Monday, March 20

Fracture revisited

I noticed that the 2007 movie Fracture was on Netflix and so I thought I'd watch it again. I hadn't seen it since August 2009, a fact I was able to recover because I wrote a blog piece about a chess position in the film. I ended the item with a question about the six captured black pieces — which weren't visible in my movie-still grab. With the better-resolution Netflix version, I took it upon myself to retake a screen snippet of the board:

So the six captured black pieces were there all along, hidden in the poor contrast of my 2009 screen grab!

Tuesday, March 7

T cube

Designed by Yavuz Demirhan, realized by Brian Menold, this recently acquired puzzle more than tests my patience. The three identical pieces (two one-by-three bars attached to a one-by-five bar) fit — without any protuberances — within the (five-by-five-by-five) cubic cage. It arrived assembled and I was careful in taking it apart, but after I had reassembled it a second time it no longer came apart as I expected! And by the time I did get that disassembled I had forgotten how it was supposed to come together. Complicating things ever so slightly is that one of the frame's twenty-four inside edges is a touch less than three units long, presumably a production flaw and not part of the design. I'm getting too old for this type of toy.

Thursday, February 23

Movin' on up

When I bragged about my 100th Leyland prime find last August, I noted that I was moving up a leaderboard of probable-prime (PRP) discoverers. I currently have 131 Leyland primes under my belt and the last few days saw me take possession of position #44 on the PRP production score list, of which the above is a snippet.

Roughly, in the range where I am searching, every new find adds .01 to my production score. So to reach position #40 I have to come up with another 27 PRPs. My current rate of production is about five or six per month. So another five months.

Friday, February 17

A definite answer

Earlier today's Futility Closet titled Ahead of Schedule (since deleted) was to me more than a little disappointing. It highlights author Jack Finney's 1973 suggestion that a flying machine invented by W. J. Lewis circa 1876 might actually have flown across the skies of New York that year. Futility Closet's Greg Ross noted that when Finney included the speculation in his 1983 book, Forgotten News, he still "hadn’t received a definite answer".

So here's a definite answer: No. A flying machine invented by W. J. Lewis never flew any American skies. Finney's New York Times piece was of course mischievously disingenuous. He failed to point out that the 30 December 1876 Frank Leslie's Illustrated Newspaper (wherein Lewis's new flying machine is featured) specifically stated that what flew during "a formal test" was a small model. As the 22 September 1877 Scientific American Supplement (also featuring the machine) pointed out: "It is an easy matter to make a small flying machine shoot up a short distance into the air by means of a spring. But to make a large machine, with a steam engine, lift itself and sustain itself in the air is a problem not yet solved."

The picture of the flying contraption was reprinted yet again in a T. C. Hepworth story called Voyages in Cloudland (Frank Leslie's Popular Monthly, September 1883) wherein the Lewis machine's "travel through the air" was still nothing more than a proposal. The 27 May 1892 Velasco (Texas) Daily Times: "Dr. W. J. Lewis of San Antonio is nearing the completion of his aerial bird. He will place his bird on exhibition when finished and proved to be a success. Its [sic] only a model and says he is sure of revolutionizing navigation."

A "San Antonio history" site has a reference for 26 September 1894: "Dr. W. J. Lewis returned to San Antonio from St. Louis where he had purchased aluminum for his new invention — a flying machine with stationary wings to be powered by a machine-drive propeller." And that led me to this 29 September 1894 (preceded by "14 years ago today") text-file entry: "Dr. W. J. Lewis, of San Antonio, who is working on a flying machine, is in St. Louis. He has been studying aeronautics for 25 years. A machine was built 12 or 15 years ago, but the friction and consequent amount of power needed were too great. Dr. Lewis has been experimenting ever since trying to reduce the friction to a minimum. He believes success is not far off. Dr. Lewis' machine is constructed of bamboo covered with silk."

