10/9!*8!*7!-6!*5!/4!+3!*2!+1!

Happy New Year!

Java fix

For the factorization of large integers I have become somewhat dependent on factordb.com and Dario Alpern's ECM Java applet. With my new Mac/OS I have, so far, gone without the latter but today I enabled Java in my web browser, only to find that my large numbers would not paste into the ECM app, nor could I copy any factors out of it. After a little searching, I finally came up with a fix: I downloaded Alpern's ECM source code, opened Terminal, gave the ECM folder-location path (using the cd command), compiled it (javac ecm.java), and ran it (java ecm). The applet appears sans browser and copy/paste work fine.

Pi continued fraction & Khinchin: regimes

Let the 'reduced geometric mean' be the geometric mean minus Khinchin (k). The first 25 reduced geometric means for the fractional part of π are:

 1 7-k                                              =  4.3145..
 2 105^(1/2)-k                                      =  7.5615..
 3 105^(1/3)-k                                      =  2.0322..
 4 2^(1/2)*7665^(1/4)-k                             = 10.5471.. max
 5 2^(2/5)*7665^(1/5)-k                             =  5.2088..
 6 2^(1/3)*7665^(1/6)-k                             =  2.9090..
 7 2^(2/7)*7665^(1/7)-k                             =  1.6891..
 8 2^(3/8)*7665^(1/8)-k                             =  1.2814..
 9 2^(1/3)*7665^(1/9)-k                             =  0.7182..
10 2^(3/10)*3^(1/5)*2555^(1/10)-k                   =  0.6755..
11 2^(3/11)*3^(2/11)*2555^(1/11)-k                  =  0.3248..
12 2^(1/3)*21^(1/6)*365^(1/12)-k                    =  0.7362..
13 2^(5/13)*21^(2/13)*365^(1/13)-k                  =  0.5977..
14 2^(5/14)*21^(1/7)*365^(1/14)-k                   =  0.3304..
15 2^(1/3)*21^(2/15)*365^(1/15)-k                   =  0.1164..
16 2^(3/8)*21^(1/8)*365^(1/16)-k                    =  0.0580..
17 2^(7/17)*21^(2/17)*365^(1/17)-k                  =  0.0075..
18 2^(4/9)*21^(1/9)*365^(1/18)-k                    = -0.0366..
19 2^(9/19)*21^(2/19)*365^(1/19)-k                  = -0.0755..
20 2^(9/20)*21^(1/10)*365^(1/20)-k                  = -0.1977.. max
21 2^(11/21)*21^(1/7)*365^(1/21)-k                  =  0.2561.. max
22 2^(6/11)*21^(3/22)*365^(1/22)-k                  =  0.2050..
23 2^(12/23)*21^(3/23)*365^(1/23)-k                 =  0.0746..
24 2^(1/2)*21^(1/8)*365^(1/24)-k                    = -0.0396.. max
25 2^(12/25)*3^(4/25)*5^(2/25)*7^(3/25)*73^(1/25)-k =  0.1504..

Notice that 1-17 and 21-23 are positive, while 18-20 and 24 are negative. Each one of these alternating-sign regimes has a maximum (distance from k): for instance, {20, 0.1977..} for the negative 18-20 regime. I have now calculated the start, end, and maximum for the first 27087 regimes (the final one incomplete because it ends beyond 3*10^9). Some regimes are quite lengthy, such as the positive 5418849-1434927964 and 1865143624->3*10^9. The so-far maximum in that final one is {2377934394, 0.00004194392..}, meaning that the geometric mean of 976 terms is closer to Khinchin than the geometric mean of 2377934394 terms!

[Fred Lunnon was kind enough to point me to Chapter III of William Feller's An Introduction to Probability Theory and its Applications (Volume 1) as a means of understanding some of the mathematics involved in all this.]

Pi continued fraction & Khinchin

As stated in my last entry, I am now able to compute billions of continued fraction terms for arbitrary constants. In fact, using my current setup, I have already charted over three billion such terms for the constant π. (Because of memory constraints, an attempt at four billion terms failed.)

There are a number of things an empiricist can do with such a collection: tally it (these occurrence counts are for exactly 3 billion terms), find the position of first occurrence, and the position of the nth occurrence, of n. (All three of these exclude the initial 3, because the initial — the zeroth — term of of a simple continued fraction may be any integer but the rest are strictly positive. This is why I do not like the Applications example in the Khinchin entry of the Mathematica documentation center.)

Additionally, what I did back in 2001 (with a measly 53 million terms) was generate a π Khinchin-approach sequence: A059101, with 27 terms. Today I added terms #28 to #36.

Home, sweet home

Yesterday, the replacement for my nine-year-old dual 2-GHz Power-PC G5 arrived and — as suggested in the final entry of my old blog — in the wee hours of this morning I purchased and subsequently downloaded the home edition of Mathematica 9.

The 27" iMac (2012) had been maxed out with what I could add at the Apple store, with the exception of 32 GB RAM which I had ordered from a third party and installed myself.

