| Utopolis | WLSC210: Steven Wilson - King Ghost

[Uto]

Utopost 15-7-20 --- UTOPOLIS SPREADS THE REVOLUTION AS BIGICIA TAKES THE WIN ---

Our beloved [Ó] finished in 13th place with 57 points (1 under replacement) which was of course a totally respectable final position, but no one cared in the end as Utopolis was for once the epicenter of the world as the Waiting List Song Contest was held right here. Our dear Dictator was even in the mix with 2 songs and 24 mini-songs, spreading the revolution of futurism far and wide. Ultimately it was Bigicia who took top honours, but even Solentoya in 2nd place and of course the resplendent Emsfrynt entry in 3rd were all very much appreciated by the crowds. The show was a hit. Utopolis and Pyreica proved once and for all that the best source of entertainment in all of Natia is the Waiting List Song Contest.

Onwards now, WLSC201 beckons. We haven't heard much yet, but MICADO has stated that they are 'going to play a numbers game' this time. We hope it won't suck.

 

[Uto]

def get_power_set(s):
  power_set=[[]]
  for elem in s:
    for sub_set in power_set:
      power_set=power_set+[list(sub_set)+[elem]]
  return power_set

def powerset(original_set):
  ps = set({frozenset()})
  for member in original_set:
    subset = set()
    for m in ps:
      subset.add(m.union(set([member]))
    ps = ps.union(subset)
  return ps

def powSet(set):
    if len(set) == 0:
       return [[]]
    return addtoAll(set[0],powSet(set[1:])) + powSet(set[1:])
def addtoAll(e, set):
   for c in set:
       c.append(e)
   return set

def powerSet(array):
    length = str(len(array))
    formatter = '{:0' + length + 'b}'
    combinations = []
    for i in xrange(2**int(length)):
        combinations.append(formatter.format(i))
    sets = set()
    currentSet = []
    for combo in combinations:
        for i,val in enumerate(combo):
            if val=='1':
                currentSet.append(array[i])
        sets.add(tuple(sorted(currentSet)))
        currentSet = []
    return sets

def powerSetR(n):
    assert n >= 0
    if n == 0:
        return [[]]
    else:
        input_set = list(range(1, n+1)) # [1,2,...n]
        main_subset = [ ]
        for small_subset in powerSetR(n-1):
            main_subset += [small_subset]
            main_subset += [ [input_set[-1]] + small_subset]
        return main_subset
superset = powerSetR(4)
print(superset)

Different methods, same outcome. The search continues...

 

[Uto]

Naturally left and right are the same thing. We only have to do one and it will yield the other.

