SENIOR MOMENTS

1—Longevity is WAY overrated!

2—The reason getting old is called the "Golden Years" is because that is the color of our underwear!  And also our pill bottles!

3—My heart used to skip a beat and go pitter-patter whenever I'd see a good-looking woman; now it's just atrial fibrillation!

4—I used to get my Second Wind at 9 PM--now I’m just breaking wind at 9 PM!

5—I quit buying Viagra because there’s just no point.

6—What’s with all the “smartphones”?  Why would people want a phone smarter than they are?  I’d be afraid I’d step out into the street and not notice the smart-car about to whack me!

7— People all just sit around in restaurants and bars wiping their phone screens with their fingers, oblivious to everything and everyone else around them!  Should those using smartphones while ignoring dinner companions be considered dumb-asses?

8—I was quite the dancer in my younger days, juking around to rock ’n’ roll.  Now my rocking and rolling are done in chairs!  Someone asked me recently if I could still “get down.”  Of course I can still “get down,” but getting up is now a serious problem!

9—I can now listen to all the loud music I want without bugging my parents!  In fact, it’s a necessity!

10—One may as well get to bed by 10 PM because the body is gonna wake up at 6 AM no matter what time one goes to bed!

11—I used to love going to fine restaurants and pounding down a big steak for dinner.  Now I just bring 2/3 of it home for later!  I’ve brought home so many “doggie bags” I’m now trying to scratch behind my ears with my feet and am howling at the moon!

12—I used to have longer hair, but about 30 years ago my hairdresser told me my bald spot would show less if I cut my hair short!

13—Those irregular red diagrams on our arms are not really cool tattoos; they are just “geezer” bruises!

14—I remember pitying the Old Grads celebrating their 50th Reunions at alumni functions, thinking I would NEVER get to be that pathetic; now I are one!

15—The body will surely age and turn to mush, but the brain and the eyes stay 19 FOREVER!

16—I used to love going into bars and restaurants and flirting with all the good-looking waitresses and bartenders; now they all address me as “sir” and ask if I want the “Senior Discount."

17—You know you are getting old when you lust after your friends’ (grand)daughters or your (grand)daughter’s friends.

18—I knew I was gonna get older, but I did not think it would happen so fast!  When I was a kid, I was desperate to become a “grownup.”  Now I am a geezer!  What happened to “grownup"?

19—Back when I was in school, I observed that the trip between Lexington and Richmond was “6 beers and 2 pit-stops long”; now it’s 2 beers and 6 pit-stops long!

20—I get my usual lengthy nap during the day, so don’t need coffee anymore to stay awake.  One may as well get to bed by 10 PM because the body is gonna wake up at 6 AM no matter what time one goes to bed!

21—Drunk driving IS reprehensible and wrong, but I can remember when it was a competitive sport!  The “trigger” BAC was 0.15% back then!!  There were fewer idiots and a lot less traffic on the roads, and cops were often kind enough to just drive someone home.  Most of us geezers are lucky to be alive today, but getting killed on the highways was considered just another acceptable risk, like BB-gunfights and cherry bombs!  “Hey, y’all!  Watch this!”

22—“Light” beer is OK now, but “3.2” beer back in the good ol’ days was nasty!

23—Fear of the contents of one’s “Permanent Record” never goes away!

24—God invented toilet tanks so we’d have a convenient shelf for our pill bottles!

25—God invented khaki pants as a malicious joke.

26—We may be in danger of losing our sense of humor as we age; some of us feel compelled to righteously demonstrate our intellectual superiority by literally responding, in detail, to the gist of mere jokes!

OR

???

26—You know when you are dealing with a “humor-challenged” geezer when he feels compelled to righteously demonstrate his intellectual superiority by lIterally responding, in detail, to the gist of mere jokes!

27--I don't do "stand-up" comedy anymore.  I have to sit down now.  And, it's a bitch to get up onstage with a walker!

MORE TRICKLE-DOWN

Below is a link to the latest graph from Wikipedia, eff. 2017, showing "Real Median Household [gross] Incomes" in the US, from 1985 to 2017.  "Median" differs from "average" because it is the true midpoint: half over/half under.  It is now almost a whopping $62K for all those American slackers out there!  HALF of ALL American households are grossing LESS than that stupendous largesse!