For the most part the setup went smoothly. I had to figure out how to do my web-sharing, resolve a will-not-fetch-mail issue, and resign myself to not using Java for now. I booted up Mathematica and asked for $MaxNumber. It suggested: 8.768126706828697*10^2711437152599256. So I knew I could do a lot better than the 180 million terms of the pi continued-fraction generated back in 2002. Requesting one billion terms, the calculation required just over one hour!

Time wasted

Since November 19, I've been trying to find the eighth term of A219325 and have only just managed to get up to five billion. Giovanni Resta has now beat me to it with 34505916416. The binary circulant that results from this number is:

1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1
1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1
1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0
0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1
1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1
1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0
0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1
1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0
0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0
0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0
0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1
1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

Keyboards

Design — as Apple (of all companies) should know — is how it works. When Tim Cook was asked recently how adept he was at using Apple's virtual keyboard, he replied: "Pretty good. I think if you stick with it a little while you get quite good at it. And the auto correction is quite good." Ouch!

Apple's virtual keyboard suffers of course from a fundamental design flaw. It fails to adequately mimic an actual keyboard by splitting it into two discrete entities, the second of which sports the numbers and some much-used punctuation (such as the apostrophe and the hyphen). This becomes a difficult-to-ignore annoyance in message chats on my iPad and would be relatively easy to fix with a properly designed, replacement virtual keyboard. I'm aware of course that space/size concerns might limit what is reasonably possible but intelligent designers would figure out a way. The reason they have not done so (unless perhaps there is a design disconnect at Apple these days) surely is to steer folk into Apple's $70 wireless keyboard accessory solution!

So, in order to better enjoy my iPad Messages chats, I purchased an Apple wireless keyboard. The first thing I grappled with was why there wasn't an obvious on/off indicator light on the keyboard. This design flaw may be overcome by noting that the caps-lock light will not come on when the keyboard is off (an extra and surely unnecessary step). The second thing I dealt with is that there is no way to send my wireless-keyboard typed blurbs without touching the Send button on the iPad. This is of course an easily fixed software limitation — except that Apple hasn't addressed the issue in the several years that people have been complaining about it! Maybe Apple really has lost its design moxie.

What's so special about 798 and 1182?

I've been working on A219357 for nine days now. I'm especially proud of my graph, where the two wayward points (798, 2164818573) and (1182, 5394998141) are easily picked out.

A long run

Continuing with Eric Angelini's digit-difference/add-subtract/iterate procedure, I have now come across a particularly long run that does not repeat a previous element (i.e., confirm that a loop has been entered) until step 175128. The starting number (linking to a 32 MB evolution) is 293613.

Update (8 Nov 2012): An even longer run that does not repeat a previous element until step 337550: The starting number (linking to a 55 MB evolution) is 294066. I've made a graph of the run.

A long loop

Eric Angelini's digit-difference/add-subtract/iterate procedure, to which I drew attention two weeks ago, continues to delight. I knew there was a length-25 loop starting with 20971:

 0 20971
 1 50232
 2 102345
 3 223459
 4 212312
 5 101102
 6 211223
 7 110212
 8 98101
 9 80983
10 170138
11 841395
12 408752
13 889984 *maximum
14 879840
15 758392
16 522717
17 217055
18 49552
19 103584
20 235927
21 111172
22 110521
23 95211
24 52103
25 20971

Now I have discovered a significantly longer loop starting with 204099163.

Update (3 Nov 2012): There exists an intermediate length-85 loop starting with 17175432.

13094

Start with 13094. This is p.
From left to right, determine the absolute differences between p's adjacent digits:

1-3 = 2
3-0 = 3
0-9 = 9
9-4 = 5
4-1 = 3     (the last digit of p minus the first one)

Collecting the resulting digits, we get q = 23953.

If q > p, compute p + q. If q < p, compute p - q. Either way, this is our new p.
Repeat:

0     13094 + 23953
1     37047 + 47434
2     84481 - 40477
3     44004 -  4040
4     39964 + 60321
5    100285 ...

The procedure was created by Eric Angelini, who presented it to MathFun on October 9. I chose 13094 to illustrate the method because this is a number for which I do not have an eventual outcome. Lesser starting numbers end up in small loops, although it may take a while (for example 199, 10853, 10886) to get there. In my graph of ten million iterations of 13094's evolution, the upward climb is relentless.

Topsy-turvy

On September 24, Apple announced that it had sold 5 million iPhone 5s in the three days since the phone's introduction. This represents a profit of one to two billion American dollars. In three days! One might have expected AAPL to do better than drop $10, that day, from its $700 previous close — and another $17 the day after.

On September 27, Research in Motion announced that it had lost $235 million in its second quarter. How did NASDAQ react to this news? RIMM went from $7.14 per share to $7.50. I guess the fundamentals were sound, in the fundamentally flawed illogic of what constitutes the American stock market system.

