Sunday, July 31, 2022

Bodie's weight

click to enlarge

The vertical scale is kilograms. Red dots are vet readings. Blue dots are home (bathroom scale) readings. I don't really trust the bathroom scale to be accurate but it will do. We just want to be cognizant of inordinate weight gain. So every two weeks Bodie looks forward to jumping into my arms. Unfortunately, the process also monitors my personal weight gain.

Saturday, July 30, 2022

Aerial action


Just beyond my neighbour's yard, a northern mockingbird lets a hawk know it's not welcome.

Friday, July 29, 2022

Don't it always seem to go ...?


It has been a year since I last received delivery of a couple of big bottles of Welch's grape juice. I should have ordered more in the following months! By the time I did, they were out of stock. I can't tell if the supply shortage is temporary or permanent.

Thursday, July 28, 2022

Cycles in Éric Angelini's sum-and-erase

Éric's article on sum-and-erase is here. I wanted a place where I could post known cycles, so I will do that in this listing [index.  name = c&start-string  (cycle length)  {precursors}]:

0.  c0  (1)  {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 00, 01, 02, 03, 05, 06, 07, 08, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, ...}

1.  c3374  (583792)  {04, 09, 25, 31, 63, 67, 69, 77, 92, 96, 99, 023, 027, 031, 040, 042, 044, 049, 067, 074, 075, 081, 082, 090, 093, 099, 105, 109, 116, 133, 138, 148, 152, 161, 162, 163, 168, 174, 194, 197, 198, 206, 216, 253, 257, 258, 285, 307, 314, 327, 352, 370, 382, 389, 398, 422, 423, 430, 463, 477, 482, 483, 496, 503, 521, 543, 544, 568, 581, 582, 590, 592, 599, 604, 605, 610, 613, 630, 635, 639, 645, 656, 665, 667, 668, 676, 681, 682, 685, 686, 688, 708, 722, 736, 737, 742, 758, 766, 773, 782, 801, 809, 810, 814, 821, 839, 841, 848, 849, 856, 858, 867, 875, 884, 885, 894, 902, 906, 923, 932, 944, 958, 977, 982, 988, 0119, 0135, 0144, 0147, 0152, 0163, 0166, 0176, 0191, 0199, 0203, 0207, 0216, 0230, 0235, 0244, 0253, 0256, 0259, 0267, 0270, 0275, 0279, 0299, 0301, 0310, 0314, 0317, 0333, 0349, 0361, 0375, 0378, 0385, 0387, 0400, 0402, 0404, 0409, 0420, 0426, 0429, 0440, 0448, 0482, 0484, 0486, 0490, 0498, 0521, 0539, 0559, 0562, 0578, 0592, 0595, 0607, 0619, 0645, 0656, 0658, 0665, 0668, 0670, 0671, 0673, 0686, 0698, 0704, 0705, 0713, 0716, 0735, 0736, 0738, 0740, 0750, 0767, 0768, 0776, 0794, 0801, 0802, 0810, 0813, 0814, 0817, 0819, 0820, 0824, 0829, 0831, 0847, 0855, 0856, 0866, 0867, 0900, 0903, 0909, 0911, 0916, 0919, 0925, 0929, 0930, 0938, 0957, 0958, 0982, 0990, 0991, 0992, 0999, 1005, 1009, 1016, 1019, 1027, 1050, 1056, 1059, 1061, 1062, 1082, 1090, 1091, 1099, 1106, 1109, 1119, 1120, 1163, 1168, 1191, 1192, 1201, 1210, 1222, 1238, 1239, 1250, 1253, 1254, 1264, 1268, 1277, 1285, 1289, 1299, 1307, 1327, 1333, 1335, 1337, 1339, 1352, 1353, 1364, 1365, 1370, 1373, 1376, 1378, 1393, 1396, 1422, 1495, 1520, 1526, 1528, 1530, 1545, 1554, 1557, 1559, 1566, 1575, 1578, 1593, 1595, 1604, 1613, 1618, 1628, 1629, 1630, 1631, 1637, 1648, 1649, 1668, 1679, 1681, 1685, 1686, 1724, 1728, 1729, 1739, 1754, 1760, 1762, 1767, 1776, 1792, 1793, 1794, 1823, 1825, 1832, 1840, 1843, 1853, 1866, 1867, 1894, 1904, 1907, 1908, 1911, 1912, 1921, 1923, 1929, 1933, 1934, 1938, 1970, 1987, 1992, 2006, 2019, 2028, 2047, 2048, 2053, 2058, 2060, 2068, 2074, 2082, 2085, 2091, 2094, 2099, 2109, 2126, 2133, 2134, 2157, 2162, 2163, 2168, 2169, 2173, 2188, 2194, 2208, 2216, 2222, 2230, 2234, 2249, 2254, 2264, 2280, 2291, 2295, 2299, 2302, 2307, 2314, 2320, 2324, 2342, 2344, 2347, 2348, 2351, 2357, 2358, 2361, 2370, 2384, 2389, 2391, 2394, 2395, 2398, 2413, 2414, 2416, 2418, 2429, 2441, 2458, 2471, 2480, 2481, 2492, 2503, 2524, 2531, 2542, 2545, 2554, 2556, 2565, 2576, 2584, 2604, 2624, 2642, 2643, 2644, 2655, 2668, 2679, 2686, 2687, 2704, 2740, 2757, 2758, 2763, 2764, 2775, 2777, 2784, 2786, 2793, 2802, 2805, 2818, 2820, 2837, 2839, 2843, 2848, 2850, 2856, 2875, 2881, 2884, 2897, 2904, 2906, 2912, 2917, 2918, 2921, 2925, 2929, 2948, 2951, 2952, 2964, 2992, 3007, 3019, 3033, 3054, 3057, 3061, 3070, 3071, 3089, 3091, 3095, 3098, 3109, 3117, 3125, 3129, 3136, 3140, 3146, 3148, 3163, 3164, 3167, 3171, 3176, 3177, 3199, 3213, 3218, 3231, 3237, 3244, 3254, 3256, 3273, 3287, 3298, 3299, 3303, 3316, 3321, 3327, 3330, 3335, 3352, 3353, 3371, 3374, 3387, 3396, 3398, 3457, 3462, 3476, 3502, 3509, 3512, 3515, 3523, 3528, 3532, 3533, 3546, 3551, 3564, 3578, 3604, 3611, 3612, 3619, 3644, 3654, 3655, 3668, 3675, 3686, 3687, 3700, 3701, 3707, 3709, 3713, 3724, 3731, 3734, 3743, 