I guess "real" means it's been adjusted to currently inflated dollars for comparison, which means that ACTUAL gross median incomes were lower back then.  I recall that the ACTUAL Gross Median Household Income in 2013 was less than $54K.  See how low it got during/after the Recession in 2008.

Don't let the steep "rise" in median incomes between 2011 and 2017 shown on the graph fool you: the entire scale of that graph is only between $50K and $62K.  Basically "chickenfeed."  I don't know how much larger they have gotten since those wonderful tax cuts last year.  

Recall that the "middle class" INCOME tax cut that Barack Obama lobbied for and signed several years ago was for married couples having joint NET TAXABLE incomes up to $700K, which is about $1 Million GROSS.  He originally proposed his income-tax cut for up to $250K TAXABLE which is at least $300K gross!  "Middle Class," indeed!  I daresay the TRUE "Middle Class" is somewhere between $55K and $70K GROSS.  Back in 2013, 75% of ALL American households were UNDER $100K.

Note also that, ON TOP OF income taxes, ALL the schmucks in the TRUE Middle Class must also pay the FICA (SS) FLAT tax of 6.2%, matched by ALL their employers paying an additional 6.2% (which, of course, indirectly whacks all workers receiving lower wages thereby).  And it is also well to note that FICA, being assessed on ALL GROSS EARNED INCOMES (wages and salaries) up to about $130K (but not over that), winds up whacking the portion of "gross" incomes being withheld and paid over for federal and state INCOME taxes!  AND, because there is no allowable income-tax deduction for FICA taxes withheld, those schmucks also get to pay INCOME taxes on those FICA taxes also withheld!  Neat!  It's like a taxation House of Mirrors!

But the swells do not pay ANY FICA on earned incomes over about $130K NOR on their passive-income dividends, interest or capital gains.  Nor should they, since SS benefits are limited.  However, I can't recall ANYONE ever discussing the adverse impact of the FICA tax bite on the economy when jabbering about how badly INCOME tax cuts are needed to further stimulate all the "Job Creators" out there!  Smells like I stepped into a pile of "trickle-down" now smeared on the bottom of my shoe!

Meanwhile, those Working Stiffs who actually spend about 100% of their shrinking net incomes into local economies get to pay proportionately higher taxes (thus leaving lower net incomes to spend) so that the Filthy Rich can get another INCOME tax cut that they will likely spend overseas on vacations, fine cars, whisky and artworks they can't possibly understand!

https://en.wikipedia.org/wiki/Household_income_in_the_United_States

11/17/18

MY SAYINGS (so far)

MY SAYINGS (so far) 2/4, 17, 4/21/18

On the difference between A-theism and ANTI-theism:

Absence of belief is not the same as belief of absence.

On drinking, drugs, addiction and recovery:

If it were not for my wonderful, dangerous life experiences, I would not be the fucking know-it-all that I am today!

I inhaled—and I like it!

On “majority” rule:

The purest form of “democracy” is a lynch mob, for everyone in attendance agrees on the outcome except for the victim!

On the rancid ubiquity of MBA’s (palindrome):

“Generic Management 101”

A BMW; a rake—EGAD!  A geek!  A raw MBA.

On getting old:

The reason old age is called the “Golden Years” is because that is the color of one’s underwear!

On gay marriage:

If two gay guys get married and call each other “husband,” does that mean they are both WRONG at the same time?

Shouldn’t gays also have to experience the pain and heartbreak of matrimony?

If one objects to gay sex, then he should, nevertheless, strongly promote gay marriage, because we all know that married people don’t have sex!

On evolution:

I get so frustrated with evolution-denying dumb-asses it makes me want to go swim in blue-green algae!

On suicide:

It is really difficult to slit one’s wrists with an electric razor!

On depression:

I get so despondent it makes me just want to go lie down.

On coveting:

The Ten Commandments prohibit coveting thy neighbor’s ass.  Well, my neighbor’s got a cute little ass, but she won’t give me the time of day!

On self-identity:

I’m Wat and you’re not!

On career choices:

Trust me: I’m a lawyer!

On “free speech”:

The First Amendment ensures the “right” to be annoyed by someone else’s utterances.

