Tuesday, December 21, 2021

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:

Thursday, December 16, 2021

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 ...



Sunday, December 05, 2021

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.

Thursday, November 18, 2021

Pandigital palindromic sums

Two days ago Éric Angelini posted on MathFun:

234567898765432 + 1000000000000000 = 1234567898765432

... noting that (ignoring the arithmetic symbols) the concatenated 47 digits are a palindrome. Éric wondered about smaller palindromic sums where all ten digits are present ("pandigital" in the sense of A171102). Here are the 24 smallest:

12076 + 38354945 = 38367021
12076 + 83854945 = 83867021
12376 + 80854945 = 80867321
12876 + 30354945 = 30367821
13086 + 27254945 = 27268031
13086 + 72754945 = 72768031
13286 + 70754945 = 70768231
13786 + 20254945 = 20268731
21067 + 38354945 = 38376012
21067 + 83854945 = 83876012
21367 + 80854945 = 80876312
21867 + 30354945 = 30376812
23087 + 16154945 = 16178032
23087 + 61654945 = 61678032
23187 + 60654945 = 60678132
23687 + 10154945 = 10178632
31068 + 27254945 = 27286013
31068 + 72754945 = 72786013
31268 + 70754945 = 70786213
31768 + 20254945 = 20286713
32078 + 16154945 = 16187023
32078 + 61654945 = 61687023
32178 + 60654945 = 60687123
32678 + 10154945 = 10187623

Thursday, November 11, 2021

What a difference five months make

Five months ago, I showcased the then-ten-largest-known Leyland primes. Here's an update:

500973  (100207,99856)   Gabor Levai          Nov 2021
500702  (100263,98600)   Gabor Levai          Sep 2021
386642   (81650,54369)   Yusuf AttarBashi     Jun 2021
386561   (80565,62824)   Hans Havermann       Aug 2021
386548   (83747,41272)   Hans Havermann       Aug 2021
386434  (328574,15)      Sergey Batalov       May 2014
302858   (84181,3960)    Hans Havermann       Nov 2021
301815   (83278,4209)    Hans Havermann       Sep 2021
301763   (64431,48250)   Hans Havermann       Sep 2021
301716   (67237,30714)   Hans Havermann       Sep 2021

The first column gives the number of decimal digits. The Leyland number of an (x,y) pair is x^y + y^x. Nine of these ten entries are new. Of course my list of all known Leyland primes is always up-to-date.

Thursday, October 07, 2021

What's so special about 6987952709035199279905674?

Éric Angelini came up with this yesterday:

abcdefghij... (letters are distinct digits):
a is divisible by 1 with remainder 0
ab is divisible by 2 with remainder 1
abc is divisible by 3 with remainder 2
abcd is divisible by 4 with remainder 3
etc.

The largest such integer would be 95674103:

9/1 leaves a remainder of 0
95/2 leaves a remainder of 1
956/3 leaves a remainder of 2
9567/4 leaves a remainder of 3
95674/5 leaves a remainder of 4
956741/6 leaves a remainder of 5
9567410/7 leaves a remainder of 6
95674103/8 leaves a remainder of 7

Much more interesting is if we dispense with the "distinct digits" limitation. Let us allow any digit. The largest integer is now 6987952709035199279905674:

6/1 leaves a remainder of 0
69/2 leaves a remainder of 1
698/3 leaves a remainder of 2
6987/4 leaves a remainder of 3
69879/5 leaves a remainder of 4
698795/6 leaves a remainder of 5
6987952/7 leaves a remainder of 6
69879527/8 leaves a remainder of 7
698795270/9 leaves a remainder of 8
6987952709/10 leaves a remainder of 9
69879527090/11 leaves a remainder of 10
698795270903/12 leaves a remainder of 11
6987952709035/13 leaves a remainder of 12
69879527090351/14 leaves a remainder of 13
698795270903519/15 leaves a remainder of 14
6987952709035199/16 leaves a remainder of 15
69879527090351992/17 leaves a remainder of 16
698795270903519927/18 leaves a remainder of 17
6987952709035199279/19 leaves a remainder of 18
69879527090351992799/20 leaves a remainder of 19
698795270903519927990/21 leaves a remainder of 20
6987952709035199279905/22 leaves a remainder of 21
69879527090351992799056/23 leaves a remainder of 22
698795270903519927990567/24 leaves a remainder of 23
6987952709035199279905674/25 leaves a remainder of 24

Wednesday, October 06, 2021

Oaklands

click to enlarge
This is my first-year high school class of 1964/1965. Last Saturday, one of these teenagers hosted a high school reunion celebration in his residence at 50 Yorkville Avenue. If one were to look roughly northwest from the top of that building, they might see something like this:

click to enlarge
I have marked the De La Salle college location in yellow. This Apple maps representation is ~2018 because construction on the townhouses (just west of Del's fussball pitch) on Avenue Road is in its starting phase. Additionally, there are now townhouses to the south of the field on Oaklands Avenue. The city of Toronto did a detailed heritage property background report in 2015. Here's a closer bird's-eye view:

click to enlarge
There is a worthwhile article on De La Salle, written in 1980 by William Stephenson, called All Things Right & Dutiful. Somewhat surprisingly for such fare, it contains a paragraph on the once-upon-a-time corporal punishment meted out to some of the students.

I was unfortunately unable to attend this 52nd anniversary (counting from our graduating year) get-together. Many of my reasons noted here were of course tongue-in-cheek.

Saturday, October 02, 2021

Top ten reasons why I am not attending my high-school reunion

#10. I don't want to belong to any club that will accept me as a member. [Groucho Marx]

#9. I'm still recovering from the last time I was talked into attending a get-together.

#8. I can't think of a bigger social evaluative threat. (Not that I care.)

#7. I am under house arrest!

#6. I flipped a coin and it came up tails.

#5. The delta-driven fourth wave (and other respiratory delights).