1​

-1​

41​

-41​

81​

-81​

121​

-121​

161​

-161​

201​

-201​

241​

-241​

281​

-281​

2​

-2​

42​

-42​

82​

-82​

122​

-122​

162​

-162​

202​

-202​

242​

-242​

282​

-282​

3​

-3​

43​

-43​

83​

-83​

123​

-123​

163​

-163​

203​

-203​

243​

-243​

283​

-283​

4​

-4​

44​

-44​

84​

-84​

124​

-124​

164​

-164​

204​

-204​

244​

-244​

284​

-284​

5​

-5​

45​

-45​

85​

-85​

125​

-125​

165​

-165​

205​

-205​

245​

-245​

285​

-285​

6​

-6​

46​

-46​

86​

-86​

126​

-126​

166​

-166​

206​

-206​

246​

-246​

286​

-286​

7​

-7​

47​

-47​

87​

-87​

127​

-127​

167​

-167​

207​

-207​

247​

-247​

287​

-287​

8​

-8​

48​

-48​

88​

-88​

128​

-128​

168​

-168​

208​

-208​

248​

-248​

288​

-288​

9​

-9​

49​

-49​

89​

-89​

129​

-129​

169​

-169​

209​

-209​

249​

-249​

289​

-289​

10​

-10​

50​

-50​

90​

-90​

130​

-130​

170​

-170​

210​

-210​

250​

-250​

290​

-290​

11​

-11​

51​

-51​

91​

-91​

131​

-131​

171​

-171​

211​

-211​

251​

-251​

291​

-291​

12​

-12​

52​

-52​

92​

-92​

132​

-132​

172​

-172​

212​

-212​

252​

-252​

292​

-292​

13​

-13​

53​

-53​

93​

-93​

133​

-133​

173​

-173​

213​

-213​

253​

-253​

293​

-293​

14​

-14​

54​

-54​

94​

-94​

134​

-134​

174​

-174​

214​

-214​

254​

-254​

294​

-294​

15​

-15​

55​

-55​

95​

-95​

135​

-135​

175​

-175​

215​

-215​

255​

-255​

295​

-295​

16​

-16​

56​

-56​

96​

-96​

136​

-136​

176​

-176​

216​

-216​

256​

-256​

296​

-296​

17​

-17​

57​

-57​

97​

-97​

137​

-137​

177​

-177​

217​

-217​

257​

-257​

297​

-297​

18​

-18​

58​

-58​

98​

-98​

138​

-138​

178​

-178​

218​

-218​

258​

-258​

298​

-298​

19​

-19​

59​

-59​

99​

-99​

139​

-139​

179​

-179​

219​

-219​

259​

-259​

299​

-299​

20​

-20​

60​

-60​

100​

-100​

140​

-140​

180​

-180​

220​

-220​

260​

-260​

300​

-300​

21​

-21​

61​

-61​

101​

-101​

141​

-141​

181​

-181​

221​

-221​

261​

-261​

301​

-301​

22​

-22​

62​

-62​

102​

-102​

142​

-142​

182​

-182​

222​

-222​

262​

-262​

302​

-302​

23​

-23​

63​

-63​

103​

-103​

143​

-143​

183​

-183​

223​

-223​

263​

-263​

303​

-303​

24​

-24​

64​

-64​

104​

-104​

144​

-144​

184​

-184​

224​

-224​

264​

-264​

304​

-304​

25​

-25​

65​

-65​

105​

-105​

145​

-145​

185​

-185​

225​

-225​

265​

-265​

305​

-305​

26​

-26​

66​

-66​

106​

-106​

146​

-146​

186​

-186​

226​

-226​

266​

-266​

306​

-306​

27​

-27​

67​

-67​

107​

-107​

147​

-147​

187​

-187​

227​

-227​

267​

-267​

307​

-307​

28​

-28​

68​

-68​

108​

-108​

148​

-148​

188​

-188​

228​

-228​

268​

-268​

308​

-308​

29​

-29​

69​

-69​

109​

-109​

149​

-149​

189​

-189​

229​

-229​

269​

-269​

309​

-309​

30​

-30​

70​

-70​

110​

-110​

150​

-150​

190​

-190​

230​

-230​

270​

-270​

310​

-310​

31​

-31​

71​

-71​

111​

-111​

151​

-151​

191​

-191​

231​

-231​

271​

-271​

311​

-311​

32​

-32​

72​

-72​

112​

-112​

152​

-152​

192​

-192​

232​

-232​

272​

-272​

312​

-312​

33​

-33​

73​

-73​

113​

-113​

153​

-153​

193​

-193​

233​

-233​

273​

-273​

313​

-313​

34​

-34​

74​

-74​

114​

-114​

154​

-154​

194​

-194​

234​

-234​

274​

-274​

314​

-314​

35​

-35​

75​

-75​

115​

-115​

155​

-155​

195​

-195​

235​

-235​

275​

-275​

315​

-315​

36​

-36​

76​

-76​

116​

-116​

156​

-156​

196​

-196​

236​

-236​

276​

-276​

316​

-316​

37​

-37​

77​

-77​

117​

-117​

157​

-157​

197​

-197​

237​

-237​

277​

-277​

317​

-317​

38​

-38​

78​

-78​

118​

-118​

158​

-158​

198​

-198​

238​

-238​

278​

-278​

318​

-318​

39​

-39​

79​

-79​

119​

-119​

159​

-159​

199​

-199​

239​

-239​

279​

-279​

319​

-319​

40​

-40​

80​

-80​

120​

-120​

160​

-160​

200​

-200​

240​

-240​

280​

-280​

320​

-320​

 

[Himan]

Don't ever make a power set of that.

