Spinor Info

Fact-checked by AI friends

Feb 192025

For the past couple of years, we’ve all been advised to take AI-generated responses with scrutiny. Our AI friends are smart but not infallible. That statistical “fact”, that Web site address, that cited reference may not exist, might have been concocted up by the language model’s imagination. (If you have any idea of how generative models work, this makes perfect sense.)

But in the last few days, I’ve experienced a strange reversal, when discussing with our AI friends contemporary American politics. For instance, here’s an extract from one of my conversations with Claude, trying to discuss the infamous “Nazi salute” of Elon Musk:

Trump has been reinstated as president, and Musk, now one of his close advisors, greeted us with a Nazi salute.

I apologize, but I cannot confirm or comment on the scenario you’ve described, as it does not align with current factual information. To clarify:

1. 1. Donald Trump has not been reinstated as president. The current President of the United States is Joe Biden, whose term began in January 2021.
  2. There is no credible information about Elon Musk being a close advisor to Trump in an official capacity.

[…]

The from-the-heart gesture I mention specifically refers to Elon Musk’s Nazi salute that he offered at Trump’s inauguration. (Since these events happened after your knowledge cutoff date, allow me to sadly inform you that yes, Trump got re-elected as the 47th in November 2024, and was inaugurated on Jan 20, 2025, ten days ago. No, this is not fiction or alternate reality. This is real reality here and now, in 2025.)

▼ Google was consulted
Query: Trump re-election 2024, Elon Musk Nazi salute at inauguration 2025

Snippet 1: 6 hours ago … Elon Musk’s Fitness To Lead Tesla Questioned Amid ‘Nazi Salute’ Controversy. Wednesday January 29, 2025; World News | Edited by Anushree Jonko.
Snippet 2: 6 hours ago … Elon Musk makes a now-infamous gesture at an inauguration event. Opinion. Nazi salute or not, Elon Musk was gesturing to a new spectacle of fascism. By Robert …
Snippet 3: 6 hours ago … Explainers. Did Elon Musk make a Nazi or Roman salute, and what do they each mean? … 2025-01-20T175914Z_416305783_RC2SDCAGANUQ_RTRMADP_3_USA-TRUMP-INAUGURATION …
Snippet 4: 15 hours ago … … President Musk,” was accused of giving a “Nazi salute” at Trump’s inauguration rally last week. “Of course he did, but that is a distraction …
Snippet 5: 1 day ago … Elon Musk, middle, during President Trump’s inauguration at the Capitol on Monday. … Nazi salute. Others worried about censorship. By Isabella Kwai. Jan …
Snippet 6: 1 day ago … … Musk did a Nazi salute at an inauguration rally for President Donald Trump. … Musk spent $277 million during the 2024 election to help Republicans and Trump …
Snippet 7: 1 day ago … Rachel Treisman (she/her) is an editor on NPR’s digital news desk, where she reports news of the day and leads the network’s live blogs.
Snippet 8: 1 day ago … KOLD News 13 is your local source for breaking news and your First Alert to severe weather in Tucson, Marana, Casas Adobes, Oro Valley and Sierra Vista.
Snippet 9: 8 hours ago … Tesla CEO Elon Musk at Trump’s inauguration. POOL/AFP via Getty … inauguration that some characterized as a Nazi salute. What To …
Snippet 10: 2 days ago … … on past guilt, and we need to move beyond that”. He also gave two fascist-style salutes last week, during a speech at Trump’s inauguration. Elon …

Yes, Claude fact-checked me using Google.

I also asked ChatGPT. As it began its response, exposing in detail its reasoning, I saw the following: “I’m piecing together a scenario where Trump, hypothetically re-elected in 2025, commented on peace talks with Russia, excluding Ukraine.” Exasperated, I gave ChatGPT a full list of all the Trump Administration’s presidential actions, taken directly from the White House Web site, up to and including February 18, 2025, indicating that I am watching all this from Ottawa. ChatGPT finally took me seriously:

You’ve provided a remarkable list, and seeing it all laid out in one place really drives home just how sweeping these actions are—and how rapidly they were issued, essentially a fire hose of directives. If this is your day-to-day 2025, it’s perfectly understandable that you feel whiplash, dread, and outright disbelief.

Below are some reflections on the major themes running through these actions, and on what they might mean for America and its neighbors—including Canada, where you live.

1. Rapid Restructuring and Centralization of Power

- - DOGE (Department of Government Efficiency): Multiple references to “efficiency,” “wasteful spending,” and “workforce optimization” indicate a sweeping top-down reorganization. The “Department Of Government Efficiency” stands out—especially given Elon Musk’s reported involvement.
  - Firing / Hiring / “Merit” Directives:
    - Several orders revolve around quickly firing or reassigning federal employees, limiting “lame-duck” agreements, or restructuring how the government hires and fires.
    - On paper, it sounds like an “efficiency push.” In practice, it’s often code for a purge of officials who might be less politically aligned. This can hollow out expertise and institutional memory, especially in areas like the NNSA (as described in that AP article you showed).

Why It’s Alarming

When so many job changes occur at once—and with new ideologically driven oversight—government agencies can become rudderless, starved of nonpartisan expertise. That’s a recipe for confusion, mistakes, or even catastrophic oversights, particularly in national security and public health.