#4. Elbow-bump performance anxiety.

#3. My dog wasn't invited.

#2. My shoes are on their last legs.

#1. Mama told me not to come. (That ain't the way to have fun.)

Wednesday, September 29, 2021

3816547290

I've been looking very hard for the earliest occurrence in print of the number 3816547290 as the solution of a famous divisibility challenge. For an explanation, see OEIS A181736. David Gauld, the author of that sequence, wrote about this number way back in December of 1984 (problem 15 on page 17, here; the following month it appeared in Games magazine, page 2). I recently asked David wherefrom he got that number. He replied that it was in the 1983 book "Les nombres remarquables" by François Le Lionnais. Indeed:

There's more! A Google book search for 3816547290 comes up with a Russian hit, Nauka i zhizn' (Science and life) - page 148, supposedly 1980:
click to enlarge
Once I figured out the trailing numbers, this did look like a bona fide mention. The snippet view, alas, showed nothing. And Google's date assignments can't generally be trusted, so I longed for an inside-the-journal look. Playing with it (try searching for 381654), I eventually conjured up this snippet:
click to enlarge
Showing a '1980' at the top-right made me hopeful that this is an actual earlier posing of the divisibility curiosity than that of Le Lionnais. If that were so, it would not be unreasonable to suppose that this dissemination was responsible for Le Lionnais (being the well-connected individual that he was) coming to be acquainted with 3816547290.

A variant of the divisibility puzzle that excludes the digit 0 appeared just prior to Le Lionnais in an "Acorn User" competition in November 1982:
Acorn User: November 1982, page 71
Acorn User: February 1983, detail from page 55
The February 1983 answer to the puzzle is significant for noting that the problem appeared in the 'Brainteaser' column of the Sunday Times (in 1982), which is how David Wells credited 381654729 in "The Penguin Dictionary of Curious and Interesting Numbers" (1986). More relevant (to me) is the assertion that it was first posed in Scientific American "five years ago". Of course! That would make it Dr. Matrix (Martin Gardner) in Chautauqua (Mathematical Games, Scientific American, December 1978, page 23):

"Jaime Poniachik of Buenos Aires, who edits an excellent Spanish puzzle magazine titled The Snark, happened to be visiting the Chautauqua Institution at the time of the ASMOF demonstration. When it was his turn to ask a question, he said he had a friend in the U.S. with a curious social security number. Its nine digits include every digit from 1 through 9, and they form a number in which the first two digits (reading from left to right) make a number divisible by 2, the first three digits make a number divisible by 3, the first four digits make a number divisible by 4 and so on until the entire number is divisible by 9. What is the number?"

Gardner's solution (Mathematical Games, Scientific American, January 1979, page 24):

"The social security number is 381-65-4729. Adding 0 at the end gives the unique solution to the same problem with the ten digits from 0 through 9."

So 3816547290 was implicitly noted as of this date and the explicit Russian mention a year or so later is no longer a surprise. In "The Magic Numbers of Dr. Matrix" (1985), Gardner cleans up the ambiguity of his "ten digits" solution by adding "..., and the ten-digit number divisible by 10." There is considerably more in the book but I will quote only a couple of paragraphs:

"Michael R. Leuze worked with a computer to examine solutions to this problem in number systems other than base 10. He found that there are no solutions in any odd base or in base 12. In base 2 there is the trivial solution 1. In base 4 there are two solutions, 123 and 321; in base 6, 14325 and 54321; in base 8, 3254167, 5234761, and 5674321. In base 14, as in base 10, there is a unique solution: 9 12 3 10 5 4 7 6 11 8 1 2 13. Leuze conjectures that there are no solutions in higher bases."

"Leuze sent a thorough analysis of the problem in negative bases. For other generalizations, see 'Progressively Divisible Numbers', by Stewart Metchette, in Journal of Recreational Mathematics, Vol. 15, No. 2 (1982-83), pages 119-22. The problem surfaced again in 'What's In a Number?', Mathematical Gazette, Vol. 67 (December 1983), pages 281-282. The editor added in a footnote that when the problem appeared in London's Sunday Times in 1982, irate readers made the same careless mistake some of my readers did — they complained that the answer was not unique because they had worked on the problem with an eight-digit calculator!"

Finally, Gardner reveals the true author of the puzzle:

"Jaime Poniachik (the person who posed the problem in my column) told me the problem had been invented by his wife, Lea Gorodisky, who worked with him on the Snark."

Wednesday, September 15, 2021

Spirit talker

Canada's Aboriginal Peoples Television Network (APTN) premieres tonight season 2 of Spirit Talker, "a documentary series that will follow Mi’kmaq medium Shawn Leonard as he travels from coast to coast using his psychic abilities to connect the living with the dead and bring hope, healing, and closure to indigenous communities." I've watched all of season 1 so I will certainly watch at least this first episode, not so much for what Shawn says and does (which is all fairly predictable, tired old shtick) but more for enlightening glimpses of behind-the-scenes. CTV News Atlantic (Halifax NS) did this promo piece (Keeping Up with Katie Kelly) introducing the series:

Katie: When you watch the show, you you [unintelligible] ... You know so much. People are shocked by what you say. Is it real? Is it all real?
Shawn: It's absolutely 100% real, yea. This isn't like a scripted show in any way. This is like... They just put me in front of people and let me do my thing.

In spite of being unscripted, Shawn's on-site production team includes some seven other people whose bread and butter depends on how good they can make Shawn look. Shawn himself is not of course an unwitting pawn of the deceased. His art, such as it is, likely goes back to his 1995 marriage to Melissa McClinchy who brought a dabbling in pseudoscience to their relationship (which lasted until 2014). Their paranormal pastime had become a public persona focus for Shawn as he strove* to incorporate his Indigenous ancestry into the act, dropping (for example) his Beaupre surname from his online identity. In 2015, Shawn celebrated an Indigenous wedding to a Bonny Martell but this ended bitterly a mere eighteen months later. Around this time he may have made "Shawn Leonard" his legal identity. The current status of his subsequent relationship to a Michelle Belanger (not the occult author), touted at one point as his fiancée, is unknown to me.

