Thursday, October 01, 2020
Monday, September 28, 2020
The red polygon atop a Google map (click on it for a better view) represents the 15 hectare confines of my time in south Weston / north Mount Dennis since March 20, with the sole exception of a trip to the vet on June 10. Yesterday, having finally received some cloth masks via Amazon, I decided to break out and walked to the yellow open-circle spot to the northwest, where I took this photo of a condo construction site:
Monday, September 21, 2020
A few days ago, Futility Closet highlighted a David Morice "Kickshaws" bit (from a 1997 "Word Ways") dealing with "root words" wherein the number of letters of a specific power of an integer written in English words is equal to that integer. This looked like something I could verify and possibly expand on. In short order, Mathematica came up with over one hundred examples. I trust of course that Mathematica is correctly providing the (American) English equivalents of the large numbers. Also, Mathematica does not ever include the word "and" in its integer wording. The solutions list begins:
Sunday, September 06, 2020
Late yesterday, I found my (to-date) largest Leyland prime: 33845^26604+26604^33845. At 149763 decimal digits, this becomes now the fifth largest known such prime:
386434 (328574,15) Serge Batalov May 2014
300337 (314738,9) Anatoly Selevich Feb 2011
265999 (255426,11) Serge Batalov May 2014
223463 (234178,9) Anatoly Selevich Jul 2011
149763 (33845,26604) Hans Havermann Sep 2020
The number is the 167th new Leyland prime discovered since I (using xyyxsieve and pfgw) started finding them two months ago. Prior to that I had found 579 new Leyland primes using Mathematica — but that took from 3 October 2015 to 3 July 2020. At my current rate of discovery, I will find my 1000th new Leyland prime on December 9, but that is likely early because I am entering large-number terrain where my finds will be slower in coming. Still, I might have it by the end of the calendar year. We'll see.
Saturday, September 05, 2020
Going behind the garden shed just prior to sunset, August 25, I had a smallish raccoon approach me atop the neighbour's back fence. It seemed not to notice me until fairly close, whereupon it retreated to that yard's maple tree. I ran in the house to fetch my camera. It was only after looking at the photos just now that I noticed the eyes.
Sunday, August 23, 2020
I had mentioned in my previous post that I was considering purchasing a new computer "if I can trade in my old kernel-panic-plagued late-2015 one". When I bought this iMac it was pretty much top of the line.
SSDs were expensive and 1 TB was as big as Apple was willing to provide at the time. The standard 8 GB RAM was going to be replaced with 64 GB purchased from Other World Computing (Apple has always been incredibly ungenerous with its memory pricing).
I experienced my first kernel panic on the new iMac on 23 December 2015, 15 days after receipt. There was another one on 9 February 2016. I seem to have been panic-free until May 8 and then more on May 14, May 21, and May 22, when I decided to do a RAM switch. In addition to the kernel panics there was other weirdness happening in my running Mathematica Leyland prime searches. For example, the Mathematica front end would lose its connection with the Mathematica kernel. Mathematica was pretty much the only thing I was running on this machine.
I tried an OS reinstall on June 13 but the situation did not improve. I should of course have brought it back to Apple before its one-year warranty ran out but I was still under the impression that it might be the third party RAM and, besides, Catherine was increasingly anxious about driving and I did not ask her for the ride.
By July 2017 I had boxed the iMac from hell and purchased a new one, the one that I am currently working on. It's been fine but the 2 TB SSD is getting full. A 4 TB SSD in a new iMac should do the trick for a few more years. Plus I can upgrade to 128 GB RAM. The idea of trading in the defective iMac seemed like a good way to reduce the cost.
Phobio is Apple's official Mac Trade In partner for U.S and Canada. When I tried to evaluate nine days ago my late-2015 iMac on Phobio's website (by entering the computer's serial number), I got this:
My device (iMac Core i7 4.0 GHz) did not appear! Selecting one of the Core i5 alternatives instead would of course end up in my iMac being undervalued and this was not fair. So I sent an email (August 14) to Phobio explaining my dilemma. No response. A followup email (August 19) noting the non-response and asking for them to "please let me know" has also not gotten a reply. At this point I am entertaining deep-Apple conspiracy theories about what is going on (and I'm not the sort of person who entertains conspiracy theories).
Strangely, my late-2014 iMac which has never had kernel panics before started to experience them in June 2019. At any rate, I will give up for the moment the idea of trading in the late-2015 machine. I'll likely still purchase a new iMac but am unsure as to when.