The 1 June 1898 Times-Picayune (from New Orleans, Louisiana) has an article that asks: "Has Dr. W. J. Lewis, of California, who is now visiting this city, discovered the principle of the flying machine?" A 30 November 1900 Macon (Missouri) Democrat newspaper article starts: "Dr. W. J. Lewis of St. Louis has invented a flying machine that flies. It is built on the order of a bird. It gives good satisfaction and by 1903 Dr. Lewis says he will have one completed — large enough to carry ..." I'll note that the 1876-1883 references all had the not-yet-doctored Mr. Lewis "of New York".

Back to Finney's 1973 speculative fiction: "So what happened after W. J. sent his machine twisting and torquing across Manhattan's skies in 1876? People just weren't a bit surprised; they'd been expecting it. Probably wondering why it had taken so long. And then, what with one thing and another, they got busy, and it just slipped the nineteenth century's mind." Give me a break!

Good mourning

Formerly, mourning was worn in England both for a longer period and of a much deeper character than is used at the present time. Two years were not considered too long a time for a father or a mother. Now custom prescribes only one year. It is also considered better form now to wear plainer and less ostentatiously heavy and expensive habiliments. Widows wear deep mourning for one year; then ordinary mourning as long a time as they may wish. Deep mourning is considered to be woollen "stuff" and crape. Second mourning is black silk trimmed with crape. Half-mourning is black and white. Complimentary mourning is black silk without crape. The different stages are less observed everywhere, outside of courts, than formerly. The French divide mourning garb into three classes, — deep, ordinary, and half mourning. In deep mourning, black woollen cloths only are worn; in ordinary mourning, silk and woollen both; and in half-mourning, black and white, gray and violet. In France, etiquette prescribes for a husband one year and six weeks; six months of deep mourning, six of ordinary, and six weeks half-mourning. For a wife, a father, a mother, six months; three deep and three half-mourning. For a grandparent, two months and a half, slight mourning. For a brother or sister, two months, one of which is deep mourning. For an uncle or aunt, three weeks of ordinary mourning, and two weeks for a cousin. While wearing deep mourning, one does not go into society, neither are visitors received. In the United States we have no fixed rules, but of late years the retirement from the world, after the loss of a near relative, has been much shortened. For one year, no formal visiting is undertaken, and no entertaining nor receiving, save in exceptional cases. Mourning (or black) is worn for a husband or a wife two years; one year deep, one year light. For parents, from one to two years; and for brothers and sisters that have reached maturity, one year. Those who are invited to a funeral, though not related, must go entirely in black, wearing black gloves and black beaver hat. To appear in hats of felt or straw, is wanting in due respect to customs.

[The Art of Dress, page 391, in The Manners That Win, Minnesota 1880.]

Thursday, February 16

Southern Ontario's great rainstorm of 1878

I got this from the Toronto Globe's Saturday, 14 September 1878 newspaper (page 8), where it is noted that it was raining steadily from late Tuesday well into Friday. Some 12 cm was reported to have fallen at Port Dover on Lake Erie. The emphasis was of course on Toronto where four lives were said to have been lost in the Don River. From my community (then village) of Weston it was reported that the iron bridge on the Grand Trunk Railway at Black Creek gave way and fell at 9 AM September 13, after fourteen hours of very heavy rain.

In many ways this was a forewarning of 1954's Hurricane Hazel and, indeed, this appears to have been the tail end of Hurricane #5 of 1878. This morning I adjusted the Wikipedia entry for that storm by replacing its September 13 extratropical placement in Virginia with one in Ontario. A remarkably modern storm path could be figured out even back then from the news of the day:

The storm originated in the Gulf of Mexico, where the barometer was low on Sept. 6th. During the latter part of that day there were high north-easterly winds and heavy rains in Florida. The disturbance hovered over Cuba and Southern Florida until the night of the 10th. It then began to travel in a northerly direction, and by the morning of the 12th it was over South Carolina, accompanied by heavy rain. During the 12th it moved at the rate of over 30 miles an hour, and by Friday morning was over the western end of Lake Ontario.

