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Comments:
<0> hello
<1> yo
<2> y0
<0> a manifold is something that looks locally like R^n
<0> could you sy that if you have to explain manifolds in 1 sentence?
<0> say
<2> R^n looks locally like R^n. Is R^n a manifold?
<0> yes
<3> yes
<3> what cl***es teach about manifolds?
<4> manifold = a space of n dimensions with coordinates characterized by a tuple of n elements
<4> IIRC
<3> n?
<3> i think n has to be finite
<2> Manyfold, is a sphere a manifold?
<4> n can be any integer
<4> hang on
<3> i don't think that a null space is a manifold, but perhaps i am mistaken
<0> perhaps better to say a manifold is something that could be wholly covered by open patches which look like open subsets of R^n
<4> http://en.wikipedia.org/wiki/Manifold
<4> the wikipedia has a good brief this time
<0> Volatile: yes a sphere is a manifold
<3> and i just made up the phrase "null space" on the spot
<0> one that needs 2 maps to be covered
<2> ah, I see
<3> reiminnian manifolds are most common, i would think
<2> riemannian? ;)
<2> he would turn in his grave if he knew how you spelled him... ;p
<3> yes. and null spaces do exist (or at least do not exist)
<4> at least can be represented, whether they exist or not :p
<3> yes
<2> the riemannian manifolds are used to describe hyperbolic geometry, right?
<3> apparently matrix operators have null spaces too
<3> Volatile: i think so, but i'm not really the right person to ask that sort of question
<3> are zero vectors are orthagonal to other vectors?
<2> yep
<3> what do they call a nonzero orthagonal vector?
<2> and to themselves
<4> so, in the Real World(tm) as we know it, what practical applications are there for riemannian manifolds ?
<2> space-time fluctuations?
<2> if ther is such a thing as a Real World(tm)
<2> there*
<5> There's a lot of evidence for it.
<2> The general theory of relativity incorporates all kinds of strange things...
<2> I'm sure quantum physics has some obscure use of it as well...
<3> you might have a large area filled with poisonous gas and want to represent the amount of poisonous gas between points as a distance
<2> hehe
<3> they might be interesting for economics, but i don't know anything about that
<2> "So... Here I am... In a room filled with poisonous gas... Gee, I wonder how much gas there is between this point and that point over there..."
<0> manyfolds are usually used in general relativity
<2> Thought so...
<0> quantum field theory is usually in flat minkowskian space-time
<0> you get very strange results considering a curved background
<6> hi all
<6> i just wanted to ask if there is a channel for algorithm questions
<6> or can i ask here
<5> If it's somewhat math related, you can ask here.
<5> Otherwise, maybe in the channel for the programming language you are using.
<6> i tought there was a channel specific for algorithm questions
<6> but not sure
<6> my question is rather simple
<6> it's about solving a sudoku with backtracking
<6> first i calculated a set of candidate numbers for every empty field
<6> the candidates set includes the intersection of the complement of the field in the 3x3 sqare the compmlement of the column and the complement of the row
<3> #ai might help you, jc-denton
<6> now if i start choosing radom numbers from this set and set them in until i figure out that i have no choice left for a field
<6> but how far do i get back then
<6> _death: thx
<6> basically i'm unsure about how to use backtracking
<7> Typically you undo the last decision and make another decision at that level if you can. Otherwise, you undo the previous decision and so on.
<7> You can think of it as doing a DFS of a decision tree.
<6> what does DFS stand for
<0> Depth first search
<3> woggle: i'm having a bit of trouble visualizing what you are talking about. is the tree already built?
<6> ah ok
<6> so i simply just choose another number for the last decision i made and then check again
<7> _death: It's implicit. Each edge represents deciding to fix a certain number in the puzzle. Each vertex represents a certain partially-filled in state of the puzzle.
<6> sounds too simple
<3> i'm going to have to look up this game
<6> the article on wikipedia is quite good
<8> % 3**163
<9> mnvl: 3**163
<8> % 3^163
<9> mnvl: 589881151426658740854227725580736348849310352832644300781946246613899173590427
<10> % 3^3^3
<9> ihope: 7625597484987
<10> % 3^(3^3)
<9> ihope: 7625597484987
<10> % 3^3^3^3
<9> ihope: Overflow[]
<11> are you crazy!
<8> wow, i didn't know mathematica could overflow
<8> % Log[3^163, 2]
<9> mnvl: Log[2]/Log[589881151426658740854227725580736348849310352832644300781946246613899173590427]
<8> % Log[2,3^163]
<9> mnvl: Log[589881151426658740854227725580736348849310352832644300781946246613899173590427]/Log[2]
<10> % Log[3^163, 3]
<9> ihope: 1/163
<8> % Log[2,3^163] \\N
<9> mnvl: No (forbidden content).
<8> % Log[3,3^163] \\N
<9> mnvl: No (forbidden content).
<8> % Log[3,3^163]
<9> mnvl: 163
<12> it's a forward slash
<8> % Log[3,3^163] //N
<9> mnvl: 163.
<8> % Log[2,3^163] //N
<9> mnvl: 258.3488876175484
<10> % No
<9> ihope: No
<8> thanx
<8> Failure02,
<10> % Not[True]
<9> ihope: False
<10> % True + True
<9> ihope: 2*True
<13> hehe
<1> haha
<8> maxint in perl must be 2^256
<12> what the
<12> :)
<1> truer than true
<13> % google
<10> :-)
<9> Rayden[SFX]: google
<10> % True + False
<9> ihope: False + True
<10> Addition is commutative, see?
<8> well that's reasonable enough
<12> % True // N
<9> Failure02: True
<13> % 5.32523532e^4
<9> Rayden[SFX]: 5.32523532*e^4
<8> @seen delta
<9> delta is in #math. I last heard delta speak 14 hours, 8 minutes and 48 seconds ago.
<10> What do you call it when f(x+y) = f(x) plus f(y) and f(x*y) = x * f(y)?
<13> % 5.32523532e^4 + 5.32523532e^4
<9> Rayden[SFX]: 10.65047064*e^4
<13> % 5.32523532e^6 + 5.32523532e^2
<9> Rayden[SFX]: 5.32523532*e^2 + 5.32523532*e^6
<13> hmm
<12> ihope: linear?
<10> So if I said that Not was such a function, Not would be a linear function?
<12> yes
<13> % True + False + True
<9> Rayden[SFX]: False + 2*True
<10> Aha... THAT's why it's called linear algebra.
<13> hmm should be False
<10> I knew it had something to do with quantum mechanics...
<10> Rayden[SFX]: why?
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