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A quote from Euler

  Yesterday I paid tribute here to a great mathematician. Today I offer a quote from him.  "To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero.  Hence there are not so many mysteries hidden in this concept as there are usually believed to be."  The significance of that observation may not be obvious outside of some consideration of the history of math, the development of calculus in particular.  But once we do a little grappling with that history, we see that Euler is making a point here that takes us back to ancient Greece.  Back to Zeno, Achilles and tortoise.  If Achilles is to catch up with the tortoise there must be a moment at which the difference between them is zero. One way of looking at the problem is to ask what is the next lower number -- one really really close to zero but still a positive number!  Euler here is saying "That is the wrong way of looking at it." Or, "don't create my...

Paying tribute to a great mathematician

Leonhard Euler (1707-1783) was surely one of the most prolific of great mathematicians. Among his contributions, we need to mention two, each of which comes down to us as a single letter: the letter e and the letter i . If we were literally to "pay"tribute, we might do so in increments of $2.72, rounding up a bit the value of irrational e.  We'll get to that. First: biography. Euler was born in Basel, Switzerland, so his life and work might fittingly be considered a riposte to the old anti-Swiss jibe (originally from The Third Man ) that Switzerland has produced nothing for all its years of peace and democracy, nothing more than the humble cuckoo clock.    Since Euler’s day and because of his work, i has stood for the simplest of the numbers that Descartes had called “imaginary.” This i refers to the square root of -1. We don’t need to bother ourselves further with the question “ what is the square root of -1?” It is i , by stipulation.    Also since Eul...

Supreme Court term

  I hereby inform my readers that I will not be doing the usual post-Supreme-Court term round-up this year.  Most Julys for many years now, I have devoted four long blog entries to the term of the US Supreme Court that has just ended.  This year, I'm not feeling it.  There have been a lot of intriguing decisions this term. I have written posts on some of they as we have proceeded.  But the elaborate round-up? No thanks.  And ...sorry to disappoint.  By the way, the fact that I have just been using the word "round-up" reminds me of the fact that one of the cases decided by the Court this term literally did involve a product named Round Up.  https://www.supremecourt.gov/opinions/25pdf/24-1068_n7ip.pdf 

To a 15 year old

    From Quora, question and answer How should I get started with philosophy? I'm 15 years old. That is a very good time for it. You might want to try to define for yourself what kind of philosophy problem most interests you and cluster your readings (and your early manuscripts) there. Many young people are driven by social/political concerns. Can philosophers say something foundational about these concerns? Can it help us get a Big Picture into which the day-to-day headlines and debates will fit? If that is what you mean by philosophy, you might want to look to John Rawls, Robert Nozick, and older figures like Thomas Paine, Edmund Burke. Others are feeling a more existential angst. What is the point of even getting out of bed in the morning? Do my actions matter? Are they determined anyway, so that I am just a ping-pong ball bouncing around? If those questions are what philosophy means to you, I suggest the essays of Ralph Waldo Emerson, and a follow-up with the work of Willi...

Four score and seven years ago

As soon as Abraham Lincoln received a favorable battle report from Gettysburg in early July 1863, he at once paired the time of year with the time in which the United States had declared its independence from its mother country, and before long Lincoln did the arithmetic.  The two events were separated by 87 years. Months passed before Lincoln spoke on the subject of that battle and its consequences (in November), but his famous address on that occasion begins with the invocation of the length of time that passed between the two events: four score and seven years.  This is likely the only reason the word "score" in that sense remains in the English language.  All of which, as we close in on the 250th anniversary of the same declaration of independence, induces me to ask: what happened just 87 years ago as I write?  That would be 1939. What happened on independence day that year? Four score and seven years ago, legendary first baseman Lou Gehrig delivered a farewell a...

The Supreme Court, equity theft and the Pung family

  In Isabellas County, Michigan, the Pung family lost its ranch style home due to a mere $2,242 in disputed taxes.  The country government sold the place for $76K at a public auction. The buyer then flipped it for $195,000.  I'm a recovering anarcho-capitalist, so I will try not to go on too much of a bender about how much this sucks.  But boy is the world of property taxation and enforcement offering up a delicious cuba libre to someone who is trying to get with the twelve steps, here!!! In May 2023, U.S. Supreme Court ruled unanimously in Tyler v. Hennepin County that home equity theft is unconstitutional. The Court determined that seizing excess value over a tax debt violates the fifth amendment's taking clause.   So was Pung simply a straightforward application of Tyler ? No such luck.  Lower courts essentially gave the Pungs the difference between the tax debt and the public auction value. But the Pungs asked the Supreme Court to affirm that (...