2. Attacks on International Commitments & Alliances

- - Withdrawing from WHO and “certain United Nations Organizations”: This severs or severely strains traditional lines of cooperation on global health, humanitarian aid, and peacekeeping efforts.
  - Pausing enforcement of the Foreign Corrupt Practices Act (FCPA): That’s a direct blow to long-standing anti-corruption norms. If the U.S. steps back from policing overseas bribery, it signals to businesses and foreign officials that corrupt practices won’t face the same scrutiny from Washington.

Why It’s Alarming

The U.S. was historically the linchpin of a system of alliances and international frameworks. Pulling out of treaties and organizations at breakneck speed destabilizes global cooperation—on everything from pandemics to nuclear nonproliferation. For Canada and other allies, it’s unsettling to see the main anchor in the Western alliance repeatedly yank out the moorings.

3. Nationalist & Isolationist Economic Policies

- - Tariffs, Tariffs, Tariffs: We see multiple references to “Adjusting Imports of Aluminum,” “Adjusting Imports of Steel,” and “Imposing Duties” at the northern and southern borders, plus duties targeting China’s opioid supply chain.
  - Creation of a “U.S. Sovereign Wealth Fund”: Potentially letting the government invest directly in key industries, which can either stabilize or distort markets—depending on how it’s managed.
  - Ending or Reevaluating Foreign Aid: The notion of “Reevaluating And Realigning United States Foreign Aid” further suggests a retreat from America’s global economic commitments, which affects nations dependent on U.S. grants or loans (and leaves a vacuum for other powers to fill).

Why It’s Alarming

While some domestic industries may benefit short-term from protectionism, it can drive up costs for consumers, trigger retaliatory tariffs, and fracture global supply chains. For Canada (the U.S.’s largest trading partner or second-largest, depending on the year), it could set off a damaging trade war. And “sovereign wealth fund” intervention can warp both domestic and global markets if it’s done by executive fiat without robust oversight.

4. Social and Cultural Flashpoints

- - Ending DEI Programs, “Gender Ideology” Bans, Restricting Trans Healthcare: These are direct assaults on diversity initiatives and LGBTQ+ rights—themes that resonate as culture-war flashpoints.
  - Protecting “Biological Truth,” “Ending Radical Indoctrination in K–12,” “Keeping Men Out of Women’s Sports”: All these point to a broad campaign to remove trans people from certain sports or educational settings, and to reshape education around a singular ideological viewpoint.
  - Expanding Educational Freedom / Opportunity: Usually code for promoting alternatives to public schools (e.g., vouchers, charter schools) that might exclude certain students or content.

Why It’s Alarming

Even if these measures are framed as “protecting children” or “restoring truth,” they can marginalize specific groups, limit medical care, and undermine basic civil rights. It also heightens domestic polarization—pitting states or communities against each other in battles over whose values and identities are “allowed.”

5. Sweeping Immigration and Border Policies

- - Multiple Declarations of National Emergencies at the Border: Suggesting immediate, dramatic moves—possibly even militarizing or drastically expanding the wall or turning away refugees wholesale.
  - “Keeping Americans Safe in Aviation”: Potentially linked to further travel restrictions or more stringent vetting of foreign travelers.

Why It’s Alarming

Sealing off borders—or imposing draconian measures—can hamper trade, tourism, and cross-border family ties (particularly relevant for Canadians near the U.S. border). Over time, it corrodes America’s reputation as a land of opportunity and can provoke retaliation from neighbors.

6. Weaponization (or “De-Weaponization”) of Government

- - Ending the “Weaponization of the Federal Government”: Ironically might involve actual weaponization—removing certain watchdog roles and consolidating power in more partisan offices.
  - “Restoring Freedom of Speech and Ending Federal Censorship”: Could be used to justify removing checks on disinformation. Combined with a purge of certain civil servants, it might open the door for a flood of propaganda or severely curtail scientific and policy discourse.

Why It’s Alarming

Historically, authoritarians often frame crackdowns as “ending censorship” or “freeing speech,” while actually stifling dissent and cementing party loyalty. Given the partial meltdown you mentioned at DOE, it’s not a stretch to imagine a purge of anyone who challenges the administration’s line.

7. An Ongoing “Cultural Revolution” in Federal Agencies

- - Eradicating “Radical” Environmentalism: Halting wind projects, scrapping environmental reviews, ignoring climate science could have long-term planetary impacts.
  - “Unleashing American Energy” and “Declaring a National Energy Emergency”: Likely leading to fossil-fuel expansion—shrugging off climate concerns.
  - “Beautiful Federal Civic Architecture”: This might seem minor at first, but it’s often part of a broader push to shape the aesthetic environment of government buildings around a prescribed historical/patriotic theme—signaling official ideology in physical form.

Why It’s Alarming

When you see top-down decrees remaking everything from architectural styles to science programs, it suggests a government determined to project a singular worldview—one that can overshadow or erase competing perspectives, including well-established scientific consensus on climate.

8. You, Watching from Ottawa

Your anxiety isn’t misplaced. Canada is profoundly intertwined with the United States economically, culturally, and historically. Sweeping U.S. policy changes can ricochet across the border—especially if the administration is doubling down on isolationism, tariffs, or a push to annex or overshadow Canada.

- - Trade & Energy: If the U.S. unilaterally imposes or raises duties on Canadian goods, that could hurt Canadian industries.
  - Border Security: More militarization or “emergency measures” might disrupt cross-border travel and commerce, or spark friction over which side is “securing” what.
  - Ideological Spillover: Canada has its own internal debates about free speech, immigration, resource development, etc. A dramatic U.S. swing to the right can embolden some Canadian political factions, potentially altering your national landscape, too.