3747, 3757, 3767, 3770, 3774, 3775, 3776, 3789, 3792, 3794, 3804, 3809, 3812, 3814, 3821, 3837, 3851, 3855, 3856, 3858, 3859, 3866, 3872, 3873, 3885, 3888, 3896, 3905, 3911, 3922, 3929, 3936, 3938, 3942, 3950, 3963, 3967, 3969, 3972, 3983, 3986, 3989, 3992, 3996, 3998, 4019, 4023, 4035, 4053, 4063, 4069, 4091, 4096, 4097, 4099, 4102, 4109, 4123, 4139, 4146, 4155, 4163, 4164, 4176, 4196, 4202, 4218, 4220, 4228, 4235, 4239, 4253, 4282, 4283, 4299, 4300, 4301, 4307, 4347, 4348, 4349, 4361, 4368, 4370, 4371, 4374, 4376, 4378, 4380, 4381, 4384, 4387, 4394, 4399, 4416, 4437, 4438, 4439, 4452, 4458, 4461, 4483, 4491, 4492, 4506, 4516, 4524, 4527, 4531, 4542, 4548, 4578, 4584, 4598, 4612, 4614, 4616, 4625, 4627, 4628, 4641, 4661, 4668, 4671, 4686, 4698, 4701, 4710, 4731, 4767, 4776, 4793, 4796, 4815, 4826, 4834, 4843, 4850, 4866, 4888, 4890, 4911, 4914, 4922, 4924, 4929, 4935, 4938, 4939, 4941, 4942, 4959, 4960, 4970, 4992, 4993, 4995, 5003, 5019, 5030, 5031, 5033, 5034, 5035, 5038, 5039, 5053, 5063, 5067, 5088, 5091, 5109, 5113, 5131, 5134, 5142, 5163, 5166, 5176, 5186, 5196, 5198, 5218, 5236, 5244, 5249, 5263, 5264, 5274, 5286, 5296, 5299, 5307, 5333, 5339, 5361, 5366, 5370, 5371, 5384, 5388, 5391, 5393, 5428, 5429, 5439, 5446, 5448, 5455, 5456, 5464, 5465, 5483, 5484, 5487, 5493, 5496, 5503, 5545, 5546, 5554, 5555, 5562, 5566, 5578, 5582, 5584, 5604, 5616, 5625, 5630, 5637, 5648, 5652, 5656, 5661, 5665, 5668, 5686, 5694, 5720, 5742, 5758, 5760, 5761, 5763, 5767, 5776, 5779, 5781, 5782, 5785, 5794, 5797, 5810, 5814, 5825, 5827, 5832, 5845, 5852, 5854, 5863, 5866, 5870, 5871, 5900, 5929, 5930, 5937, 5938, 5964, 5979, 5982, 5992, 5997, 6004, 6005, 6014, 6019, 6021, 6040, 6041, 6050, 6056, 6065, 6078, 6091, 6099, 6100, 6104, 6106, 6107, 6109, 6130, 6134, 6155, 6160, 6174, 6177, 6225, 6235, 6236, 6237, 6244, 6252, 6253, 6263, 6268, 6277, 6286, 6287, 6288, 6298, 6299, 6300, 6307, 6309, 6318, 6321, 6351, 6370, 6372, 6377, 6379, 6404, 6405, 6416, 6417, 6429, 6430, 6440, 6453, 6461, 6473, 6485, 6489, 6490, 6499, 6545, 6554, 6559, 6569, 6572, 6578, 6588, 6595, 6596, 6605, 6610, 6623, 6628, 6641, 6659, 6680, 6682, 6691, 6698, 6705, 6713, 6714, 6718, 6723, 6743, 6753, 6781, 6794, 6803, 6804, 6806, 6812, 6823, 6826, 6830, 6834, 6837, 6852, 6854, 6860, 6862, 6873, 6894, 6899, 6904, 6913, 6915, 6916, 6922, 6923, 6929, 6938, 6942, 6949, 6961, 6968, 6975, 6986, 6992, 6994, 6999, 7008, 7019, 7035, 7037, 7056, 7067, 7073, 7076, 7078, 7080, 7084, 7087, 7091, 7099, 7102, 7109, 7147, 7150, 7158, 7163, 7174, 7178, 7187, 7195, 7205, 7227, 7230, 7235, 7240, 7244, 7253, 7260, 7263, 7272, 7279, 7288, 7294, 7297, 7299, 7305, 7318, 7340, 7358, 7361, 7365, 7366, 7377, 7385, 7458, 7490, 7493, 7495, 7499, 7502, 7508, 7516, 7517, 7526, 7529, 7530, 7542, 7547, 7561, 7563, 7571, 7574, 7578, 7581, 7587, 7604, 7611, 7614, 7620, 7621, 7626, 7627, 7635, 7655, 7657, 7662, 7668, 7672, 7675, 7680, 7682, 7686, 7703, 7706, 7708, 7714, 7718, 7722, 7729, 7737, 7751, 7754, 7758, 7762, 7765, 7773, 7798, 7824, 7825, 7833, 7841, 7849, 7860, 7863, 7866, 7892, 7904, 7909, 7912, 7920, 7929, 7931, 7936, 7938, 7940, 7941, 7942, 7945, 7950, 7958, 7978, 7987, 7990, 7992, 7999, 8001, 8009, 8010, 8012, 8013, 8017, 8019, 8024, 8029, 8031, 8041, 8047, 8053, 8067, 8090, 8091, 8100, 8108, 8109, 8129, 8143, 8152, 8156, 8160, 8162, 8163, 8173, 8179, 8180, 8204, 8224, 8229, 8234, 8235, 8239, 8242, 8244, 8253, 8256, 8279, 8292, 8299, 8307, 8313, 8323, 8324, 8331, 8332, 8341, 8344, 8358, 8361, 8369, 8370, 8374, 8385, 8391, 8401, 8402, 8403, 8407, 8408, 8422, 8436, 8446, 8452, 8456, 8464, 8480, 8492, 8506, 8517, 8518, 8527, 8531, 8534, 8537, 8561, 8562, 8566, 8581, 8604, 8626, 8633, 8644, 8647, 8657, 8662, 8669, 8672, 8679, 8692, 8696, 8707, 8716, 8723, 8724, 8726, 8727, 8731, 8736, 8742, 8765, 8767, 8770, 8772, 8776, 8788, 8791, 8794, 8810, 8835, 8840, 8851, 8878, 8887, 8891, 8893, 8905, 8918, 8929, 8938, 8944, 8952, 8961, 8976, 8981, 8983, 8992, 9002, 9006, 9017, 9020, 9025, 9029, 9038, 9044, 9058, 9060, 9077, 9088, 9092, 9104, 9105, 9128, 9143, 9144, 9149, 9163, 9178, 9180, 9182, 9189, 9194, 9198, 9211, 9227, 9229, 9235, 9244, 9247, 9253, 9272, 9284, 9288, 9292, 9302, 9307, 9336, 9347, 9361, 9362, 9363, 9370, 9377, 9379, 9382, 9389, 9397, 9398, 9407, 9416, 9435, 9444, 9462, 9468, 9475, 9478, 9483, 9508, 9516, 9518, 9556, 9565, 9567, 9568, 9578, 9583, 9604, 9615, 9617, 9618, 9626, 9633, 9641, 9645, 9658, 9662, 9668, 9686, 9688, 9689, 9698, 9704, 9707, 9709, 9710, 9749, 9750, 9761, 9767, 9770, 9776, 9790, 9794, 9801, 9866, 9870, 9902, 9914, 9918, 9922, 9937, 9938, 9968, 9970, 9974}

