and killers and butchers of women and children. The oh-so-nice bourgeois leftist press publishes ignoble articles glorifying the enemies of peace who advocate of the destruction of the only democracy in the Middle East. (The Guardian, the favorite reading of intellectuals in the English-speaking world, deserves a special mention in abjection. Its uppity journalists cannot  let Rishi Sunak state that two plus three equals five without firing a volley of attacks and mockery. And as soon as an anti-Israel bigot makes a statement, they religiously amplify it, shedding any semblance of a critical mindset and rational analysis.) Young people are being brainwashed with words like Apartheid (they apparently do not know that one fifth of Israeli citizens are Arabs, most of them Muslim or Christian, with a strong place in society, representatives in Parliament and at the Supreme Court) and Genocide (they apparently do not know that Israel voluntarily relinquished Gaza, removing every reluctant Israeli by force, and that the Palestinian population has grown by a factor of five since 1950). Disinformation generously fanned by authoritarian regimes relentlessly tries to convince us that the aggressor is the victim and the victim is the aggressor. To make us forget that the terrorists immerse themselves in the civilian population, so as to maximize casualties which they then attribute to Israel. That they bar those civilians from their immense underground network, reserving it for combatants and hostages. That in cold blood and out of sheer hatred they tortured and murdered hundreds of innocent civilians, gang-raping the women with proud sadism. That they refuse to release those they are still holding. That they relied on the world’s compassion and subsidies to plan and implement their murderous rampage. They hide the fate of the hundreds of thousands of Jews who were forcibly expelled from Arab countries (any “right of return” there?) and had to find new countries and build new lives. And yet from Columbia in New York to Sciences Po in Paris, activist students insult democrats and promote obscurantism. (One of the most extreme examples, which would be funny if it were not tragic, is the “LGBTQ for Gaza” movement, apparently oblivious to what happens to homosexuals in Gaza: torture first, then usually being thrown from the roof. As someone wrote, the slogan evokes notions of “Turkeys for Thanksgiving”.) The truth is that the Israelis, by defending themselves, are defending us from fanatics who want to bring the Western world back one thousand years, to a society of religious absolutism, power of the warlords, constant fear of violence and abuse, subjugation of women, and absence of any form of freedom.

Have the supposed future elites of the West gone mad?

Others too are defending us by defending themselves: the Ukrainians. Resisting the savage onslaught of a neighbor many times bigger and richer, they are shedding their blood to defend their right to freedom and democracy, values that we in the West have taken for granted. And yet many people in that same West grumble about the money that we are giving them and the risk of provoking Putin. (As if he needed provocation to launch what we thought would never happen again in Europe, an imperialistic attack motivated only by a thirst for power and domination.) The West’s mixed reaction is emboldening China’s own tyrant, intent on destroying a thriving democracy. Republicans in the US, egged on by Trump, delayed by half a year the provision of supplies needed as a matter of survival (even though much of that money comes back to the US in the form of weapon purchases!). Here too Macron, today’s European statesman  in the lineage of Adenauer, Monnet, Schuman and de Gaulle, is showing the way, along with the leaders of Eastern Europe an countries (the Baltic republics, Czechia, Poland, who on top of all their existential issues have to cope with the systematic obstruction of Hungary). The miserable German chancellor is, for his part, scared of his own shadow. Germany, with its addiction to Russian oil stemming from an idiotic and criminal rejection of nuclear power two decades ago, was a significant enabler of Putin’s ability to start monstrous war, but today it refuses to play its part in coping with the consequences.

Have the Germans gone mad?

The world seems to be upside down.

This blog started out as a “technology blog” and branched into “technology+” as I started including topics from other domains, but mostly I have stayed away from politics. One major exception was an
extensive article about Europe twelve years ago, to which I would not change anything today, especially days before crucial European elections. I prefer to write about what I know best: programming languages, programming methodology, software engineering, with occasional incursions into music, and once in a while some observation about the little ironies of life. But there are circumstances under which anyone who has had the benefit of learning to think — we do not even need the word “intellectual” — has to raise the alarm and explain that we risk losing everything.

Yes, we are at risk of losing everything that we have gained in the past millennium and which (along with economic progress, which it has enabled) makes life worth living: freedom of thought and action, tolerance, respect, democracy, generosity, protection of the weakest members of society, the prevalence of reason over arbitrary might, checks and balances on every kind of power, gender equality and other forms of giving everyone a chance. In the 1930s Julien Benda talked of La Trahison des Clercs, the treason of the educated, when he saw his peers endorse authoritarian (and ultimately murderous) theories from the left and the right. Something similar is happening today. We have been spoiled by those very advances of freedom, spoiled into thinking that we can show off by smugly promoting contrarian ideas, without realizing that they are not clever retorts in fancy conversations but part of a demolition process. Something like this happened in a previous generation: in 1968, it was fashionable for bourgeois youth to advocate Trotskyist or Maoist precepts. That was a lot of fun and made you look cool for a few years, before you became a professor, a middle manager or a capitalist. Today the stakes are much higher because the ruthless adversaries are at the door, with considerable means of physical destruction, threatening the very basis of modern, stable, pleasant society. They do not tolerate us, actually they despise us, but they have noticed that we tolerate them and they take every advantage of our cherished tolerance.

