I wish someone would translate Lord of the Rings into English.
Monthly Archives: October 2014
Summus
I’m interested in digit-sums and in palindromic numbers. Looking at one, I found the other. It started like this: 9^2 = 81 and 9 = 8 + 1, so digitsum(9^1) = digitsum(9^2). I wondered how long such a sequence of powers could be (excluding powers of 10). I quickly found that the digit-sum of 468 is equal to the digit-sum of its square and cube:
digsum(468) = digsum(219024) = digsum(102503232)
But I couldn’t find any longer sequence, although plenty of other numbers are similar to 468:
digsum(585) = digsum(342225) = digsum(200201625)
digsum(4680) = digsum(21902400) = digsum(102503232000)
digsum(5850) = digsum(34222500) = digsum(200201625000)
digsum(5851) = digsum(34234201) = digsum(200304310051)
digsum(5868) = digsum(34433424) = digsum(202055332032)
digsum(28845) = digsum(832034025) = digsum(24000021451125) […]
digsum(589680) = digsum(347722502400) = digsum(205045005215232000)
What about other bases? First came this sequence:
digsum(2) = digsum(11) (base = 3) (highest power = 2)
Then these:
digsum(4) = digsum(22) = digsum(121) (b=7) (highest power = 3)
digsum(8) = digsum(44) = digsum(242) = digsum(1331) (b=15) (hp=4)
digsum([16]) = digsum(88) = digsum(484) = digsum(2662) = digsum(14641) (b=31) (hp=5)
The pattern continues (a number between square brackets represents a single digit in the base):
digsum([32]) = digsum([16][16]) = digsum(8[16]8) = digsum(4[12][12]4) = digsum(28[12]82) = digsum(15[10][10]51) (b=63) (hp=6)
digsum([64]) = digsum([32][32]) = digsum([16][32][16]) = digsum(8[24][24]8) = digsum(4[16][24][16]4) = digsum(2[10][20][20][10]2) = digsum(16[15][20][15]61) (b=127) (hp=7)
digsum([128]) = digsum([64][64]) = digsum([32][64][32]) = digsum([16][48][48][16]) = digsum(8[32][48][32]8) = digsum(4[20][40][40][20]4) = digsum(2[12][30][40][30][12]2) = digsum(17[21][35][35][21]71) (b=255) (hp=8)
digsum([256]) = digsum([128][128]) = digsum([64][128][64]) = digsum([32][96][96][32]) = digsum([16][64][96][64][16]) = digsum(8[40][80][80][40]8) = digsum(4[24][60][80][60][24]4) = digsum(2[14][42][70][70][42][14]2) = digsum(18[28][56][70][56][28]81) (b=511) (hp=9)
After this, I looked at sequences in which n(i) = n(i-1) + digitsum(n(i-1)). How long could digitsum(n(i)) be greater than or equal to digitsum(n(i-1))? In base 10, I found these sequences:
1 (digitsum=1) → 2 → 4 → 8 → 16 (sum=7) (count=4) (base=10)
9 → 18 (sum=9) → 27 (s=9) → 36 (s=9) → 45 (s=9) → 54 (s=9) → 63 (s=9) → 72 (s=9) → 81 (s=9) → 90 (s=9) → 99 (s=18) → 117 (s=9) (c=11) (b=10)