On the difference between Donald Trump and Godzilla:

One is a huge, ill-tempered reptile with a big tail, small forelegs, orange skin and weird orange scales on its head, and it goes around stomping on helpless people, bellowing and baring its teeth a lot; the other is just a Japanese movie dinosaur.

On scary images:

Considering that all Presidents probably lie is horrifying, like thinking about your grandparents having sex!  You just don’t want to BELIEVE IT!  (Too bad somebody told Donald Trump!  About the lies, not the sex!  Well, that is a horrifying image, too!)

On bestiality:

The Rev. Rick Warren is one of those “Wrong-Wing” hyper-Christians who gave the invocation at Barack Obama’s first Inauguration, and who declares that “gay sex is like sex with animals.”  I have a couple of issues with that: (1) how does he know that? and (2) I really resent it because I AM NOT GAY!

On reproductive choice:

If a male wishes to express his anti-choice opinions about pregnancy and childbirth, he should first be able to extrude a fully-inflated football through his anus!

On outer space:

Black holes suck!

On abuse of power:

Most Democrats employ intrusive govt. to save us from ourselves, while most Re-Pubes employ intrusive govt. to save themselves from the rest of us!

On cutting-edge surgical developments (Johns Hopkins):

Dicks On Ice!  Coming soon at a major transplant center near you!

On buoyancy:

Imagine my surprise to learn that malfunctioning chainsaws and weed-eaters don’t float!

On growing up (Rockwell Kent):

“Doing as one is told” is a great characteristic in a child and a horrible characteristic in an adult!

This year:
May our 20/20 hindsight become our 2020 FOREsight!

Democrats who've lost touch (most current Democrats):

Chardonnay Democrats!

ON THE BUS--OR NOT

The brilliant author Tom Wolfe died May 15, 2018 at age 88.  I have read most of his books.  He was a native of Richmond, Va.  I did not think he was THAT old.  I always regarded him as young and “hip.”  I guess that means I’m pretty old, too!

One of his earliest works is Electric Kool-Aid Acid Test, being about the LSD-fueled wild journeys of Ken Kesey and his gang of “Merry Pranksters” in the early 1960’s, back and forth across the US in a psychedelically painted school bus named "Further."  Reading that book moved me to pursue a thorough reading of the published works of Ken Kesey, now dead, whose most well-known book is probably One Flew Over The Cuckoo’s Nest, later made into a great movie starring Jack Nicholson and Louise Fletcher.  I have a photo still from that movie autographed by Jack Nicholson.

In the mid-1990's I went to the Smithsonian Institution in Washington, DC to hear Ken Kesey speak in a presentation sponsored by the Resident Associate Program, of which I was then a member.  Kesey was also rather well-known to most as having been an aggressive experimenter with drugs of all kinds, including psychedelic mushrooms and LSD. However, on the night he was at the Smithsonian, he seemed rather straight and sober.

Prior to the start of his talk, I saw Kesey "meandering" in the lobby of the auditorium where he was to speak. I approached him, and I asked him first if he was, in fact, not "Mr. Kesey," to which he replied he was. I then asked if the Smithsonian had been trying to get him to donate his old bus to them for display.

Kesey said that the folks with whom he had been speaking there had wanted to display the bus, but he said to me, "Y'know, that bus is rusting away in my back yard and is almost completely gone now!" I said that was no surprise to me; then he said (which I knew) that they had shot a lot of 16-millimeter film on those bus rides, and they had a tape recorder patched into the bus's electrical system. Unfortunately, the tape recorder would speed up when the bus engine speeded up, then it would slow down again when the engine slowed down. Kesey said they had been unable to "sync" the film to the tape, but the emerging digitized sound technology was holding out some promise.

(Indeed, subsequent to Kesey's death, his son has managed to produce DVD's of those films with the digitized sound track intact.)

Anyway, Kesey said he had proposed to the Smithsonian officials an idea they were not very warm to--to create a long, narrow theatre with two rows of bus seats therein, with those films projected onto a far wall for viewing by visitors who would be seated in those seats and who might, in some small way, be able to share the experience of "being on the bus."

He then looked at me and said, "Y'know, it was not about the ride; it was about the trip!"