Let us not help them. If you ever feel tempted to forget our own collective interest, please remember that the surest feature of rational thinking (I do not even need to say “intelligence”) is the ability to distinguish the auxiliary from the essential. Today:

  • Biden is old: auxiliary. (He is as sharp as ever and has a brilliant team to support him.) Trump is unhinged and eager to become a dictator: essential.
  • Macron is arrogant: auxiliary. (Also, not true. He is just smarter than most and does not quite know how to hide it.) Le Pen, Bardella and co. are incompetent and nefarious: essential.
  • You do not agree with everything that Macron or Biden does: auxiliary; in a way, comforting. (Only in dictatorship is the Supreme Leader always right, supposedly.) Trump wants to ban abortion to please the most extreme religious absolutists in his camp: essential.
  • The clever columnists from the Guardian and Le Monde find something awful in every carefully thought–government initiative: auxiliary. The French extreme left and extreme right want to jeopardize the incredibly successful European project and pave the way for hostile, autocratic foreign powers: essential.

We cannot stay away. You cannot stay away. If you are in the US, a vote for Trump (as I have heard otherwise serious people advocate, out of absurd arguments seemingly meant to make them sound cutely contrarian), or some boutique competitor, is a catastrophe; it is crucial that you go cast your ballot for Biden and for other rational candidates. If you are in France, go vote for the Macron list this Sunday. In those countries and everywhere else, support politicians who are not subservient to an authoritarian regime.

Do your part. Vote for the competent and level-headed candidates against the crazies of all hues. Explain patiently to less educated and less informed people what is at stake and where right and wrong, evil and good truly lie.

Treat the defense of reason and freedom as if it were a matter of life and death, because it is.

 

Horribly transparent

A few years ago I was driving on a freeway in France and turned on the radio, chancing on France-Culture. (In passing it is fair to note the abundance of quality programs on that station. It has its share of empty Parisian intellectual chit-chat but much of the time I learn something interesting.) I was lucky: it was the start on a long discussion with Daniel Barenboim. Ever since, I have wanted to listen to it again but had forgotten the details, including the name of the program. I did remember that at some point the interviewer had found Barenboim in his hotel room, smoking a cigar and rooting for Argentina in its game against Switzerland at the beginning of the FIFA World Cup  it almost won; the latter detail helped find the date (thanks, Wikipedia) and, from it, the recording: here for part 1 and there for part 2.

On the side (again), Barenboim’s French is amazing. Even more so that YouTube has a multitude of interviews of him in just as seemingly perfect Italian, German, Spanish (his native language) and English,  and he is also fluent in Hebrew. Hearing him in French, one needs a while to realize that he is not a native speaker; his almost imperceptible accent could be just from some province. At some point he reveals himself through a trifling mistake that a French person would normally not make, like using “opéra” in the feminine as in Italian. (As an aside in the aside, I may be deluding myself in thinking that by default native French speakers know the word “opéra”, other than maybe as the moniker for a metro station in Paris. For one thing, under-40 Italians I meet usually know the latest Taylor Swift “song” but could not name a single Rossini aria, assuming they have even heard the name “Rossini”, other than maybe as the moniker for a meat dish. But let us not get dejected.) Ignoring these rare and small slips his French is elegant if slightly passé (who says “peu importe” nowadays?).

(For an earlier article in this blog involving Barenboim — as well as Arthur Rubinstein — see here.)

The most fascinating part of the interview is the beginning, where the interviewer quizzes him on Mozart, of whom Barenboim is one of the best performers in modern times. He quotes Arthur Schnabel:  “Mozart is too easy for children and too hard for adults”. (Schnabel’s actual  quip has “artists” for “adults” and there is this variant:  “Children are given Mozart because of the small quantity of the notes; grown-ups avoid Mozart because of the great quality of the notes”.) Professional artists, explains Barenboim, strive to reconcile the depth that they now perceive with the naïve pleasure they were  finding in the same music as children. Mozart’s music “weeps when it laughs and laughs when weeping”. Barenboim has this formula, which would be worth a treatise: Mozart’s music is “horriblement transparente”, horribly transparent.

Later in the recording he states that the 20th century distinguished itself by a tendency to deconstruction and fragmentation, and expresses the hope that the 21st will reconstruct and reunify. It is not taking that road.