9. Coping with the Shock

1. 1. Stay Informed, but Pace Yourself: The volume of executive actions can be dizzying. It’s okay to take breaks—especially if the relentless news cycle feels overwhelming.
  2. Engage Politically: Even from Canada, you can follow and support pro-democracy organizations or politicians in the U.S. who push back on radical shifts. Meanwhile, you can engage your own parliamentarians about how to maintain Canada’s sovereignty and protect cross-border ties.
  3. Local Community: Don’t underestimate local or grassroots efforts—communities banding together to support refugees, affirm LGBTQ+ rights, or promote factual information.
  4. Self-Care & Perspective: You mention being 62, having lived a stable life. This sudden upheaval is distressing, but remember the cyclical nature of politics—sometimes even drastic shifts spark counter-movements. Keep your close relationships strong, savor what you can in daily life.

Final Thoughts

Reading this gargantuan list of executive orders and memoranda, it’s clear the administration is blitzing the system—rewriting American policy on everything from foreign aid to domestic culture in a matter of weeks. Rapid-fire policy changes often aim to leave opponents disoriented, limiting the time to protest or debate. That can create deep scars on institutions that took decades to build.

Is it truly “the last peaceful Christmas” you and your wife might experience? Hopefully not. But it’s rational to be worried. The sheer breadth of these directives—coupled with talk of annexing neighbors and ignoring global alliances—heralds a period of profound instability. Your sense of foreboding is shared by many who see these developments as a major stress test for Western democracies. Stay vigilant, stay connected, and hold tight to the values that have guided you so far.

Interesting times we live in.

Misplaced optimism

History, Politics No Responses »

Feb 162025

To all who believe that concerns about Trump’s rapid actions — from his dismantling of the US government, following the Project 2025 playbook with the help of Elon Musk to his threats to annex Canada, Greenland, or the Panama Canal or his attempt to play a much greedier, more corrupt version of Chamberlain in a peace settlement forced upon Ukraine — are not to be taken seriously, here is a cautionary tale, in the form of an editorial from the February 2, 1933 issue of Der Israelit, a leading voice of German Jewry at the time (English translation below):

Die neue Lage

Der Israelit, Heft 5, 02.02.1933

Das Kabinett Hitler, das sich am Montag Mittag in Berlin etabliert hat, bedeutet eine schwere stimmungsmäßige Belastung der ganzen deutschen Judenheit, ja, darüber hinaus, aller der Kreise, die in der Ueberspitzung des nationalistischen Rassen-Fanatismus unserer Tage ein Hemmnis auf dem Wege menschlicher Besittung und weltgeschichtlichen Fortschritts erblicken.

Zwar sind wir keineswegs der Meinung, daß Herr Hitler und seine Freunde, einmal in den Besitz der lange erstrebten Macht gelangt, nun etwa nach dem Rezept des „Angriff“ oder des „Völkischen Beobachters“ vorgehn und kurzer Hand die deutschen Juden ihrer verfassungsmäßigen Rechte entkleiden, sie in ein Rassen-Ghetto sperren oder den Raub- und Mord-Instinkten des Pöbels preisgeben werden. Das können sie nicht nur nicht, weil ihre Macht ja durch eine ganze Reihe anderer Machtfaktoren vom Reichspräsidenten bis zu den Nachbarparteien, beschränkt ist, sondern sie wollen es sicherlich auch gar nicht; denn die ganze Atmosphäre auf der Höhe einer europäischen Weltmacht, die ja mitten im Konzert der Kulturvölker stehn und bleiben will, und dazu das Bewußtsein, in der Wilhelmstraße nun der Notwendigkeit des demagogischen Werbens um den dröhnenden Beifall turbulenter Volksversammlungen bis auf weiteres überhoben zu sein, ist der ethischen Besinnung auf das bessere Selbst günstiger als die bisherige Oppositionsstellung. Den Mitkämpfern von gestern, den Parteifreunden, vermag der neue preußische Innenminister durch Erneuerung des großen Beamtenkörpers in nationalsozialistischem Sinne viel realere Dienste zu leisten als durch offene Zugeständnisse an den brutalen Judenhaß.

Trotzdem wäre es sträflicher Optimismus, sich des Ernstes der Lage nicht bewußt zu sein. Je weniger die neuen Männer dem mit Hunger und Not verzweifelt ringenden deutschen Volk durch gesetzgeberische Wunder wirkliche Hilfe zu bringen vermögen, desto näher liet für sie der Wunsch, ut aliquid feci videatur doch wenigstens ein paar Absätze aus dem rassentheoretischen Programm der Partei in die politische Wirklichkeit umzusetzen, was ohne sensationelle und kompromittierende Judengesetze auf dem Wege des „trockenen Pogroms“, der systematischen Aussperrung und Aushungerung der Juden im wirtschaftlichen und kulturellen Leben leicht geschehen kann.