Disclosure: I do not use a mobile phone nor have I ever put money into the stock market.

56 by 2's

two nonillion
nine trillion thirteen
one hundred thousand three hundred
thirteen billion forty-three million forty-three
?
one hundred twenty-one million two hundred thirty-six thousand six hundred thirty-six

One, two, three, four

What is the smallest English number expression that has one letter occurring once, two letters occurring twice, three letters occurring three times, and four letters occurring four times?

wordthreepeating

1, 21, 1000013, 4000414, 131256, 21445566, ________________.

Coverage

BBC news anchor this morning: "Give us the background to it. What's at the centre of it?"

Flagpole

oneseventhreesixfiveeleveneightninetwothirteenfourtentwelvesixteenfifteentwentysixfourteeneighteenseventeennineteentwentyonehundredeleventwentyonetwentyfivetwentytwotwentythreetwentyfourtwentyeightthirtyeightthirtytwentyseventwentyninethirtyonethirtyseventhirtythreethirtytwofortytwothirtyfourthirtyfivethirtysixthirtyninefortyfortyonefortythreefortyfivefortysevenfortyfourfortysixfiftyfourfortyeightfortyninefiftyonefiftysevenfiftyfiftytwofiftythreeonehundredtwelvefiftyfivefiftyeightfiftysixfiftyninesixtysixtyonesixtythreesixtyfivesixtysevensixtyfoursixtytwoseventyfoursixtysixsixtyeightsixtynineseventyseventyoneseventytwoseventythreeseventyfiveseventysixseventysevenseventyeightseventynineeightysixeightyfoureightyoneninetyfoureightythreeeightyeightytwoeightyfiveeightyseveneightyeighteightynineninetyeightninetythreeninetyninetyoneninetytwoninetyfiveninetysixninetysevenonehundredfiveninetynineonehundredonehundredtwoonehundredoneonehundredthreeonehundredfouronehundredsixonehundredeightonehundredsevenonehundrednineonehundredtenonehundredthirteen...

This is the top of the flagpole of Eric Angelini's English flagpole sequence. If we subtract the indices from the sequence, we get: 0, 5, 0, 2, 0, 5, 1, 1, -7, 3, -7, -2, -1, 2, 0, 10, -3, 0, -2, -1, -1, 89, -2, 1, -3, -3, -3, 0, 9, 0, -4, -3, -2, 3, -2, -4, 5, -4, -4, -4, -2, -2, -2, -1, 0, 1, -3, -2, 5, -2, -2, -1, 4, -4, -3, -3, 55, -3, -1, -4, -2, -2, -2, -1, 0, 1, -3, -6, 5, -4, -3, -3, -3, -3, -3, -3, -2, -2, -2, -2, -2, 4, 1, -3, 9, -3, -7, -6, -4, -3, -3, -3, 5, -1, -5, -5, -5, -3, -3, -3, 4, -3, -3, -2, -4, -3, -3, -2, -1, -3, -2, -2, 0, ... Herein, the positions of the zeros are: 1, 3, 5, 15, 18, 28, 30, 45, 65, 113, ... In effect, these are the indices of the flagpole sequence where a(n) = n. It turns out that the majority of flagpole sequence numbers lie on that line — of the first 1000000 terms, 688153. Within this region, the largest spacing between consecutive on-the-line terms is between term #321947 (=321947) and term #411273 (=411273). This large gap is due to the demand for the letter L exceeding the local supply. A much larger gap will begin ~10^9 when demand for the letter M exceeds its local supply.

Bye bye Birdo

Just a few hours shy of a 492-day stay with us, Harry Vance attempts to put a reluctant Birdo into her carrier. I will miss her anticipation of the microwave beep, half-way (or so) through my one-minute milk heat-ups, and the imitation squeaks as the window blind by her cage came up in the morning. Birdo's vocal repertoire included coughing, sneezing, and a hearty nose-blowing whenever I brought a hankie up to my face. She arrived with a couple of well-worn, two-note whistles but Catherine eventually taught her the theme to The Andy Griffith Show, which fell into disuse after I taught her I Was Kaiser Bill's Batman — phrases of which became our back-and-forth contact calling. She could do a sparrow, robin, or gull, a cat or a dog, and would not hesitate to join in at the first hint of laughter. Birdo's "English" included yeap (guessing correctly, occasionally, the answer to a query being asked of someone else), naow (said with a snarl), c'mere, c'mon, good girl, and of course Har-ree followed by — in a different voice — Birdo. She had a mock people-speak but the monologue was largely unintelligible. Catherine tried once to get her to do a happy wheee but it came out incredibly cranky when she finally succumbed to it. Birdo would greet you with a cluck and thank you with a coo. When she really wanted your attention, she'd let out an ear-piercing smoke-alarm. She had an impossible-to-describe, funny bit that we called the 'dying-parrot'. Watching her grapple with falling-asleep had me conjecture that birds evolved the behaviour to rest on one leg, with the head tucked into the back, so as to make the mathematics/mechanics of balancing that much easier. (I'm aware of the heat-loss theory but I'm not buying it as anything more than a modest advantage in limited circumstances. On the other hand, trying to maintain one's balance with a minimum of thought/correction is, high up — where a bird is likely to find itself at night, a matter of some gravity.) As for having a parrot as a room-mate, I'm now aware of how much dander and feather fluff (such) a bird generates each and every day and this detritus becomes a cleaning-burden far beyond the confines of the cage.