Perhaps a good indicator of Shawn's reach is this photograph ...

... taken from his Facebook header, impressive for the sheer number in his pre-pandemic Spirit Talker "Tribe" online course group and (of course) their gender bias. I have mentioned Shawn once before in my blog, here. Apparently season 3 of Spirit Talker (with an Ontario focus) is already half-way done.

* Shawn is still striving. In the Katie Kelly interview he states: "I'm a very proud Mi'kmaq person." Then, as if to justify the assertion: "I never grew up on reserve. I grew up near to the reserve in Shubenacadie, Nova Scotia." This must be his stock response when folk on the reserves that he visits ask him which reserve he is from.

Saturday, September 11, 2021

Hurricane Larry

Hurricane Larry landfall @ 1:20 AM, local time
This image shows the "Larry makes landfall on Newfoundland" advisory location as we moved this morning into the 20th anniversary date of the 9/11 attacks. It is not lost on me that on the attack's 9th anniversary, 11 years ago (also a Saturday), my brother-in-law Larry passed away. The hurricane's landfall is 37 km east-southeast of St. Bernard's.

A CBC news story on the hurricane mentions a "statement" that said "Larry made landfall at 1:30 a.m. NT just west of Long Harbour, N.L., on the Avalon Peninsula." I have no reason to suppose that my National Hurricane Center landfall location is incorrect, so the "just west of Long Harbour" translates to "50 km west of Long Harbour". That's on the other side of Placentia Bay at that latitude, on the Burin Peninsula. So not really a very good description. I'm aware that the official location coordinates might themselves be subject to error bars (especially this far north when much of the eye wall will have dissipated) but that is an entirely different discussion.

CTV's (Canadian Press) version of the event has Larry "arriving near South East Bight around midnight local time, according to the National Hurricane Centre in Miami." South East Bight is very close to the landfall coordinates and when one is looking for a location place-name, it will do. But what about the "midnight local time"? The NHC's summary has "1150 PM AST" (Friday) ... "0350 UTC" (Saturday). Why did the NHC use AST? Likely because that (currently) is Miami time. Technically Miami is in the EDT time zone, but Eastern Daylight Time = Atlantic Standard Time. Coordinated Universal Time is 4 hours ahead of Atlantic Standard Time. But right now, Atlantic Canada is observing Atlantic Daylight Time so landfall would have been at 12:50 AM ADT. Furthermore, Newfoundland Time is an additional half-hour ahead, so 1:20 AM local time. What made the Canadian Press think that AST was local time? It's an easy mistake to make if you have no patience for diligence.

Thursday, September 09, 2021

My 1500th Leyland prime find

This morning I found my 1500th Leyland prime. My 1000th was only eight months ago! I have 579 red values found using Mathematica (from 3 October 2015 to 3 July 2020), followed by 921 blue values found using xyyxsieve & pfgw64 (from 6 July 2020 on). Compared to my graph for the 1000th, everything is compressed: horizontally by the addition of eight months, vertically by the addition of eighteen integers ranging from 300000 to 301441 decimal digits and two more composed of 386548 and 386561 decimal digits.

Wednesday, September 01, 2021

Ad war

I had been fighting a battle with Google ads for I don't know how long. If it was an animated gif and had an x in the top-right corner, I would smash that x, click "send feedback" and choose "not interested in this ad" from the four options.


When I initially started this, I chose "ad was inappropriate" to more properly indicate my feeling that anything animated was an annoyance — distracting me from reading the page — but the nuance was always that there was something more politically incorrect about the ad and I gave up on the sentiment. Sometimes, after I had flagged a handful of identical such ads on the same page with "not interested", I would finally do a "seen this ad multiple times". And in spite of Google assuring me that it would try to stop showing me these ads, I would in fact see the same stupid ads from the same advertisers again and again.

Early this morning I finally gave up on the experiment. The only noticeable change over all these many months had been that I was seeing more ads for women's apparel. So much for artificial so-called intelligence. I'm now using the Magic Lasso ad-blocker extension in Safari and all I can say is: Why didn't I do this a long time ago?

Thursday, August 19, 2021

Opening day

The FreshCo that (two months ago) I anticipated opening, opened today. I was there just after 9 AM checking it out. I had washed my hair and changed my hole-riddled T-shirt so that folk wouldn't mistake me as a harbinger of a zombie apocalypse. It was the first time in over seventeen months that I have been inside a grocery outlet! I picked up a couple of 2L milks, a couple of 750G yogurts, one head of lettuce, a chunk of beef, and a few smaller items. These were distributed in two bags that I had brought to the store. The ten-minute walk home was somewhat tiring, my back apparently no longer suited to such a task. One sour note (noticed after I got home) was that the box of Milk-Bones I purchased only because it was shelf-tagged at $1.25 (a very good price) showed up as costing $2.49. The $5-off opening special (on orders over $35) made up for that annoyance.

Wednesday, August 11, 2021

The Huron and Ontario ship canal

After the Frederick Moffat house aside in my last blog article, I wondered about other early settlers in my neighbourhood, in particular those on my street: Sykes Avenue. Additionally, I wondered about the street name's origin. A possibility soon emerged: William Sykes (1815-1872) who in his later years became resident engineer of the Huron and Ontario Ship Canal Company in Toronto. An 1869 prospectus of that venture is made available by Kingston's Queen's University, here. A more-than-interesting aspect of the proposed canal was its debouchure near Toronto:

"The Southern division will commence in the Humber Bay, at a point about 25 chains west of the mouth of the Humber River, where it is proposed to make three lift locks in the solid ground, elevating the canal 45 feet and carrying it, by means of a stone aqueduct, over the Lake Shore Road, Great Western Railway and side road. From the Northern extremity of this aqueduct, the canal will be continued, through the solid ground, to the village of Lambton, a distance of three miles, where it will join the river and receive its water supply. Following the valley of the Humber River for about three miles farther, to Weston, it will there intersect the Grand Trunk Railway, which is carried over the valley of the Humber by a viaduct about 60 feet above the water level. There the canal will be brought, by the necessary excavation in the bed of the stream, underneath the Railway, at a level to afford 100 feet clear headway for the passage of masts of vessels; its elevation to the natural level being effected, after passing beneath the viaduct, by three lift locks."