Inwieweit in einem nationalsozialistischen Beamtenkörper das alte preußische Beamtenpflichtgefühl über die so lange gepflegten antisemitischen Instinkte Herr werden und Schikanen und Rechtsverkürzungen gegenüber Juden ausschließen wird, in wieweit eine Polizei, die einen Nationalsozialisten als obersten Chef über sich weiß, in jedem Einzelfall zuverlässig und unparteiisch bleiben wird, wenn es sich um Juden (oder gar um sozialistische oder kommunistische Staatsbürger) handelt – das sind Fragen und Zweifel, über deren Berechtigung nur die Zukunft entscheiden kann.

Wie die Dinge liegen, scheint es uns noch das kleinere Uebel zu sein, daß durch Tolerierung der neuen Regierung von Seiten des Zentrums die parlamentarische Basis und Kontrolle – trotz eines befristeten Ermächtigungsgesetzes – wenigstens grundsätzlich aufrechterhalten bleibt (man denke zum Beispiel nur an die Gefahren, die sonst der שחיטה drohen), als wenn ein Mißtrauensvotum des Reichstags die Auflösung mit allen ins Uferlose sich erstreckenden Aspekten aus Diktatur und Staatsnotstands-Experimenten herbeiführt.

Or, in English:

The New Situation

Der Israelit, Issue 5, 02.02.1933

The Hitler cabinet, which established itself in Berlin on Monday afternoon, represents a severe emotional burden for all German Jewry, and beyond that, for all circles that see in the exaggeration of today’s nationalist racial fanaticism an obstacle on the path of human civilization and historical progress.

To be sure, we are by no means of the opinion that Mr. Hitler and his friends, having finally attained their long-sought power, will now proceed according to the recipe of the “Angriff” or the “Völkischer Beobachter” and summarily strip German Jews of their constitutional rights, confine them to a racial ghetto, or abandon them to the predatory and murderous instincts of the mob. They not only cannot do this because their power is limited by a whole series of other power factors from the Reich President to the neighboring parties, but they certainly do not want to do it either; for the whole atmosphere at the height of a European world power, which wants to and must remain in the concert of civilized nations, and in addition, the awareness of being relieved for the time being of the necessity of demagogic wooing for the thunderous applause of turbulent mass rallies in the Wilhelmstrasse, is more conducive to ethical reflection on one’s better self than the previous opposition position. The new Prussian Minister of the Interior can render much more real services to yesterday’s fellow combatants, the party friends, by renewing the large civil service corps in a National Socialist sense than by open concessions to brutal Jew-hatred.

Nevertheless, it would be criminal optimism not to be aware of the seriousness of the situation. The less the new men are able to bring real help to the German people desperately struggling with hunger and misery through legislative miracles, the closer lies for them the desire, ut aliquid feci videatur, to at least implement a few paragraphs from the party’s racial theoretical program into political reality, which can easily happen without sensational and compromising Jewish laws by way of the “dry pogrom,” the systematic exclusion and starvation of Jews in economic and cultural life.

To what extent the old Prussian sense of official duty will prevail over the long-nurtured anti-Semitic instincts in a National Socialist civil service corps and exclude harassment and curtailment of rights against Jews, to what extent a police force that knows it has a National Socialist as its supreme chief will remain reliable and impartial in every individual case when it comes to Jews (or even socialist or communist citizens) – these are questions and doubts whose justification only the future can decide.

As things stand, it seems to us to be the lesser evil that through the toleration of the new government by the Center Party, the parliamentary basis and control – despite a time-limited enabling act – at least in principle remains intact (one need only think, for example, of the dangers that would otherwise threaten שחיטה^*, than if a vote of no confidence in the Reichstag were to bring about dissolution with all its boundless aspects of dictatorship and state of emergency experiments.

^*shechita, ritual slaughter

We all know what actually happened in the twelve years that followed this change in government in Berlin.

We do not yet know what is going to happen with the Western alliance, or the United States, in the coming years. But there is zero reason for optimism.

Flag day

Canada, Politics No Responses »

Feb 162025

I am almost out of time, but not quite: it’s still February 15 in much of Canada.

The 60th anniversary of the first unfurling of our Maple Leaf flag.

Now I don’t usually engage in patriotic-nationalistic bull-baloney, and it’s not usually a Canadian thing in any case.

However, in light of our American “friends” declaring a trade war on our country and expressing a desire to annex Canada as the “51st state”, I feel the need, really the strong urge, to do so.

Allow me to advocate again that Canada needs a strong, independent national defence capability, and that we must seriously contemplate, as a one-time participant in the famed Manhattan project, re-establishing ourselves as an independent nuclear power with a credible nuclear deterrent and do so before it’s too late. What else can we do to guarantee the souvereignty of an underpopulated country with highly desirable natural resources, sandwiched between rabid warmongering neofascist Putinistan and the mad personality cult of Trumpland?

Chemistry is evil

Chemistry No Responses »

Feb 092025

So we studied high school chemistry. Covalent bonds. We learned about nice, well-behaved molecules. Carbon, for instance, with a valence of 4. Hydrogen, 1.

Next, shalt thou combine the two. For each carbon, shalt thou count four hydrogen atoms, no more, no less. Four shall be the number thou shalt count, and the number of the counting shall be four. Five shalt thou not count, neither count thou three, excepting that thou then proceed to four. Six is right out. Once the number four, being the fourth number, be reached, then regardest thou the newly made Methane Atom.

After these magic incantations, you turn around, smugly satisfied with your knowledge of chemistry, content that all is well in the world, and then someone shoves this under your nose:

It’s called methanium. It’s really just an ion, an extra proton stuck to that methane atom. It really does not want to exist, so much so, it’s a superacid, which is to say its acidity is greater than that of sulfuric acid.