Time warp

I tend to be a little obsessive about the accurate reporting of place and time (as a corollary to my obsession about the accurate reporting of fact). For that reason, twice a year (at the beginning and end of DST), I photograph a display of my presumably-accurate computer clock, before and after I have reset my digital camera's date/time setting to the correct time, so that if ever I might wish to report the actual time that a photograph was taken, I can translate the camera-clock time (in the EXIF data) into real time.

For example, when I did this album of a Toronto Wildlife Centre goose rescue, I had to subtract 2 minutes and 34 seconds from the photos' time stamps because the camera clock had gained that much since I last calibrated it in March.

By coincidence, it was back in March when my iPhoto additions first no longer appeared in the 'photos' section of the application. The pictures were still accessible through the 'events' section and I put the matter down to an application bug resulting from the sheer number of photos (over 44000) it had to display on my aging infrastructure.

This morning, I noticed that the date stamp for a recent picture had the year as 2011. In the four-and-a-half months since I last calibrated the camera clock I had never noticed that the year was incorrect. The photos had in fact all been added to the 'photos' section of iPhoto, but they were back in 2011 where I never once occasioned to look. Fortunately it was easy to correct all of the bad dates in a batch date/time adjustment.

Jump for joy

I came across R.L. Burnside by way of Lightnin' Malcolm (who I caught on a WNED/PBS show last week). This Burnside video from 1978 says it all:

See my jumper, lawd, hangin' out on the line
See my jumper, lawd, hangin' out on the line
Know by that, something on my mind

Would'na been here baby, lawd, if it had'na been for you
Would'na been here baby, lawd, if it had'na been for you
Way down here, way you wanna do

Fix my supper baby, lawd, let me go to bed
Fix my supper baby, lawd, let me go to bed
This white lightnin' done gone to my head

The uninnuendoed meaning of jumper is a smock (on a clothes-line), as evidenced by just such an article of clothing being washed/starched/ironed in a couple of other blues numbers.

Going the distance

The Gar Creek mudslide on the morning of July 12 had me, at the time, trying to accurately place the disaster on Google Earth. Unlike bimmjim, one of the commenters to the Yahoo! retelling of that news, I knew that Johnsons Landing was (obviously) slightly north of where Google Earth spotted the location. David Petley (who writes a landslide blog) had the correct map placement, verifiable by this helpful graphic.

The Fairmont Hot Springs mudslide on July 15 had some in the media trying to relate this event to the Gar Creek one by proximity. The National Post headlined it as 45 km away. I had already measured the distance as ~78 km (as the crow flies) and decided to let the Post know of its error. Incredibly, this evening's CBC - The National suggested that the distance between the locations was only 30 km (at 4:50 into the broadcast), which had me remeasure the damn thing in case I had made some dumb mistake. A little later, I chanced upon Brad Giffen (a CTV news-channel anchor) using the 45 km figure. What is this contagion?

Update: At least one subsequent story got it right.

Lies, damn lies, and family history

It can be a little unsettling at times to see things from someone else's perspective.

Marlene Frost and I are once again doing a little bit of recreational genealogy. In our research, I came across the email address of a great-grandson (Paul) of the Irish couple whose descendants we are attempting to chart. So I thought I would share with him the state of our current tree in the hope of having him correct any errors that we might have made and, moreover, contribute some particulars of his own immediate family. I mentioned that we were trying to figure out where the parents of a local minor celebrity (Bob) fit into the tree.

Paul replied that Bob was his (first) cousin. I objected, pointing out that newspaper accounts had named Bob's father as someone other than Paul's suggested uncle and, additionally, those accounts provided information that allowed one to deduce, with a little digging, the name of Bob's mother, which was not the name of Paul's uncle's wife. Paul replied that my newspaper accounts were "somewhat in error" and repeated his mantra that Bob's father was his uncle.

If nothing else, Paul's insistence did convince me that Bob was in that branch of the family tree. I now believe (for a variety of reasons) that Bob is Paul's cousin, once removed — not his uncle's son but, rather, his uncle's grandson. That an individual so close to the scene of the action can get it so wrong speaks volumes about the fictions that must permeate some of our family histories.

Perspective

It can be a little unsettling at times to see familiar scenes from an altered perspective. Maps are no exception, as I rediscovered today in examining the melting ice in Hudson Bay. How long will it take you to find Hudson Bay in this image of NASA's White Marble?