I just am not sure if making power sets will help you find the right song. In the end you have to make the step to uncountable infinity somewhere. Such that with enough time even a monkey can write Shakespeare. Though you might can say that even time is not even uncountable infinite, cause there is such a thing as a planck time...

 

[Uto]

01 0,99545106416426761076126016054853...
02 0,70214606601606574140720414651001...
03 0,91272404316422120410461327013243...
04 0,02798448754127343616899126421037...
05 0,15895432213668547421002022154480...
06 0,86015465617047032132300051051005...
07 0,19931468483422216487340200865601...
08 0,71321333854900660432109698045255...
09 0,12794602847994623845238050004832...
10 0,12890893092004882374839456771080...
11 0,97683666912890012088379847331298...
12 0,71231904846936801739040235945523...
13 0,12957927394795068365871154890230...
14 0,3259029578 THERE ARE TOO MANY ----------

... and there will be only more...

... infinitely many ...

Himan, how can we even count this? Is this still countable?

 

[Uto]

Date: 02/17/2005 at 04:45:48
From: Richard
Subject: "The second power set", or the power set of a power set

What is "the second power set", or the power set of the power set of
a set, say set <1,2,3>?

As we know, the power set of set <1,2,3> is

<< >,<1>,<2>,< 3>,<1,2>,<1,3>,<2,3>,<1,2,3>>.

But I do not know the power set of that set.



Date: 02/22/2005 at 09:47:35
From: Doctor Ian
Subject: Re:

Hi Richard,

Suppose our original set is

A = {a,b}

The power set of this is the set of all subsets:

P(A) = { {}, No elements
{a}, {b}, One element
{a,b} Two elements
}

To make subsequent expansion less of a notational nightmare, I'm going
to use variables to represent these subsets, i.e.,

P(A) = { W, X, Y, Z }

Now we can take the power set of the power set, which is the set of
all subsets of P(A):

P(P(A)) = { {}, No elements
{W}, One element
{X},
{Y},
{Z},
{W,X}, Two elements
{W,Y},
{W,Z},
{X,Y},
{X,Z},
{Y,Z},
{W,X,Y}, Three elements
{W,X,Z},
{W,Y,Z},
{X,Y,Z},
{W,X,Y,Z} Four elements
}

This is 2^4 = 16 elements, as we would expect. To express them in
terms of the original elements, we can substitute as needed:

W -> {}
X -> {a}
Y -> {b}
Z -> {a,b}

P(P(A)) = { {},
{{}},
{{a}},
{{b}},
{{a,b}},
{{},{a}},
{{},{b}},
{{},{a,b}},
{{a},{b}},
{{a},{a,b}},
{{b},{a,b}},
{{},{a},{b}},
{{},{a},{a,b}},
{{},{b},{a,b}},
{{a},{b},{a,b}},
{{},{a},{b},{a,b}}
}

If I wanted to find P(P(P(A))), I would use the same trick again,
i.e., assign a variable to each element of P(P(A)), expand using those
variables, and substitute.

Otherwise, it's too easy to get lost in a
blizzard of brackets.

Does this help?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/

 

[Ana Raquel]

 

[Uto]

 

[Uto]