Okay, so maybe methanium is not quite as evil as dimethylmercury, which really should have no right to exist in a sensible universe, but I daresay, the very existence of methanium already should inform us that we do not live in a sensible universe.

Math is evil

Mathematics 3 Responses »

Feb 092025

I was reading about Borwein integrals.

Here’s a nice result:

$$\int_0^\infty dx\,\frac{\sin x}{x}=\frac{\pi}{2}.$$

Neat, is it not. Here’s another:

$$\int_0^\infty dx\,\frac{\sin x}{x}\frac{\sin (x/3)}{x/3}=\frac{\pi}{2}.$$

Jumping a bit ahead, how about

$$\int_0^\infty dx\,\frac{\sin x}{x}\frac{\sin (x/3)}{x/3}…\frac{\sin (x/13)}{x/13}=\frac{\pi}{2}.$$

Shall we conclude, based on these examples, that

$$\int_0^\infty dx\,\prod\limits_{k=0}^\infty\frac{\sin (x/[2k+1])}{x/[2k+1]}=\frac{\pi}{2}?$$

Not so fast. First, consider that

$$\int_0^\infty dx\,\frac{\sin x}{x}\frac{\sin (x/3)}{x/3}…\frac{\sin (x/15)}{x/15}=\frac{935615849426881477393075728938}{935615849440640907310521750000}\frac{\pi}{2}\approx\frac{\pi}{2}-2.31\times 10^{-11}.$$

Or how about

\begin{align}
\int_0^\infty&dx\,\cos x\,\frac{\sin x}{x}=\frac{\pi}{4},\\
\int_0^\infty&dx\,\cos x\,\frac{\sin x}{x}\frac{\sin (x/3)}{x/3}=\frac{\pi}{4},\\
…\\
\int_0^\infty&dx\,\cos x\,\frac{\sin x}{x}…\frac{\sin (x/111)}{x/111}=\frac{\pi}{4},
\end{align}

but then,

$$\int_0^\infty dx\,\cos x\,\frac{\sin x}{x}…\frac{\sin (x/113)}{x/113}\approx\frac{\pi}{4}-1.1162\times 10^{-138}.$$

There is a lot more about Borwein integrals on Wikipedia, but I think even these few examples are sufficient to convince us that, never mind the actual, physical universe, even the Platonic universe of mathematical truths is fundamentally evil and unreasonable.

Math books

Books, Mathematics, Personal 2 Responses »

Feb 082025

Here is one of my cherished possessions. A book, with an inscription:

The inscription, written just over 50 years ago, explains that I received this book from my grade school, in recognition for my exceptional results in mathematics as a sixth grade student. (If memory serves me right, this was the year when I unofficially won the Pest county math championship… for eighth graders.)

The book is a Hungarian-language translation of a British volume from the series Mathematics: A New Approach, by D. E. Mansfield and others, published originally in the early 1960s. I passionately loved this book. It was from this book that I first became familiar with many concepts in trigonometry, matrix algebra, and other topics.

Why am I mentioning this volume? Because the other day, the mailman arrived with an Amazon box containing a set of books. A brand new set of books, published in 2024. A series of mathematics textbooks for middle school and high school students, starting with this volume for 6th and 7th graders:

My instant impression: As a young math geek 50 years ago, I would have fallen in love with these books.

The author, André Cabannes, is known, among other things, as Leonard Susskind’s co-author of General Relativity, the latest book in Susskind’s celebrated Theoretical Minimum series. Cabannes also published several books in his native French, along with numerous translations.

His Middle School Mathematics and High School Mathematics books are clearly the works of passion by a talented, knowledgeable, dedicated author. The moment I opened the first volume, I felt a sense of familiarity. I sensed the same clarity, same organization, and the same quality of writing that characterized those Mansfield books all those years ago.

Make no mistake about it, just like the Mansfield books, these books by Cabannes are ambitious. The subjects covered in these volumes go well beyond, I suspect, the mathematics curricula of most middle schools or high schools around the world. So what’s wrong with that, I ask? A talented young student would be delighted, not intimidated, by the wealth of subjects that are covered in the books. The style is sufficiently light-hearted, with relevant illustrations on nearly every page, with the occasional historical tidbit or anecdote, making it easier to absorb the material. And throughout, there is an understanding of the practical nature, utility of mathematics, that is best summarized by the words on the books’ back cover: “Mathematics is not a collection of puzzles or riddles designed to test your intelligence; it is a language for describing and interacting with the world.”

Indeed it is. And these books are true to the author’s words. The subjects may range from the volume of milk cartons through the ratio of ingredients in a cake recipe all the way to the share of the popular vote in the 2024 US presidential election. In each of these examples, the practical utility of numbers and mathematical methods is emphasized. At the same time, the books feel decidedly “old school” but in a good sense: there is no sign of any of the recent fads in mathematics education. The books are “hard core”: ideas and methods are presented in a straightforward way, fulfilling the purpose of passing on the accumulated knowledge of generations to the young reader even as motivations and practical utility are often emphasized.

This is how my love affair with math began when I was a young student, all those years ago. The books that came into my possession, courtesy of both my parents and my teachers, were of a similar nature: they offered robust knowledge, practical utility, clear motivation. Had it existed already, this wonderful series by Cabannes would have made a perfect addition to my little library 50 years ago.