Déjà vu all over again

The CBC's Kelly Crowe wrote an article using this Yogiism only last month. Today, Crowe storied Real water needs for The National (the print version is here). By contrast, Snopes' Eight Glasses debunk first appeared on 6 February 2001 and Heinz Valtin's 8 × 8 review on 8 August 2002. There's no news like old news.

How big is my baby?

Arms outstretched: "So big!"

I caught this particular scene from the 1932 William Wellman film on TCM this morning and went about googling — unsuccessfully — for some reference (I vaguely remember its German counterpart played by my mother with one of her charges) to this baby teaching game.

I'll see you again

     Thomas Powers was a man of great mystery. He was taciturn to the greatest degree and would say nothing about himself. Mrs. Wolcott said that he came to her home in the later part of February from Philadelphia. For a long time she knew him simply as "Mr. Powers". He would say nothing about himself. He was a man of very peculiar habits in that he seemed at times utterly oblivious of his surroundings. While he did not rudely repel any advances to conversation with him, he would quietly withdraw. He did not care to talk about any of his work and when the conversation drifted toward that channel he would leave the room. He was a man of good habits, always coming home early and Mrs. Wolcott says that not over two or three nights did he remain out of the house after 9 in the evening, coming home early and immediately going to bed. About three weeks ago he was sitting alone in the sitting room, through which Mrs. Wolcott passed. She made some remark to him and when he looked up she noticed that his eyes were red. She asked him if he was ill and he said:
     "No, Mrs. Wolcott. I'm not sick but I'm awfully homesick. I've never had a home since I was a child."
     He broke into crying and Mrs. Wolcott asked him to come and make himself more at home and not all by himself. He seemed to cheer up and commenced to visit. He said again that he had no home and said he was afraid he might lose his position here. He told Mrs. Wolcott that he liked the place very much and hoped he could remain. Mrs. Wolcott tried to cheer him up and he burst into another fit of weeping.
     Once he asked Mrs. Wolcott if she thought that any one would know him in Watertown. He would give no reason for his making such a strange statement. Since Sunday he had acted queerly. He seemed to lose his appetite and when Mrs. Wolcott asked him if he was sick he said he had not been well in two years, but that there was nothing serious. While the rest of the family might be talking and laughing loudly, he would drop off to sleep, oblivious of his surroundings and the noise.
     On Wednesday night he ate little for supper and left the house about 7. A postal card from his brother was on the table and it was carried to him. He did not look at it, but simply slipped it in his pocket. With one of the boarders he walked to a cigar store, bought a cigar and said, "I'll see you again."

Watertown Daily Times: 3 April 1909

That was on 31 March 1909. Thomas Powers jumped into the Black River from Watertown's Court Street bridge. Except for the evening's darkness and the swiftness of current, his northwest view — downstream — would have looked something like this:

It would be 1915 days (five and a quarter years) before Thomas would be seen again: on the shore of Lake Ontario, near where Stoney Creek empties into it, 32 km southwest of Watertown. The trip downriver and through the lake would have been at least 50 km.

Thomas' suicide might have gone unnoticed were it not for the concern of his brother, James, who offered on April 10 — after a week of fruitless searching — a $100 reward for the finding of the body. On that same day another person, Thomas Blacklock, jumped off the Court Street bridge — but this would not become known until June 7, a couple of days after a Joseph Kellar, who had faked a suicide off the bridge on May 2, was found alive and well. Blacklock's body, found in Dexter on May 21, had been claimed — and buried — as that of Kellar.

References:

     Watertown Daily Times: April 2 — Thomas Powers is still missing

     The Syracuse Herald: April 11 — James Powers offers $100 reward

     The Syracuse Post-Standard: April 12 — the reward spurs search for a body

     Watertown Daily Times: April 15 — a fake body is chased down the river

     The Syracuse Post-Standard: May 3 — did Joseph Kellar jump into the Black River?

     Watertown Daily Times: May 21 — a body is found in the river at Dexter

     The Syracuse Post-Standard: May 22 — the body is identified as Joseph Kellar

     Watertown Daily Times: June 2 — James Powers increases the reward

     The Syracuse Herald: June 5 — Joseph Kellar is alive; claims he did not fake suicide