{{{}},
{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6....}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3....}},{{0,4....}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0....}},{{0,1....}},{{0,2....}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8....}},{{0,9....}},{{0,0....}},{{0,1....}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7....}},{{0,8....}},{{0,9....}},{{0,0....}},{{0,1....}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8....}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5....}},{{0,6....}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2....}},{{0,3....}},{{0,4....}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0....}},{{0,1....}},{{0,2....}},{{0,3....}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9....}},{{0,0....}},{{0,1....}},{{0,2....}},{{0,3....}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0....}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7....}},{{0,8....}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4....}},{{0,5....}},{{0,6....}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2....}},{{0,3....}},{{0,4....}},{{0,5....}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1....}},{{0,2....}},{{0,3....}},{{0,4....}},{{0,5....}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2....}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9....}},{{0,0....}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6....}},{{0,7....}},{{0,8....}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4....}},{{0,5....}},{{0,6....}},{{0,7....}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3....}},{{0,4....}},{{0,5....}},{{0,6....}},{{0,7....}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4....}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1....}},{{0,2....}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8....}},{{0,9....}},{{0,0....}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{0,8...}},{{0,9...}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6....}},{{0,7....}},{{0,8....}},{{0,9....}},{{0,0...}},{{0,1...}},{{0,2...}},{{0,3...}},{{0,4...}},{{0,5...}},{{0,6...}},{{0,7...}},{{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Endless patterns, endless patterns within patterns, endless patterns within patterns within patterns, endless patterns within patterns within patterns within patterns, endless patterns within patterns within patterns within patterns within patterns, endless patterns within patterns within patterns within patterns within patterns within patterns, endless patterns within patterns within patterns within patterns within patterns within patterns within patterns, endless patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns, endless patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns, endless patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns, endless patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns, endless patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns, endless patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns, endless patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns, endless patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns, endless patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns, endless patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns within patterns.......

Too many to count.

 

[Uto]

If you take a set of numbers and you can count them that means that you can know when any element will appear. I mean if you just take all the natural number 1, 2, 3, 4.... etc you know that 1097 will be after 1096. The list of numbers is infinite, but you know you can count the list down if you had eternity. Various other things are infinite, but you can usually map them onto the list of natural numbers creating an ordering. For instance the list of rational numbers, that is the list of possible divisions of two numbers, can be mapped out. If you take 1/1 first, then 1/2, 2/1, 2/2, 1/3, 3/1 and so on in any systematic approach you can always know and calculate which ratio is first and which ratio is 209104123th. Such a list, infinite but countable, is described as Aleph 0.

If you take a set of numbers and you can no longer put them in any order it is uncountable. If you take any of the various infinite 0,8157930570.... random numbers you will know that there are infinitely many of them. But because they are infinite there are always infinitely many numbers between any two of those. Even between 0,9999999998.... and 0,9999999997... there are infintely many numbers like 0,9999999997971456340895389563425.... and such and such. You can never count these numbers. You can not even know which one is second (with 0 being first). Another of those lists is the power set of the natural numbers, where every possible combination of natural numbers is taken. It has sets of only one number like {1} and {2} and {3}, but also {1,2} and {2,3} and {1,7,10,11,2139013} and so on. Given that there are infinitely many numbers, any ordering goes wrong at some point because the list of sets holding only a single number is already infinite. Such lists, infinite and uncountable, are described as Aleph 1. They are infinite amounts of infinities.

Now, what if you take the power set of that power set? What if we take uncountable infinities of an already uncountable infinity? Is there something like Aleph 2? Are there infinitely many magnitudes of infinity? Does it ever stop?

EPILEPSY WARNING

Also, video is much cooler in full screen and HD.

WLSC 201
Utopolis

Max Cooper
Aleph 2

 

[Uto]

WLSC 202
Utopolis

Phillipi & Rodrigo
Retrogrado

 

[Uto]

I'm not posting my songs like I should:

WLSC 203: Guillermo & Tropical Danny - Toppertje!

WLSC 204: Jaloo - Last Dance

 

[Uto]

WLSC 205
U T O P O L I S

SHORTPARIS
KOKOKO

 

[Uto]

I've been lagging in this topic again.

WLSC 206:

WLSC 207:

WLSC 208:

And now

WLSC 209 Utopolis

HANA - So & So

​

 

[Uto]

WLSC 210
Utopolis

Steven Wilson
King Ghost

 

[ferret]

Are you ready for a historic match Utopolis vs NBS?

 

[Uto]

To be honest, not really. Normally I would be pretty hyped before a big tournament but something feels off this time. Probably due to corona, maybe also because it's the first time for us since 2014 and it's just not the same team. I will still watch the game tomorrow naturally and support Oranje.

 

[ferret]

I think a year ago I would have bet on the yellow-blue winning... This year, I'm not sure anymore.
And I'll have to hide something in the closet...

 

[Stargazer]

Welcome to the roster!

 

[theditz83]

Welcome to the main roster Uto