When he wrote this, Earth had twice the number of species of plants and animals that now survive. Human population was 3 billion (up from 750,000 200 years earlier p. 211) (and rising by one billion per 12 years, as it has ever since).
Speed of sound in surface ocean at 0ºC is 1543 m/s; in air at 0ºC, 332 m/s. p. 54.
Reef-forming coral won't grow below about 70ºF. p. 59. [Nor will they survive more than tiny concentrations of atmospheric CO2, which dissolves in seawater, becomes acid, and kills coral.] Polyps range from pinhead- to pea-size. They extend their tentacles only at night. p. 62. When a moray bites it doesn't let go: you have to cut its head off. p. 69. Sea urchins walk at night. p. 70. Probably the greatest hazard of the reef is sunburn. p. 75.
Minimum rainfall for a tropical rainforest is about 80 inches/year. p. 101. Zero to 10 inches/year is desert. Deserts lie in latitudes where winds blow toward the equator. p. 123.
Forest and sea are similar in having sunny high layers, grading down to dark depths, with appropriately-adapted communities of living things at each level.
In northern woods, the mosquitoes biting you are apt to be all of the same kind; while in the rain forest, almost every bite will be from a different species of mosquito, if that is any comfort. p. 105.
The ants poured on in their tens of thousands, swept through our snake pit, and left us with skeletons. p. 110.
Some male moths can locate a female of their species a mile away, and fly directly to her. pp. 177, 186.
To a dog, the silently approaching vampire bat would sound like a boiler factory falling in out of the sky. p. 184.
Look at the human brain as a product, a consequence, of the use of tools, the development of culture. pp. 219-228.
Southeast Asia seems to be the original home of a surprising number of domesticated plants and animals. p. 237-239.
This, I think, will be terrific for a middle-school kid. Benjamin expresses enthusiasm for, and enjoyment of, math. Conversational tone, a little humor.
Trigonometry, Pythagorean triples, trig functions, finding heights of trees and mountains, law of cosines, law of sines, Hero's formula, trigonometric identities, radians, graphs of trig functions
Imaginary number i, Euler's number e, e^(i theta) notation, polyhedrons, complex arithmetic, compound interest, exponential functions, logarithms
Calculus: optimization, differentiation, derivatives of products of functions, quotients of functions, polynomials, exponentials, trig functions; chain rule; Taylor series
The sum of the cubes of the first n integers is the square of the sum of the first n integers: Sum[i^3, {i, 1, n}] = (Sum[i, {i, 1, n}])^2 = (1/4)(n^2)(n + 1)^2 https://www.wolframalpha.com/input?i=... p. 12
How to find the day of the week for any date. pp. 65-70.
Sierpinski triangle: a fractal pattern of the odd (black) and even (white) numbers in Pascal's triangle: https://www.wolframalpha.com/input?i=... pp. 92-94. The larger the triangle, the more nearly white it is.
Wilson's theorem: n is a prime number if and only if (n - 1)! + 1 is a multiple of n. p. 144.
If p is an odd prime number, then 2^( p - 1) - 1 is a multiple of p . (Fermat. p. 145) A number that has this property, but is not prime, is called a pseudoprime.
Connecting the midpoints of any quadrilateral always produces a parallelogram. p. 150.
There are over 300 proofs of the Pythagorean Theorem. p. 174. Benjamin gives us five of them.
Three points on a circle, two of them forming the diameter, are a right triangle. Proof p. 185.
Central angle theorem: For any two points X and Y on a circle centered at O, the angle XPY at /any/ point P on the major (larger) arc of the circle, from X around to Y, will be half of the angle XOY. The angle XQY at any point Q on the minor arc of the circle, from X to Y, will be 180 degrees minus the angle XPY. p. 186.
Area of circle of radius r = pi r^2. Proofs pp. 187-188.
Ellipse, semimajor and semiminor axes a and b: (x/a)^2 + (y/b)^2 = 1 p. 189.