It is difficult to imagine the plan's impact on Weston had it ever come to pass. How might history have been changed, for example, in light of the flooding caused by the hurricanes of 1878 and 1954? This section of the canal's meander ends up in Lake Simcoe, called "Lac Taronto" by early French map-makers who appropriated an Aboriginal word referring to the area between the eastern part of Orillia and Atherley. The proposed canal's waterway route from Toronto to Lake Simcoe (shown in red) mirrors in part a supposed Toronto Carrying Place trail.

There exists a perceptual mechanism known as "figure—ground": We focus on the former to the exclusion of the latter. I believe now that the Carrying Place trail is such a figure, the ground (ironically) being its nearby waterways. This figure has been honed by far too many occasions of uncritical thinking, relying largely on the portion of the trail (from Bloor Street to Weston) with which we are most familiar. I gave a hint of the problem that this entails in my 2017 article on Weston's origin "across the river":

"There's another plaque at the northwest corner of Little Avenue and Weston Road ... detailing — in a map — the 'Toronto' Carrying Place, a portage trail running from the Humber River at Bloor Street to the Holland River, a considerable journey. You may be forgiven if you think that the dashed line segments represents an actual path, but in fact we know very little about the journey. The trail is just a supposed connection between the start and end points, ignoring the many places along the way where a canoe might sensibly be set in water."

In fact, the trail isn't the figure; it's the ground. The waterway route is the real figure! The supposed "trail" is really just a bunch of portage elements, of which the stretch from Bloor Street to Weston misleads one into thinking that this is all about walking, not canoeing; that this is all about a land route starting in Toronto, not a waterway route ending in Taronto.

Update: I have discovered that the Huron and Ontario ship canal is a decade-later rehashing of the Georgian Bay canal proposed by R.B. Mason and Kivas Tully in 1858. The chart/map "shewing the several proposed routes of the Toronto & Georgian Bay ship canal between the city of Toronto and Lake Huron" is from their survey. Embarrassingly, what I had taken to be the figure of Indigenous roads in the Huron & Ontario ship canal folded-map segment (which lacked the legend) turned out (by reference to the Toronto & Georgian Bay ship canal map) to be the ground (ridges) of watersheds. It is actually an interesting correspondence: The ridge of a watershed is high terrain that encounters no flowing water. This is ideal for a no-maintenance transportation corridor!

Friday, August 06, 2021

The recycling ghost

My pre-dawn walk with Bodie this morning was to go (on the sidewalk, left to right in the photo) past these two bins on the Sykes-side of the once Frederick Moffat house. [The linked obituary suggests that his Denison (not Dennison) Rd. W. residence was "Corralyn" which (instead) appears to have been his cottage on Peninsula Lake.] The sloping-concrete section in front of the driveway is noteworthy to me because back on February twenty-second I apparently slipped here on the ice. As I regained consciousness that morning, a sore spot on the back of my head was firmly planted into the sidewalk. Bodie, dragging his leash, was several metres ahead so I hadn't been out long. It did not appear that he was the least bit concerned, nor that he was about to help get this Timmy out of the unwell.

The overturned green bin is a known sign of raccoon mischief. As I approached, the lid on the mostly-closed blue recycling bin opened up. Slightly startled, I decided to traverse the terrain on the street side of the bins, instead of the sidewalk. I snapped the photo of the still-dark crime scene after I had gone past, hoping to illuminate the perpetrator.

Saturday, July 17, 2021

What goes up

My previous post managed to ensnare Ray Chandler into helping extend OEIS sequence A293355, which had reached term #384. Ray has access to "yafu" which allows him to factor large integers quickly. Sadly, I don't know how to get that program to run on my Mac. At any rate, thanks to Ray's persistent effort, he was able to extend the sequence past a local maximum at #398 and then down the other side to a point where the numbers were finally small enough that I could once again automate the procedure in Mathematica. The downslope reaches a local minimum at #923, then rises again, slowly and erratically:

click to enlarge
The ratios graph (that I had previously posted to term #384) extends now past term #3280:
click to enlarge
It clearly shows the differing "resonances" about which I had speculated.

Sunday, July 11, 2021

The unknown soldier

I have been cleaning up my primary iMac's virtual "desktop" for a week or so. One of the files thereon was a tabular listing of OEIS sequence A293355 up to term #291. When I submitted the sequence back in 2017, I included a listing of terms only up to #250, so clearly it was something I was extending at the time and hoping to extend even further. But other projects got in the way.

I had a look at term #291 and found that factordb had it fully factored in its database. If we have the full factorization of a sequence term, one may find the subsequent term by applying an algorithm to that factorization. If it's an easy factorization I can even automate the procedure in Mathematica and have it determine several terms at once. Unfortunately when one is trying to fully factorize a 90-plus-digit number, chances are that the second-largest factor is itself large (say, > 30 digits) and this makes it difficult for Mathematica to find in a reasonably short amount of time.