801 (s=9) → 810 (s=9) → 819 (s=18) → 837 (s=18) → 855 (s=18) → 873 (s=18) → 891 (s=18) → 909 (s=18) → 927 (s=18) → 945 (s=18) → 963 (s=18) → 981 (s=18) → 999 (s=27) → 1026 (s=9) (c=13)
Base 2 does better:
1 → 10 (s=1) → 11 (s=2) → 101 (s=2) → 111 (s=3) → 1010 (s=2) (c=5) (b=2)
16 = 10000 (s=1) → 10001 (s=2) → 10011 (s=3) → 10110 (s=3) → 11001 (s=3) → 11100 (s=3) → 11111 (s=5) → 100100 (s=2) (c=7) (b=2)
962 = 1111000010 (s=5) → 1111000111 (s=7) → 1111001110 (s=7) → 1111010101 (s=7) → 1111011100 (s=7) → 1111100011 (s=7) → 1111101010 (s=7) → 1111110001 (s=7) → 1111111000 (s=7) → 1111111111 (s=10) → 10000001001 (s=3) (c=10) (b=2)
524047 = 1111111111100001111 (s=15) → 1111111111100011110 (s=15) → 1111111111100101101 (s=15) → 1111111111100111100 (s=15) → 1111111111101001011 (s=15) → 1111111111101011010 (s=15) → 1111111111101101001(s=15) → 1111111111101111000 (s=15) → 1111111111110000111 (s=15) → 1111111111110010110 (s=15) → 1111111111110100101 (s=15) → 1111111111110110100 (s=15) → 1111111111111000011 (s=15) → 1111111111111010010 (s=15) → 1111111111111100001 (s=15) → 1111111111111110000 (s=15) → 1111111111111111111 (s=19) → 10000000000000010010 (s=3) (c=17) (b=2)
The best sequence I found in base 3 is shorter than in base 10, but there are more sequences:
1 → 2 → 11 (s=2) → 20 (s=2) → 22 (s=4) → 110 (s=2) (c=5) (b=3)
31 = 1011 (s=3) → 1021 (s=4) → 1102 (s=4) → 1120 (s=4) → 1201 (s=4) → 1212 (s=6) → 2002 (s=4) (c=6) (b=3)
54 = 2000 (s=2) → 2002 (s=4) → 2020 (s=4) → 2101 (s=4) → 2112 (s=6) → 2202 (s=6) → 2222 (s=8) → 10021(s=4) (c=7) (b=3)
432 = 121000 (s=4) → 121011 (s=6) → 121101 (s=6) → 121121 (s=8) → 121220 (s=8) → 122012 (s=8) → 122111 (s=8) → 122210 (s=8) → 200002 (s=4) (c=8) (b=3)
648 = 220000 (s=4) → 220011 (s=6) → 220101 (s=6) → 220121 (s=8) → 220220 (s=8) → 221012 (s=8) → 221111 (s=8) → 221210 (s=8) → 222002 (s=8) → 222101 (s=8) → 222200 (s=8) → 222222 (s=12) → 1000102 (s=4) (c=12) (b=3)
And what about sequences in which digitsum(n(i)) is always greater than digitsum(n(i-1))? Base 10 is disappointing:
1 → 2 → 4 → 8 → 16 (sum=7) (count=4) (base=10)
50 (s=5) → 55 (s=10) → 65 (s=11) → 76 (s=13) → 89 (s=17) → 106 (s=7) (c=5) (b=10)
Some other bases do better:
2 = 10 (s=1) → 11 (s=2) → 101 (s=2) (c=2) (b=2)
4 = 100 (s=1) → 101 (s=2) → 111 (s=3) → 1010 (s=2) (c=3) (b=2)
240 = 11110000 (s=4) → 11110100 (s=5) → 11111001 (s=6) → 11111111 (s=8) → 100000111 (s=4) (c=4) (b=2)
1 → 2 → 11 (s=2) (c=2) (b=3)
19 = 201 (s=3) → 211 (s=4) → 222 (s=6) → 1012 (s=4) (c=3) (b=3)
58999 = 2222221011 (s=15) → 2222221201 (s=16) → 2222222022 (s=18) → 2222222222 (s=20) → 10000000201 (s=4) (c=4) (b=3)
1 → 2 → 10 (s=1) (c=2) (b=4)