Drawing an ellipse: p. 190.
Approximate formula for the circumference of an ellipse, semimajor and semiminor axes a and b: pi( 3a + 3b - sqrt( (3a + b)(3b + a) ) ) Notice that if a = b = r, it's a circle, circumference 2 pi r. Srinivasa Ramanujan (1887-1920). p. 191.
Volume of sphere = (4/3) pi r^3
Area of sphere = 4 pi r^2
Cone of height h, on a circle of radius r, slant height s (s^2 = r^2 + h^2):
Volume of cone = pi r^2 h/3
Area of cone = pi r s p. 192.
Volume of a pizza, radius z, thickness a, V = pi z z a p. 193.
Pythagorean triples: For a right triangle, short sides a and b, hypotenuse c: Where a, b, c are whole numbers, they're called a "Pythagorean triple."
For any two positive integers (m, n), m > n, the numbers a = m^2 - n^2 b = 2mn c = m^2 + n^2 are a Pythagorean triple. Notice that a^2 + b^2 = c^2. p. 205.
Every Pythagorean triple can be created by some choice of (m, n). p. 205.
Law of cosines: for any triangle, sides a, b, c, angle C opposite side c: c^2 = a^2 + b^2 - 2 a b cos C proof p. 216.
Area of any triangle, sides of lengths a, b form angle C: area = (1/2) a b sin C proof p. 217.
Law of sines: for any triangle, sides a, b, c, opposite angles A, B, C: (sin A)/a = (sin B)/b = (sin C)/c proof pp. 217-218.
Hero's formula: for any triangle, sides a, b, c, semiperimeter s = (a + b + c)/2, area of triangle = Sqrt[ s(s - a)(s - b)(s - c) ] p. 219.
Trigonometric identities sin^2 x + cos^2 x = 1 many others p. 225.
For any polyhedron with a number F of flat faces, a number E of straight-line edges, and a number V of vertices, F + V = 2 + E p. 232
Multiplying complex numbers: The magnitude (length) of the product is the product of the magnitudes. The argument (angle) of the product is the sum of the arguments. Dividing complex numbers, divide the lengths and subtract the angles. p. 240.
e^(i theta) = cos theta + i sin theta e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! + … cos x = 1 - x^2/2! + x^4/4! - x^6/6! + … sin x = x - x^3/3! + x^5/5! - x^7/7! + … p. 251
Checkmate in Berlin: The Cold War Showdown that Shaped the Modern World, Giles Milton, 2021, 377 pages, Dewey 943.155, ISBN 9781250247568
The story of Checkmate in Berlin: The Cold War Showdown that Shaped the Modern World, Giles Milton, 2021, 377 pages, Dewey 943.155, ISBN 9781250247568
The story of postwar Berlin, told in a series of personal anecdotes. Easy to read.
The Soviet army fought and raped its way into Berlin, securing full control April 30, 1945. The American and British armies finally occupied their assigned sectors nine weeks later, July 4. The Soviet army had spent those nine weeks looting and destroying everything they could, and establishing Communist control of Berlin's civilian government, judiciary, and police. p. 85. The author gives us little explanation for the Western allies' delay.
From Stettin on the Baltic to Trieste on the Adriatic, an iron curtain has descended across Europe. --Winston Churchill, March 5, 1946 speech: https://winstonchurchill.org/resource... Map, Stettin to Trieste: https://www.google.com/maps/dir/Stett... Iron Curtain: https://en.wikipedia.org/wiki/Iron_Cu... The Russians admire strength, despise military weakness. p. 165. They must be confronted with total resolve. --George Kennan, Feb. 22, 1946 in his famous long telegram: https://nsarchive2.gwu.edu/coldwar/do... where he also tells us, "Russian rulers have invariably sensed that their rule was relatively archaic in form, fragile and artificial in its psychological foundation, unable to stand comparison or contact with political systems of Western countries." p. 167.
