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...
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As you probably remember from my frequent recent mentions, I've been working my way through a book on probability, statistics, and the philosophy of science, STATISTICAL INFERENCE AS SEVERE TESTING, by Deborah Mayo. This will be my last quote from that book. From p. 367, "It is supposed in many fields of social and biological science that nearly everything is related to everything: 'all nulls are false.' Meehl dubbed this the crud factor." What follows is a description of a psychology survey done by the University of Minnesota in 1966 in which all of the following showed some degree of (often low though statistically significant) correlation -- attitudes toward school, leisure activities, educational plans, parents' occupations, siblings, birth order, family attitudes. religious preferences, MCAT scores, etc. Every null hypothesis is false. Mayo tells us that Meehl here is also eager to explain that this is not what statisticians call a "Type 1 error...
Basic timeline for the development of primates -- with highlights selected from an intentionally anthropocentrc point of view: up to three million years ago. The earliest primates, called the Plesiadapiformes, are said to have speciated out of the Euarchonta very soon after the dinosaur-eliminating Comet struck, about 66 million years ago (MA). Soon after (63 MA) the Plesiadapiformes differentiated into the so-called wet-nosed and the dry-nosed primates. We will ignore the wet-nosed in what follows. The dry nosed are represented on today's earth by both the Great Apes and us humans. One distinctive feature of the dry-nosed branching? It can't metabolize vitamin C. We, and millions of years of ancestors, have had to include fruits bearing that vitamin in our diets. We then skip forward to 30 MA. Around this time some of the dry-nosed primates made it to South America. Perhaps the area was connected with Africa here: but on one hypothesis that wouldn't have been necessary...
There was a time in the history of life on earth before predation. Scientists talk about an Ediacaran period in the history of our planet. It is named for the Ediacara hills in Australia, where some of the key fossils were found. Also, for the phonetically curious, the proper pronunciation is Ee-dee-ac-aran. Rhymes with Me - he- wrack -Iran. Anyway, the creatures of the Ediacaran did not eat each other. They were without eyes, claws, or antennae: no means for watching, seizing, or evading each other. Beginning around 635 million years ago, continuing until 542 million, Ediacaran biota had simple lives as they crawled along the sea floor, eating such organic matter ("the mat" as Peter Godfrey-Smith calls it) that had built up there. Eventually dying and contributing to that mat. Ediacaran biota did have nervous systems. The fact itself indicates that nervous systems aren't entirely about sensing and reacting to the outside. The biota didn't have to react to ...
The philosophy of Henri Bergson, summarized. (I may have done this before but I can't find that post now, so we'll try again.) Time is real and important: it cannot without loss be treated in Einsteinian fashion as a particular dimension of space; Because time is real, novelty and free will are also realities: the future contains surprises that could not even in principle have been determined by calculation from the facts existing today; One must make a sharp distinction between intelligence and intuition. Intelligence is very useful — it is a survival mechanism for humans — but it cannot grasp the essence of reality, the movement of time. Intelligence geometricizes, which is why intelligent people often find themselves denying the first two propositions; As a philosophy of biology, Bergsonism asserts too that there is something about life that escapes mechanistic formula: that life and its evolution can never be explained as so much organic chemistry. Bergson populariz...
Back in 2003, an intelligent-design advocate named Francis Beckwith wrote a book, Law, Darwinism, and Public Education, published by Rowman and Littlefield. Although Beckwith was clearly out of sympathy with Darwinism, the point of the book wasn't about biology. It was about the establishment clause of the first amendment of the Constitution. Beckwith's view was that "intelligent design" was an alternative scientific hypothesis, and that accordingly it is appropriate -- and not even remotely an official establishment of religion -- to teach that hypothesis as one distinct from Darwinism within public schools. That book might have gone unnoticed -- like lots of other books saying the same thing -- had it not been taken up by an enthusiastic review (technically a "book note,") in the Harvard Law Review for January 2004. The reviewer, one of the student editors of the HLR, was Lawrence VanDyke. The note, appearing in such a high-visibility periodical...
The question for the day, how closely related are these two contentions, by MP: 1. "While tacit knowledge can be possessed by itself, explicit knowledge must rely on being tacitly understood and applied. Hence all knowledge is either tacit or rooted in tacit knowledge. A wholly explicit knowledge is unthinkable." 2. "The information in DNA could no more be reduced to the chemical than could the ideas in a book be reduced to ink and paper: something beyond physics and chemistry encoded DNA."
A recent anthology by philosophers of science challenging the "modern synthesis" in evolution draws an intelligent review from NDPR, here: https://ndpr.nd.edu/news/challenging-the-modern-synthesis-adaptation-development-and-inheritanc/ What had to be brought together was some sort of Darwinian account of evolution on the one hand and Me ndelian genetics on the other. The late 1930s and early 1940s were key, and the gelling of the synthesis involved a seminal book by Theodosius Dobzhansky in 1937, and another by Ernst Mayr in 1942 The term "modern synthesis" was attached to such work in the subtitle of a book by Julian Huxley, also in 1942. I'll quote the review directly for some institutional history: During this period significant institution building was taking place, coupled with theoretically significant gate-keeping. The Committee on Common Problems of Genetics, Paleontology, and Systematics, supported by a United States National Res...
Both Plato and Aristotle believed in a tripartite human soul Was that just a coincidence, just a symptom of the attraction that the number three has for the human mind? or is the classification in the one case more similar to the other than might first appear? In Plato's view, the soul contains an appetite, a spirit, and an intellect. These correspond to the classes in an idealized city, where the appetite corresponds to the ordinary working stiffs, the spirit corresponds to the warriors (sometimes called "guardians"), and the intellect to the philosopher kings (sometimes also, confusingly, called "guardians"). In the world of fantasy, the three levels correspond to Dorothy's friends: where the appetite might be represented by the sentimental tin man, the guardian spirit by the lion, and the intellect by the scarecrow. What about Aristotle? He wrote of the vegetative soul, the sensitive soul, and the (uniquely) human soul. The vegetative functions o...
It is easy to fall into thinking about inherited traits in a very reductionist way: to mentally assign to each trait a gene of its own along that famous double helix. Thus, the gene for blue eyes may lie next to the gene for left handedness, and then there's the gene for brown hair, for a large nose, and so forth. But it doesn't work that way. You aren't a bundle of atomistic traits. You are a whole, and the genome that produces you, produces you as a whole. Much of what you inherit, then, you inherit only through patterns that one can only 'see' if one zooms out from such a gene-by-gene look, to look at the whole genome. Here's a relevant story from CELL. http://www.sciencedirect.com/science/article/pii/S0092867417310061?via%3Dihub I learned of this indirectly. I became aware a couple of weeks ago that there exists a suspicion in some quarters that Jeremy Bentham, the notorious inventor of utilitarian ethics and the Panopticon, may have been on the au...