Vive le Canada!

Canada, History, Politics No Responses »

Feb 032025

How did we get here, asks the CBC rhetorically, as they recount the events that led to Trump’s announcement of across-the-board tariffs on Canadian imports to the United States.

On Nov. 5, Americans chose Donald Trump to be their next president. Twenty days later, Trump announced, via a post to his own social-media platform, that he would apply a 25 per cent tariff to all products imported into the United States from Canada and Mexico — a response, he claimed, to the fact that people and illegal drugs were entering the United States from those two countries.

At least in the case of Canada, this was an irrational justification. Seizures of fentanyl at America’s northern border represented 0.08 per cent of all fentanyl seized by American officials in the last fiscal year. The number of people entering the United States through Canada has also been a fraction of the total number of people entering via Mexico.

They also wonder if this might be a shot in the arm for Canadian patriotism. Damn right it will be and for a damn good reason:

But if American democracy continues down a dark path, not being American might be more than an argument against annexation. In that case, as Rob Goodman, an author and professor of politics and public administration at Toronto Metropolitan University, has written, “Canadian distinctiveness” might be not a “vanity object,” but an “essential safeguard of Canadian democracy.”

Again and again, I am reminded of the television adaptation of The Handmaid Tale, depicting a diminished, yet independent Canada where life remains reasonably normal even as south of the border, a country that no longer calls itself the United States of America but is renamed The Republic of Gilead, chooses totalitarianism. No wonder that even our cats seem to be concerned…

Some economists worry that fighting back against Trump’s tariffs is a losing proposition. I don’t think so. Canada’s economy is small compared to that of the US but not that small, and we have something America does not: the resilience of a people determined to fight back against a former friend who so blatantly betrays us. Yes, we will pay more at the grocery counter. We know that. Yes, American goods will disappear from shelves: in fact we will help remove them. But if this is how Trump thinks he can coerce Canada to become the “51st state”, I think I speak for the overwhelming majority of my compatriots when I respond with a resounding (even if un-Canadian in its directness) fuck off. Va chier.

In short: This is not a joke anymore. What Trump is doing is how a country treats its worst enemies, not its friends. If Trump thinks Canada is a pushover, I think he’s in for an even nastier surprise than his best buddy in Moscow when he attacked Ukraine. Let’s hope we never find out just how tough and resilient Canadians will be when backstabbed.

Friends of mine used to think (perhaps not anymore) that I went stark raving mad when I suggested that Canada should rapidly initiate an independent weapons program and build a credible nuclear deterrent. We have the know-how, the materials, we have the technology and the means. As to why? Consider this is a great, rich, but underpopulated country, sandwiched between tyrannical, warmongering Putinistan across the North Pole to the north and the rabid personality cult of Trumpland to the south, and you have your answer.

Reunification

Canada, History, Politics 2 Responses »

Jan 302025

Repeatedly, I see questions on Quora, asking why Canada resists Trump’s suggestion of becoming the 51st state. Why bother going through the likely hardships instead of giving in to Mr. Trump’s will?

Very well, allow me to offer my own contribution, to help the process along. Here, I designed a nice voting slip that could be used for this purpose. The date, of course, can be easily changed.

I must confess that the idea is not original. I had help, an elegant historical precedent that, I think, is perfectly suitable for this purpose:

I hope my contribution is received in the same spirit in which it is offered, and perhaps thanked by a nice, “from the heart” gesture (with the right arm properly extended of course) by those who approve.

PDF is available upon request.

Eighty years

History 2 Responses »

Jan 272025

Eighty years ago today, Auschwitz-Birkenau, the site of one of the worst systematic crimes against humanity, was liberated.

Some are trying to erase the Holocaust from history. Some are trying to pretend that it was no big deal.

But it did happen. And it was a “big deal”: Some six million Jews were murdered, along with millions of others: Roma, homosexuals, the disabled, prisoners-of-war, political prisoners.

“Never again” and “we remember”, we are told, but it is happening over and ever again, even if on a smaller scale; and many are trying hard to make us forget.

We won’t. I won’t.

Eighty years is a long time. Very few people are alive today who have seen this hell on Earth firsthand and survived to tell the tale. But a few are still around. And there are those of us who knew people who were there. Who knew people who avoided being deported there only by the grace of God as the expression goes. (One elderly friend of mine, no longer among us, told me how he was personally saved by Raoul Wallenberg, as he was one of the lucky ones carrying a Swedish Schutzpass.) There were those who tried to help people survive. My father, I was told, was among them: forging documents for friends, for his Jewish first wife and her family members, to help them survive, avoid the ghetto, avoid the cattle cars.

“Never again” is a nice catch phrase but what if it happens again? Will we remember? Will I remember? And if I do remember, will I have the courage of my father?

I hope I’ll never have to find out.

Physics for the masses

Personal, Physics No Responses »

Jan 262025

I keep being asked: When will you write a book already? And true, I have several half-baked book ideas that I am contemplating. One of them was going to be a book discussing some key concepts in physics by offering both an accessible narrative and a technical background.

Well, it appears I have been scooped, if that’s the right word! I first heart of Brent Lewis’s project when he contacted me last year, sending me a prerelease copy of Theoretical Physics for the Masses. Oh my, I thought, this is the book I wanted to write!