In occupied Berlin, natives starved and froze; the occupiers were fed and warm. "The social status of any German in our zone today, is on a level comparable to a negro in Mississippi." p. 208.
Despite the warnings of men who knew the Soviets, the Truman and Atlee governments continued ordering their forces to appease Stalin until he blockaded Berlin, June 24, 1948. p. 241. No food nor fuel could enter the city. There would be no electricity, no clean water, no working sewers. Stalin was trying to force the Western allies out. Berlin had been getting 13,500 tons of supplies daily by rail, including 6,000 tons of coal. Subsistence minimum was 4,500 tons, including 641 tons of flour, 150 of cereal, 106 of meat and fish, 900 of potatoes, 51 of sugar, 10 of coffee, 20 of milk, 32 of fats, 3 tons of yeast, 38 tons of salt. By spring 1949, the airlift was bringing in 8,000 tons a day. pp. 248, 262, 285, 287, 297. Berlin was 2.4 million people. p. 252.
The Western allies knew something the Soviets didn't: they knew where the gas mains and electric lines were, thanks to mayor Ernst Reuter's having smuggled them the prints. The allies tapped the mains and cables: eastern Berlin supplied some power to the west. p. 262.
Western Berlin established its own police force: 1100 officers came to the west side; 900 stayed on the east. p. 263.
Luftwaffe mechanics maintained the airlift planes. p. 270. A plane took off or landed every 90 seconds, round the clock, using 450 planes. For Easter Sunday 1949, they did something special: 13,000 tons on 1,400 flights in 24 hours. p. 269, 298.
Fog halted the airlift Nov. 3, 1948 to early January 1949. pp. 286-291.
For months as the Soviets blockaded Berlin, the West continued supplying the Soviets coal, iron, steel, machinery, chemicals, rubber, textiles, tools, and spare parts. Finally, the American commandant began a counter-blockade of the east. p. 295.
A Russian-speaking American spy learned that the Soviets were unprepared to use their military against the West. p. 296.
Stalin ended his siege, May 12, 1949. p. 301. The Western allies signed off on a West German constitution the same day. West Berlin was not part of West Germany. pp. 312-313.
The West won West Berlin. p. 301.
NATO was formed April 4, 1949: Belgium, Canada, Denmark, France, Iceland, Italy, Luxembourg, the Netherlands, Norway, Portugal, the United Kingdom,and the United States, allying to counter Soviet aggression. p. 311. West Germany joined, 1955. p. 313. In response, the USSR formed the Warsaw Pact with Poland, Albania, Bulgaria, Czechoslovakia, East Germany, Hungary,and Romania. p. 314.
In 1961, East Germany walled off West Berlin, to prevent easterners escaping. p. 314.
You can successfully shout down your opponent only if your words are backed by overwhelming threat of force. They will use force only if they have a more-than-reasonable chance of succeeding. --Col. Frank Howley, commandant of Berlin's American sector, 1947-1949.
Troy: The Greek Myths Reimagined: Volume III of Mythos, Stephen Fry, 2021, ISBN 9781797207070, Dewey 398.20938, 288 pages.
Outstanding. Clear, entertaiTroy: The Greek Myths Reimagined: Volume III of Mythos, Stephen Fry, 2021, ISBN 9781797207070, Dewey 398.20938, 288 pages.
Outstanding. Clear, entertaining, lighthearted retelling of /The Iliad/. Stands alone; no need to have read volume I or II.
Heracles sacked Troy when King Priam was a boy. It rebuilt. p. 34.
Helen was given in marriage by lottery among her suitors. Menelaus won.
Just then Agamemnon approached, favoring Odysseus with a dark glare. "Your bright idea, I suppose?" p. 70.
"Go on!" said Odysseus, daring to nudge Agamemnon in the ribs. "Marry Clytemnestra! What could possibly go wrong?" p. 72.