LET THEM EAT CAKE! (Joke)

Regarding MASTERPIECE CAKE SHOP vs. COLORADO; oral arguments were heard in early December of 2017 before the US Supreme Court:

The case concerns the refusal of Jack Phillips, who claims to be a devout Christian, refusing to bake a wedding cake for a gay male couple in Colorado.  The Colorado Civil Rights Commission had held that, as a business, the Shop cannot refuse to DO BUSINESS with anyone pursuant to a prohibited discrimination.  Phillips asserts that his First Amendment right to freedom of religion prevents the Colorado government from forcing him to violate his fundamental moral and religious beliefs.

I have a serious observation about that: I assume that Phillips objects primarily to the manner in which gay men purportedly have sex.  If so, he should hurry to bake the cake and do everything he can to expedite the marriage, because we all know that married people don't have sex!

THE Memo

… or, much ado about nothing.

The text of THE Memo (cobbled together by congressional Republicans) was published in The Richmond Times-Dispatch on Feburary 4, 2018, so I decided to read it a couple of times.  One must get information "from the horse’s mouth” if at all possible.  I must admit that I have not seen any of the classified material that purportedly undergirds the “damning” conclusions in the Memo concerning the recent machinations about the "Foreign Intelligence Surveillance Act" (FISA), but I doubt there is any “there” there.  The Memo's “conclusions” are pretty much bootstrap fluff that amount to the same-ol’/same-ol’.  We’ve heard all that blustering crap before.  But for a couple of minor revelations therein concerning "sources and methods," I really don’t understand why the Memo was classified material in the first place!

I must first get something off my chest: most Democrats have really blundered in their response to the Memo.  Their near-hysterical reactions have basically invested the thing with much more significance than to which it is entitled.  I realize they had no way to know in advance what the Memo would say, but they behaved as if it would likely be a serious condemnation of Robert Mueller's "Russia" investigation, James Comey, Rob Rosenstein, et als.  RELAX!  Calm down!  The Memo is utter nonsense.  Democrats, however, seem incapable of playing things “cool.”  They need to take a chill-pill, but I doubt they will.  They seem to think they will achieve political advancement with their self-righteous, histrionic, paw-wringing contortions.

I feel somewhat hypocritical even defending the FBI or Justice Department because I have been seriously concerned about the establishment of the FISA courts and the wanton, gratuitous, routine spying on Americans by the federal Security State.  But the incongruity of REPUBLICANS worrying about government spying is just too much of an incredible provocation for me to resist.  What is WRONG with that picture?  Not that Democrats are rushing to defend our rights against such stuff.  They have carefully avoided expressing any concerns about government spying, also.  They seem to be buttressing the work of the Security State!  So, I don’t trust Democrats any more than I trust Republicans.  Neither group is committed to protecting us from wanton government snooping.

The document that I read in no way presents anything credible along the lines of what Donald Trump and many others have said about it.  It is certainly no exposé of anything significant, and it does not validate any hostility toward the FBI or the Justice Department nor any of the prominent persons thereabout.  Carter Page is the central figure in the Memo.  He is identified in the Memo as a “volunteer advisor to the Trump presidential campaign” that did not get cranked up until 2016, so it is curious that the Trump campaign engaged Page AFTER he had been under  close investigation for his machinations with the Russian government since 2011!  The Memo takes up as the FISA court was approached to issue (renew?) a warrant for “electronic surveillance” (wiretaps) of Page.  The Memo seems to imply that the initial Page wiretap was first sought in 2016, not in 2011.  Such warrants must be renewed every 90 days under FISA.

As someone else pointed out in criticizing the revelations of "sources and methods," the Memo does impugn the work of a British spy, Christopher Steele, who compiled a “dossier” that was allegedly used to buttress the FISA wiretap warrant.  Steele was purportedly employed by the Democratic National Committee and the Hillary Clinton campaign, which facts were apparently not revealed to the FISA court.  Part of Steele’s mission was to dredge up negative information on Trump’s dealings in Russia.  Steele had been "methodically" used by the FBI as a “reliable source” in the past, but his overt ties to the Hillary Clinton campaign and some indiscretion with Mother Jones Magazine (properly) cost him his FBI connections.  So what?  The Memo asserts that none of this was revealed to the FISA court in the wiretap application and should have been.  As a major justification, the Memo asserts that Andrew McCabe, the Deputy Director of the FBI, testified under oath that the 2016 wiretap warrant would not have been sought without the “Steele dossier information,” [my emphasis] but of course there is no way to know if there were other sources for that information, or that other information might have been sufficient.  So, "but for" Steele's corrupt work, Carter Page would have been totally vindicated?  That is what Donald Trump is claiming for himself, but I failed to see either vindication.  Sometimes what is NOT said is every bit as important as what is said.