4 = 10 (s=1) → 11 (s=2) → 13 (s=4) → 23 (s=5) → 100 (s=1) (c=4) (b=4)
977 = 33101 (s=8) → 33121 (s=10) → 33203 (s=11) → 33232 (s=13) → 33323 (s=14) → 100021 (s=4) (c=5) (b=4)
1 → 2 → 4 → 13 (s=4) (c=3) (b=5)
105 = 410 (s=5) → 420 (s=6) → 431 (s=8) → 444 (s=12) → 1021 (s=4) (c=4) (b=5)
1 → 2 → 4 → 12 (s=3) (c=3) (b=6)
13 = 21 (s=3) → 24 (s=6) → 34 (s=7) → 45 (s=9) → 102 (s=3) (c=4) (b=6)
396 = 1500 (s=6) → 1510 (s=7) → 1521 (s=9) → 1534 (s=13) → 1555 (s=16) → 2023 (s=7) (c=5) (b=6)
1 → 2 → 4 → 11 (s=2) (c=3) (b=7)
121 = 232 (s=7) → 242 (s=8) → 253 (s=10) → 266 (s=14) → 316 (s=10) (c=4) (b=7)
205 = 412 (s=7) → 422 (s=8) → 433 (s=10) → 446 (s=14) → 466 (s=16) → 521 (s=8) (c=5) (b=7)
1 → 2 → 4 → 10 (s=1) (c=3) (b=8)
8 = 10 (s=1) → 11 (s=2) → 13 (s=4) → 17 (s=8) → 27 (s=9) → 40 (s=4) (c=5) (b=8)
323 = 503 (s=8) → 513 (s=9) → 524 (s=11) → 537 (s=15) → 556 (s=16) → 576 (s=18) → 620 (s=8) (c=6) (b=8)
1 → 2 → 4 → 8 → 17 (s=8) (c=4) (b=9)
6481 = 8801 (s=17) → 8820 (s=18) → 8840 (s=20) → 8862 (s=24) → 8888 (s=32) → 10034 (s=8) (c=5) (b=9)
1 → 2 → 4 → 8 → 16 (s=7) (c=4) (b=10)
50 (s=5) → 55 (s=10) → 65 (s=11) → 76 (s=13) → 89 (s=17) → 106 (s=7) (c=5) (b=10)
1 → 2 → 4 → 8 → 15 (s=6) (c=4) (b=11)
1013 = 841 (s=13) → 853 (s=16) → 868 (s=22) → 888 (s=24) → 8[10][10] (s=28) → 925 (s=16) (c=5) (b=11)
1 → 2 → 4 → 8 → 14 (s=5) (c=4) (b=12)
25 = 21 (s=3) → 24 (s=6) → 2[10] (s=12) → 3[10] (s=13) → 4[11] (s=15) → 62 (s=8) (c=5) (b=12)
1191 = 833 (s=14) → 845 (s=17) → 85[10] (s=23) → 879 (s=24) → 899 (s=26) → 8[11][11] (s=30) → 925 (s=16) (c=6) (b=12)
1 → 2 → 4 → 8 → 13 (s=4) (c=4) (b=13)
781 = 481 (s=13) → 491 (s=14) → 4[10]2 (s=16) → 4[11]5 (s=20) → 4[12][12] (s=28) → 521 (s=8) (c=5) (b=13)
19621 = 8[12]14 (s=25) → 8[12]33 (s=26) → 8[12]53 (s=28) → 8[12]75 (s=32) → 8[12]9[11] (s=40) → 8[12][12][12] (s=44) → 9034 (s=16) (c=6) (b=13)
1 → 2 → 4 → 8 → 12 (s=3) (c=4) (b=14)
72 = 52 (s=7) → 59 (s=14) → 69 (s=15) → 7[10] (s=17) → 8[13] (s=21) → [10]6 (s=16) (c=5) (b=14)
1275 = 671 (s=14) → 681 (s=15) → 692 (s=17) → 6[10]5 (s=21) → 6[11][12] (s=29) → 6[13][13] (s=32) → 723 (s=12) (c=6) (b=14)
19026 = 6[13]10 (s=20) → 6[13]26 (s=27) → 6[13]45 (s=28) → 6[13]65 (s=30) → 6[13]87 (s=34) → 6[13][10][13] (s=42) → 6[13][13][13] (s=45) → 7032 (s=12) (c=7) (b=14)
1 → 2 → 4 → 8 → 11 (s=2) (c=4) (b=15)
603 = 2[10]3 (s=15) → 2[11]3 (s=16) → 2[12]4 (s=18) → 2[13]7 (s=22) → 2[14][14] (s=30) → 31[14] (s=18) (c=5) (b=15)
1023 = 483 (s=15) → 493 (s=16) → 4[10]4 (s=18) → 4[11]7 (s=22) → 4[12][14] (s=30) → 4[14][14] (s=32) → 521 (s=8) (c=6) (b=15)
