2022, for example

As we entered the current calendar year, James Propp (in a math-fun forum) noted a Dan McQuillan tweet on the embedding of the integer 2022 in its base-three representation:

2202220

The property is not the sole domain of 2022, but rather of a sequence of such integers wherein 2022 is the sixteenth term. James wanted to find out if this sequence was infinite. His argument had it that for length-d integers there should be slightly more than d solutions. Actual number of solutions for d up to 26 are:

3, 3, 6, 4, 4, 0, 0, 3, 3, 10, 0, 15, 14, 20, 8, 13, 20, 25, 9, 21, 14, 20, 23, 17, 8, 18.

That's 281 solutions altogether, thus far. Here are the last 18 (26-digit) solutions:

12011102001112020010002201020010222122111111112022112

12011102001112020010010002110100202102022110210022001
12120120221001100110120020101011000001200201100221210

12120200122001222012202121222002101201220202020112112

12121211002200121012200100101222020222010202110221012

12121211010102002200002122022001122122022111002211220

12121211102211101101221101122010121002020112121202201

12121211110112212210222021122222211212101012002120022

12121211202222011121002000222100101122011102212211110

12121211210200212010210010102210210002222221002210221

12121221220001002121001110110111221111010011221120222

12121222012222220211020021122201211121212110012112122

12121222020000010000010220110120001111001100122121202

12200002021122110111202210110110201200122021112110022

100202112102120012102220200111102002122102011100001122

100202112102120102102210221000121021121102121111011222

100211210200212022120220202012210222011001201111010120

100211210200212022120221010210222021011222010102002111

[last updated 28 March 2022]

A coincidence of dates

Every few years I manage to discover something previously unknown in my genealogical meandering. Recently it was the children of Wilhelmine Elisabeth Havermann Rademacher on an Ancestry website. Note that the site incorrectly positions her among the children. Elisabeth (known as Sette) was a sister of my grandfather Friedrich (known as Fritz) Havermann (1869-1945).

Sette's children are welcome additions to my personal "Havermann" family tree. There was another piece of information on that Ancestry website: Elisabeth's death date is given as 17.05.1943, supposedly in Arnsberg. A search for that specific date yields a number of hits related to Operation Chastise, wherein the dam at the Möhne reservoir was destroyed. Many of the deaths from the resulting flood occurred in Neheim (which, since 1975, is a part of Arnsberg). Neheim is not only where I was born, but also (I believe) the hometown of my grandaunt Elisabeth Rademacher. If Sette was a casualty of that flooding, this was not something of which I had been previously aware. Mind, prior to my father's death, his aunts and uncles (and their offspring) generally were not something of which I recall being really conscious. If he had ever talked about any of them, it failed to make a sufficient impression on me (i.e., that they were his relatives).

My research associate, Marlene Frost, has Ancestry access and was able to dig up the 1928 and 1936/37 address directories for Neheim showing that Elizabeth and some of her children lived at Möhnestraße 11, not far from the Möhne river (downstream from the reservoir). The Möhne joins the Ruhr in Neheim. Sette's death informant, instead of providing particulars, had simply made a reference to the Möhnekatastrophe, hence the date.

Möhnetalsperre 17 May 1943 (Fotarchiv Ruhrverband)

How not to communicate one's GPS location

Alas, Apple has made the ad unavailable. "The owner of this Apple Watch has taken a hard fall and is not responding to their watch. The emergency location is latitude 47.7, longitude -117.5, with an estimated search radius of forty-one metres."

Bob B. (presumably no relation to the unfortunate Amanda A. [video ad also now unavailable] who flipped her car in fast-rising, muddy water) was knocked unconscious mountain biking in a forest just west of Spokane WA with his watch supposedly making the 911 call. No doubt countless targets of the advertisement will ask Google Maps for the location of the coordinates:

Wow! Exactly on a bicycle-friendly road in a wooded area. But there is something amiss. To achieve such pin-point accuracy one needs precision somewhat beyond the given tenths of a degree latitude/longitude. 47.7000 N, 117.5000 W would do it, although the 41-metre search radius suggests 47.700 N, 117.500 W is probably sufficient. A GPS location is likely given in degrees/minutes/seconds (not decimal degrees) and this would have the desired accuracy. I am not acquainted with the Apple Watch emergency-call GPS specifics but I will point out that by approximating the location as 47.7 N, 117.5 W (dropping the terminal zeros), it implies an error box of ~7.5 km east-west and ~11.1 km north-south. That's a search-area of over 8300 hectares! Poor Bob.

47.7º N, 117.5º W, approximation error box (in magenta), click to enlarge

Telephone puzzler

Local calls appeared to be getting through on our home-phone landline but not long-distance calls, as evidenced by a handful of instances over the course of a month. I was certain that the problem lay in some distant Bell relay device and that the technician likely wouldn't have to come into the house. I was wrong.

Ekene, technician, connecting a new cable to a nearby Bell hub

Snow

Early this morning, coming home after the dog-walk. Twelve hours later we had ~40 cm.

10*9*8+7+6+5+4*321

Happy New Year!

The adventure begins (fingers crossed)

photo/ornament courtesy ScienceSocks

Wildlife

coyote under the streetlight, click to enlarge

Spotted walking from Clouston Avenue through Denison Park on this morning's dogwalk, a furtive coyote has just left the north end of park and is about to walk up Denison Road West. I managed to get a lot closer to a fox that I saw on Sykes Avenue back on November 27:

YYZ

From high above my abode in south Weston, courtesy the latest version of Mathematica, a graphic representation of Canadian and U.S. flight paths yesterday that started or ended at nearby Toronto Pearson International Airport. Zooming in ...

Weston Station

click to enlarge

In the above Toronto transit map, Weston Station is clearly marked on the UP Express and GO Line Service routes, heading northwest out of (downtown) Toronto. As one might expect, it is just south of the extended horizontal line connecting Lawrence West (University, line 1) and Lawrence (Yonge, line 1) subway stations.

Roy Murray wrote an article on WestonWeb.ca about Castlepoint's "Weston Park" proposed development right beside Weston Station, pointing us to a YouTube video by Castlepoint Numa on the project. I watched it on December 2nd and noticed that the location of Weston Station had been moved southeast so as to appear much closer to Eglinton Ave. W. in Mount Dennis. So I decided to make a YouTube comment pointing that out: "There's a transit map at 0:50 to 0:55 where Weston Station pops up at an incorrect location. It's actually a good deal further northwest. Presumably the disingenuous placement is meant to convince the target of this propaganda piece of the station's proximity to the Eglinton Crosstown corridor."

click to enlarge

I noticed today that my comment had been removed and comments turned off.