tag:blogger.com,1999:blog-7307840825023135484.post1963623394124168492..comments2012-02-07T15:48:38.662+13:00Comments on Arcadian Pseudofunctor: Higgsy CodesKeahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-7307840825023135484.post-85429288564349322052012-01-01T17:16:16.239+13:002012-01-01T17:16:16.239+13:00Actually, $3$, $5$, $7$ and $11$ are all nice Galo...Actually, $3$, $5$, $7$ and $11$ are all nice Galois primes.Keahttps://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-90503336236019088132012-01-01T14:31:05.219+13:002012-01-01T14:31:05.219+13:00Mitchell, remember that there are no stringy compa...Mitchell, remember that there are no stringy compactifications in what we are doing. No a priori classical spaces or algebras. No ad hoc AdS spaces. The dimension $26$ just happens to be the dimension of the traceless part of the exceptional octonion Jordan algebra. The dimension $24$ is a triplet of octonions, or the $24$ non diagonal paths on a tetractys. <br /> <br />Now I am musing over this sequence $1,5,21,77,253,759$. It has nice prime factors, namely $3$, $5$, $7$, $11$ and $23$, which includes the $(5,7,11)$ of the exceptional Galois groups, and $11$ and $23$ as lengths for the ternary and binary codes.Keahttps://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-12299231393032199162012-01-01T09:59:50.931+13:002012-01-01T09:59:50.931+13:00Mitchell, we are not doing the same thing, so curv...Mitchell, we are not doing the same thing, so curvature will not arise in quite this way. If you want, we have 3+3 dimensions to start with. There are various 6x6 formalisms for GR which will probably turn out to be relevant. Louise's cosmology, which I use heavily, is already dS, not AdS.Keahttps://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-43614567167169753532012-01-01T02:57:07.816+13:002012-01-01T02:57:07.816+13:00Welcome back... I don't know how this moonshin...Welcome back... I don't know how this moonshine Higgs venture will work out, but let's bear in mind that the bosonic string compactified on the Leech lattice is apparently equivalent to quantum gravity in (2+1)-dimensional anti-de-Sitter space, with black hole entropies equal to j-function coefficients. Don't ask me how we get from there to quantum gravity in (3+1) dimensions with a positive cosmological constant; but AdS3 could be a slice of AdS4, and you could get dS4 from AdS4 by adding a constant energy density throughout space. Or maybe it works the other way round - first you uplift from AdS3 to dS3, and then dS3 is a slice of dS4; the latter is how it works in Silverstein et al's "Hologravity".Mitchellhttps://www.blogger.com/profile/10768655514143252049noreply@blogger.com