Swap

Éric Angelini's blog post last Friday (Underline, reproduce) motivated me to attempt to solve

S9 = ninth, twentieth, thirtieth, fourth, ninetieth, sixth, seventh, eighth, ...

... wondering how many swaps (of "first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, …") were needed to produce it. It stymied me for a day or so but (using a combination of manual and Mathematica step-throughs) I eventually got this:

S9 = ninth, twentieth, thirtieth, fourth, ninetieth; sixth, seventh, eighth, first, tenth, second, twelfth, fifteenth, thirtyeighth; thirteenth, fifth, eleventh, eighteenth, nineteenth, seventeenth, twentyfirst, twentysecond, fourteenth; twentyfourth, twentyfifth, twentysixth, twentyseventh, twentyeighth, sixteenth; third, thirtyfirst, thirtysecond, thirtythird, thirtyfourth, thirtyfifth, thirtysixth, thirtyseventh, twentythird; thirtyninth, fortieth, fortyfirst, fortysecond, twentyninth; fortyfourth, fortyfifth, fortysixth, fortyseventh, fortyeighth, fortyninth, fortythird; fiftyfirst, fiftysecond, fiftythird, fiftieth, fiftyfifth, fiftyfourth; fiftyseventh, fiftyeighth, fiftyninth, sixtieth, sixtyfirst; sixtysecond, sixtythird, sixtyfourth, sixtyfifth, fiftysixth; sixtyseventh, sixtyeighth, sixtyninth, seventieth, seventyfirst, seventysecond; seventythird, seventyfourth, seventyfifth, seventysixth, seventyseventh, seventyeighth, sixtysixth; eightieth, eightyfirst, eightysecond, eightythird, eightyfourth, eightyfifth, eightysixth, eightyseventh, seventyninth; eightyninth, eightyeighth, ninetyfirst, ninetysecond, ninetythird, ninetyfourth, ninetyfifth, ninetysixth, ninetyseventh, ninetyeighth, ninetyninth, onehundredth; ...

In case you are still wondering what this is all about, the sequence of written-out ordinals reproduces itself if you take its 9th, 20th, 30th, 4th, 90th; 6th, 7th, 8th, 1st, 10th, 2nd, 12th, 15th, 38th; 13th, etc. letters. I have replaced commas with semicolons where the spelling of each ordinal ends. The semicolon after "onehundredth" indicates the end of "thirtyeighth".

So I told Éric that there were 24 swaps, i.e. red-lettered ordinals (where the number does not correspond to its position in the sequence). But in my mind "swap" has a strong sense of pairwise exchanges, which is not the case here. There are three such pairwise exchanges: Positions 1 with 9, 3 with 30, and 13 with 15. But the rest are more involved. Position 14 goes to 38, which goes to 23 (which goes to 14). Position 2 goes to 20, which goes to 17, which goes to 11 (which goes to 2). Finally, position 5 goes to 90, which goes to 88, which goes to 79, which goes to 66, which goes to 56, which goes to 54, which goes to 50, which goes to 43, which goes to 29, which goes to 16 (which goes to 5).

Update: I've calculated 11001 indexed terms for

S10 = tenth, eighteenth, twentyeighth, ninetieth, fifth; second, seventh, eighth, ninth, first, sixth, eleventh, eleventhousandth, fourth, fifteenth; fourteenth, seventeenth, twelfth, third, sixteenth, twentyfirst, twentysecond, twentythird, twentyfourth, twentyfifth, twentieth, twentyseventh; ...

In the linked file, the 1098 red entries are indicated by an asterisk at the end of the line.

Man versus nature

two men with leaf blowers (across the street, last Thursday)

same driveway (left) this morning

Doctor in the Tardis

After a decade-long hiatus of not seeing my family doctor, on September 27 I had my first appointment with a new doctor. After taking down some of my personal information we agreed to my doing a blood test and an Ontario Health fecal immunochemical test. In an October 13 phone appointment, he relayed the bad news: My cholesterol was high, which when combined with my family history of stroke (my father had one) suggested medication. When I indicated reticence to go on meds he allowed me a three-month reprieve of diet and exercise followed by a retest. To add insult to injury, the fecal test proved abnormal, inviting a colonoscopy. I suggested that the result was a false positive based on contamination with hemorrhoidal bleeding.