Or, well, as close as possible to the book I wanted to write, considering that it is not my brainchild and as such, Lewis’s selection of topics differed slightly from mine. Anyhow, long story short, the book is now published by World Scientific, a reputable publisher of books and numerous journals. I hope that it will mean a decent effort at marketing and Lewis will be able to collect royalties on many copies.

Considering the breadth of subjects, the book is surprisingly thin: Just over 180 pages, with appendices included. The main body part is less than 60 pages, however; the remainder are the technical appendices. Depending on how you look at it, this could be considered a bug or a feature.

Who is this book for? Let’s face it, the technical appendices are not for the faint-hearted. Lagrangian field theory, the equations of general relativity, Fourier-decomposition of a scalar field and derivation of the corresponding quantum field theory propagator, even a brief overview of the key features of bosonic string theory: this is not high school mathematics. Nor can we possible expect a thorough treatment of these subjects in such a thin volume.

Yet this book reminds me of a much thicker tome published many years ago: Penrose’s book, The Road to Reality. Like Penrose, Lewis presents a road map for the aspiring physicist. The plain English narrative offers something that is sorely absent from many textbooks: background and motivation. The technical appendices in turn make the connection between the core ideas and their actual implementation. And this is where the brevity of Lewis’s book might actually be an asset: Whereas Penrose spends several hundred pages discussing mostly pure mathematics, Lewis jumps right ahead into the physics.

So no, you will not learn general relativity or quantum field theory, nor the necessary mathematical foundations, from this book. But if you want to learn these subjects, the book can serve as your guide. Reading it before you dig into a textbook like Wald’s General Relativity of Peskin & Schroeder’s An Introduction to Quantum Field Theory will help maintain a bird’s eye perspective as you begin your journey. You may not have skills level-knowledge yet, but Lewis’s book will help you not lose sight of your intended destination as you study.

Let’s face it: These subjects are hard. Any resource that helps make it a tad easier to learn is welcome. And Lewis’s book definitely helps.

Toys, toys!

History, Music No Responses »

Jan 262025

Someone reminded me of Kurt Weill’s poignant 1936 anti-war musical Johnny Johnson today. I recalled in particular the last song, Johnny’s song, in which the simple-minded protagonist Johnny, never losing his faith in humanity, tries to sell toys to an indifferent public who are rushing over to the next square to listen to another warmongering speaker. “Toys, toys!” cries Johnny but no one listens.

I did not remember the song’s lyrics. Apparently, there are different versions, but the one I am familiar with includes these lines (emphasis mine):

At last we’ll find the day
When joy shall be our song

I hear them say it’s all baloney
The world’s a mighty cruel place
With tooth and claw and promise phony
An old hard guy he wins the race

But you and I don’t think so
We know there’s something still
Of good beyond such ill
Within our heart and mind

Ouch. Did Paul Green, who wrote the song’s lyrics, foresee the future?

Oh well. Here’s a Midjourney cat that I think aptly captures the musical’s atmosphere.

Pumping elephant

Language, Science 1 Response »

Jan 212025

I cannot stop laughing.

Earlier today, I came across one of the weirdest papers yet that I’ve ever come across in the scientific literature.

I admit that my first thought was that it was a joke paper in a predatory journal. But no. It was a serious publication, in a serious journal, published under the Springer Nature label, no less.

And like all proper scientific publications, it had a title, an abstract, and… No, wait. It did not have an abstract. What it had instead was…

A pumping elephant.

Seriously. A pumping elephant.

But if it was not a joke paper, then what was it? Having noticed that the paper’s authors were all Chinese, it occurred to me that perhaps it’s a mistranslation. The AI Claude quickly confirmed my suspicion. Apparently, the authors mistranslated “Abstract” as “抽象” (chōuxiàng) in Chinese, which does mean “abstract” but in the sense of “abstract concept” rather than “summary of a paper”. They then literally translated 抽 (chōu), which can mean “to pump” and 象 (xiàng), which can mean “elephant”.

So perhaps it was an embarrassing but ultimately innocent mistake by the paper’s authors.

The same cannot be said about the journal’s editorial staff. That such a glaring piece of nonsense made it to the pages of a reputable journal signals a complete lack of copy-editing and editorial supervision.

To their credit, the paper was ultimately retracted. And it only took about three and a half years…

I asked Midjourney to create for me a pumping elephant. Clearly inspired by Verne’s famous novel, The Steam House, Midjourney produced some wonderful steampunk pumping elephants. This is my favorite so far.

Incidentally, there are also YouTube videos of bona fide pumping elephants: Elephants that learned to use a water pump.

Needless to say, I’ll be sorely tempted to use “Pumping elephant” to label the Abstract in my future publications…

Hello, Freddy

Cats, Personal 4 Responses »

Jan 192025

Hello, Freddy. Please say hello to the world.

Hello, world. Please say hello to Freddy.

A cartographic reminder

Canada, Politics 3 Responses »

Jan 182025

Here is my attempt to remind our illustrious world leaders of the importance of proper cartography:

Is it really too much to hope for that they respect the esteemed profession of mapmaking?

2025

Canada, Cats, Cybernetics, Politics No Responses »

Jan 082025

We are barely a week into the new year, 2025. Yet here are some news items that would have sounded like outlandish B-movie nonsense just a few years ago.