Monday, August 10, 2020
A year ago today I charted the expected progress on my five-year indexing-the-Leyland-primes project. Having a few days ago finished interval #10, I anticipate intervals #11 to #13 to be done by September, and #14 by October, all thanks to Mark Rodenkirch's xyyxsieve and pfgw.
|my current work sheet|
As I am no longer burdened by my previous reliance on Mathematica 9, I may even update everything to macOS Catalina one of these days. A new iMac is also being considered (if I can trade in my old kernel-panic-plagued late-2015 one). After I've finished interval #14, I will have tabulated all Leyland primes up to 103013 digits. Interval #15 will start there and continue on to the end of interval #28, reaching 150000 digits:15 L(40945,328) - L(41507,322) 6612071 105334 (5e9) 6 Aug 28 - Sep 30
16 L(41507,322) - L(222748,3) 13527824 217348 (5e9) 12 Sep 3 - Oct 10 ~
17 L(222748,3) - L(45405,286) 33460389 536426 (5e9)
18 L(45405,286) - L(48694,317) 69041008
19 L(48694,317) - L(44541,746) 43871809
20 L(44541,746) - L(49205,532) 45659518
21 L(49205,532) - L(49413,580) 18377349 287809 (e10)
22 L(49413,580) - L(49878,755) 54608684
23 L(49878,755) - L(144999,10) 11614904 182243 (e10)
24 L(144999,10) - L(145999,10) 8050111 126465 (e10)
25 L(145999,10) - L(146999,10) 8094919 127396 (e10)
26 L(146999,10) - L(147999,10) 8139747 128441 (e10)
27 L(147999,10) - L(148999,10) 8184494 128015 (e10) 12 Sep 27 - Nov 7 ~
28 L(148999,10) - L(149999,10) 8229120 129812 (e10) 12 Aug 31 - Oct 11 ~
The column after the interval is the number of Leyland numbers between the end-points of that interval, followed by how many of those remain after sieving to the subsequent quantity (in brackets). This is followed by the number of iMac-mini cores working on primality testing and the start and finish dates (~ added if in the future). Initially, in addition to intervals #15 and #16, I will be having a go at interval #28 in order to up my PRPTop production score.
Tuesday, July 21, 2020
Saturday, July 11, 2020
Saturday, June 20, 2020
Tuesday, June 09, 2020
Monday, June 08, 2020
Sunday, June 07, 2020
Thursday, June 04, 2020
Sunday, May 24, 2020
Sometimes attributed to Groucho Marx, quote investigator "Garson O'Toole" (Gregory F. Sullivan) got it right in 2010 when he traced the core of the quotation to Anthony Oettinger, quoting from Oettinger's September 1966 Scientific American article touching on the subject of grammar by computer (time flies vs. fruit flies; the complication is mentioned as early as 1963 in the Harvard Alumni Bulletin). O'Toole: "By 1982 or before someone juxtaposed the sentences to yield a funny combination which was then assigned to Groucho Marx."
The April 1975 issue of Computers and People already had the juxtapositioning. Lawrence M. Clark wrote "Computer Programs that Understand Ordinary Natural Language" (pages 14-19, 23; page 14 reproduced here, quotation boxed in green). It gets better. Clark's three sentences appeared already in the November 1966 issue of Computers and Automation (different title, same publication). Neil Macdonald (a pseudonym for Edmund Berkeley) wrote a short "Research on Meaning in Programming Languages" (page 10, reproduced here). It is "peach" instead of "banana" but that is not as important as the date.
Saturday, May 23, 2020
Cruickshank and Nason's "History of Weston" has the school "about a quarter-mile from the Main Street" which would put it closer to Rosemount Ave. than to Elm St. To resolve the location, I looked at a 1913 map that showed structures:
The red brick building in the middle of the above is my candidate for the Grammar School. Look at all the empty lots around it. To further convince myself:
Note that there is a slight forward protrusion of the left part of the building which matches the outline in the map. Finally, a 1924 map shows that the building is no longer there. Looking at the location today, one would see this.
Saturday, May 16, 2020
This morning a couple of ovenbirds crashed into our kitchen deck-door glass. The one on its side righted itself after a couple of minutes and they both just lay there in obvious shock. Here's a closeup of the upright one:
Catherine looked it up and said to just leave them for a few hours. And indeed, three hours later they were gone. This has happened before, twenty or more years ago (I am guessing), and — somewhat remarkably — the two birds that crashed into the door back then were also ovenbirds!
