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Only three suitable division rings exist: the real numbers, the complex numbers and the quaternions. The fist two are contained in the last one. Thus the most elaborate separable Hilbert space is a quaternionic Hilbert space. “Division algebras and quantum theory” by John Baez. http://arxiv.org/abs/1101.5690

Also most scientist do not notice what separable stands for. It means that eigenspaces of operators can only contain a countable number of eigenvalues. For example operators whose eigenspaces contain all rational numbers may exist, but operators whose eigenspaces contain all (or a closed set of) real numbers can only exist in a non-separable Hilbert space, such as a Gelfand triple. By the way, each infinite dimensional separable Hilbert space owns a Gelfand triple.

Another fact that hardly anyone knows is that quaternionic number systems, coherent sets of quaternionic numbers and continuous quaternionic functions exits in 16 versions that only differ in their discrete symmetry sets. This is due to the four dimensions of quaternions. For example quaternionic number systems exist in left handed and right handed versions.

]]>Besides alt history driven by different outcomes of wars, etc. there are tales based on alternate tech. Pavane by Keith Roberts has an England where “land trains” filled the niche of cars and trucks. Phillip K. Dick’s Man in the High Castle shows the effects of a WWII won by the axis powers, including suborbital rocket travel and a US west coast dominated by Japanese culture. And a Jules Verne novel was rediscovered recently where he envisioned 20th century life. Not really alt history but a very retro view of how things might have gone.

I’d like to see a book where Darwinian selection is discovered centuries before the industrial revolution. Farmers were building up breeding methods for a long time…

]]>-Albert Camus, The Plague, Part 2 ]]>

At first glance the weak value argument in the first paper seems sound, I think they really pin-point a mistake there, but I don’t think that this mistake applies to most of the sampling that goes under the name ‘weak measurements’ (I may be wrong though, as I really haven’t paid much attention to this field).

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