When the Greeks had been at Troy almost ten years, and the greatest heroes were dead:
Once more an agonizing stalemate loomed, and once more Agamemnon turned in frustration to his prophet Calchas.
"What do the swallows and sparrows tell you now, you old fraud?"
"Only a foolish leader blames his messengers, and the King of Men, the great one I serve, has never been a fool.
" … My lord, we need Philoctetes."
On Lemnos, Odysseus and Diomedes found Philoctetes, still in perpetual agony from the wound that would not heal. Seeing Odysseus, who had persuaded the Greeks to leave him there, he raised his bow.
"Go on," said Odysseus. "Shoot. I'm sure I deserve it. We left you to rot. Better we all die here forgotten. Why choose glory and fame in Troy when death awaits us whatever we do? Might as well end it here in this stinking lair as on the field of battle. One way we live forever in posterity--in statues, songs, and stories--the other we are forgotten. But so what? What has posterity ever done for us?"
"Damn you, Odysseus," gasped Philoctetes, "If we do die together here, I'll probably be cursed to spend the afterlife with you endlessly jabbering on in my ear." pp. 201-202.
A great story, well retold.
"Dark human passions of selfishness, fear, and hatred counterbalanced by kindness, friendship, love, and wisdom. The field is still open for someone to portray all that better than Homer, but so far on my journey through life I have yet to see it done." --Stephen Fry p. 241.
1200 BCE: The Trojan War was fought with bronze weapons. p. 14. [The making of iron weapons was a military secret of Hittites, beginning 1300 BCE, according to Asimov's Chronology of the World, p. 43. "Iron has been discovered for the evil of mankind." --Lichas the Lacedemonian, quoted in Herodotus' History, Volume 1. At Patroclus' funeral games, Polypoetes won a lump of meteoric iron by throwing it farther than even great Ajax could manage. The Iliad, Gareth Hinds, p. 227 (book 23). Fry's version doesn't mention it.]
/The World Remade: America in World War I/, G.J. Meyer, 2016, 651 pages, ISBN 9780553393323, Dewey 940.3
The author's previous, /A World Undone: The St/The World Remade: America in World War I/, G.J. Meyer, 2016, 651 pages, ISBN 9780553393323, Dewey 940.3
The author's previous, /A World Undone: The Story of the Great War, 1914-1918/, is of the whole war. /The World Remade/ is a political and military history of the U.S. involvement in the war. p. xvi.
Very readable.
The U.S. actually fought during only about the last half-year of the war. At home, Americans became less free. Main changes:
The government's assault on speech, assembly, due process, and fairness.
The widespread public approval of that assault.
The official telling of lies, and the eager embrace of those lies.
The Espionage Act of 1917 is still in force. The government uses it against whistleblowers: people who reveal facts of official misconduct the government wants hidden from the public.
We've lost our sense that our political system is improving. p. 572.
All the countries of Europe were afraid of their neighbors' intentions. Each felt the need to mobilize their military for defensive purposes. Decision-making power flowed away from the politicians, to the generals. pp. 12-22.
Germany, afraid of being crushed between France and Russia, rushed to attack France first, through the softest route: Belgium. pp. 25-26.
Britain, France, and Russia intended to take vast Middle Eastern, African, and Pacific territory from the Ottoman, Austro-Hungarian, and German empires. They bribed Italy, Romania, and Japan to join with promises of territory. They kept their intentions secret, especially from the Americans. All the belligerents inflamed their own people with exaggerated promises of the fruits of victory. pp. 161-162.
There is evidence that British officials deliberately put the Lusitania in danger of German torpedo attack, to try to bring the U.S. into the war. pp. 126-127.
Britain and France were determined to make peace talks impossible, to get the U.S. into the war. p. 160. Wilson's secretary of state, Robert Lansing, treasonously urged Britain and France to make demands that would make peace talks impossible. p. 163. Colonel House also told Britain and France not to take seriously Wilson's call for peace talks. p. 163.