2.  c083433  (120621)  {092, 245, 351, 395, 413, 433, 468, 571, 802, 0382, 0479, 0588, 0594, 0691, 0848, 0884, 0902, 0920, 1038, 1142, 1170, 1369, 1380, 1412, 1421, 1433, 1479, 1482, 1560, 1584, 1645, 1666, 1701, 1710, 1802, 1848, 1884, 1986, 2096, 2148, 2235, 2251, 2325, 2352, 2450, 2477, 2512, 2521, 2555, 2601, 2634, 2649, 2688, 2761, 2955, 2970, 2999, 3358, 3479, 3510, 3519, 3538, 3544, 3583, 3699, 3702, 3769, 3779, 3797, 3802, 3848, 3884, 3917, 3949, 3981, 3994, 4012, 4103, 4112, 4121, 4122, 4138, 4160, 4165, 4183, 4286, 4650, 4707, 4770, 4790, 4792, 4802, 4825, 4870, 4909, 4933, 4990, 5078, 5108, 5277, 5427, 5479, 5602, 5786, 5802, 5808, 5823, 5848, 5880, 5884, 6335, 6353, 6385, 6411, 6456, 6465, 6479, 6491, 6591, 6645, 6669, 6694, 6696, 6802, 6848, 6884, 6946, 6964, 6966, 7014, 7098, 7228, 7282, 7291, 7444, 7579, 7588, 7597, 7759, 7802, 7816, 7848, 7884, 7903, 7946, 8002, 8020, 8021, 8288, 8376, 8428, 8479, 8482, 8708, 8780, 8828, 8842, 8870, 8882, 9134, 9168, 9273, 9277, 9515, 9551, 9581, 9802, 9806, 9848, 9884, 9999}