Electoral humiliation for a Kennedy

A poor third place finish for a Kennedy. And in the State of New York, no less -- the state where former Attorney General Bobby Kennedy served as US Senator. from his election in November 1964 until his assassination almost four years later.  The primary campaign for the Democratic nomination to be the Congress critter from the 12th district NY -- midtown Manhattan, along with both the upper East and West sides -- was the first ever political campaign for Jack Schlossberg.  Schlossberg is the son of Caroline Kennedy, and so he is the grandson of a President and the grand-nephew of the aforesaid AG and Senator.  Whatever.  Micah Lasher won with 39 percent of the vote. The second-place finisher was Alex Bores, with 35 percent. Schlossberg was far behind with just 10 percent. George Conway was in the mix, too.  [At least Schlossberg beat Conway].  Voting turnout was likely key here.  Lasher drew his strength from the Upper West side (pictured) where votin...

An important economist: not a celebrity

  One of the important financial economists writing today is Mohamed El-Erian, who grew up as the son of an Egyptian diplomat and was the deputy director of the IMF for three years in the 1990s. He is quite well known to folks like me, who look to his analyses to guide our work reporting day to day events.  But he is not well known at all to the "general public," where that term is taken to mean the sort of people who know that Paul Krugman or Robert Shiller are important economists.  I'm old enough to remember when Friedman and Galbraith were the economists whose name came to the tongue of many non-economists. They both passed away in the first decade of the new millennium, and the public attention has done what it does ... it has passed on. I may say more about El-Erian's non-celebrity work soon.  For now, I will only lay down that he has recently said that on June 24, "The most notable price action in US markets" was the fall by 9 basis points of US gover...

The Mosquitoes of Gilligan's Island

I just had a revelation about Gilligan's Island . Regular fans will remember that Gilligan would from time to time mention his favorite rock group The Mosquitoes. Eventually, the group itself visited the island, looking for a relaxing getaway after a difficult tour. Like all guest stars, the band left in a manner that didn't help the core seven castaways at all.  Anyway, it is obvious that the group was conceived as a Beatles parody. The insectile name, to start with,  The fact that the group appears to have had a single with the lyrics "don't go in there, yeah yeah yeah." It was not subtle parody.  But what only recently occurred to me was the clever way that the names of the members of the fictional group mirror the real-world names of the Fab Four.  The Mosquitoes had four members (of course): Bingo, Bango, Bongo, and Irving. Note that three of those names would be quite unusual for any of the men one meets on the street in any city in the Anglophonic world. ...

A random philosophical troika

   An odd philosophical troika of philosophers in early modern Britain comes to mind today for no good reason.  Locke, Berkeley, Hume. I saw a random post in Quora asking for a brief summary of the significant contributions of each "the" three major philosophers.  No more specific context. I have no idea how one would pick THE troika the querent had in mind, But this is one troika if great significance. To summarize their “significant contributions” is a considerable task — or three different tasks, EACH considerable. But it does seem that together the three of them tell a tragic story.  In essence we can say this (ignoring the politics of Locke or of Hume, and the vision theory of Berkeley): Locke: Accepted a dualist picture of the world in which minds, conceived of as properties of souls, are intangible beings that must come to grips with a material world around them. His contribution was to think through this material world in Newtonian terms — what he called...

There's something happening here

I always thought that was the name of the song!  (Spoiler alert: I was wrong.)  The Buffalo Springfield classic that begins with those two haunting chords. It wasn't about anti-war protests. At least (in the wake of the death of the author) you can make it about that if you will.  The catalyst for the creation of the song was the Sunset Strip curfew in Los Angeles in late 1966.  It has taken me sixty years to learn this.  Who knows how much learning is ahead for me?  For what it's worth.  

Excitement in the air

  I don't know about you, dear reader, but there are some of us who feel some excitement on the morning of 'decision days' in June.   The US Supreme Court is typically trying to clear its dockets ahead of its summer break, and this is when the hotly contested cases and the publicly most awaited make their appearance. Hence the fun.  "Is today the day they release their birthright citizenship decision? or a re-affirmation of central bank independence? or the weapons-for-the-stoners case?" Last Thursday did turn out to be the day for the weapons-for-stoners case. That came out right, as far as concerns the parties directly involved, though the precedential significance seems to be small. This morning? It is another announced decision day and the excitement is back. Okay, nerdy perpetual law student fun....  

Taking the week off

  As you may have noticed, dear reader, I have for a long time been presenting new blog posts every Tuesday, Wednesday, Thursday and Friday. Yet today is Thursday and this is the first post this week.    My apologies if you are disappointed.  I hope to be back to a regular schedule next week. 