When I downloaded the photos for this article, I noticed that the time-stamp didn't seem right. I soon realized that I had forgotten to set the daylight-saving time option on my camera back on March 8. Which meant that I had 209 recent photos in my Apple Photos app that needed to be adjusted by one hour. Fortunately, Photos makes this easy. Unfortunately, the app hung ~70% through the process:
So I force-quit and relaunched the app to see what had been accomplished. I could see that some of the photos had added the hour but many had not. Worse, Photos had not gone through the 209 photos sequentially by date, but rather, somewhat haphazardly — a few each day. This is no doubt some sort of optimization procedure that utilizes multiple cores for speed gain (the same thing happens when one is importing photos from the camera). What Apple Photos did not realize is that my Mathematica was already utilizing all four cores on my Mac to calculate a ParallelTable. Perhaps this is why the application crashed.
Anyways, I now had to step through each day's photos and try to determine which ones had been adjusted and which had not. I had the camera's sequential photo numbers and the fact that many of the shots had been taken within minutes of each other to help me in this endeavour. However, for days (and parts of a day) where I had only taken one photo, this did not help. It took me another hour or so to step through my backup and check each photo's original time. Only later did I notice that the get-info on even the modified-time photos still showed the original time stamps.
All in all, it took me longer, I think, to correct all that Exif (when did they stop using all-caps?) data than it took those birds to recover. Moreover, I had to add an hour to the "posted" time on my Echo Beach post because I had originally cheated by back-timing that post to match the then-thought-to-be-correct photo time (to give it a more stream-of consciousness feel).
Thursday, May 14, 2020
Two months ago we were strapped in for a year-or-two rollercoaster ride. Many bought into the lockdown as a necessary — but decidedly time-limited — mitigation. Two months at home seems to be about as much as the public can bear. It will be an interesting summer.
Sunday, May 10, 2020
Thursday, May 07, 2020
|0 1 2 3 4|
|5 6 7 8 9|
If you think of the downward-moving "lines" as particles, a lot of "physics" happens as the particles collide. How many different particles can you distinguish?
Saturday, May 02, 2020
This typewritten table of the decimal expansions of powers of two up to 2^115 dates to when I was fourteen years old. My fascination then with powers of two almost certainly arose as a consequence of having encountered the wheat and chessboard problem. I would have calculated the numbers by hand and the typing layout suggests a slight obsession with presentation decorum, a handicap I've endured to the present day. The digit after the power is the digital root.
I recently had occasion to extend OEIS sequence A305942, the number of decimal powers of two having exactly n digits zero. For any given n, that number is fairly constant (on average a little over 33) but there is significant variation. For n up to 295000, I have found a zero-count as high as 62 and as low as 11. Checking other digits in the same range, I find a high of 65 and a low of 8 (see below). These extrema are outliers of course and statistics might suggest that we can find larger-than-65 and smaller-than-8 examples, if only we chart n large enough. But bear in mind that my current database of n up to 295000 is based on powers-of-two decimal expansions up to 2^10000000. It is not a fast computation.
This graph (click on it to get a better view) shows the number of occurrences (the blue points) of the digit 7 in decimal powers of two from 9100000 to 9240000. The green line represents the value 275923. Although (due to the size of the points and the thickness of the line) it may seem that there are dozens of points on the line, there are in fact only eight (at powers 9141747, 9143624, 9155434, 9163531, 9168298, 9171371, 9174454, and 9190491).
Saturday, April 25, 2020
|Basic ingredients. Good for what ails ye.|
"As a general rule, those who think they know everything about a subject really know very little about it; those who know most feel their lack of knowledge, and are always anxious to learn more."
— The Abstainers' Advocate (1894)
Around 1960, Harold Pullman Coffin cleverly rephrased this as: "The fellow who thinks he knows it all is especially annoying to those of us who do." There's a quotation website that annoyingly confuses this newspaper columnist with creationist Harold Glen Coffin. All of the quotations are Pullman's but the photo and the bulk of the bio is for Glen!
Saturday, April 18, 2020
They reduced the 8 cans of green beans that I ordered to 0 cans, 8 cans of lentils to 4, and 8 big containers of yogurt to 3. That's ok. I had ordered 4 two-litre containers of 1% milk. I was brought 4 one-litre containers but they charged me for the two-litre containers. That's not ok. The plain bagels that I ordered were replaced with sesame seed bagels, which might be ok but I won't know till I try one. The 8 PC white-cheddar mac & cheese boxes that I ordered were replaced with KD regular mac & cheese. I thought that was going to be ok but I just made myself a couple of boxes and it's inedible (although I did eat a bit and now I'm feeling queasy). I'm going to have to throw that out and hide the other 6 boxes.