1891 = 861 (s=15) → 871 (s=16) → 882 (s=18) → 895 (s=22) → 8[10][12] (s=30) → 8[12][12] (s=32) → 8[14][14] (s=36) → 925 (s=16) (c=7) (b=15)
1 → 2 → 4 → 8 → 10 (s=1) (c=4) (b=16)
16 = 10 (s=1) → 11 (s=2) → 13 (s=4) → 17 (s=8) → 1[15] (s=16) → 2[15] (s=17) → 40 (s=4) (c=6) (b=16)
1396 = 574 (s=16) → 584 (s=17) → 595 (s=19) → 5[10]8 (s=23) → 5[11][15] (s=31) → 5[13][14] (s=32) → 5[15][14] (s=34) → 620 (s=8) (c=7) (b=16)
2131 = 853 (s=16) → 863 (s=17) → 874 (s=19) → 887 (s=23) → 89[14] (s=31) → 8[11][13] (s=32) → 8[13][13] (s=34) → 8[15][15] (s=38) → 925 (s=16) (c=8) (b=16)
1 → 2 → 4 → 8 → [16] (s=16) → 1[15] (s=16) (c=5) (b=17)
1 → 2 → 4 → 8 → [16] (s=16) → 1[14] (s=15) (c=5) (b=18)
5330 = [16]82 (s=26) → [16]9[10] (s=35) → [16][11]9 (s=36) → [16][13]9 (s=38) → [16][15][11] (s=42) → [16][17][17] (s=50) → [17]2[13] (s=32) (c=6) (b=18)
1 → 2 → 4 → 8 → [16] (s=16) → 1[13] (s=14) (c=5) (b=19)
116339 = [16][18]52 (s=41) → [16][18]75 (s=46) → [16][18]9[13] (s=56) → [16][18][12][12] (s=58) → [16][18][15][13] (s=62) → [16][18][18][18] (s=70) → [17]03[12] (s=32) (c=6) (b=19)
1 → 2 → 4 → 8 → [16] (s=16) → 1[12] (s=13) (c=5) (b=20)
100 = 50 (s=5) → 55 (s=10) → 5[15] (s=20) → 6[15] (s=21) → 7[16] (s=23) → 8[19] (s=27) → [10]6 (s=16) (c=6) (b=20)
135665 = [16][19]35 (s=43) → [16][19]58 (s=48) → [16][19]7[16] (s=58) → [16][19][10][14] (s=59) → [16][19][13][13] (s=61) → [16][19][16][14] (s=65) → [16][19][19][19] (s=73) → [17]03[12] (s=32) (c=7) (b=20)
Performativizing Papyrocentricity #29
Papyrocentric Performativity Presents:
• Sky Story – The Cloud Book: How to Understand the Skies, Richard Hamblyn (David & Charles 2008)
• Wine Words – The Oxford Companion to Wine, ed. Janice Robinson (Oxford University Press 2006)
• Nu Worlds – Numericon, Marianne Freiberger and Rachel Thomas (Quercus Editions 2014)
• Thalassobiblion – Ocean: The Definitive Visual Guide, introduction by Fabien Cousteau (Dorling Kindersley 2014) (posted @ Overlord of the Über-Feral)
Or Read a Review at Random: RaRaR
Thalassobiblion
Ocean: The Definitive Visual Guide, introduction by Fabien Cousteau (Dorling Kindersley 2014)
A big book for a big subject: the sea. But “guide” isn’t the mot juste. “Encyclopaedia” is better, because the book covers all aspects of oceanography and marine life, drawing on physics, chemistry and biology to describe everything inorganic from waves and icebergs to whirlpools and underwater volcanoes, everything organic from a beautiful flower like beach morning-glory, Ipomoea imperati, to a grotesque fish like the Pacific blackdragon, Idiacanthus antrostomus. The flower is on the shore, the fish is in the abyss, but both of them descend from a single ancestor.