An odd insight

I just realized something.  I've always been kinda nerdy, but I've never fit in even among my fellow nerds.  Why not?  Perhaps because Dante's DIVINE COMEDY was for me what THE LORD OF THE RINGS was for the 'normal' nerd. Hmmmmm. 

MAHA beats MAGA

The coalition that put Donald Trump into office twice is coming unravelled. That judgment is of the jigsaw-perceiving sort.  One of its pieces is the recent Republican Party primary in Iowa.  https://www.wsaw.com/video/2026/06/03/lahn-wins-iowa-gop-governor-race-turek-takes-democratic-senate-primary/   "Make America Healthy Again," a loose grouping itself, of people who read Ivan Illich and those who just want to be able to drink unprocessed (raw) milk without governmental interference, of people who are sure vaccines cause autism and those who believe pesticides are destroying the food, from the granola eaters on the left to the granola eaters on the right including some who have made that transition personally -- MAHA ending up (as that acronym suggests) more-or-less aligned with MAGA during the last presidential election campaign. This year, in the mid-terms, that alignment has come apart.  In the Iowa Republican primary for Governor, MAHA backed Zack Lahn, w...

Comment on the Sen quote

  I noted yesterday, that in writing his work on collective choice Sen had apparently read not only the work of John Rawls (which was inevitable), but responses to Rawls about the humans-only nature of the deliberations Rawls imagines behind the veil of ignorance. We are supposed to imagine ourselves as ignorant of our social class, race, and native intelligence, but presumably cognizant of the fact that, when the veil is lifted, we will turn out to be humans.  The responses wondered why the species barrier is that strong. What piques my interest is that Sen refers to these critiques (he does not source them specifically -- admittedly it is a bit of a digression from the main line of his thought) as half in jest and half serious.  Hmmmm.  Has Peter Singer written in response to Rawls? If he has, (and I'm too lazy to look into it right now) then I can easily imagine Singer making the point Sen emphasizes in dead earnest, utterly without jesting.  What Sen sees...

A quote from Amartya Sen

  Amartya Sen, an economist/philosopher, was born in November 1933 and he is still with us. He may be the single most important philosopher alive.  One of his works is COLLECTIVE CHOICE AND SOCIAL WELFARE. Or, perhaps, you might count this as two of his works.  The first book of that title was published in 1970, then a much expanded and re-written version appeared in 2017. I'd like today to quote a bit from the 2017 edition, in which Sen is with some sympathy discussing the work of John Rawls.  He says (this is a footnote): A half-jocular, half-serious objection to the criteria of fairness of Rawls and others often runs like this: Why confine placing oneself in the position of other human beings only, why not other animals also? Is the biological line so sharply drawn? What this line of attack misses is the fact that Rawls is crystallizing a rule of fairness that our value system does seem to have, rather than constructing a rule of fairness in vacuum based on notion...

An unreported alien landing

  An alien recently landed his UFO in Vatican City. Pope Leo went out to meet him personally.  Leo, "I just want to know one thing.  Does your world know Jesus Christ as Savior?"  Alien, "Oh, yes.  He visits us about once every seven years.  We throw a big party when he arrives, then he preaches and heals amongst us. When Jesus has decided it is time to leave, our leaders declare a national holiday and there is a big send-off parade. We tell him we look forward to the next visit" Leo, "Really?  He only visited this planet once, more than two thousand years ago."  Alien, "Hmmm.  Did you give him a nice send-off?" 

"Oh, she bit her dog, eh?"

I haven't seen either of the recent WICKED pics.  I don't plan to see them. Years ago I had some interest in the OZ fantasy world.  Back when it meant the Frank Baum books on the one hand and the 1939 movie on the other.  The Baum books were written as an allegorical take on the monetary debates of Baum's day. The word "Oz" itself suggests ounces, the standard measurement for gold. The notion of a "yellow brick road" suggests gold bricks, and perhaps that an insistence on a gold standard was leading the farmers of the US, the Kansans, toward danger. And so forth.  Of course the Garland movie didn't do much with the allegory -- It could have, since the '39 movie came out between FDR's abandonment of the gold standard (1933) and his partial reinvention of it by way of Bretton Woods (1944) -- but it didn't.  Personally, I have never asked myself prequel-producing questions like "how did the monkeys learn to fly" or "why does ...