So I went back and forth (between Mathematica and factordb) yesterday trying to extend A293355 beyond term #291. Incredibly, every time I put a difficult-to-factor term into factordb it came back with the number fully factored! This was, clearly, no coincidence. Someone, three-or-so years ago, was also extending the sequence. Except that when they entered a term it did not come back fully factored. Instead they had the time-consuming task of factoring the number by other means. Whoever it was soldiered on, extending the sequence to term #384 which contained a 115-digit composite that my hero was apparently unable to resolve (unless, tragically, they succumbed in the battle). I submitted the updated, much larger "b-file" (an indexed tabular listing) to OEIS. The point of A293355 was to present an infinitary aliquot sequence (the one here starting with 6216) that seemed to evolve into monotonically increasing (never decreasing, by magnitude) terms. The actual term-by-term increases are much more interesting than the conjecture might suggest:

click to enlarge
Perhaps the sequence is just in some sort of "resonance" (for lack of a better word) that will eventually be disturbed by an unkind factorization — one that portends a much more chaotic future.

An abundance of additional terms (July 17): What goes up

Thursday, July 01, 2021

O Canada!

The Globe, Toronto, Saturday, 13 May 1911
Historic Home of a Vanished Canadian People
by Janet Grant Needham (1866-1939)

Canada is making history every day through her wealth of natural resources, agriculture, mines, and her tide of immigration. "Forward" is the keynote of our land from sea to sea. Nevertheless there is a spot in the very heart of this great Dominion where history has been made already; the thousands of her inhabitants have come and gone, their records sealed and closed. We, too, have our Herculaneum and Pompeii offering a rich treasure to the excavator. The savage Huron people are gone, but they have left traces of their race.

It seems a far cry to the summer of 1615, when Samuel de Champlain, in response to a promise he had made to a band of fur-trading Hurons at their rendezvous, "Falls of St. Louis", set out to assist them in their wars against the fierce Iroquois ("Voyage de Champlain", page 276). Besides giving aid from a sense of duty against these raiders, who terrorized every other tribe, he thought it would open a way for their conversion, for to Champlain "the saving of a soul was more than the winning of an empire". Notwithstanding, this promise was the fatal mistake of his Indian policy, producing the lasting enmity of the Iroquois and the ultimate extermination of the Huron race. He brought out from France the same year four Recollect friars, one of the three branches of the Franciscan Brotherhood. Father Joseph Le Caron elected to come to the Hurons. Arrayed in the habit of his order, a coarse grey garment girdled at the waist by a stout cord, a peaked hood, sandals of wood an inch in thickness, he gathered without delay his church equipment and left the spot where now stands Montreal, accompanied by twelve Frenchmen and a few savages. Eight days later, early in July, Champlain, with two Frenchmen and ten savages, followed. Both parties journeyed up the Ottawa and Mattawa Rivers, over a short portage to Lake Nipissing, near the spot where North Bay is built, down the French River, past Byng Inlet and the rocky east coast, and through the island enchantment of the Georgian Bay to its extremity, landing on the first day of August a few miles west of Penetanguishene. Passing through a country abundant with raspberries, grapes, plums, squashes, Indian corn and wild rice, through village after village of unpronounable names where now are Sturgeon Bay, Fesserton, Victoria Harbor, Coldwater and other towns, they reached a large village, Carhagouha, with triple palisades thirty-five feet high, situated near the locality where Waubaushene now stands. There they overtook Le Caron. In these wilds on August 12 Father Joseph said the first Mass in the Huron country, holding the Host high above his kneeling countrymen and the awe-stricken savages. A cross was planted at this spot. The explorer proceeded thirty-five miles to Cahaigue, the capital, with 200 cabins. The warriors assembled gladly welcomed him.

On September 1 all was in readiness, and 2200 warriors, decorated with war paint and with small supplies of smoked fish and wild rice, passed by Lake Couchiching through the Narrows connecting it with Lake Simcoe, out by the Trent waters to Lake Ontario. They crossed at the eastern end and soon stood before the camp of the astonished Iroquois, who defeated and put to rout the panic-stricken Hurons. The Iroquois never forgave this assault. Champlain, twice wounded, wintered with a friendly chief on the shore of Lake Simcoe. Towards spring he visited the Tobacco Nation, or Petuns, in the Collingwood district, then finally left these parts. This is our first knowledge of the Huron Nation.

"Quelles hures!" (What hyenas!) exclaimed an astonished Frenchman, attracted by the fantastical modes of dressing their hair, chief of which was the head shaved, leaving a ridge of bristles from the forehead over the crown to the neck, hence the word "Hurons". The original name was Ouendat. Tourists or the curious may see to-day at the Narrows (two and a half miles from Orillia) the "fishing weirs" used in Champlain's time and to which he refers. They are of heavy tamarac driven into the mud a great depth, exposing only six inches, and in an excellent state of preservation considering the lapse of nearly 300 years. The population at this time was 10000 huddled in eighteen villages varying in size from three or four hamlets to twelve acres, one even fifteen.

Let us look into a Huron cabin or long house. It is 100 feet long, built of young sapling supports placed at intervals, curving towards the centre, and over which are laid sheets of bark. A foot space is left the entire length at the top to admit light and for the escape of smoke more or less always present. The place is thronged with beings, for it is the home and common property of ten families, each averaging six. On the ground, at intervals down the centre, are five fires fed with fat pine logs. Round about are hung weapons, ornaments and clothing on long arms of wood. A broad shelf of bark, on supports, is built along both sides three feet from the ground, under which is firewood. Around the fitful gleams of the fires are grouped on a winter's night battle-scarred warriors and women, feasting, cooking, gambling, dancing or idly jesting; young men eager for the fray, girls decorated with ornaments, unruly children, aged, feeble squaws, the "burden-bearers", besides numerous half-starved dogs. During a snow-storm the smoke is so dense the inmates breathe with nostrils to the ground.