And that ancestor may have evolved in the sea. It certainly moved there before it gave rise to flowers and fish. This big subject is also a very important one: the sea is central to the evolution and continued existence of life on earth. Only the sun matters as much, but some marine life could potentially survive the disappearance of the sun:
Hydrothermal vents are similar to hot springs on land. Located near ocean ridges and rifts, at an average depth of 2,100m (7,000ft), they spew out mineral-rich, superheated seawater. Some have tall chimneys, formed from dissolved minerals that precipitate when the hot vent water meets cold, deep-ocean water. The mix of heat and chemicals supports animal communities around the vents – the first life known to exist entirely without the energy of sunlight. (pg. 188, “The Open Ocean and Ocean Floor”)
The deep ocean is a fascinating and little-known place: much nearer than the other side of the earth, but much harder to get to. Like climbing mountains, plumbing the abyss is difficult and dangerous. It’s interesting that both endeavours have been dominated by a particular group of human being: both the highest and lowest points on the planet were first reached by white males. Fabien Cousteau, who introduces this book, continues the tradition. He’s the grandson of Jacques Cousteau (1910-97), who popularized diving and marine biology for millions of people. Jacques saw huge advances in marine technology and science and his son and grandson have seen more. But the discoveries are still coming: as Fabien points out, it’s estimated that “over 90 per cent of the world’s biodiversity resides in its oceans”.
Discomedusae by Ernst Haeckel
Some of that biodiversity left the water for the land and evolved new forms. Some of those new forms went back to the water, like the ceteceans and sea-snakes. Like human beings, they’re descended from fish, the most varied of all vertebrate groups. But some marine life never left its cradle. Where else can you find the beauty and strangeness of groups like the jellyfish? Radial symmetry is a marine speciality and when H.P. Lovecraft was inventing his aliens, he looked to under-space as much as outer:
But to give it a name at this stage was mere folly. It looked like a radiate, but was clearly something more. It was partly vegetable, but had three-fourths of the essentials of animal structure. That it was marine in origin, its symmetrical contour and certain other attributes clearly indicated; yet one could not be exact as to the limit of its later adaptations. The wings, after all, held a persistent suggestion of the aerial. How it could have undergone its tremendously complex evolution on a new-born earth in time to leave prints in Archaean rocks was so far beyond conception as to make Lake whimsically recall the primal myths about Great Old Ones who filtered down from the stars and concocted earth life as a joke or mistake; and the wild tales of cosmic hill things from outside told by a folklorist colleague in Miskatonic’s English department. (At the Mountains of Madness, 1931)
Lovecraft would have enjoyed Ocean as much as Jacques Cousteau. It closes with a detailed “Atlas of the Oceans”, with maps of the ocean floor all around the world. Before that, you can learn how the Corryvreckan whirlpool nearly killed George Orwell in 1947, where to find manganese nodules, why so many deep-sea creatures are red and what the narwhale’s horn really is. You can also feast your eyes on photography that records everything from microscopic plankton to swirling hurricanes hundreds of kilometres across. Big subject, big book. Beautiful subject and beautiful book too.
Spijit
The only two digits found in all standard bases are 1 and 0. But they behave quite differently. Suppose you take the integers 1 to 100 and compare the number of 1s and 0s in the representation of each integer, n, in bases 2 to n-1. For example, 10 would look like this:
1010 in base 2
101 in base 3
22 in base 4
20 in base 5
14 in base 6
13 in base 7
12 in base 8
11 in base 9
So there are nine 1s and four 0s. If you check 1 to 100 using this all-base function, the count of 1s goes like this:
1, 1, 2, 3, 5, 5, 8, 5, 9, 9, 11, 10, 15, 12, 14, 13, 15, 12, 17, 14, 20, 19, 20, 15, 23, 19, 22, 22, 25, 24, 31, 21, 25, 24, 24, 27, 33, 27, 31, 29, 34, 29, 36, 30, 34, 35, 34, 30, 40, 33, 36, 35, 38, 34, 42, 37, 43, 40, 41, 37, 48, 39, 42, 42, 44, 43, 48, 43, 47, 46, 51, 42, 53, 44, 48, 50, 51, 50, 55, 48, 59, 55, 55, 54, 64, 57, 57, 55, 60, 57, 68, 60, 64, 63, 64, 59, 68, 58, 61, 63.
And the count of 0s goes like this:
0, 1, 0, 2, 1, 2, 0, 4, 4, 4, 2, 5, 1, 2, 2, 7, 4, 8, 4, 7, 4, 3, 1, 8, 4, 4, 6, 8, 4, 7, 1, 10, 8, 7, 7, 12, 5, 6, 5, 10, 4, 8, 2, 6, 7, 4, 2, 12, 6, 9, 7, 8, 4, 11, 6, 10, 5, 4, 2, 12, 2, 3, 5, 14, 11, 13, 7, 10, 8, 11, 5, 17, 7, 8, 10, 10, 8, 10, 4, 13, 12, 10, 8, 16, 8, 7, 7, 12, 6, 14, 6, 8, 5, 4, 4, 16, 6, 10, 11, 15.