3.  c222227222772202078  (1723)  {695, 825, 905, 0655, 0857, 0864, 1385, 1857, 2695, 3078, 3285, 3857, 4189, 4857, 5778, 5787, 6054, 6504, 6685, 6856, 6857, 6865, 7864, 8265, 8459, 8572, 9005, 9050, 9857}

4.  c332  (14072)  {323, 332, 3238, 3283, 3328, 5133, 7132}

5.  c3933  (10538)  {333, 3339, 3393, 3933}

6.  c5464644657500000011711019071641751  (49)  {243, 2439, 6782}

Roughly, in order of precursor frequency. Strictly speaking, the bold numbers are not precursors (to cycles) but, rather, cycle terms themselves. I include them for the sake of completeness. Are there any more cycles?

Update: In a 14 Sep 2023 video seminar, Neil Sloane @38:33 mentions Michael Branicky finding (in my notation) c00020203143 (20173) and c00660657510634435617071915 (46), precursors not mentioned.

Saturday, July 23, 2022

My tired lip, Angela

I don't recall when exactly I read Martin Gardner's article on mnemonics [Scientific American, October 1957; 'The Scientific American Book of Mathematical Puzzles & Diversions', 1959; reprinted as 'Hexaflexagons and Other Mathematical Diversions', 1988] but it was likely sixty years ago when I lived on Claremont Street and came across the 1959 book on puzzles and diversions, borrowed from what must have been the 'Boys & Girls Library' at Manning Ave. & Robinson St. I didn't get into Martin Gardner and Scientific American as an obsession until a few years later, December 1967 being my first store-purchased issue.