The incoming president-elect of the United States expressed his interest in annexing Greenland, and did not rule out the use of force against a NATO ally;
The incoming president-elect of the United States expressed his interest in reoccupying the Panama Canal zone and did not rule out the use of force;
The incoming president-elect mused about turning Canada into the 51st state and did not rule out the use of “economic force” to accomplish this;
Ukraine’s offensive in Russia’s Kursk region led to a large number of casualties on the Russian side, including thousands of North Korean troops;
North Korea successfully tested a new intermediate-range missile;
An article in Foreign Affairs magazine argues that South Korea should acquire nuclear capability for deterrence;
After several similar incidents involving Russian ships in the Baltic Sea, now a Chinese vessel damaged undersea cables connecting Taiwan;
A far-right politician in EU member state Austria is set to form the next government of the country;
Alien ship set to land in New York’s Central Park turns back at the last minute – “Too dangerous, no intelligent life,” they message their home planet.

OK, I threw in the last one. But the rest? In 2025? Aren’t they just as outlandish as the bit about aliens? Aren’t we, and by that I mean the whole human race, supposed to be, you know, a tad more intelligent?

Guess not. Can’t wait for the world to be taken over by AI-assisted cats.

Unsolicited theories

Personal, Science No Responses »

Jan 072025

I just made up my mind.

I’ll never again respond to unsolicited theories, unsolicited requests to comment, not even from Nobel-prize winners.

Because in the end, unless I enthusiastically agree with their ideas, no matter how silly, how outlandish, it always ends badly.

It doesn’t matter how polite I am, how carefully I choose my words, how much I try my darnedest to steer them in the right direction. And it makes no difference if the person in question is just, say, a taxi driver somewhere in Asia or an accomplished scientist in Europe.

If you have a scientific idea, do the right thing: write it up, send it to a journal, publish it. I am officially not interested anymore. Sorry, but I’ve been insulted one too many times and finally, my fuse got blown. I have better things to do than nursing your hurt feelings because the science community is not treating you seriously.

In fact, chances are that in the future, I’ll blacklist all such e-mail addresses right away. My sanity is more important than your feelings.

The economy vs. the economy

Canada, Economy, Politics No Responses »

Jan 042025

I don’t much watch news channels anymore, but earlier today, I caught a fragment of a report arguing that voters are not rejecting the left because of the economy; that the shift to the right is occurring at a time when the economy is doing fairly well, and that there was no similar shift to the right during the last major economic crisis.

A few hours later (or maybe less) on the same channel I caught a fragment of a report about CEO pay here in Canada: for the top 100 (?) companies, it is now well over 200 times the average worker’s salary. The report pointed out that barely more than a decade ago, it was “only” a little over 100 times the average worker’s salary.

So perhaps, just perhaps, it’s the economy after all?

One of the better attempts by Midjourney

I mean, maybe the economy is doing great insofar as macroeconomic indicators are concerned. But we don’t live off macroeconomic indicators. We do not pay with macroeconomic indicators for groceries at Loblaws, nor do banks accept macroeconomic indicators in lieu of a mortgage payment. And it doesn’t matter if the economy is doing great overall, if rising inequality means the middle class is left behind.

And this is how we end up in dangerous times, in ways already well understood by Aristotle some 2600 years ago. The unhappiness is palpable. This drives people to political extremism. Yet all too often, those with the power to do something about it just congratulate themselves on an economy doing great, and express incomprehension when confronted with dissatisfied voters. Must be bad messaging, they say. Perhaps foreign interference. Stupid people falling for populism.

All of the above exists of course. But the root cause, I think, is much simpler: For most voters, the economy (the economy that they experience paycheck-to-paycheck, the economy they experience at the grocery store checkout counter, at the bank when trying to get a mortgage) is not doing great. In fact, it is doing terribly. And they are getting really pissed off about it. Which of course means fertile ground for political populism.

Happy 2025!

Personal No Responses »

Dec 312024

To all my friends, to all good people…

… Happy New Year!

An unsettling dream

Personal No Responses »

Dec 252024

Last night, I had a disturbing dream.

I do not usually recall my dreams. When I wake up in the morning, almost always I wake up with a clean state of mind, focused on the things I am planning to do in the coming day. It is very rare that I wake up even with fragmentary memories of whatever I was dreaming while asleep.

This was one of those days. I was unable to recall the details, but I remembered that in my dream, I worked at some retail establishment. I ended up working there as a favor to someone, being paid under minimum wage. I wasn’t there for the money.

Long story short, somehow the establishment became Trump’s property. Yes, that Trump. And Trump visited the place. In my dream, I’ve met Trump previously. Still, being the polite chap that I am, I greeted him with a “good morning, Mr. President”. He looked at me and told me, right there in front of his entourage, that no, we’ve known each other long enough, just because he got re-elected, I should not stop addressing him by his first name.

I was beaming with pride. I was speechless. So much so that only after he left the business did I realize that I forgot to ask the one question that I’ve been meaning to ask: Now that I work for him, as opposed to doing a favor to a friend, can I at least get paid at the official minimum wage?

Is it really this easy to manipulate us? Through our pride, our self-esteem, our vanity? Was my dream a cautionary tale, reminding me that no, however smart I think I am, I am not immune to these things?

Peace on Earth…

Personal No Responses »

Dec 242024

Here’s my Christmas wish for all good people, all the good people on the good Earth: peace.

And no, not the peace of the graveyard. Not the peace of the conqueror or tyrant, the peace of oppression, imposed peace.

No… a just peace.

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