The Memo also asserts, incorrectly I think, that FISA wiretap applications “should include information potentially favorable to the target of the FISA application that is known to the government.”  I practiced criminal-defense law for about 12 years and have never known of any obligation put upon any prosecutorial operation to reveal “favorable” information about a suspect.  If there is known EXCULPATORY information that shows that a suspect is INNOCENT, then I think it would be bad faith to thus proceed.  But there is NOTHING in the published Memo that suggests that there was ever ANYTHING FALSE asserted against Carter Page, nor did it contain any EXCULPATORY information seemingly withheld.  True, the DNC and Clinton connections make Steele look bad, but they don’t suggest Page’s INNOCENCE!  There is NOTHING in the Memo that suggests that Steele’s information procured a phony wiretap.  There is NOTHING in the Memo that suggests that any information ever obtained by the FISA wiretaps demonstrated Page's INNOCENCE!  Even if Steele is totally prejudiced against Page, the FISA courts issued wiretap warrants against Page numerous times, so there must have been SOMETHING going on!  But the Memo tells us nothing of that.

If Donald Trump were capable of feeling embarrassment about anything at all, he ought to be embarrassed that the tepid contents of the Memo do not in any way vindicate his silly bloviations about it.  But Trump has never demonstrated he is thus capable, so I guess he is also incapable of shame, REGARDLESS of what his thugs and sycophants do.  I am not going to hold my breath, waiting for him to act “presidential” for a change!  I hope Robert Mueller will eventually tell us what we need to know.

And, speaking of “shame,” EVERYONE I grew up with was scornful of “brown-nosers”!  They were the scum of the Earth, dismissed derisively!  What has happened to all those people I grew up with?  Where are they now?  If there was EVER someone who almost begs people to “brown-nose” him, it is Donald Trump, and there are scads of such earnest little “puppies” out there, all lined up to just burrow right on in!  And I am talking about people with advanced degrees and a fair amount of presumed intelligence!

Good grief!

HEARD IT THROUGH THE GRAPEVINE

[The following e-mail was sent to a Catholic friend 9/20/17:]

Some time ago I had heard that "Immaculate Conception" pertained to the conception of the Virgin Mary herself within the womb of St. Anne (Jesus’s grandmother), to keep the Virgin “sinless.”  Apparently, the Holy Church’s leaders (all male) seem to have had a problem with even the “Missionary Position,” as ordinary conception via S-E-X would be “dirty” and riddled with “Original Sin."  UGH!  Many of us faithless goy have mistakenly believed the phrase referred to the Virgin Birth itself, also “sinless” (poor Joseph), but I was finally corrected in my misunderstanding.  It seems that Church leaders are straining to make all the weird doctrines that have been dreamed up over the centuries fit into the human perceptions of reality, and I think that’s an unfortunate, misdirected waste of time and effort.

https://en.wikipedia.org/wiki/Immaculate_Conception

Dare we infer that, because Adam & Eve likely had S-E-X after they ate the apple (and saw the light), that “Original Sin” (which I have NEVER really understood) is related to having done the “nasty”?  Should we infer that Cain & Abel were conceived without S-E-X?  I don’t remember if they were born before or after “The Fall,” which is supposedly when “Original Sin” attached.  Might it relate to the OBVIOUSLY occurring incest that HAD to have happened if ALL humanity is descended therefrom?  My Sunday-School teachers could NOT answer these questions!

I can accept that someone might personally feel that S-E-X would taint an otherwise “sinless” conception and birthing, though I could never agree with that, but was it REALLY necessary for the Pope (Pius IX) to jump through his own asshole to solemnly pronounce the matter as “official” doctrine back in 1854, or thereabouts?  I don’t remember reading that nonsense in the Bible!  My former German professor, who is also an ordained Episcopal priest, was able to read Greek and Latin, and he told me once that the translation from Greek attributed to the English word “virgin” could also be translated as “young girl,” NOT NECESSARILY a “virgin” in the sexless sense.

