Monthly Archives: April 2013

Vibrancy and Vileness

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Every so often you come across a news-story that isn’t just horrifying in itself but offers a sickening glimpse into the wilful neglect and toxicity of a so-called “civilized” state and its so-called “justice” system. Here’s a story like that from Scandinavia:

Rapist is sentenced to six-and-a-half years in prison

The Iraqi man (35) arrived in Norway in 2003. Now he has been convicted of sexual assault twice. The 35-year-old Iraqi has now been sentenced to six-and-a-half years in prison and ordered to pay NoK 300,000 [$52,000/£34,000] in damages after he was arrested for participating in a gang rape in Slottsparken [the park surrounding the Royal Palace in Oslo] in October 2011. The 35-year-old also committed a particularly degrading rape at Rådhusplassen [the town square] in November 2005. On that occasion he raped a 27-year-old woman behind some pallets with granite slabs. When the victim resisted, the man put his hand over her mouth and nose and told her that he would kill her.

The woman who was raped in Slottsparken told police that she was raped by several men and that she feared that she would be killed. She is unsure of how many men who raped her, but she knows that none of the rapists used condoms. As a result she was given HIV-prevention drugs and pregnancy-termination drugs. The relationship with her fiancé came to an end and she attempted to commit suicide after the ordeal. Today she is afraid to meet men who look foreign.

(Translation of Aftenpost story, “Seks og et halvt års fengsel for voldtektsmann”, 2nd April, 2013)

But “horrifying” is perhaps understating it. I’m left shaking my head in disgust and asking one urgent question: Why, in the name of decency and justice, was this obnoxious woman not prosecuted and punished severely for her blatant auto-incitement to racial hatred and xenophobia / allophobia? Her wilfully selfish attitude reeks of toxic white privilege and obdurate refusal to sensitively engage issues around the Other. Shame on you, Norway, for creating a society in which such corrosive and egocentric individuals can exist. To flush their hateful ideology from your so-called “nation”, I suggest that you immediately double immigration from Iraq – and go on doubling it for as long as it takes. And double immigration from Somalia, Haïti and the Congo too. Until you do that, you can count yourself a thoroughly failed state.

A Slap on the Wrist — original translation, which is adapted slightly above

Sumbertime Views

by in 666, Digit-sums, Mathematics, Number of the Beast and tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Like 666 (see Revelation 13:18), 153 (see John 21:11) appears in the Bible. And perhaps for the same reason: because it is the sum of successive integers. 153 = 1+2+3+…+17 = Σ(17), just as 666 = Σ(36). So both numbers are sum-numbers or sumbers. But 153 has other interesting properties, including one that can’t have been known in Biblical times, because numbers weren’t represented in the right way. It’s also the sum of the cubes of its digits: 153 = 1^3 + 5^3 + 3^3 = 1 + 125 + 27. So 153 is a cube-sumber or 3-sumber. The other 3-sumbers are 370, 371 and 407. There are 4-sumbers too, like 1,634 = 1^4 + 6^4 + 3^4 + 4^4, and 5-sumbers, like 194,979 = 1^5 + 9^5 + 4^5 + 9^5 + 7^5 + 9^5, and 6-sumbers, like 548,834 = 5^6 + 4^6 + 8^6 + 8^6 + 3^6 + 4^6.

But there are no 2-sumbers, or numbers that are the sum of the squares of their digits. It doesn’t take long to confirm this, because numbers above a certain size can’t be 2-sumbers. 9^2 + 9^2 = 162, but 9^2 + 9^2 + 9^2 = 243. So 2-sumbers can’t exist above 99 and if you search that high you’ll find that they don’t exist at all. At least not in this house, but they do exist in the houses next door. Base 10 yields nothing, so what about base 9?

4^2 + 5^2 = 45[9] = 41[10]
5^2 + 5^2 = 55[9] = 50

And base 11?

5^2 + 6^2 = 56[11] = 61[10]
6^2 + 6^2 = 66[11] = 72

This happens because odd bases always yield a pair of 2-sumbers whose second digit is one more than half the base and whose first digit is the same or one less. See above (and the appendix). Such a pair is found among the 14 sumbers of base 47, which is the best total till base 157 and its 22 sumbers. Here are the 2-sumbers for base 47:

2^2 + 10^2 = 104
3^2 + 12^2 = 153
5^2 + 15^2 = 250
9^2 + 19^2 = 442
12^2 + 21^2 = 585
14^2 + 22^2 = 680
23^2 + 24^2 = 1,105
24^2 + 24^2 = 1,152
33^2 + 22^2 = 1,573
35^2 + 21^2 = 1,666
38^2 + 19^2 = 1,805
42^2 + 15^2 = 1,989
44^2 + 12^2 = 2,080
45^2 + 10^2 = 2,125

As the progressive records for 2-sumber-totals are set, subsequent bases seem to either match or surpass them, except in three cases below base 450:

2 in base 5
4 in base 7
6 in base 13
10 in base 43
14 in base 47
22 in base 157
8 in base 182*
16 in base 268*
30 in base 307
18 in base 443*

Totals for sums of squares in bases 4 to 450

Totals for sums-of–squares in bases 4 to 450 (click for larger image)

Appendix: Odd Bases and 2-sumbers

Take an even number and half of that even number: say 12 and 6. 12 x 6 = 11 x 6 + 6. Further, 12 x 6 = 2 x 6 x 6 = 2 x 6^2 = 6^2 + 6^2. Accordingly, 66[11] = 6 x 11 + 6 = 12 x 6 = 6^2 + 6^2. So 66 in base 11 is a 2-sumber. Similar reasoning applies to every other odd base except base-3 [update: wrong!]. Now, take 12 x 5 = 2 x 6 x 5 = 2 x (5×5 + 5) = 5^2+5 + 5^5+5 = 5^5 + 5^5+2×5. Further, 5^5+2×5 = (5+1)(5+1) – 1 = 6^2 – 1. Accordingly, 56[11] = 11×5 + 6 = 12×5 + 1 = 5^2 + 6^2. Again, similar reasoning applies to every other odd base except base-3 [update: no — 1^2 + 2^2 = 12[3] = 5; 2^2 + 2^2 = 22[3] = 8]. This means that every odd base b, except base-3, will supply a pair of 2-sumbers with digits [d-1][d] and [d][d], where d = (b + 1) / 2.