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 problematic. 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    2.8 MB   >>>    31.7 MB
34    1217729    4.3 MB   >>>    50.0 MB
35    1854561    6.6 MB   >>>    78.3 MB
36    2805381   10.0 MB   >>>   121.7 MB
37    4219909   15.1 MB   >>>   188.1 MB
38    6321000   22.7 MB   >>>   289.2 MB
39    9415676   34.1 MB   >>>   441.8 MB
40   13976362   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 billion
one hundred
one million
six billion
six hundred
six million
ten billion
ten million
two billion
two hundred
two million

five billion
five hundred
five million
four billion
four hundred
four million
nine billion
nine hundred
nine million
one thousand
one trillion
six thousand
six trillion
ten thousand
ten trillion
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
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.

Wednesday, June 16, 2021

A nearby grocery

FreshCo site @ 55 Denison Rd. E. (aka 1500 Jane St.), looking west
Click on the image for a much better look! A bird's-eye view of Jane St. (left to right near the bottom) and Denison Rd. E. (from the prominent zebra-stripe pedestrian crossings at Jane St. to Weston Rd., just past the curved underpass at the railway corridor). The green arrow points to the empty-field location of a now almost-ready FreshCo grocery outlet that is about a ten-minute walk from my home (the yellow arrow at the top). By the way, this is the exact location of what was once The Moffat Stove Company.

I only learned about the new grocery on Monday, so I took Bodie there for a look:

They are hiring next week so I expect the store opening in a month or two.

Wednesday, June 09, 2021

Big time

Nine months ago, I showcased my then-largest Leyland prime find. Things have changed a bit. Here are, as of today, the top ten known Leyland primes:

386434  (328574,15)      Sergey Batalov       May 2014
300694  (110610,523)     Hans Havermann       Jun 2021
300468   (63722,51915)   Hans Havermann       Jun 2021
300337  (314738,9)       Anatoly Selevich     Feb 2011
300035   (67594,27465)   Hans Havermann       Jun 2021
300000   (70599,17756)   Hans Havermann       Jun 2021
265999  (255426,11)      Sergey Batalov       May 2014
223463  (234178,9)       Anatoly Selevich     Jul 2011
172940  (104608,45)      Norbert Schneider    Jun 2021
149984   (45728,1905)    Hans Havermann       Oct 2020

The first column gives the number of decimal digits. The Leyland number of an (x,y) pair is x^y + y^x. Half of the entries have been found in the last seven days!

Monday, June 07, 2021

Much ado about UFOs (UAP)

I'm increasingly annoyed by the lack of skepticism in the current round of media hype about UFOs (UAP). Randall Munroe (xkcd) and Michael Shermer explain what should be obvious:

Wednesday, June 02, 2021

Kelly Rapids

click on the image for a better look
This is a screen grab of Google maps' depiction of a twisting section of Kelly Rapids that appears to be the de facto border hereabouts between the Canadian province of Quebec and the American state of Maine. Very noticeable is the straight-line segmented border approximation of the waterway, as though it was created on a much lower-resolution map. Also noticeable is a small section of the stream that appears to have taken a different, more-northerly route, thus inadvertently ceding some Canadian land to the Americans!