I was reminded of this by Futility Closet's recent 'Words and Numbers' which adjusts slightly Gardner's version (above) and gets into some π mnemonics. I had myself created one of these back then: "My tired lip, Angela, my lip." Twelve digits. Not too shabby and I recalled it after all these years, although I did attempt at first to place the 'tired' in front of the second 'lip'. I also remembered that the final p=9 wasn't actually π's twelfth digit but a rounding-up approximation. There is a much more intensive explanation/application of this particular use of mnemonics, here.

Saturday, July 16, 2022

The fire at #3

1:25 AM (click to enlarge)

aftermath, in the light of day

Police said that this was arson, by a woman walking south on (very nearby) Weston Road.

Friday, July 01, 2022

The Townsend fire

Allan Reed and Frances Montgomery were married in 1937 in a Goderich Presbyterian church. Their third child, Eleanor, was born 8 January 1944 in nearby Dungannon, having been preceded by her siblings James and Jewel. A good Christian upbringing was no doubt an integral part of all three children's lives. Nevertheless, Eleanor found herself pregnant at age 17. She was Mrs. Pat Moorehead a decade later when Canadian Queen of the Fiddle was released. Eleanor's daughter, Catherine, was soon to be part of Eleanor's circa-1973 marriage to Graham Townsend, musician extraordinaire, and the 1975 birth of a half-brother, Graham (Gray) Jr.


The young Gray picture (above) is taken from a YouTube video where he is wearing dark glasses. It is well known that Graham Sr. was visually impaired from birth. Not well known is the fact that Graham's father, Fred Townsend, also struggled with poor eyesight in his youth and, by the time he reached his twenties, became convinced that he was going blind. In the 1901 U.K. census, Fred's mother, Alice Townsend (1878-1962), as well as Alice's mother, Dinah, are both described as "partially blind". Dinah's husband, William Townsend (1833-1921) is described as being "blind since 1864".

Gray at age 14

In 1984, Catherine had her first child, making Eleanor a grandmother. In 1991, Eleanor's mother, Frances, died at the age of 76. A year or so later, the Townsends moved to Barrie. In 1993, Catherine had a second child, Isabella, by a second-marriage to a Mr. Monti, who is otherwise unknown to me.

Gray at age 19

On 25 October 1998, at the Orangeville Convention Centre, hundreds of musicians and fans turned out to pay tribute to Graham and Eleanor Townsend. None too soon. On 3 December 1998, Graham Sr. died at age 56 from the effects of colon cancer after struggling with it, stated one source, for two years. According to Donna Douglas, Graham "had sought out alternative therapies", somewhat surprisingly, "with the financial help of friends in the music industry". On 22 December 1998, Eleanor's father, Allan Reed, died at age 72. A week or so later, Catherine Monti is preparing to give birth to her third child. Her older offspring "is away at camp" (possibly a mental health treatment facility) and the younger one, Isabella, is with gran'ma Eleanor. Perhaps Mr. Monti drove Isabella to the Townsend home in Barrie. Perhaps Eleanor picked her up in Dungannon.

In the wee hours of 31 December 1998, a fierce fire gutted the Townsend home at 56 Springdale Drive. The remains of 54-year-old Eleanor and 5-year-old Isabella were found in the living room, dead (it was determined later) from smoke inhalation. 23-year-old Gray managed to escape. "Isabella Johnson, a neighbour and friend who has lived next door since the Townsends moved in about six years ago, said she was awakened by Gray's yelling. She then heard a 'popping' noise as the fire engulfed the home..." [Montreal Gazette: 2 January 1999]. Gray ended up in the hospital with undisclosed injuries. It seems plausible that he had received burns. But how exactly, I have not come across anyone mentioning.