Having studied 3 foreign languages, I am firmly leery of hearsay translations.  Way too many human beings put their own spin on stuff like that.  I cannot buy the notion of utterly inerrant translations via the “spirit” of God having infused the translator!  Seriously!  Jesus did NOT speak Elizabethan English, despite what many would fervently believe!  Of course, I don’t know about any of that, but it seems that a LOT of declared Christians (not just Catholics) are obsessed with all the “rules and regulations” and hocus-pocus and less so with just accepting and following the teachings of Jesus.

SPEAKING OF “hearsay,” one should read the so-called “Jefferson Bible.”  Thomas Jefferson was classically educated at William & Mary and was fluent in Greek and Latin.  He did his own translation of the New Testament from Greek, and being also LEGALLY trained, he applied the English Rules of Evidence thereto, excluding ALL hearsay but for some narrative to tie things together.  It pretty much boils down to just a small, distilled recital of the teachings of Jesus! The MOST INTERESTING part of it, however, is that it ENDS at the Crucifixion, NOT the Resurrection (which is hearsay)!  I think that every account of the Risen Jesus in the New Testament is written in the 3d-person.  I don’t recall ANY passage where one directly declares that he/she has PERSONALLY seen the Risen Jesus—it is always written in the passive voice: he “was seen”; the wounds “were seen,” etc.  Hearsay.

Finally, the metaphor about “The Fall” seems to be that one should remain fat, dumb and happy and do what (s)he is told, then God will be nice to you.  But if you DARE open your eyes and question what is going on, you will be PUNISHED for your uppity ways!  The Evil Snake will BITE YOU!  That is hogwash, as far as I am concerned!  I well KNOW that one must trade clueless “happiness” for being dreadfully aware of all the misery and suffering and evil going on, but I prefer unhappy KNOWLEDGE over STUPID happiness!  I don’t need a “devil” to blame to let human assholes off the hook, either!

I heard it through the grapevine!

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.

ALICE

    I have recently been reading a lot about the “Golden Ratio,” 1.61803 …, known by the Greek letter ϕ (pronounced “fee,” not “fye”), a mathematical ratio or proportion frequently found in nature by which many plants and animals grow and/or expand.  It is also manifest in certain architecture, art, music and science, and it has even been implicated in the behavior of the stock market!  The first known enunciation of it was by Euclid, the ancient Greek mathematician, who observed that any straight line cut at a certain point would manifest a ratio of the entire line to the longer segment as the longer segment is to the shorter segment.  It is known in German as the “Goldene Schnitt” (Golden Cut).

    The Ratio also represents the relationship of the numerical sequences in the “Fibonacci Series,” originally stated by Leonardo Fibonacci, a 16th Century Italian mathematician, who posited the Series about the reproduction of a pair of rabbits in captivity.  The Series is defined as each sequential number therein being the sum of the two preceding numbers in the Series, e.g., 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, etc.  The Golden Ratio, an irrational number that does not repeat nor is evenly divisible by any integer, is also expressed in the design known as the “Golden Rectangle,” which is considered a rectangular proportion that is inherently pleasing to the human eye.  The ratio of the shorter side to the longer side calculates out to the Golden Ratio, and it is allegedly manifest in playing cards, index cards, the Parthenon façade, and many other examples.

_________________________________ 

    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!

    That hidden math progression is rather intriguing, and though I have read the original Alice, I did not pick up on any of that until I had read Livio’s exposition. . It makes me wonder if there might be other math riddles in Alice In Wonderland.

    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)

da VINCI'S GOLDEN RATIO

For the past month or so I have been reading and have almost finished Math and the Mona Lisa, which I bought back around 2004 when it was first published by a long-ago friend, Bülent Atalay, who is a theoretical physicist and who teaches at U.Va., Mary Washington University and Princeton University.  Atalay is also an accomplished, published artist.

