Friday, November 18, 2022
Spotted early this morning walking west down our street, just as Bodie and I were leaving for our walk. Already too distant to be distinct by the time I managed the photo, I have added a helpful arrow. At the bottom of the shot are some of the two dozen bags of leaves where our driveway meets the road, ready for today's yard-waste pickup. Resourceful squirrels will tear the paper off the bottom of the bags in order to steal the mostly dry leaves. I've had to re-bag one of them because it was beyond repair.
Wednesday, November 16, 2022
Saturday, November 05, 2022
Friday, November 04, 2022
Éric Angelini came up with this idea of listing products (one per line) where the multipliers introducing the line are the positive integers and the smallest possible multiplicands (after the initial line) are deduced from the products, given that the concatenations of the products (to the right of the equal signs) must be the same as the concatenations of the multipliers and multiplicands (in order, to the left of the equal signs), from the beginning, as far as it will go.
On the MathFun mail list, Éric shared Gilles Esposito-Farese's version that makes the multipliers the nonnegative integers (up to 50), instead of the positive-integers versions shown on Éric's blog:
0 * 0 = 0
1 * 0 = 0
2 * 5 = 10
4 * 63659 = 254636
5 * 119 = 595
For some reason Gilles skipped 3. Which makes his output for lines 4 to 50 incorrect. Ouch!
Here is my correction:
0 * 0 = 0
1 * 0 = 0
2 * 5 = 10
3 * 846 = 2538
4 * 1 = 4
5 * 1283 = 6415
6 * 2 = 12
7 * 1194673 = 8362711
8 * 118342264792783 = 946738118342264
9 * 88 = 792
10 * 7839881 = 78398810
11 * 7127164651933786 = 78398811171271646
12 * 432781551 = 5193378612
13 * 332908885487176222196 = 4327815511333290888548
14 * 512587299724651848 = 7176222196145125872
15 * 664831 = 9972465
16 * 11550979 = 184815664
Friday, October 14, 2022
I don't watch a lot of Netflix, likely because after wading through a bunch of popular/trending items I don't find anything palatable. Yesterday I tried a different approach. I looked through the critically acclaimed films and (eventually) came across The House:
Although the movie left me slightly discombobulated, I thought it generally worthwhile. For some reason, about half-way through, Harry Mathews' The Sinking of the Odradek Stadium came to mind. I once owned a copy of it. In the early 1980s (I think), I lent it to Brad (I think), a workplace acquaintance. I lost track of Brad at some point. I never got the book back!
Tuesday, September 13, 2022
|27 March 1943: click to enlarge|
|5 July 1947: click to enlarge|
Sunday, September 11, 2022
As expected, one of my slower processes has rediscovered (this afternoon) Gabor Levai's 1000027-digit Leyland prime. I thought that it might be a good time to see how far I've come. It seems that I've completed about 49% of the numbers that I wanted to test since I started 132 days ago, so, on average, I'm testing about 220 numbers per day. It means that, at best, I'll be done by February 2023 but a lot depends on my transferring processes from my three slow computers to others as they become available.
I had installed differing operating systems on those machines to see what would happen. I saw no improvement. So I'm thinking now that the slow speed arises from the fact that these three Mac minis were purchased (in order to save money) with only 8 GB RAM, which may be insufficient for the task at hand (it had been adequate for testing 300000-digit numbers). I will now terminate three of the six processes on each machine to see if there is any speed improvement on the remaining three processes. Later this month I will have completed 14 processes on two other machines, which allows me to transfer the 9 terminated processes.
Thursday, September 01, 2022
This morning, a 23-minute power interruption allowed a couple of Toronto Hydro employees to do some maintenance work on a close-to-my-home transformer. I have all 18 computers (104 processes currently working on my million-digit Leyland prime search) on battery back-up units but the amount of time here was just long enough to shut down seven of them (39 processes). Another 5 to 10 minutes might have killed them all.
By early afternoon I had saved the output of the interrupted programs and reinitialized their new search ranges. Three of the seven affected computers were the ones that were taking 18.5 hours per candidate in my May 27 reality check, so I installed new (differing) operating systems on those machines, hoping for a speed improvement. I won't know for a couple of days if that will pan out.
Saturday, August 27, 2022
Back on April 20, I developed a terrible toothache that came to be associated with a swollen lower-right jaw. Over the next five days I consumed more Acetaminophen and Ibuprofen pills than likely I had over several decades. On April 25, my dentist (whom I had not seen since December 2019 because of the pandemic) had a look.
He prescribed a seven-day regimen of Amoxicillin. Within 24 hours the situation improved. He also recommended that I see an endodontist, which I did on May 10. The endodontist gave me three options: do nothing, have a certain dead tooth pulled, or let him do a root canal that involved (at least, pending complications) two three-hour sessions. I don't know that I can last one three-hour session. The last time I had a root canal the doctor left me alone for ten or so minutes and I chose that time to have a panic attack! Unfortunately, that set in motion similar feelings of anxiety, subsequently, every time that I have had my mouth worked on in a dentist's chair.
Mulling over my options, I did nothing over the course of the summer. On July 7, I managed to complicate things by breaking off part of a tooth in the upper-left part of my mouth. As annoying as this was, I did not see my dentist about it. Around August 20, I noted that the area around my dead tooth was getting reinfected. Salt-water rinses were not helping. Fortunately, this time the formation of the abscess was not accompanied by pain and, by August 22, I felt that my own body was dealing with it and that, perhaps, the worst was over. Nevertheless, I was fearful that my immune system was not capable of conquering the bacterial pathogen and I thought it prudent to see if I could acquire an antibiotic.
Constrained somewhat by my unwillingness to travel any distance, I thought that making an appointment with my family doctor right here in Weston was an option. He could write me a prescription and I could get it filled nearby. But my call to his office on August 23 did not go as planned. The receptionist, upon discovering that my last appointment had been way back in November 2012 (I was as surprised as she was: Had it really been that long?) felt that she needed to ask the doctor if he wanted to engage with me. The next day she left a message with their (apparently new) policy: My family doctor was not taking back patients he hasn't seen in over five years due to being overburdened with Covid. Wow, I managed to not only lose my family doctor, but I'm also responsible for my wife losing her family doctor (same doctor, it has probably been five years since she has seen him)!
On August 25, I decided to give my dentist a call. My wife had suggested that they might be able to have a repeat of my April 25 prescription filled at a local dispensary and I should ask about that. They were busy and I had to leave a message. I gave my name and mentioned my previous appointment with the dentist on April 25 and asked about the possibility of filling a repeat of the prescription that I got then, but locally. I forgot to leave my phone number. There was no reply, so the next morning, Friday, I phoned again. The assistant/receptionist who answered tied my request to the previous day's call by noting that her inability to parse my full name had her calling back someone else for the reply. I provided the local Shoppers Drug Mart address and phone number. She said that she still had contact the dentist about all this but if she didn't get back to me that day, she would get back to me on Monday.
I spent the rest of Friday making my potato/carrot/spinach soup complemented with some lentils, roast-beef gravy, and leftover frozen bits from a long-ago spiral ham. I had several bowlfuls and tried to get some late-afternoon shut-eye. When I came to later that evening, I was feeling much better! The swelling in my gums had receded a little and I had the sense that my immune system was going to be able to handle this after all. Perhaps it was some remnant antibiotic in the ham!