The nLab experiment has begun

As I mentioned before, I put up a page on quantum channels over at nLab.  I suggested to Bob Coecke that he get one of his grad students to put up pages on categorical quantum mechanics and Aleks Kissinger has agreed to take up the task.  So, quantum mechanics and quantum information theory are beginning to develop a broader presence on nLab which is a good thing.  Plus, I’m making more progress on the quantum channel front and the format is more to my liking than MathOverflow.  If you’re interested in making a contribution, check out the site.

Categorical Quantum Mechanics

Well, I’ve thrown up a page at nLab for quantum channels since the only quantum-related pages over there (so far) were mostly field theory stuff.  It already got a community edit to make it look better (!) which is cool.  Now I just have to convince Bob Coecke and the other categorical people in quantum information-related fields to start using it (John Baez already uses it).  I figure this might be a good way to work my way through my Birkhoff theorem stuff with some assistance.

More on the nature of mathematics

The debate is heating up (in a good way) over at FQXi where I posed a question about the nature of mathematics.  While presently remaining agnostic on the issue, I want to emphasize why this is even a question at all since a number of people seem fairly wedded to the fact that mathematics is invented.  That may still be true, but there are certain aspects of mathematics that simply cannot be invented.  For instance, it is well-known that many animal species have the ability to do basic arithmetic (adding and substracting) and one of Pavlov’s experiments with dogs demonstrated that they have a fairly sophisticated ability to distinguish between certain geometrical objects.  In fact (and this doesn’t surprise me in the least), monkeys perform about as well at mental addition as college students.  Interestingly enough, what sets humans apart appears to be language.  Even though chimpanzees, for instance, can outperform humans at tracking numbers and remembering sequencing, the level of specificity possessed by humans is not possessed by any other species.  We are the only ones who assign symbols to numbers.  I find this utterly fascinating, particularly in light of my recent FQXi essay.

Thus, the questions that come to mind are two-fold.  First, perhaps some mathematics is inherent (discovered) but that some is invented.  Is the difference discrete or continuous?  Is there a gradual change from inherent to invented?  Second, is this really a question of language and, if so, how much of mathematics is a language?  It clearly can’t all be since monkeys, for example, don’t have language.  And what is it about language that can suddenly transform something from real and inherent to something that is invented and beyond the realm of possibility?  Is this just further evidence that mathematics is really a language and just a language?  If so, what do we call the logical rules of addition and subtraction that seem to be understood by many creatures?

Algorithmic thermodynamics & Eddington

John Baez and Mike Stay have written an interesting paper combining algorithmic information theory with statistical mechanics.  Looks to be an interesting read.  Incidentally, while over at the n-Category Café, I stumbled across an old (and very interesting) post on dimensional analysis.  One of the comments indicated that Clive Kilmister had died.  This is certainly possible, though I’m very surprised I hadn’t heard of it.  The last time I saw Clive (which was admittedly six years ago) he was alive, well, and spritely.  Alas it is nevertheless possible that he has passed on, though I sincerely hope not.  Clive – along with Ted Bastin, Pierre Noyes, Frederick Parker-Rhodes, and John Amson – founded the Alternative Natural Philosophy Association (ANPA).  They were essentially the successors to Eddington (which explains why I know them since my dissertation was on Eddington’s Fundamental Theory not to mention that John Amson is a retired St. Andrews mathematics professor who I had the pleasure of lunching with one afternoon at his home in Crail while I was working on my dissertation).  They are/were interesting folks and a testament to the great tradition of off-beat foundational work that exists in the UK.  I sincerely miss that.

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