After an investigation by Barrie police and the Fire Marshal's Office, it was "revealed the fire was deliberately set by [Eleanor Townsend] in her vehicle which was parked in the garage" [Toronto Star: 16 March 1999]. "She was distraught over the death of her husband Graham, ... She was on prescription medication at the time of the fire, Detective Bryan Shultz said in a news release." As previously explained, the death of her husband was not a surprise and there is evidence that she was actually coping rather well: "Following the death of her husband, [Eleanor] Townsend said in an interview last month that she planned to work with her son at getting her late husband's works recorded" [Montreal Gazette: 2 January 1999]. The bit about being "on prescription medication" strikes me as not being obviously relevant. They should perhaps have stated the kind of prescription and how much of it was in her system. Instead, for a "fire [that] was purposely set in the seat of a car, parked in the garage of the house" [The Globe and Mail: 17 March 1999], what might have been her motive? Would not Eleanor taking care of her granddaughter and (presumably) looking forward to another grandchild have been important factors to consider? The authorities surely must have had additional evidence that implicated her.

It appears that they did. The official opinion may have had something to do with statements made by Gray: "'Mum was really not well and I was trying to keep things together when dad died', said her son, ..." [The Globe and Mail: 17 March 1999]. In fact, a family friend, Steve Fruitman, described Gray as being "terribly despondent over his father's death" [Gerry Taylor, New Brunswick Telegraph Journal: 5 January 1999], a situation not unlike the one Gray ascribes to his mother. Since it was thought important to point out that Eleanor was on medication, what about Gray? When he was in the hospital after the fire, were blood tests performed to examine his drug and alcohol levels?

Barrie fire chief Jim Lemieux had suggested that "Eleanor Townsend at first escaped the fire, but it seems she realized Isabella was trapped inside 'and went right back in'" [Toronto Star: 1 January 1999]. This is echoed in Taylor's Telegraph Journal article, but it included Gray in the escape: "The fire, of undetermined origin, was well advanced before Eleanor and her 23-year-old son, Gray, awakened and rushed from the house. Outside, Eleanor remembered that her five-year-old granddaughter was still asleep in the house and rushed back inside where she perished with the child." This information could only have come from Gray.

Ten weeks later: "[Gray] lived with [Eleanor Townsend] and she alerted him to the fire. He escorted his mother and his niece Isabella on to the deck at the back of the house. At some point, after being separated from her son, [Eleanor] Townsend and Isabella re-entered the home ..." [Toronto Star: 16 March 1999]. It appears that the story had changed. Neither version addresses how Gray might have sustained injuries but at least the later account has him taking charge and implies that Eleanor was aware of the fire before he was. "Family members said they believe Ms. Townsend went back into the house to look for the family dog and the girl followed her. The dog died in the fire." [The Globe and Mail: 17 March 1999]. That would have been Eleanor's brother, Jim Reed, and and his then-wife, Marina, showing that they were not prepared to doubt Gray's retelling of his escape from the fire.

A comment from someone Gray was dating "in the early 90s" [taken from the Gray-at-age-19 video] suggests that he "was patient, charming, disciplined and loved to teach. He also ran 5 miles a day every morning!" Perhaps all that ended with the move to Barrie. A new home, perhaps new friends. Had Gray finished high school yet? Was he, like his grandfather, struggling with increasingly bad eyesight and was, as a result, unable to get a driver's license? Did he resent his mother, Eleanor, being able to drive a vehicle at her whim, spending time with her daughter and grandchildren?

Gray died in 2003, presumably a short time after making available "a number of reel to reel tapes of material that Graham and Eleanor had taped on various occasions that were never released before" [Randy Morrison: liner notes on the 2004 album 'The Talented Townsends']. Somewhat remarkably (for an individual who is the product of musical royalty and is himself an entry in The Canadian Encyclopedia), I am not aware of anyone detailing anything concrete about his personal life after the fire or the circumstances of his death.

Update: Marlene Frost, my genealogy research partner, managed to acquire for me Randy Morrison's email. Randy kindly informed me that Gray died on the day of "New Year’s Eve of an overdose of pills and alcohol". That would have been the fifth anniversary of the day of the fire. And while Randy said that Gray's vision was fine (I had conjectured that Gray was going blind as a reason for some emotional turmoil that might have made him set fire to Eleanor's car), Randy understood Gray to have been bipolar: "Graham had to really keep a watch on him and after Graham died Gray was really lost and out of control."

Final thought: Graham Sr. had died. Presumably the Townsend estate now belonged to Eleanor. She may have had a will, or not. What happens to the estate after her death? She had two children, so maybe it was split between them. Or maybe Gray gets it all. One thing seems certain: Eleanor being named as the person who set the fire surely facilitated the transfer of insurance money for the burned-out house.