     The Syracuse Post-Standard: June 5 — Kellar's handwriting matches suicide note

     Watertown Daily Times: June 7 — the body is identified as Thomas Blacklock

     Watertown Daily Times: July 7 — the Thomas Powers search resumes

     Watertown Daily Times: July 8 — diving apparatus has arrived

     Watertown Daily Times: July 9 — the bell diver nearly drowns

     The Syracuse Post-Standard: July 10 — coroner doubts Thomas Powers suicide

     Watertown Daily Times: July 10 — the diving continues

     Watertown Daily Times: July 12 — bell divers abandon the search

     Watertown Daily Times: 30 June 1914 — a body is found June 28 in Lake Ontario

     The Lowville Journal and Republican: 9 July 1914 — how the body was identified

With her babe in her arms

     Watertown, Aug. 10. — Mrs. John Powers this morning swore out a warrant for the arrest of her husband, who she claimed was drunk, disorderly and abusive. Powers was arrested and lodged in jail. He will be brought before Recorder Cobb Monday morning.
     Mrs. Powers was seen at her home at No. 41 Morrison street, and told her story to The Herald man. Their home up to three months ago was at Munningar, West Mead county, Ireland. John was a good worker but spent all his money for drink. She thought if she could get her husband away from the influences of their old town he would do better, so they sailed for America. After a few days in New York city they went to Kingston, Ont., and from there to this city, where they have been only two months. About a month ago she complained of him but nothing was done.
     Friday night John did not return at the usual hour and when he knocked for admittance at 4 o'clock this morning she started with fear to let him in, but before she reached the door he had got in through a window and began to threaten her and she fled to the neighbors.
     She walked the streets with her babe in arms till a warrant could be procured. She also stated that they had had nothing to eat for two days and that he had spent all his week's wages but $3 for drink, when he was arrested. She said she wanted to be freed from him, declaring that she could earn a living better without him. Mrs. Powers will apply to Mrs. N.C. Walker to have four of her five children admitted to the Orphans Home.

The Syracuse Sunday Herald: 11 August 1895

References:
     Watertown Daily Times: 10 August 1895 — another version
     Watertown Daily Times: 12 August 1895 — the follow-up
     Watertown Daily Times: 17 September 1895 — conclusion

Exercise:
     Determine a history of the Mullingar Powers' children and their descendants.

Snake catches toad

A little wildlife drama on our (the east) side of the Raymore weir on the Humber.

Samsung A.I.

A message to Samsung-Canada's online product support:

I ordered this TV from FutureShop and received it on 17.03.2012. The accompanying remote (AA59-00463A) did not work. Fortunately I have another Samsung TV and was able to use it to set up the TV and confirm that this was not a battery issue. I continued to play with the remote in the hopes that some minor jiggling or such would cause it to work, but it will not function.

I contacted FutureShop to see if they would replace the defective remote but they said I would have to ship back the entire TV and they would replace that. That struck me as the height of sillyness so, instead, I searched online for a replacement remote. I found one that looked like it at Amazon and purchased it.

It works fine, but it turns out that it is not identical to the one that came with the TV. The Amazon remote (BN59-01042A) has some different button designations and lacks the SLEEP button that I want.

How can I exchange my defective remote for one that works?

The reply:

Thank you for contacting Samsung Customer Care.

We understand that the remote control supplied with the TV is not working and the you have purchased another remote control that is not the exact unit for the TV model.

We are sorry to hear that.

We recommend you access the below link for some troubleshooting steps to isolate the issue when the remote control is not working.

http://bit.ly/IuXkVS

You will need to isolate if the issue is with the remote control or the IR sensor on the TV.

The TV will be exactly compatible with the remote control part number that is labeled under the battery in the battery compartment of the remote control. The compatible remote control is AA59-00463A as also listed by you.

To replace the remote control with the correct part number, you need to contact the store from you purchased it.

Thank you for contacting Samsung.
Kind regards,
Andy
Samsung Customer Care

The following day I received another email from Samsung titled ‘Thanks for signing up with Samsung’ and stating: “Thank you for your interest in Samsung. Now that you've joined us, you'll be in the know about everything Samsung...” I did not of course sign up — I asked for product support. There was a “click here to unsubscribe” notice near the end, so I did and, after confirming my wish to be removed from their mailing list, was greeted with “We're sorry to see you go. Please allow 7-10 business days for us to process your request.” Oh my!

Shazam

On 27 June 2010, I asked for help identifying a particular piece of music. Today I managed to find out — well, because there's an app for that! The song turns out to be Mac Thornhill's 1988 Who's Gonna Ease The Pressure:

I was able to understand a little better the words in some of the tune's remixes: What I took to be "who's gonna be the best of..." is actually "who's gonna ease the pressure of...". Why, of course! I'm still hoping to resolve a couple of SAUNZ in my lyric transcription.

Eight

845534401, 83565065201, 829144019201, 834854554601, 854516148301, 866422665701, 878554044001, 889419071111, 890750408711, 891079866601, ...

Each of these is a prime equal to a multiple of its reversal plus-or-minus a prime smaller than itself in exactly 8 ways (A182239). For example:

845534401 = 104435548 *  3 + 532227757
          = 104435548 *  5 + 323356661
          = 104435548 *  6 + 218921113
          = 104435548 *  8 +  10050017
          = 104435548 *  9 -  94385531
          = 104435548 * 11 - 303256627
          = 104435548 * 14 - 616563271
          = 104435548 * 15 - 720998819

All ten of our numbers begin with an 8. What will be the first term that does not?