Wilson's "neutrality" so obviously favored the Allies, as by accepting Britain's blockade of Germany to starve her people, that Germany could not trust Wilson as a peacemaker. p. 162.
Britain cut Germany's North Sea communications cables, including those to New York, August 4, 1914, before even declaring war, so that only British-French-Russian propaganda could reach the U.S. p. 27. Britain denied U.S. reporters access to the front, so that only British lies about German atrocities would reach the U.S. p. 175. "Germans are monsters." Irrational hatred is more easily turned on than off: it became an obstacle to postwar peace. p. 180.
William Jennings Bryan had such a following in the Democratic Party that Wilson offered him the post of secretary of state. With their hero in the administration, Bryan's many partisans would be less inclined to criticize. p. 96. Wilson then ignored Bryan's attempts to reach a negotiated end to the European war. pp. 100-103, 105-109. Bryan resigned, rather than support Wilson's march to enter the war. pp. 107-109.
For daring to speak against the draft, or for belonging to labor organizations or progressive or populist political parties, hundreds of people were arrested and prosecuted, subject to decades-long prison sentences and ruinous fines, under the Espionage Act of 1917 and the even-more-unconstitutional Sedition Act. p. 430. Wilson's Justice Department arrested and charged 166 senior officers of the Industrial Workers of the World, of disloyalty under the act. p. 336. The postmaster general was empowered to, and did, shut down antiwar, pacifist, critical, progressive, socialist, labor, Lutheran, Catholic, and foreign-language periodicals. School districts banned the teaching of German. Progressivism as a political force was disintegrating. The Department of Justice recruited 250,000 vigilantes to report their neighbors' inadequate loyalty. pp. 257-258, 274-291, 319-320.
Attorney General Palmer, 1919-1921 and his henchman J. Edgar Hoover, unleashed police riots on thousands of unoffending "aliens." The American public applauded. pp. 534-540.
Massachusetts governor Calvin Coolidge used 6,700 soldiers to crush a labor strike by Boston police, who were working 83-hour weeks for wretched pay. Americans made him president for it. p. 547.
Senator Robert La Follette was early to see what many would understand only later: war sends more power flowing to those Americans who already have most of it.
La Follette by contrast was as tireless and effective a champion of the rights of ordinary citizens as the American political system has ever produced. He fought to take power from Big Money and put it in the hands of voters. He won antitrust laws, direct election of senators, utility and bank regulation, better wages and working conditions, restrictions on child labor, progressive income taxes, protection of Native American woodlands from the predations of timber companies. He opposed discrimination against blacks, Asians, and Jews, and championed voting rights for women. The masters of industry and finance saw him as a serious threat. He interfered with the efforts of banks, railroads, packing companies, mill owners, and trusts, to steal the fruits of working people's labor. "The supreme issue is the encroachment of the powerful few on the rights of the many." pp. 194-199.
William Jennings Bryan likewise spent his life crusading for those on the losing end of the American dream. Bryan believed that the prime duty of pietists was to side with the common man and woman in their perpetual battle with the defenders of privilege, corruption, and big money. p. 81.
For businessmen, to choose fast fat profit, rather than the common good, was a no-brainer. p. 261. War profiteers wallowed in wealth. pp. 267, 332. Most of the spending was of borrowed money, which transferred more wealth to rich financiers. p. 267. Federal spending went up by a factor of 24 during the war; most of it borrowed. p. 353. For ordinary Americans, the cost of living inflated faster than wages. p. 353. Price inflation spiked to 100% per year. After the war, corporations reduced workforces, demanded 12-hour days, cut wages, denied union recognition. pp. 498, 533. "I can hire one-half the working class to kill the other half." --robber baron Jay Gould. p. 293. The U.S. spent $33 billion on the war, 1917-1918. In 1919, 20% of U.S. workers were at some point on strike. p. 533.
