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Lettris is a curious tetris-clone game where all the bricks have the same square shape but different content. Each square carries a letter. To make squares disappear and save space for other squares you have to assemble English words (left, right, up, down) from the falling squares.
Boggle gives you 3 minutes to find as many words (3 letters or more) as you can in a grid of 16 letters. You can also try the grid of 16 letters. Letters must be adjacent and longer words score better. See if you can get into the grid Hall of Fame !
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The string theory landscape or anthropic landscape refers to the large number of possible false vacua in string theory. The "landscape" includes so many possible configurations that some physicists[who?] think that the known laws of physics, the standard model and general relativity with a positive cosmological constant, occur in at least one of them. The anthropic landscape refers to the collection of those portions of the landscape that are suitable for supporting human life, an application of the anthropic principle that selects a subset of the theoretically possible configurations.
In string theory the number of false vacua is commonly quoted as 10500. The large number of possibilities arises from different choices of Calabi-Yau manifolds and different values of generalized magnetic fluxes over different homology cycles. If one assumes that there is no structure in the space of vacua, the problem of finding one with a sufficiently small cosmological constant is NP complete, being a version of the subset sum problem.
The idea of the string theory landscape has been used to propose a concrete implementation of the anthropic principle, the idea that fundamental constants may have the values they have not for fundamental physical reasons, but rather because such values are necessary for life (and hence intelligent observers to measure the constants). In 1987, Steven Weinberg proposed that the observed value of the cosmological constant was so small because it is not possible for life to occur in a universe with a much larger cosmological constant. In order to implement this idea in a concrete physical theory, it is necessary to postulate a multiverse in which fundamental physical parameters can take different values. This has been realized in the context of eternal inflation.
Some physicists, starting with Weinberg, have proposed that Bayesian probability can be used to compute probability distributions for fundamental physical parameters, where the probability of observing some fundamental parameters is given by,
where is the prior probability, from fundamental theory, of the parameters and is the anthropic selection function, determined by the number of "observers" that would occur in the universe with parameters . These probabilistic arguments are the most controversial aspect of the landscape. Technical criticisms of these proposals have pointed out that:
Various physicists have tried to address these objections, and the ideas remain extremely controversial both within and outside the string theory community. These ideas have been reviewed by Carroll.
Vilenkin and collaborators have proposed a consistent way to define the probabilities for a given vacuum.
A problem with many of the simplified approaches people have tried is that they "predict" a cosmological constant that is too large by a factor of 10–1000 (depending on one's assumptions) and hence suggest that the cosmic acceleration should be much more rapid than is observed.
Although few dispute the idea that string theory appears to have an unimaginably large number of metastable vacua, the existence, meaning and scientific relevance of the anthropic landscape remain highly controversial. Prominent proponents of the idea include Andrei Linde, Sir Martin Rees and especially Leonard Susskind, who advocate it as a solution to the cosmological-constant problem. Opponents, such as David Gross, suggest that the idea is inherently unscientific, unfalsifiable or premature. A famous debate on the anthropic landscape of string theory is the Smolin-Susskind debate on the merits of the landscape.
The term "landscape" comes from evolutionary biology (see Fitness landscape) and was first applied to cosmology by Lee Smolin in his book. It was first used in the context of string theory by Susskind.