Galway, England

My father-in-law, John Edward Powers, likes to play up his Irish roots, even though his mother's parents were both born in France, his father's mother, Agnes Sullivan, born in Toronto ON, and his father's father, David Edward Powers, born in Sandy Creek NY. Agnes Sullivan's parents may have come from northern Ireland but David Edward Powers' parents were from county-unknown. So the genealogically-minded members of the Powers clan were excited, last year, to find David Edward's uncle, Michael Powers. At the time, I asked John if he knew anything about his Irish roots. A new priest at his church had asked him the same thing and John had to admit that he did not know. But in the following days he thought about it and a word came to him (from, hopefully, his parents/grandparents and not some movie that got stuck in his mind). The word was Connemara.

Two-and-a-half weeks ago, Marlene Frost shared with me her discovery of an obituary for Michael Powers that mentioned his place of birth: Galway, Ireland. Yesterday, I found another one that (sort-of) confirmed the location. We're making progress!

Say it ain't so

"They say that in 7.6 billion years our sun will balloon up to a size larger than the Earth's orbit, thus vaporizing the planet."
"When?"
"In about 7.6 billion years."
"Man! That's a relief. I thought you said '7.6 million years'."

Overheard at the check-out of the supermarket this morning, in the context of 'why worry, be happy', a simplified variant of the preceding old joke: "They say, we're all gonna be dead in a million years."

A Female Lothario.

   An Irish girl named McCormick, residing in Hamilton, Canada as a servant has been guilty of a series of very strange acts. In her capacity as servant she would with a very art-address ascertain the feelings of almost every lady relative to the tender passion, telling them that Mr. —, a dry goods clerk, or a lawyer, &c. was desperately in love with them, and that he would contrive to see them on a certain night. When the night appointed came, the young gentleman would come, in the shape of Miss McCormick in male apparel. In three different cases was the question popped, and accepted; in one the wedding garment made. This fun was tried once too often, and the gay creature was locked up in jail.

Scientific American: New York, January 9, 1847.

Not surprisingly, perhaps, there are a handful of online references to this story. The original appeared in the 26 December 1846 Hamilton Spectator. In January 1847, any number of other newspapers reprinted it, including, on January 11, the Hagerstown Torch Light and the Monday morning New York Herald.  Dan Akeson (who suggests that no copies of the original Hamilton Spectator story exist) published, in 1990, a book on Eliza McCormick making the outrageous claim that she transgendered herself into nineteenth-century Tory backbencher, John White.

Scientific American cover art

Taking a cue from Rick and Mary Parsons' Scientific American cover art website, I decided to collate twenty-one special covers from 1896 to 1909, complementing a previously done gallery of Scientific American covers from May 1948 to August 1987.

$2.92

A somewhat remarkable thing happened this morning. I went to the nearby variety store (which I rarely do) to purchase a couple of 'rolls' of peppermint Certs (in preparation for tomorrow morning's dentist visit). I don't get a lot of opportunities to get rid of change so I already had a rough idea of how much I had in my wallet prior to the vendor telling me that it was going to cost me $2.92: Just a little more than I had hoped. Should I pull out a five? I wondered, but I kept on counting: one loonie, seven quarters, one dime, one nickel, and two pennies. It was the exact amount of change that I had!

Female Appellation.

When Eve brought woe to all mankind
Then Adam called her wo-man ;
But when she woo’d with love so kind
He then pronounced her woo-man.
But now with folly and with pride
Their husband’s pockets trimming,
The ladies are so full of whims
That people call them whim-men.

Scientific American: New York, December 19, 1846.

The Ladies' Repository has it in their September 1865 issue (on p.176). The 22 February 1868 Once A Week (also p.176) wonders who the author was. Joseph Hodges Choate used it in his 22 December 1880 speech (The Pilgrim Mothers), which may have helped propel it into the next century.

We have a winner

I wrote my first blog entry here on 31 December 2010. On 18 January 2011, I wondered how long it would take to get my first comment. That comment came today! Total elapsed time: 451 days, 13 hours, 50 minutes.

Grammatical Tautology.

I’ll prove the word that I’ve made my theme,
Is that that may be doubled without blame ;
And that that that, thus trebled, I may use,
And that that THAT that critics may abuse,
May be correct. Farther—the dons to bother—
Five THATs may closely follow one another !
For be it known that we may safely write
Or say, that that THAT that that man wrote was right :
Nay, e’en, that that THAT that THAT that followed ;
And that that THAT (that that THAT that began)
Repeated seven times is right !—Deny’t who can.

Scientific American: New York, November 28, 1846.

cf. That.

Plocondragobbleiferous.

In a descriptive article, now going the rounds, the following high flown sentence occurs : “Through the mountain gorges stray the sullen bear and tawny moose, while the beautiful deer feeds along the solitary waters, and the treacherous panther screams in the tangled thicket.”

Scientific American: New York, November 6, 1846.

