Prime Evil Cats
Category theorists are fond of replacing the counting numbers by sets, in the category Set. The trouble is that prime numbers don't make a lot of sense for ordinary sets. If I buy 3 oranges and 5...
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Ribbon Review
Why you should love the Field with One elementIn the theory of $F$, matrices are no longer interpreted as linear operators for complex number Hilbert spaces. If we can do quantum mechanics without...
View ArticleQuirky Quasars
The 2009 paper by David Elbaz, Quasar induced galaxy formation: a new paradigm?, discusses the theory that supermassive black holes are responsible for galaxy formation. The team looked at the quasar...
View ArticleCycles of Time
Penrose's new book, Cycles of Time, is due out soon. This discusses his own thermodynamic cosmology, in which there are slowly decaying masses and information loss. Wrong for sure, but a step in the...
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Quirky Quasars II
The Arp heresy is the hypothesis of intrinsic redshift for quasars, which are believed to be ejected from galaxies. An alternative, using a simple redshift-distance relation, is to drop the assumption...
View ArticleQuote of the Month
From Zuska: You are not supposed to notice sexist behavior, and everything in our society is carefully designed to help you understand and accept it as natural and just the way things are and evolution...
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M Theory Lesson 306
The (wreath) product used in the theory of the field with one element is between the symmetric group $S_d$ and $d$ copies of the $n$-th roots of unity. For $\mu$ the primitive $n$-th root, an element...
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M Theory Lesson 307
Such Hermitian matrices provide a basis for all $3 \times 3$ Hermitian $1$-circulants in the form Since the eigenvalues of each basis matrix take the values $(1,1,-1)$, the eigenvalues of the sum are...
View ArticleMagic Motives
The most fashionable of all phrases amongst real mathematicians studying QFT, occasionally mentioned here, are the words motivic cohomology. This is supposed to be the mother of all cohomology...
View ArticleJob Hunting
There is one Kiwi government source of science funding for which I am still eligible to apply. Other countries have similar funding processes. However, in order to apply for such grants I require a...
View ArticleSo Few
Thanks to FSP for mentioning the Breaking Through Barriers website. Their new report on the problems faced by women in science contains basic suggestions on what science departments can do to improve...
View ArticleMagic Motives II
If sets and vector spaces are secretly the same thing, and spaces are built out of these new sets, then there should be one big category of spaces that has everything in it, including invariants!For...
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M Theory Lesson 308
Any elementary matrix, denoted $E_{ij}$, can be expressed as a Fourier transform of the democratic matrix. In the $3 \times 3$ case, the nine choices for $F$ give the $9$ elementary matrices. Thus any...
View ArticleMeanwhile
Well, it seems that no matter how hard you try, you just can't keep a good woman down: a second peer reviewed AIP paper was just accepted for publication; I have just finished a first draft of my scary...
View ArticleQuantum Computation
A well funded industry these days is research into the real world implementation of small sets of carefully chosen quantum operations, combinations of which are able to closely simulate any quantum...
View ArticleQuote of the Day
Courtesy of the small grocery shop near my place, which places a thought for the day on the chalkboard outside, no matter the weather: The Emperor will not judge you by your medals and diplomas but by...
View ArticleMeanwhile II
So I've found a suitable proof reader for my book, am busy hunting down literary agents, and am making progress with exciting, although naturally temporary, alternative career options. Now if, and it...
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M Theory Lesson 309
Recall that much of the tribimaximal mixing literature discusses small finite groups, such as $S_3$ and $A_4$. For example, Ernest Ma considers a $2 \times 2$ representation of the six element group...
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M Theory Lesson 310
Permutations may be represented by symmetric braids. A category theorist would usually draw a diagram like indicating that the braid crossing goes neither over nor under, and that one can slide strands...
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M Theory Lesson 311
Under the correspondence between ribbon twists and roots of unity, as in there is a matching of particle ribbon diagrams to matrices, giving in particular Observe how two copies of each $1$-circulant...
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