2007 September 6 – 2:09 pm
I was trying to understand Wick rotation by applying it in the case of a finite-dimensional Hilbert space, and came up with something strange. The way I’ve worked it out, it seems to map classical observables to quantum states! I’ve never heard anything like that before.
Say we have an -qubit Hilbert space . [...]
2007 February 3 – 2:55 am
I’m looking at multiplicative intuitionistic linear logic (MILL) right now and figuring out how it’s related to braided monoidal closed categories (BMCCs).
The top and bottom lines in the inference rules of MILL are functors that you get from the definition of BMCCs, so they exist in every BMCC. Given a braided monoidal category C, [...]
2007 January 31 – 9:44 pm
A rig is a ring without negatives, like the nonnegative integers. You can add and multiply them, multiplication distributes over addition, and you’ve got additive and multiplicative identities 0 and 1.
There’s another rig, called the “rig of costs,” that everyone uses when planning a trip: given two alternative plane tickets from A to B, [...]
2006 December 1 – 11:59 pm
LIGO, the Fool’s Golden Ratio and Stonehenge’s Platonic solids 1600 years before Plato.
http://math.ucr.edu/home/baez/week241.html
The last post was all about stuff that’s already known. I’ll be working in my thesis on describing the syntax of what I’ll call simply-typed quantum lambda calculus. Symmetric monoidal closed categories (SMCCs) are a generalization of CCCs; they have tensor products instead of products. One of the immediate effects is the [...]
I finally got it through my thick skull what the connection is between lambda theories and cartesian closed categories.
The lambda theory of a set has a single type, with no extra terms or axioms. This gives rise to a CCC where the objects are generated by products and exponentials of a distinguished object, the [...]