The bigger the numbers get, the bigger the discrepancies get. Sometimes the discrepancy is dramatic. For example, suppose you represented the prime 1014719 in bases 2 to 1014718. How 0s would there be? And how many 1s? There are exactly nine zeroes:
1014719 = 11110111101110111111 in base 2 = 1220112221012 in base 3 = 40B27B in base 12 = 1509CE in base 15 = 10[670] in base 1007.
But there are 507723 ones. The same procedure applied to the next integer, 1014720, yields 126 zeroes and 507713 ones. However, there is a way to see that 1s and 0s in the all-base representation are behaving in a similar way. To do this, imagine listing the individual digits of n in bases 2 to n-1 (or just base 2, if n <= 3). When the digits aren’t individual they look like this:
1 = 1 in base 2
2 = 10 in base 2
3 = 11 in base 2
4 = 100 in base 2; 11 in base 3
5 = 101 in base 2; 12 in base 3; 11 in base 4
6 = 110 in base 2; 20 in base 3; 12 in base 4; 11 in base 5
7 = 111 in base 2; 21 in base 3; 13 in base 4; 12 in base 5; 11 in base 6
8 = 1000 in base 2; 22 in base 3; 20 in base 4; 13 in base 5; 12 in base 6; 11 in base 7
9 = 1001 in base 2; 100 in base 3; 21 in base 4; 14 in base 5; 13 in base 6; 12 in base 7; 11 in base 8
10 = 1010 in base 2; 101 in base 3; 22 in base 4; 20 in base 5; 14 in base 6; 13 in base 7; 12 in base 8; 11 in base 9
So the list would look like this:
1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 2, 0, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 0, 0, 0, 2, 2, 2, 0, 1, 3, 1, 2, 1, 1, 1, 0, 0, 1, 1, 0, 0, 2, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 0, 1, 0, 1, 0, 1, 2, 2, 2, 0, 1, 4, 1, 3, 1, 2, 1, 1
Suppose that these digits are compared against the squares of a counter-clockwise spiral on a rectangular grid. If the spiral digit is equal to 1, the square is filled in; if the spijit is not equal to 1, the square is left blank. The 1-spiral looks like this:
Now try zero. If the spijit is equal to 0, the square is filled in; if not, the square is left blank. The 0-spiral looks like this:
And here’s an animated gif of the n-spiral for n = 0..9:
She-Shell
Joachim Wtewael (sic), Perseus Rescuing Andromeda (1611) (mirrored)
When I first came across this painting in a recent edition of Arthur Cotterell’s Classic Mythology,* it had mutated in two ways: it was mirror-reversed (as above) and Wtewael’s name (pronounced something like “EET-a-vaal”) was printed “WIEWAEL”. At least, I assume the painting was mirror-reversed, because almost all versions on the web have Andromeda on the left, which means that Perseus is holding his sword in his right hand, as you would expect.
I think I prefer the mirrored version, though I don’t know whether that’s because it was the first one I saw. In either version, it is a rich and dramatic painting, full of meaning, seething with symbolism. It’s displayed in the Louvre and if French etymology had been a little different, I could have called it La Conque d’Andromède. Here is the commoner version:
*Mythology of Greece and Rome (Southwater 2003).