So I spent a month researching the matter and, this afternoon, saw him in order to share my findings. I decided ahead of time not to get into the family-history-of-stroke matter which I saw as confirmation bias on his part (he didn't even know at what age my father had the stroke). The diet-and-exercise bit is of course something to be suggested regardless (as it is generally worthwhile), not as a designed-to-fail antidote to statins. I wasn't going to get into that either as it evidenced a desire to get me on meds and I didn't want to be confrontational. At any rate, the matter was moot as I had found sources that suggested (in the absence of cardiovascular disease, diabetes, etc.) that I had no need to be on meds.

First, I presented Dr. Ian Neeland's (22 Dec 2020) podcast quotation of "10 years on a statin with low LDL cholesterol might decrease your risk [of heart attack, stroke, etc.] by 20 percent" as being (for me) a negligible benefit. Next, I presented Robert M. Kaplan's (3 Apr 2019) opinion piece on preventing heart disease, starting with some absolute risk-of-dying meta-analysis statistics and concluding with "... observations on people over the age of 70 do not show any statistically significant statin-related reductions in deaths from any cause."

Throughout most of the session my doctor seemed overly defensive, mildly angry perhaps. He interrupted me several times, explained that he was following guidelines, and cautioned me on cherry-picking data. He closed the door to the hallway at one point. Much more was said but I choose here to be brief.

I had run out of my 15 minutes and I hadn't yet dealt with the fecal test. I asked for a couple more minutes. I explained my false-positive belief, suggested that it didn't matter anyways because I had "a very low long-term risk of colorectal cancer" based on a (19 Sep 2013) study on long-term colorectal-cancer incidence and mortality. I finished with Michael Bretthauer's "gold-standard trial" that had colonoscopies cutting cancer risk by only a fifth with no significant reduction in colon cancer mortality. How do you like them apples cherries?

New Jersey

Rogue Amoeba has updated their Audio Hijack to version 4.3 and I had been meaning to upgrade my 3.7 app for a while now. Tipping the scale was a "transcribe" block that I thought might prove interesting in attempting the lyrics to Dave Van Ronk's Garden State Stomp. There were two available options for the transcription: high accuracy which, in spite of the lengthy time that it took, proved abysmal, and low resources which, utilizing an AI-based Large Language Module, was just as bad, only with added nonsense.

Places per line are 4/4/12 (times 4 = 80). Lyrics/spelling as per the video:

Allamuchy, Hacklebarney, Rockaway, Piscataway.
Ho-Ho-Kus, Secaucus, Lower Squankum, Fair Play.
Wanamassa, Succasunna, Manumuskin, Plumbsock, Bivalve, Buckshutem,
  Turkey Foot, Macanippuck, Jugtown, Febletown, Nummytown, Rahway.

Wickatunk, Manunka Chunk, Mantua, Mizpah.
Manasquan, Raritan, Matawan, Totowa.
Whippany, Parsippany, Penny Pot, Hackensack, Batsto, Nesco,
  Metedeconk, Peapack, Loch Arbour, Egg Harbor, Swinesburg, Caviar.

Cheesequake, Boy Scout Lake, Moonachie, Tenafly.
Netcong, Watchung, Pluckemin, Mount Misery.
Bardonia, Ironia, Colonia, Weehawken, Manahawkin, Mantoloking,
  Mahalala, Pennsauken, Dutchtown*, Ironbound, Frelinghuysen, Lodi.

Hardscrabble, Double Trouble, Picatinny, Montague.
Muckshaw Pond, Ockanickon, Espanong, Ocean View.
Navesink, Shabakunk, Ongs Hat, Jumbo, Wortendyke, Water Witch,
  Blue Ball, Ringoes, Matchaponix, Delawanna, Wawayanda, Timbuctoo.

* which Van Ronk seems to pronounce Ducktown.