Wednesday, February 15

An unfortunate typo

A gentleman, named Mr. John Boyle, came into town yesterday, by the Northern Railroad, in search of Mrs. Margaret Thompson, a relative of his, and a resident of the village of Weston. Mrs. T., accompanied by one of her children, came to this city on Monday last, to superintend the sale of some farm produce, and intended to return the same evening, as circumstances of an urgent nature required her presence at home. Yesterday morning Mr. Boyle observed that her cows had not been attended, and remarking other things about the house which indicated the absence of the mistress, he resolved to make every possible search for her, but without success up to yesterday evening. Mrs. Thompson is a widow, and possessed of considerable property. She is described as wearing deep mourning, about 27 years of age, and of very prepossessing appearance. Mr. Boyle requested the Police to aid him in making enquiries regarding her whereabouts.

[The Globe: Toronto, Friday, 6 October 1854. The marks around the article title were already on the newspaper page prior to its being photocopied, so I wasn't the first to notice.]

Thursday, February 2

With multiplicity

It may be noted in Tuesday's "what's so special about 10928094208 in base 77" A281335 curio that the factorization contained an exponent. Arithmeticians have another way of expressing factors that have greater-than-one exponents and that way is called "with multiplicity". For example, in base 43 the smallest solution to A281335 is 10969263:

(3,8,41,23,6) = 3^6 * 41 * (8,23)

But if we insist that the factors be expressed with multiplicity:

(3,8,41,23,6) = 3 * 3 * 3 * 3 * 3 * 3 * 41 * (8,23)

Which is no longer a solution. So I created another OEIS sequence, A281336, to deal with that situation. In base 43 the smallest solution to A281336 is 12505821873:

(1,42,2,41,3,29,35) = 3 * 29 * (42,1,41,2,35)

Yes, there is no multiplicity in this particular example but that is not a necessity. As with my other sequence, I have an even bigger number as a solution for a smaller base (37) but have yet to discover it.

Wednesday, February 1

14 houses gone

The effects of 1954's Hurricane Hazel reached southern Ontario on Friday, October 15 and proceeded overnight into Saturday, October 16. One of the photographs published by the Toronto Daily Star on Monday, October 18 (page 5) was this:

Printed atop the picture was "14 houses gone, 35 people dead". (On page 1 it is 36 dead.) The montage was credited to Eric Cole and Ed Parker, though I'm not sure either one took the aerial shot. Here are three more photos scrounged from the Net that set the floodwater scene; two aerials and a remarkable ground view (credited to the Weston Historical Society, here) from the river's other side:

In the ground-view image, the submerged part of Raymore is on the far left and near the top. The two somewhat submerged structures in the right-half of the picture would be on the east (Weston) side of the Humber river. To their left, three large trees obscure Gilhaven Avenue, clearly visible (from the air) in the middle image, where you can see those trees on the other side of the river. To the left of the trees is a toppled bit of bridge abutment that is still there.

The 35 dead is still generally touted as the Raymore Drive "drowned" contribution to the total Canadian fatality count. A memorial plaque at the site instead suggested 32. Of course the Star newspaper's locations of the lost houses was conjectural. Another recreation (showing additional houses lost) suggests a different layout.

There are aerial maps of Toronto (1947-1992) so one can sort-of see what was lost and where. [I'll share my versions of 1947, 1950 and 1956.] There's a much-too-fast simulation of the disaster from the Toronto and Region Conservation Authority which (I expect) has positioned correctly all of the houses (seen in this screen grab from the Weston side of the river):

The TRCA has of course very good elevation data and this likely played an important role in their rising-water simulation. Alas, it's useless in helping us decide which houses were "lost". The story told is that a 1950-built footbridge across the river (seen in the above near the bottom right) lost its abutment on the Raymore side and the still connected wire ropes — now in the water — proceeded to collect debris in an arc emanating from the Weston side. Much water was thus redirected towards the unlucky buildings. The irony is that this bridge replaced a much-less sturdy earlier version (called in the article a swing bridge) that was deemed unsafe. Betty Kennedy (in her 1979 "Hurricane Hazel") called the replacement bridge a swing bridge also. This had me more than a little confused.  But a CBC radio interview (the site has an incorrect broadcast date) has an unidentified man calling it a swing bridge as well, so there should be no doubt that that is what the footbridge was called.