Old jokes

... Being already old when they were published 165+ years ago! I endeavoured to make the transcription very accurate, so if you detect typos you might want to check the original pdfs to verify that these are indeed sics. I did number the jokes (there are 63 altogether) so that any particular one may be referenced thereby. Some of the humour may well escape the average person at first reading. Some of it may even escape a more concerted effort at understanding. Some of it is no longer funny.

iBooks

I had a scare later in the day as my iBooks app began crashing repeatedly at startup. There are a number of forums on the 'net dealing with the issue and, sadly, Apple has been unable to fix things in the good long while that folk have been complaining about it. I was afraid to delete (and replace) the app because I thought that that might delete my 3246 pdfs as well, but that turned out not to be so.

iPad

As suggested here on February 15, my new Apple TV and iPad arrived on Wednesday (five weeks after my suggestion), 47 minutes apart: Apple had promised differing arrival dates and the items were shipped separately (using different carriers). Catherine and I were on our way home from Long Point at the time, so John (and Alice) did the receiving honours.

The iPad was remarkably easy to set up: I had envisioned some networking issues since my primary home network is ethernet and the iPad is WiFi, but that was not to be. More difficult proved to be the transfer of my 3246 Scientific American Weekly pdfs to it (it took a full night and day) but by last night it was good to go. Remarkably, iBooks won't keep the visual-bookshelf in alphabetical order (the list-display does) which suggests the developers never imagined someone keeping thousands of documents on the tablet.

I'm having fun exploring the apps. They are all free so far but that will change soon enough. Curious about my iPad's navigational ability, I made (using Trails Lite) a drunkard's around-the-block walk: Apparently I have crowd-sourced WiFi positioning only, not true GPS.

Happy trails to you

One of my current preoccupations is the extension of an idea that Eric Angelini mentioned to Sequence Fanatics eleven days ago. I wondered what would happen if we allowed the "digit trail" of a negative number to be the negatives of that number's digits. For starting numbers greater than ten, this had the resulting sequence oscillate between negative and positive territory, with each "run" taking another shot at hitting zero. The number of steps needed to get to the first zero is A208059. I subsequently extended the concept to other bases. Eric did a nice job of summarizing (in French) all of this.

Apple TV

No, not the television that Apple will introduce later this year but the 720p digital media receiver that I purchased, four weeks ago, along with a fifth-generation AirPort Extreme transmitter. The idea was to allow my new television access to the many movies and TV shows I'd amassed on my computer, without the painfully-slow process of putting them on those USB flash (thumb) drives that I acquired back then. (In retrospect, I shouldn't have bought those two extra 128GB ones.)

The problem was that the seven-and-a-half-year-old wireless card in my eight-and-a-half-year-old Power Mac G5 (Dual 2GHz) wasn't up to speed and, as a result, I was encountering fatal errors watching my movies. Thankfully, the Apple-TV receiver remembered where I left off, but it was annoying at best and unwatchable at worst.

So, yesterday, I purchased a 100-foot ethernet cable (75-foot was all I needed, but Tiger Direct didn't have 'em) to bridge the gap between the diametrically-opposite corners of our main floor. I then spent the better part of half a day (until the wee hours of this morning) configuring my Local Area Network so that the Apple TV and Catherine's iMac (upstairs) were getting internet while my chesswanks.com domain was still pointing to my computer. It shouldn't have been that difficult.

Apple TV will likely get updated next month, which is fine: I'm all in. And I will surely complement my now-enhanced LAN with an iPad 3!

A061205 quintuples, anyone?

One month ago, Franklin T. Adams-Watters asked about numbers that occur more than twice in A061205. The result was A203924, to which, yesterday, I added a link to my augmented table of 21313 terms. The majority of these are the third and fourth terms of A061205 quadruples: 101556 being the smallest, appearing at positions 156, 273, 372, and 651. There are 10554 quadruples in my less-than-ten-million position search-range, so these account for 21108 of the entries. The remaining 205 are taken from 67 A061205 triples, 24 sextuples, and 7 octuples.

A solution may be said to be "trivial" if all of its position numbers end in zero. (A non-trivial solution allows for an infinite number of trivial ones by multiplying all of its position numbers by the same power of ten.) After looking at the 40 non-trivial A061205 triples in my table, I conjectured that an odd-tuple exists if the product of a number multiplied by its reversal is either the square of a palindrome or, less frequently, the square of ten times a palindrome.

This insight allowed me to create a table of A061205 triples well beyond my original search range and held out the hope of finding a quintuple, if ever the palindrome could be got at in more than one way. Alas, my program is still considerably brute-force-ish: It searches for a palindrome in the square root of a number multiplied by its reversal. It might well be more efficient doing this the other way 'round.

Saving grace

I (finally) got my big-screen TV last week. I had hoped to have an over-the-air antenna attached to it so that I could watch HD without having to engage my evil Rogers cable. But it was not to be. I tried attaching one of my hard-drive docks to the USB port on the TV but it didn't recognize it. So today I bought a 64GB Lexar flash drive from FutureShop and it saw that just fine: The saving grace! It worked so well that I just ordered two more (128GB each) flash drives from Amazon. The second movie I watched was Lola rennt (1998), at a paltry 368 lines of resolution — but at least the subtitle file had been finely honed by yours truly. The picture shows a scene from the first movie that I watched.