The brain of the Huron-Iroquois has been proved to be larger than that of any other tribes of American aborigines, with doubtful exceptions. They spoke the same dialect, used the same system of warfare, customs of marriage and ceremonies in burial of their dead; besides, their long houses were after the same style — all indicating that they were descendants of one common stock, though deadly enemies. The Huron Nation was divided into four great tribes or clans, located in townships as follows: — Bear clan in Tiny, Wolf in Tay, Heron or Cord people in Medonte, and Falcon or Rock people in Oro — overlapping, naturally others. (Tiny, Tay and Flos townships are named after Lady Colborne's three lapdogs.) The 35th Regiment, Simcoe Foresters, carry on their uniforms to this day the Bear totem. The Hurons were an agricultural people, clever and ingenious, but much behind the Algonquins in the work of ornamentation and bone needle work. Established custom with them was law, and, though proud, vindictive, selfish, great thieves and gamblers, they were witty and social. Much generosity and harmony prevailed amongst them, thus enabling thousands of these untamed creatures to live in peace. Sagard ("Le Grand Voyage aux Pays des Hurons, 1632") distinguishes the Hurons, Algonquins and Montagnais as the nobles, burghers and paupers of the forest. The Iroquois, more than the Hurons, reached the highest civilization possible under benighted conditions; in short, they were the aristocracy, yet this raised them very little above the animal. Mission work among the aborigines has many dangers and much to shock the finer feelings of the cultivated missionary, and that at our own doors proved no exception. The first settlers came in 1819, a band of fugitives from Lord Selkirk's Red River expedition. This was added to greatly in 1832 by other settlers. With the agriculturist at work, comes definite information regarding the haunts and habits of these people. Soon were brought to the surface great quantities of pottery, cooking utensils, strings of wampum, arrowheads, stone and French tomahawks. After the troubles of 1837 a great flood of immigration took place. So thickly settled now is the county that one is safe in saying the average farmer has given or thrown away bushels of curios and relics, apart from collections made by interested persons.

The public is greatly indebted to Mr. Andrew Hunter, M.A., of Barrie, for constant archaeological research in securing accurate information in Huron locations and "finds". The late David Boyle, and Mr. J.H. Hammond, Orillia, have also given valuable services. The latter has most of his collection of 3000 pieces in Toronto Museum. Perfect relics are now becoming rare. The Hurons occupied the higher lands and ridges. Over 400 sites have been located, though not all inhabited at the same time. These can easily be detected by the very black soil and ash pits three or more feet thick, though covered by forest. Farmers frequently come upon mounds or depressions in the ground which prove to be ossuaries or burial pits containing human skulls averaging 200, face downwards and to the east, justifying the belief held by many, from this and their ashpits, that the Hurons were sun worshippers. Their custom was to place bodies on scaffolds. At intervals of ten years the remains were collected by the clans and deposited in pits ten feet square, with wampum, axes, pipes, beaver skins, colored beads, native beads, French articles, parcels of hair, brass kettles (tomahawks in the bottom), and whatever was held most precious by them. The whole was accompanied by solemn yet frenzied ceremonies; says one "like demons from the lower world let loose". Strange to say, numerous Mexican shells were often found in these pits. An ossuary on the farm known as the Michael Braden property in Medonte was fifteen feet in diameter, containing from 700 to 1000 remains, also seventeen copper kettles two feet wide at the top, in good condition, and later used by the early settlers. An ossuary equally large, containing 1000, was found on the Oliver farm near Barrie. A great tree had grown over it. To date 140 of these ossuaries have been carefully catalogued, indicating a population of at least 25000.

The Algonquins, inhabiting more the southern district in small numbers, used single burial in circular pits, sufficient only for a crouching position. Only once is this found among the Hurons, and that in Medonte. There are evidences, too, of hasty burial conforming to neither form — where battles have been fought, arrows and tomahawks found.

Tuesday, June 22, 2021

Now hear the word of the Lord

This is part 3 of my "Weston Bones" trilogy (part 1: Dem bones, part 2: Dem dry bones). The story thus far is that on 28 April 1911, the well-preserved 50-or-more-year-old bones of 14 adult individuals were dug up here:

Weston bones site behind 5 Bellevue Cres. near Weston Rd. (click to enlarge)

On 1 May 1911, Rowland Betty Orr (1852-1933), superintendent of the Ontario Provincial Museum, visited the site and proclaimed them to be the 300-or-more-year-old remains of "Indians". The assertion was pure invention. Regardless, an expert opinion had been rendered and the myth of an Indian burial ground on the east side of the Humber river took root. It may have been promulgated at the Ontario Historical Society where Orr was to become president. More recently, the idea has been promoted by the Weston Historical Society, for example, by Barb Shiells in 2009 here, and by Chris Menary in 2018 here:

The 1937 "History of Weston" (Cruikshank & Nason) noted the existence of an Ojibway burial place just south of Farr's Mills (on the west side of the Humber) still being used as late as 1825. One would think that they would have mentioned the Weston bones site, which wasn't just close to Weston but actually within the town's border. They didn't!

The Bellevue Crescent bones site was never properly investigated. As such it is one of unknown date and culture. Victor Konrad catalogued it in 1973, along with a supposed Scarlett Road "settlement" that he erroneously placed near the Weston bones location. Given the absence of credible scientific information and the presence of incompetent archaeological opinion, writers such as Glenn Turner (The Toronto Carrying Place, 2015) have simply repeated the empty echo-chamber reverberations of the native "ossuary" myth. The latest to do so (seemingly with a vengeance) is Edward Brown, a freelance Toronto writer who published an interesting article on the Weston bones in the Toronto Star last Saturday. In light of the well-researched background to the article, one may wonder why Brown failed to disclose the true nature of the Weston bones. I shall explain.