I'll do a listing of Raymore house numbers (even — river side — first) and the fatalities that I believe are associated with those dwellings:

#134: Girodat   Paul, Mary Beedham [found Oct 29]
#136: Newing   * Caroline Annie Beavan, * Gerald Norman [found Oct 22], ... 
          Salt   * Vera Frances [found 30 Jul 1955          \ ... Gerald John [found ~31 Jul 1955]
#138: Topliss   Annie May Martin, Albert
#140: Boyd   James
          Hall   Kenneth 
          LeBlanc   Alice
          Peasley   Lambert, Doris, Sylvia, (Shirley)
#142: Smith   John Clive, John William, Grace Anne Dunn [found Oct 30]
#144: Gillan   George H, Helen Stimson [found Oct 24, (child)
#148: Edwards   Joan I Jesson, Carolyn JKenneth Charles [found Oct 31], Frank K, John C
          Neil   Jean R Edwards, Susan L, Adele B, Darlene S [found Oct 24 
#152: McGarvey   Philomina Johnson, Jacqueline, Donald
#154: Brough   * Wilhelmina Helen Campbell

#143: Babbage   * Claude
          Jeffries   Edward Albert, Elizabeth Mrs. Thomas Sr.

  unbracketed number of people mentioned and assumed dead: 36
  italics: 4 missing Dec 19543 missing Aug 1955: a misreport, or who else was found?
  magenta: 3 declared dead by two newspapers on Oct 18 but no further mention found

The Toronto Star, Oct 18, page 2, misreported Caroline Newing as Katherine. Caroline's obituary gives her maiden name as Bevan. It was Beavan.

A Shirley Peasley is reported missing in the Globe and Mail, Oct 18, page 2. I found no further mention of her and can only assume that it was meant to be Sylvia.

"One Gillen child" is listed after the George and Helen 'missing' entries in the Globe and Mail, Oct 18, page 2. By the time the Toronto Star came out that day there was no such mention. I have no obituary for George, but Helen's mentions no child — nor does their combined memorial cemetery headstone.

"... and one adult, name unknown" accompanies a missing Kenneth Edwards in the Globe and Mail, Oct 18, page 2. In all likelihood this is an uninformed, duplicate reporting of the then-missing John Neil (who was in fact very much alive). Perhaps the connection hadn't at that point been made because John's dead wife Jean was reported at 148 Raymore while Kenneth's dead wife Joan was misreported at 248 Raymore.

Mrs. Thomas Jeffries Sr. is declared dead in the Toronto Daily Star on Oct 18, page 2, while the earlier Globe and Mail, Oct 18, page 2, had "Mrs. Tom Jefferies" missing — but there is a dead "unidentified woman, about 60" on page 1 that may well have been her. No obituary — but I have this mention. I'm still looking for her. I've got an 1885 Toronto-born Albert Edward Jeffries but his father's name isn't Thomas.

Afterthoughts: The 15 Aug 1959 Globe and Mail had a story on Thomas McGarvey having been charged with the holdup of a drug store, noting that in 1954 he "saw the water snatch his mother and sister". The article ends with his "father and a brother" having "escaped". [I have the obituary for his brother Donald.] The 13 Mar 1963 Toronto Daily Star reported on a gas explosion at a home on Raymore, ending the short article with: "During Hurricane Hazel, 23 persons on Raymore Dr. drowned." [Presumably a transposition typo.]

Tuesday, January 31

What's so special about 10928094208 in base 77?

One of my current recreational arithmetic side projects is creating a b-file (a longer list of the sequence) for OEIS A281335. 10928094208 is the smallest solution in base 77:

(4,2,67,10,58,31) = 2^10 * 31 * (58,4,67)

The digits of the number (on the left) are matched by the digits of its factorization (on the right). The solution for base 73 is an even bigger number — but I haven't yet figured it out!