I have had an abiding interest in the “Fibonacci Series” and the related mathematical “Golden Ratio” for many years.  I started out as a physics major in college, but I decided to switch to the dreaded “social sciences” because I hit the “brick wall” of calculus, in which I was sadly lacking.  I  did pass the intro physics course, but barely.  Nevertheless, I have enjoyed continuing to dabble in that stuff as a layperson.

The main premise of Atalay’s book is to explore the wonderful conjuncture of math, science and art in the person of Leonardo da Vinci, who painted The Last Supper and the Mona Lisa and also explored and enunciated many scientific truths.  One of da Vinci’s main thrusts was to study the occurrence of the so-called “Golden Ratio” or “Golden Section,” expressed as the Greek letter ϕ (phi, pronounced “fee,” not “fye”), which is mostly a rectangular proportion that is frequently manifest in both art and nature and is inherently pleasing to most viewers’ eyes.  The mathematical ratio for ϕ is 1.618 : 1, being the mathematical ratio of the long side of the rectangle to the short side and which also happens to be manifest in a string of numerals called the “Fibonacci Series,” first expressed by Leonardo of Fibonacci, a contemporary of da Vinci, discussed below.

The Golden Rectangle is reflected in the façade of the Parthenon, the proportions of playing cards, 5 x 8 index cards, etc.  It is also manifest in certain ratios of human figures as in the human face and the height of the navel to the overall height of the figure!

The essence of the Golden Ratio is that as any such structure or body gets larger and larger (like a plant or tree adding buds or branches or a growing chambered nautilus), it does so logarithmically by adding an exact “SQUARE” to such a previous “rectangle,” sized equivalent to the long side of that previous rectangle, such that the resultant and larger combined rectangular structure is 1.618 larger than the square being so tacked on!  And, the previous rectangle happens to be 0.618 of that same square, the mathematical inverse of ϕ (1/ϕ)!  Then the resultant combination of the prior “Golden Rectangle” added to the new square becomes it’s own “Golden Rectangle”!  Consider: if the value of the added “square” is arbitrarily stated as “1,” then the combination is 1.0 + 0.618 = 1.618!

The “Fibonacci Series” is defined as the series of numbers in which each is the total of the two preceding numerals.  Leonardo de Fibonacci expressed it as a pair of rabbits maturing then breeding in a closed space, then the resultant pair of offspring mature and also breed two offspring, and the first pair breed again, all of which then mature and breed further, etc.  The Series is: 0,1,1,2,3,5,8,13,21,34,55,89,144, etc.  Above 5 and 8, dividing the next higher number by the immediately lower number closely yields the Golden Ratio.  (The ratio expressed by 5 and 8 is 1.6, pretty close!)  Atalay shows a photo of a stained-glass window at the UN created by the famous artist, Marc Chagall, which has 5 square panes x 8 square panes, being itself such a manifestation of the Golden Ratio.  Consider adding “squares” beginning with 8 x 8, then 13 x 13, then 21 x 21, etc. in a spiral fashion, and the growth” pattern mentioned above is readily apparent.  As a growing body may be restricted by physical space (like the nautilus shell), it may well be forced to spiral out to the side as it grows.  So, the new growth produces a “SQUARE” of sorts because new tissue must spread more or less equally in all directions, and that is basically what a “square” is—it is spread out from side to side and end to end equally, and it is going to be defined in scope by the size of the existing tissue from which it emanates.

Years ago I read H. E. Huntley’s book, Divine Proportion, about these topics.  I also want to read Mario Livio’s book about the same thing.  Years ago another friend also gave me Jay Hambidge’s book, Dynamic Symmetry, etc. which explores how the Golden Ratio is manifest in the proportions of ancient Greek pottery.  Several years ago I attended a lecture by Roger Penrose, the theoretical physicist.  I bought his book, Emperor’s New Mind, about the math of interlocking tiles and geometric figures.  I tried to read the book at the time but found too difficult to continue.  I am fascinated by mathematical “coincidences” found in nature.  I also am reading a book, Physics for Gearheads, which has a lot of interesting material related to auto mechanics.  I am a certified auto mechanic as well as a retired lawyer and auctioneer.

Some of this stuff may be over the reader’s head.  Atalay’s book has been a tough slog for me, but I really want to know about it all.  Leonardo da Vinci was an amazing individual whose contributions to both art and science cannot be overstated.

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