Brown's incredibly competent research uncovered the existence of a cranium bone fragment that had apparently become part of a 1911 Westminster Presbyterian Sunday School cornerstone time capsule, recovered in 1956. In 2011 the Weston Historical Society ceded the capsule's contents to an archaeologist in the hopes of a Huron-Wendat reburial. Brown's discovery that this reburial had not yet taken place presented him with all that he needed to compose his newspaper article. June is National Indigenous History month and June 21 is National Indigenous Peoples day. In light of the recent finding of 215 children's remains in unmarked graves at a former British Columbia "residential" school, the article pretty much writes itself! Brown's only job now is to sell the reader on the idea that the bone fragment is Aboriginal. For an accomplished writer like Brown that should be a piece of cake.

"... what became of the disinterred remains, and has their memory been honoured? Answers proved hard to come by and disappointing."

We are ready for the con:

" ... the [Sunday school] site they chose to build on was sacred ground. ... [in spring 1911] ... Hart had disturbed a Huron-Wendat ossuary dating from the late Iroquoian era. At peace for roughly half a millennium, bodies of 30 individuals buried 60 centimetres deep were exposed."

Calling the site sacred ground is presumptuous. To Indigenous people "sacred" means something different than it does in Anglo-Christian culture. At any rate, we don't know that the burial was Huron-Wendat, nor that the bones had been there for 500 years. We do know that it was only 14 individuals buried 45 cm deep. This is Brown's first use of the word "ossuary" and (in his mind) more individuals and a deeper burial will bolster that implant. Brown's 30 individuals and 60 cm comes from the 28 April 1911 Toronto Daily Star article. My 14 individuals and 45 cm comes from 29 April 1911 Globe article. In light of the rampant speculation ("that there are probably scores of skeletons still uncovered", in the Globe), there is little doubt that the Star had already turned that fantasy into a reader-inviting headline. The Star's "two feet" from the surface became the Globe's "eighteen inches". Any numbers aficionado (of which I am one) will tell you that the latter is not only more accurate, but still within the former's error bars. The inflation of Orr's 300+ years to ~500 years is an important subterfuge because the 300 years is still within the framework of the French presence in Ontario. At any rate, I've already stated that Rowland Orr's opinion amounts to nothing. The bones could have been 50 years underground or 5000. I am not arguing that the bones aren't Aboriginal. I am simply saying that we do not know that they are.

"Upon his visit, Orr helped himself to a pair of skulls for study and preservation at the Ontario Provincial Museum."

So clever! Here's how the Globe's 2 May 1911 article stated it: "Dr. Orr secured two skulls to take measurements of their various dimensions and also to preserve as curios." The 29 April 1911 Globe article had already suggested that "an examination of the skulls themselves reveals unmistakable aboriginal anatomical features". That's a somewhat remarkable off-the-cuff observation for a reporter to make! Brown replaces the "measurements" with "study", fearing no doubt that the former might lead to an examination of craniometry in anthropology in those days. And of course Brown mustn't mention the preservation "as curios" because that would give away Orr's game of collecting relics not for the museum, but for his personal stash. With a deft replacement of words, Brown manages to shield Orr from any hint of either racism or impropriety. The man is just a scientist doing his job. I don't really understand why Ed Brown felt that he needed to do this. Orr was a product of his culture at the time.

Brown indicates that he tried to track down Orr's "samples" but was unsuccessful. In fact, Orr may already have lost his skulls in 1917 when his 1914 "Laidlaw Room" was dismantled and the collections stored away at the direction of the provincial government. A final observation: In Brown's version, Orr "helped himself" to the two skulls. In the newspaper report, he "secured" them. It is never explicitly stated but, is there any doubt that these are the two "splendid skulls ... rescued from the depredations of the innocent pillagers by Mrs. Frank Munshaw"? How ironic! Rescued from innocent pillagers only to have them taken from her by a not-so-innocent pillager. And even more ironic: Brown's word replacement stratagem (for once) got it right! Orr helped himself.

"Author Glenn Turner ... speculates, 'The ossuary on Weston Road may have been a local village cemetery or a communal Feast of the Dead pit.'"

The second mention of "ossuary". As previously noted, there was no native settlement on the east side of the Humber in Weston. Turner's "Feast of the Dead pit" is "a deep pit lined with beaver robes". That it definitely was not.

"Kapches recalled a visitor showing up ... 'There was a (portion of a) cranium, I assume from (the) ossuary in the cornerstone box.' ... From 30 skeletal remains, only a bone fragment the size of a large scallop shell can be accounted for today."

The third mention of "ossuary". Another mention of 30 individuals. Are we there yet?

"Ward 5 [councillor] Frances Nunziata ... was unaware an Indigenous ossuary had been disturbed in 1911. ... In consultation with Indigenous partners in the community, Nunziata committed to start the process of assigning a commemorative plaque for the site. Over a century later, a process is in motion granting the bones of Weston reverence long ago denied."

The fourth mention of "ossuary". I think we are there! When Nunziata finally unveils that plaque, I'm betting that it will include the word "ossuary". Maybe even the number 30. And perhaps Edward Brown will be at the unveiling. If he is, he can pat himself on the back and say: "Well done, lad. Well done!"

Frances Nunziata, April 2018

Monday, June 21, 2021

14- to 40-letter integer names

In my previous posting, I set up a dictionary of American English integer names (by letter count) and illustrated the concept with alphabetically-sorted sections for each of the letter-counts from 3 to 13. Now I intend to do the same for letter-counts from 14 to 40, but first a couple of caveats. Starting with 10^306, there is not a lot of agreement on what the 10^3n power names should be, so I will limit my naming to integers less than that. Also, I have little confidence that the program I wrote to generate the lists captures every integer name in that range. At some juncture the number of terms may simply be a lower bound. For my 14- to 40-letter names that bound is followed by a link to the sorted integer-name text file. For 33- to 40-letter files, they are compressed, which means they will likely download to your computer after clicking on the link, ready for you to decompress and open in a text editor (one that — hopefully — is capable of handling these gargantuan files).