"The interests that control steel, oil, shipping, munitions, mines, will dominate; government will be in their hands." --Woodrow Wilson. Having said so, Wilson quickly acted to make it true. pp. 344-345. Four executives of Bethlehem Steel took $2.1 million in personal bonuses in 1918. p. 350.
U.S. private soldiers were paid $30/month in combat. French privates earned $3/month. p. 411.
Some 9 million soldiers died as a result of combat: 2 million German, nearly 2 million Russian, 1.5 million French, 1 million Austrian, .8 million Turkish, .7 million British, .5 million Italian, .25 million Romanian, .25 million Serbian, .053 million American. p. 464.
Maybe 50 million people worldwide died of the war-spread influenza pandemic (including 675,000 Americans). Few civilians knew that in fall 1918, thousands of soldiers were dying of influenza: military authorities censored news as bad for morale. p. 407. Only neutral Spain did not censor news. Hence it was called the "Spanish" flu. The third-worst pandemic in history began in Haskell County, Kansas, January 1918. It spread around the world by U.S. troops and people they infected. By August 1918, it had become quite lethal.
President Woodrow Wilson knew that a decisive defeat of either side would make a stable postwar Europe impossible. p. 163. "Upon a triumph which overwhelms and humiliates, cannot be laid the foundations of peace." --Woodrow Wilson, 1/22/1917. p. 168.
Everywhere except the United States, it could be hard to distinguish the fruits of victory from the price of defeat p. 464.
1919: From the Rhine to the Pacific, Finland to Arabia, scarcely a border was not in dispute. p. 463. Many civil wars erupted. pp. 470-472.
Sometimes with the best intentions and sometimes not, the Supreme Council (Wilson, Clemenceau, Lloyd George) gradually turned Europe into a mass of festering geopolitical wounds. p. 478.
Why did President Wilson take the United States into the war in 1917? He feared that the United States, and he as president, would have no major part in the postwar settlement. p. 209. For Wilson, the thought of being on the outside while other men decided the fate of the world would have been unbearable. p. 212.
President Woodrow Wilson could find it impossible to imagine that those who disagreed with him might sometimes be right. Those who don't see what's real, collide with it. pp. 6-7. Europeans weren't particularly grateful for his lofty postwar preachments. p. 8. Wilson's Democratic Party lost both houses of Congress, November 5, 1918. p. 10. It was necessary to never disagree with Wilson on any subject about which he appeared to have made up his mind; the president would reject not only the contrary opinion but the person who offered it, and the rejection could prove permanent. Wilson needed unqualified praise. He hungered to be considered great. pp. 31-32. Wilson's one friend and adviser, "Colonel" House, likewise mistook his, House's, own prejudices for facts. p. 35. Wilson cut off close friends when they displayed independence of thought or action, and denounced anyone who declined to do as he demanded. p. 46. After William Jennings Bryan resigned as secretary of state in 1915, Wilson heard no voices to question his decisions. p. 109. "Wilson is a man of high ideals and no principles." --Lindsey M. Garrison, onetime secretary of war. p. 130. Wilson is "a ruthless hypocrite, who has no convictions that he would not barter at once for votes." --former president Taft. p. 155. Wilson is "unscrupulous and dishonest." --former Republican senator Elihu Root. pp. 284, 492-493. President Wilson condemned German-Americans, Irish-Americans, and other "hyphenates." p. 156.
Wilson nearly brought the U.S. to war with Mexico in 1913. A U.S. gunboat prowling the Mexican coast put ashore for water, without asking permission. U.S. sailors were arrested, then released with apology. Wilson demanded that Mexico give the U.S. flag a 21-gun salute. The Mexican president offered a mutual salute of each others' flags. Miffed, Wilson ordered U.S. marines to capture the port of Veracruz. Many men died on both sides. pp. 97-98.
The 53,000 U.S. soldiers who died of combat wounds, plus the 51,000 who died of illness, composed .1%, not .01%, of the 103-million U.S. population of 1917. p. 464.
Thomas Ray
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