Performativizing Papyrocentricity #28
Papyrocentric Performativity Presents:
• Himmelangst – No Empty Chairs: The Short and Heroic Lives of the Young Aviators Who Fought and Died in the First World War, Ian Mackersey (Phoenix 2012)
• Arioch’n’Roll – The White Stuff: Archetype, Anomie and Allegorical Albinism in the Music of Hawkwind, 1972-81, Dr Miriam B. Stimbers (University of Nebraska Press 1996)
• Jewels in the Skull – The Art Book, Phaidon (Second edition 2012) (posted @ Overlord of the Über-Feral)
Or Read a Review at Random: RaRaR
Hip-Hop Hermeneuticized
The Guardian undertakes a close hermeneutical analysis of some respected figures in the rap community and their complex and challenging lyrical interrogation of issues around neo-liberal capitalism:
In contemporary America, success in overcoming adversity (and often systemic racism) is most often represented in financial terms, and it’s a recurring theme in hip-hop. Consider Kanye West:
I treat the cash the way the government treats AIDS
I won’t be satisfied til all my niggas get it, get it?Or Dr Dre:
Get your money right
Don’t be worried ’bout the next man – make sure your business tight
Get your money right
Go inside the safe, grab your stash that you copped tonight
Get your money right
Be an international player, don’t be scared to catch those red eye flights
You better get your money right
Cause when you out there on the streets, you gotta get it – get itOr even TI himself:
Regardless what haters say I’m as real as they come
I’m chasin that paper baby however it come
I’m singin a song and movin yay by the ton
I bet you never seen a nigga gettin money so young.
Erythrosight
John Atkinson Grimshaw (1836-93), Autumn Morning.
Jewels in the Skull
The Art Book, Phaidon (Second edition 2012)
An A to Z of artists, mostly painters, occasionally sculptors, installers and performers, with a few photographers and video-makers too. You can trace the development, culmination and corruption of high art all the way from Giotto and Fra Angelico through Van Eyck and Caravaggio to Auerbach and Twombly. But the modernist dreck heightens the power of the pre-modernist delights. A few pages after Pieter Claesz’s remarkable A Vanitas Still Life of 1645 there’s Joseph Cornell’s “Untitled” of 1950. One is a skull, watch and overturned glass, skilfully lit, minutely detailed, richly symbolic; the other is a wooden box containing a “frugal assortment of stamps, newspaper cuttings and other objects with no particular relevance to each other”. From the sublime to the slapdash. Over the page from Eleazar Lissitzky’s Composition of 1941 there’s Stefan Lochner’s The Virgin and Child in a Rose Arbour of 1442. One is like a child’s doodle, the other like a jewel. From the slapdash to the sublime.
And so it goes on throughout the book, with beautiful art by great artists following or preceding ugly art by poseurs and charlatans. But some of the modern art is attractive or interesting, like Bridget Riley’s eye-alive Cataract 3 (1961) and Damien Hirst’s diamond-encrusted skull For the Love of God (2006). Riley and Hirst aren’t great and Hirst at least is more like an entrepreneur than an artist, but their art here is something that rewards the eye. So is Riley’s art elsewhere, as newcomers to her work might guess from the single example here. That is one of the purposes of a guide like this: to invite – or discourage – further investigation. I vaguely remember seeing the beautiful still-life of a boiled lobster, drinking horn and peeled lemon on page 283 before, but I wouldn’t have recognized the name of the Dutch artist: Willem Kalf (1619-93).
Willem Kalf, Still Life (c. 1653)
Elsewhere, I was surprised and pleased to see an old favourite: John Atkinson Grimshaw and his Nightfall on the Thames (1880). Many more people know Grimshaw’s atmospheric and eerie art than know his name, because it often appears on book-covers and as illustrations. If Phaidon are including him in popular guides with giants like Da Vinci, Dürer, Raphael and Titian, perhaps he’ll return to his previous fame. I certainly hope so.
Finding Grimshaw here made a good guide even better. The short texts above each art-work pack in a surprising amount of information and anecdote too. What you learn from the texts raises some interesting questions. For example: Why has one small nation contributed so much to the world’s treasury of art? From Van Eyck to Van Gogh by way of Hieronymus Bosch and Jan Vermeer, Holland is comparable to Italy in its importance. But only in painting, not sculpture or architecture. There aren’t just patterns of pigment, texture and geometry in this book: there are patterns of DNA, culture and evolution too. Brilliant, beautiful and banal; skilful, subtle and slapdash: The Art Book has all that and more. It puts jewels inside your skull.
Elsewhere other-posted:
• Ai Wei to Hell — How to Read Contemporary Art, Michael Wilson
• Eyck’s Eyes — Van Eyck, Simone Ferrari
• Face Paint — A Face to the World: On Self-Portraits, Laura Cumming
Overlord In Terms of Core Issues Around Maximal Engagement with Key Notions of the Über-Feral 