I asked for a refund on the missing milk. I didn't ask for compensation on the mac & cheese because I reported the problem before I tried it. On the plus side, they did deliver all 24 rolls of toilet paper that I ordered!
Update: I went back to the site and asked for a refund on the mac & cheese. After all, it's a business transaction, so why should I shoulder the burden of their mistake? Incredibly, Instacart Support (who seems to be the go-between here) not only refunded the mac & cheese, but also all 4 of the two-litre milks — it should only have been 2 of them. They call it their "customer happiness refund". In return, they hoped I would check their "Good, I'm satisfied" support followup (as opposed to "Bad, I'm unsatisfied"). How could I refuse.
Monday, April 13, 2020
Thursday, April 09, 2020
Wednesday, April 08, 2020
Tuesday, April 07, 2020
Saturday, April 04, 2020
I've been spotting cottontails in the neighbourhood on my morning walks for some weeks now. At least that's what I think they are. In and around Denison Park, along Denison Rd. W., even on Sykes Ave. For decades there's been nary a sign of these critters around here. The coyotes came first. Now rabbits. Makes perfect sense!
Thursday, April 02, 2020
Saturday, March 28, 2020
Thursday, March 26, 2020
The scheduled arrival for the order was this morning. I was waiting for it by the front steps. When the order was brought to me I asked about the tap limit. I think he said $50. Damn! My original order was for just over $80. But wait, where's the toilet paper? They didn't include it, which put my total owing under $50. But my tap didn't work for some reason so I had to push the buttons.
Sunday, March 22, 2020
This morning, after a four-and-a-half-day wait, I found my 500th and 501st Leyland primes. The above graph extends what I showed for my 200th find. I have now surpassed Anatoly Selevich's 475 such finds that he computed from January 2003 to July 2011.
Generally, I'm happy with the ongoing search. My 54 dedicated Mac-mini cores have been supplemented in the last few months by 6 cores on my old Mac Pro and 4 on a more recent iMac, which have been working on interval #8 to gain time on the overall computation, the length of which I now realize I did not correctly calculate. More specifically, the three Mac minis that have been working the upper half of interval #14 since early October 2019 were thought to complete their task by July of this year. Instead, they will run for a full year, until October 2020. In effect, that pushes the overall expected spring-2021 completion date to the fall of that year.
Thursday, March 05, 2020
11 says: "In position 1 is a 1."
41 says: "In position 4 is a 1."
61 says: "In position 6 is a 1."
83 says: "In position 8 is a 3."
113 says: "In position 11 is a 3."
101 says: "In position 10 is a 1."
Of course, each added prime must be the smallest possible that has not already been used. There's a few early surprises hinting at things to come: 11, 41, 61, 83, 113, 101, 151, 181, 233, 223, 263, 293, 353, 383, 419, 401, 479, 467, 541, 1009, 599, 631, 661, 691, 727, 751, 787, 797, 809, 877, 907, 919, 967, 991, 9001, 1031, ... Term #20 is 1009 because to the end of term #19 we have 53 digits/positions and term #19 says that the next digit (position 54) is a 1. So we need a prime starting with 1 and 1009 is the smallest one that keeps the growing sequence truthful. Term #20 also dictates that in position 100 is a 9. So when we get to term #34 = 991, we now have 99 digits/positions and so the next prime must start with a 9. Why not 997? Because that says that in position 99 is a 7 and we already know that in position 99 is a 1. So we must travel all the way up to 9001 to keep things honest. And that may have repercussions when we get to position 900.
I eventually wrote a Mathematica program that seemed to work extending the sequence. But it was taking a long time finding term #1447. So I had a look at how far it had gotten. Term #1446 was 190901 taking up positions 7006-7011. Perusing the list of prior terms, I saw that positions 7012-7020 and 7022-7024 were already assigned with digits: 191737191?371... Stepping through, 19 is prime, as is 191, but these lie: position 1 is not 9; position 19 is not 1. Continuing, no more primes up to 191737191. Then we can try 1917371911, 1917371913, 1917371917, 1917371919, replacing the ? with 1, 3, 7, 9, but these are not prime either. So we attach the next digit, 3, and replace the ? with 0, 1, 2, 3, ..., 9. We need not go further than 5 because 19173719153, finally, is prime!
So I managed to figure out term #1447 before my program did! In fact, it would not have found it because I had my initial search go up to only 104395301. Here's a graph (click on it) of 1500 terms: