[The following e-mail was sent to a Catholic friend 9/20/17:]
Wednesday, September 20, 2017
HEARD IT THROUGH THE GRAPEVINE
[The following e-mail was sent to a Catholic friend 9/20/17:]
Thursday, September 7, 2017
APOLOGIES TO KEATS (Poem)
Imagine what Keats MIGHT have said had he desired to address the issue of mathematical proportion implicit in Greek vases:
Its base is but a starting place,
In height but insignificant,
Yet stately stands the lovely vase
Its form is just magnificent!
On top, its mouth flares from the heart.
Considering Its size,
The whole but greater than the parts;
Proportions yield surprise.
Wednesday, August 16, 2017
ALICE
_________________________________
Dr. Mario Livio published a book about The Golden Ratio. Dr. Livio is an astrophysicist who, until 2015, was the director of the Space Telescope Science Institute, associated with the Hubble Telescope. Livio is discussing the nature of various historical number systems and how they used “bases” different than our own. Some cultures have used “base-5” (as with the abacus in China) and some even have used “base- 60” which, though awkward, probably accounts for the manner in which time and circles are divided into degrees, minutes and seconds. (Sixty just happens to be the lowest number evenly divisible by 1, 2, 3, 4, 5 and 6, as well as 10, and 12, 15 and 20.)
Most Western cultures have used “base-10,” and the perfect example is a vehicle odometer. Recalling my own elementary-school arithmetic, we learned to put numerals in columns, starting from right to left, as ones, tens, hundreds, thousands, etc. An odometer has a series of little “wheels,” with black numerals on a white ground, except that the rightmost “wheel” (showing tenths of miles) has white numerals on a black ground. The odometer, moving from right to left, thus shows on each “wheel” tenths of miles, miles, tens of miles, hundreds of miles, thousands of miles, etc.
Livio discusses the nature of various historical number systems and how they used “bases” different than our own (which is “base-10”). Some cultures have used “base-5” (as with the abacus in China) and some even have used “base- 60” in the past which, though awkward, probably accounts for the manner in which time and circles are divided into degrees, minutes and seconds. (Sixty just happens to be the lowest number evenly divisible by 1, 2, 3, 4, 5 and 6, as well as 10 and 12.)
Livio then cites a passage from Alice’s Adventures In Wonderland by “Lewis Carroll,” the pen name of Charles Dodgson, who lectured on mathematics at Oxford! In an observation totally unrelated to the “Golden Section” Alice, agonizing over the strange things she has encountered, frets:
“I’ll try if I know all the things I used to know. Let me see: four times five is twelve, and four times six is 13, and four times seven is—oh, dear! I shall never get to twenty at that rate!”
Crediting famous mathematician Martin Gardner’s The Annotated Alice, Livio points out that Alice’s bizarre math (4 x 5 = “12”) “works” IF “base-18” is used and would, therefore, be equivalent to our “20”: 1 (x 18) plus 2 left over! “1-2”! And 4 x 6 = “13” IF “base-21” is used, since our “24” may be thus expressed as 1 x 21 + 3 left over!
So, I decided to play around with Alice’s (Dodgson’s) “system” and, recalling my elementary-school “times table” for “4,” I noted that every equation implied therein might be stated thus: 4 x 7 = “14”; 4 x 8 = “15”; 4 x 9 = “16”; 4 x 10 = “17”; 4 x 11 = “18”; 4 x 12 = “19”; 4 x 13 = 20; 4 x 14 = 21; 4 x 15 = 22; etc. In our base-10 system, those equations respectively “equal” 28, 32, 36, 40, 44, 48, 52, 56 and 60, but if the number “base” that Alice implicitly referenced is incremented by “3” for each succeeding equation (starting with base-21, then base- 24, base-27, base-30, base-33, base-36, base-39, base-42, base-45, etc.) then Dodgson’s equations can make sense! Consider: “4 x 7 = 14” works if “base-24” is used: “1-4” yields 1 x 24 + 4 “ones” left over = 28! “4 x 8 = 15” works if “base-27” is used: “1-5” yields 1 x 27 + 5 “ones” left over = 32! “4 x 9 = 16” works if “base-30” is used: “1-6” yields 1 x 30 + 6 “ones” left over = 36! “4 x 10 = 17” works if “base-33” is used: “1-7” yields 1 x 33 + 7 “ones” left over = 40! “4 x 11 = 18” works if “base-36” is used: “1-8” yields 1 x 36 + 8 “ones” left over = 44! “4 x 12 = 19” works if base-39” is used: “1-9” yields 1 x 39 + 9 “ones” left over = 48! “4 x 13 = 20” works if “base-42” is used: “2-0” (“1-0” + 10 “ones”) yields 1 x 42 + the 10 “ones” left over = 52! “4 x 14 = 21” works if “base 45” is used: “2-1” (“1-0” + 11 “ones”) yields 1 x 45 + 11 left over = 56! Whew! Mind-bending!
I think that the ORIGINAL version of Alice is also written on two levels: one for children and the other for adults. I think the “adult” version is a vicious satire on the dominant British culture of the day! I was quite amused while reading it. I also think that the Uncle Remus Tales by Joel Chandler Harris satirizes Southern US culture.
Most of us started with the Walt Disney versions of both in our childhoods. However, I think Walt missed those subtle viewpoints.
(8/16/17--updated 12/11/22; 4/29/24)
Saturday, July 8, 2017
da VINCI'S GOLDEN RATIO
Monday, June 19, 2017
PUTIN & POLITICS
(From an e-mail sent to friends 6/17/17.)
There has recently been a SUGGESTION that Russia may have tried to mess with the actual vote-tallies in the 2016 Presidential Election! That would be reprehensible and actionable, in my opinion, if true. It transcends the issue of “stupid people” being manipulated by ALLEGED Russian meddling with e-mails and other media. Hillary Clinton DID write and send those surreptitiously disclosed e-mails, though! Vladimir Putin did not invent those!
GOLDEN RATIO & SQUARES
(E-mail to a friend 6/17/17. Updated 2/7/18.)
I have been reading a lot, lately, about the Golden Ratio (ϕ = 1.618) and the Fibonacci Series which, as you know, is manifest in nature in many ways.
SHUT THE F*** UP!
I have concluded that there is WAY too much attention being paid to the many peccadilloes of Donald Trump, and that we should ALL just shut up about him. He is NOT going to change nor reform.
I agree with Trevor Noah of “The Daily Show” that there is so much silly stuff coming from Donald Trump that a whiplash injury may well result from jerking one’s head back and forth trying to comprehend all the absurd words and deeds of Donald Trump.
I propose that a 30-day period of self-imposed total silence about Trump be observed from June 20 to July 20. He may well be unable to bear the burden of being utterly ignored and thus have a meltdown! We owe ourselves at least THAT much!
I hereby express my gratitude in advance to those who refrain from pointing out that I have already violated my own suggestion!
Tuesday, April 11, 2017
SEVEN PILLARS of (FREQUENTLY IGNORED) WISDOM
CHAPTER LVIII
These areas had climatic differences so marked that they made two countries, two races almost, with their respective populations. The shore Syrians lived in different houses, fed and worked differently, used an Arabic differing by inflection and in tone from that of the inlanders. They spoke of the interior unwillingly, as of a wild land of blood and terror.
Beyond them were the strange sights of villages of Christian tribal Arabs, under sheikhs. They seemed very sturdy Christians, quite unlike their snivelling brethren in the hills. They lived as the Sunni about them, dressed like them, and were on the best terms with them.
East of the Christians lay semi-pastoral Moslem communities; and on the last edge of cultivation, some villages of Ismailia outcasts, in search of the peace men would not grant. Beyond were Beduin.
The Greek Church prided itself on being Old Syrian, autochthonous, of an intense localism which might ally it with Turkey rather than endure irretrievable domination by a Roman Power.
The Jews were of varied sorts. Some, Hebrew scholars of the traditionalist pattern, had developed a standard and style of living befitting the country: while the later comers, many of whom were German-inspired, had introduced strange manners, and strange crops, and European houses (erected out of charitable funds) into this land of Palestine, which seemed too small and too poor to repay in kind their efforts: but the land tolerated them. Galilee did not show the deep-seated antipathy to its Jewish colonists which was an unlovely feature of the neighbouring Judea.