14        158   DoAEIN-14.txt   
15        342   DoAEIN-15.txt   
16        586   DoAEIN-16.txt   
17        913   DoAEIN-17.txt   
18       1490   DoAEIN-18.txt   
19       2365   DoAEIN-19.txt   
20       3884   DoAEIN-20.txt   
21       5940   DoAEIN-21.txt   
22       8629   DoAEIN-22.txt   
23      12386   DoAEIN-23.txt   
24      17637   DoAEIN-24.txt   
25      26311   DoAEIN-25.txt   
26      39639   DoAEIN-26.txt        1.2 MB
27      59630   DoAEIN-27.txt        1.9 MB
28      90362   DoAEIN-28.txt        3.0 MB
29     137202   DoAEIN-29.txt        4.8 MB
30     212043   DoAEIN-30.txt        7.7 MB
31     329857   DoAEIN-31.txt       12.3 MB
32     513102   DoAEIN-32.txt       19.8 MB
33     794646   DoAEIN-33.txt.zip    2.8 MB   >>>    31.7 MB
34    1217729   DoAEIN-34.txt.zip    4.3 MB   >>>    50.0 MB
35    1854561   DoAEIN-35.txt.zip    6.6 MB   >>>    78.3 MB
36    2805381   DoAEIN-36.txt.zip   10.0 MB   >>>   121.7 MB
37    4219909   DoAEIN-37.txt.zip   15.1 MB   >>>   188.1 MB
38    6321000   DoAEIN-38.txt.zip   22.7 MB   >>>   289.2 MB
39    9415676   DoAEIN-39.txt.zip   34.1 MB   >>>   441.8 MB
40   13976362   DoAEIN-40.txt.zip   51.4 MB   >>>   672.1 MB

Thursday, June 17, 2021

A dictionary of American English integer names (by letter count)

From 3 letters to 13 letters, but leaving out the (numerical) definitions:

one
six
ten
two

five
four
nine
zero

eight
fifty
forty
seven
sixty
three

eighty
eleven
ninety
thirty
twelve
twenty

fifteen
seventy
sixteen

eighteen
fifty-one
fifty-six
fifty-two
forty-one
forty-six
forty-two
fourteen
nineteen
sixty-one
sixty-six
sixty-two
thirteen

eighty-one
eighty-six
eighty-two
fifty-five
fifty-four
fifty-nine
forty-five
forty-four
forty-nine
ninety-one
ninety-six
ninety-two
seventeen
sixty-five
sixty-four
sixty-nine
thirty-one
thirty-six
thirty-two
twenty-one
twenty-six
twenty-two

eighty-five
eighty-four
eighty-nine
fifty-eight
fifty-seven
fifty-three
forty-eight
forty-seven
forty-three
ninety-five
ninety-four
ninety-nine
one billion
one hundred
one million
seventy-one
seventy-six
seventy-two
six billion
six hundred
six million
sixty-eight
sixty-seven
sixty-three
ten billion
ten million
thirty-five
thirty-four
thirty-nine
twenty-five
twenty-four
twenty-nine
two billion
two hundred
two million

eighty-eight
eighty-seven
eighty-three
five billion
five hundred
five million
four billion
four hundred
four million
nine billion
nine hundred
nine million
ninety-eight
ninety-seven
ninety-three
one thousand
one trillion
seventy-five
seventy-four
seventy-nine
six thousand
six trillion
ten thousand
ten trillion
thirty-eight
thirty-seven
thirty-three
twenty-eight
twenty-seven
twenty-three
two thousand
two trillion

eight billion
eight hundred
eight million
fifty billion
fifty million
five thousand
five trillion
forty billion
forty million
four thousand
four trillion
nine thousand
nine trillion
one decillion
one nonillion
one octillion
seven billion
seven hundred
seven million
seventy-eight
seventy-seven
seventy-three
six decillion
six nonillion
six octillion
sixty billion
sixty million
ten decillion
ten nonillion
ten octillion
three billion
three hundred
three million
two decillion
two nonillion
two octillion

eight thousand
eight trillion
eighty billion
eighty million
eleven billion
eleven million
fifty thousand
fifty trillion
five decillion
five nonillion
five octillion
forty thousand
forty trillion
four decillion
four nonillion
four octillion
nine decillion
nine nonillion
nine octillion
ninety billion
ninety million
one billion, one
one billion, six
one billion, ten
one billion, two
one centillion
one hundred one
one hundred six
one hundred ten
one hundred two
one million, one
one million, six
one million, ten
one million, two
one septillion
one sextillion
seven thousand
seven trillion
six billion, one
six billion, six
six billion, ten
six billion, two
six centillion
six hundred one
six hundred six
six hundred ten
six hundred two
six million, one
six million, six
six million, ten
six million, two
six septillion
six sextillion
sixty thousand
sixty trillion
ten billion, one
ten billion, six
ten billion, ten
ten billion, two
ten centillion
ten million, one
ten million, six
ten million, ten
ten million, two
ten septillion
ten sextillion
thirty billion
thirty million
three thousand
three trillion
twelve billion
twelve million
twenty billion
twenty million
two billion, one
two billion, six
two billion, ten
two billion, two
two centillion
two hundred one
two hundred six
two hundred ten
two hundred two
two million, one
two million, six
two million, ten
two million, two
two septillion
two sextillion

By American English we mean to exclude the conjunctive use of "and". As befits a dictionary, the integers are sorted alphabetically in each letter-count grouping. In such ordering, a word separator (a space or a hyphen) precedes any letter of a longer expression that starts the same. For example, "eight undecillion" precedes "eighteen thousand". The 13-letter entries introduce the comma, which functions to separate differing 10^3n power regimes. The counts (4, 4, 6, 6, 3, 13, 22, 35, 32, 36, 89) differ from A121064 only in the 89 for the 13-letter count. That is because our larger number range allows for "centillion" (of which there are 4) to finally show up. As we go beyond 13 letters, we expect such intrusions to increase.