A brief history of Google/Alphabet since 2020

  . Mid-2020, the firm (ticker symbol still GOOG) performed a stock split. In July 2021, Alphabet announced Intrinsic, a new robotics software company.  In November 2021, the formation of a new company, Isomorphic Labss, to promite the use of artificial intelligence in the pharmaceutical world.  August 2024, a US district court found Google guilty of violating antitrust law by using unlawful tie-ins to maintain its dominance in what remains its signature product, the search engine. No drastic remedy will be attempted, because the courts notices that the market has been taken over by AI/LLMs of late, and Google has no dominance there.  April 2025, another US district court finds Google guilty of illegally monopolizing parts of what is called the adtech stack, I.e. online advertising technology.  November 2025, the parties to the adtech case made their final arguments to the court in the eastern district of Virginia as to the proper remedies it should order. ...

A brief history of Google to 2019.

Without getting fancy, here are some key dates: 1996: Larry Page and Sergey Brin experiment with a new type of search engine.  In those ancient days search engines simply ranked results by how often a searched-for term appears on a web page.  But Page and Brin are after something a bit more sophisticated, a range of metrics that cumulatively determine how important the searched items are on a particular page. They literally used a friend's garage as an office while working on this idea. A cliche is born, the garage-born web business.  1998: The new business is formally created when Page and Brin persuade a co-founder of Sun Microsystems to pony up $100,000 so they can incorporate, set up shop in Menlo Park and hire their first employee.  2002: Yahoo offers to buy out Google for $3 billion.  Google holds to a valuation of $5 billion, and the talks end without result. Also this year, in a display of the mainstreaming of the verb form of their name, an episode of t...

An unpublished BROWN v. BOARD concurrence

  I believe at some point I have mentioned in this blog that David O'Brien authored a book about an unpublished opinion written by Justice Robert H. Jackson that would have served as a concurrence to the court's opinion in the famous 1954 case, BROWN v. BOARD. The court's opinion was expressed in a unanimous vote and a single opinion by Chief Justice Earl Warren, declaring that the old rule that allowed "separate but equal" treatment in education facilities, i.e. segregation by race in schools, was a rule no longer. A follow-up decision the next year addressed the issue of remedy: it ordered states to desegregate their schools with all "deliberate speed." (Jackson was dead by that time.) Jackson never published his concurrence because the Chief Justice lobbied hard to dissuade him from doing so. It was Warren's considered view that on a matter so pressing the Court must speak with one voice. I bring it up again because I would like to offer a quota...

Parmenides and the moon

 There is a new book out about the Greek philosopher Parmenides, the central figure of the Eleatic school. Well, it is listed as a 2025 publication.  I, for one, will call that "new" given the antiquity of the subject matter.  It is an anthology titled simply, Parmenides: New Perspectives , edited by A.G. Long and Barbara M. Sattler. The Eleatics may have made their greatest impact on subsequent philosophy through Parmenides' disciple Zeno. The simplistic view (my view) is that Parmenides took a position that seemed, simply, nuts. There is no change, no motion, and no division in the word, there is only Being.     Zeno provided arguments for that position that made it seem less nutso, by making the common sensical world of change, gaps, and differences itself seem oddly paradoxical. That conventional understanding makes Zeno seem the more interesting figure in that dyad.  But the Long/Sattler book offers "new perspectives". One of them is that Parmenid...

Artificial Intelligence and the word "quietly".

People are looking for "tells".  What is a quick way to tell when I am reading AI slop, rather than something some real human has composed?  One of the better tells is the frequent use of the adverb "quietly" in metaphorical contexts. LLMs have received a level of publicity out of proportion to their role within the AI world (see the above Venn diagram) in part because they impact and indeed may threaten the livelihood of people like me. So we, because loquacious folk, talk about it. LLMs, large language models, have quietly developed the tick of using the word "quietly" a lot. You may recently have read about how a certain individual has "quietly" become important in deliberations of Congress, or how Stephen King has "quietly" amassed some large number of acreage of Maine real estate, or some whatever. "Quietly" does a lot of work for these models. It sounds as if it is saying something about something conspiratorial or trick...

Thomas writing for eight? Really?

Prelude: for those who were paying close attention to my haiku last week: yes, I did have the procedure done and, yes, things turned out well.  There is nothing nasty growing inside my butt. Prelude complete.  Anyway: I don't want to say much here about the ROYAL CARRIBEAN case issued by the US Supreme Court last week, in part because I may have something to say about it two months from now, as part of my annual round-up of  all things SCOTUS.  I'll only for today note that the case has Justice Thomas writing for the court, as one of an eight-member majority thereof, with Justice Kagan the sole standout.    And my only point is to ask a question. Does anyone know of another decision within the last couple of years that came down just that way?  In many politically sensitive cases, one gets a 6-3 lineup.  Sometimes the split consists of appointees of Presidents of the Republican Party versus those of Presidents of the Democratic Party, as in LOUISI...