Schrödinger’s cat

November 8, 2011

I usually read novels in bed, as my brain tends to be too tired to take in any more information for the day.  So the fact that this is the third post I am starting with a reference to a popular science book makes me think that perhaps I have not been working hard enough…

The book in question is The Emperor’s New Mind, by Roger Penrose.  The main thesis of this wonderful book is, apparently (and in a very small nutshell), that the mind does not work like a computer*.  However, I am currently about 3/4 of the way through it, and this has not yet been touched upon!  Rather, over 400 pages or so, Penrose has valiantly attempted to explain Turing machines, classical mechanics, relativity, quantum theory and cosmology to the interested (and, one must assume, quite dedicated) layperson.  I can only assume that all this is going to coalesce into a grand theory of Mind, but it does so far seem like quite an ambitious project.  Having tried to achieve this kind of comprehensive introduction to even the smallest of mathematical subjects myself in previous posts (you might have noticed that I have long since given up trying to do this), I have great respect for Penrose’s tenacity.  I find that the problem with this type of enterprise lies in trying to tread the line between being impenetrable to non-mathematicians, and boring for mathematicians.   While The Emperor’s New Mind is a great book, I think it is safe to say that it probably falls on the former side of this line; it is perhaps not entirely suitable for bedtime reading.

Anyway, I have just been reading Penrose’s take on the maltreated feline of this post’s title, and it got me thinking, so I thought I would discuss it.  The cat in question is a paradox which Erwin Schrödinger came up with in order to show the absurdity of trying to apply quantum theory at the classical physical level (that is, the everyday world with which we interact, as opposed to the exceedingly odd quantum level of subatomic particles).   This is, of course, a massive and complex subject, and I will only provide the merest of scrapes of its surface!  If you happen to be a pedantic physicist, then please do comment on any inaccuracies in what follows.

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Mathematicians and religion

September 26, 2011

Where was I?  Well, last week* we established, among other oddities, that diclofenac is bad for the religion of Zoroastrianism.  That post didn’t really have anything to do with mathematics (although I did at least attempt to tenuously link it chaos theory), so I will make up for it by at least mentioning some mathematicians this week, if not actual mathematics.  However, I will stick with the topic of religion for the time being.

This is partly inspired by a book I’ve just read: Galileo’s Daughter, by Dava Sobel.  It doesn’t really match up to Longitude, but is a good read nonetheless.  It is really about the life and work of Galileo Galilei, although Sobel gives us the hard science and history in a more easily digestible form, by interweaving commentary on his relationship with his daughter.  She seems to have been a quite extraordinary woman: sent to a convent at age thirteen due to her illegitimacy (and hence lack of marriage prospects), she spent her whole life in extreme poverty within those walls,  but still managed to be a doctor, playwright, composer, musician and prolific correspondent in the little time she had which wasn’t dedicated to prayer, labour and general suffering.

Anyway, one of the things which struck me most about Galileo’s life was his relationship with the all-powerful Catholic church at this time.  He was a very devout Catholic: publicly, of course (claiming Catholicism is, after all, preferable to torture and painful death), but more surprisingly, given the utter ignorance and persecution he suffered at the hands of the Inquisition, he remained privately devoted to the church.  He even said, near the end of his life:

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The Cardinality of the Continuum

February 24, 2010

A nice grand title to pique your interest!  After some thought and a couple of conversations, I have decided to keep this blog very much aimed at the layman; the thinking being that I don’t particularly want to write hard maths in my spare time, mathematicians don’t particularly want to read hard maths in their spare time, and non-mathematicians definitely don’t want to read hard maths ever.

My PhD supervisor recently appeared on a BBC programme about infinity, which, while good viewing, was rather over-ambitious, and so had to skip over some interesting stuff.  I thought I’d fill in some of the gaps in this post.  So what is this continuum?  Technically a continuum can be anything that is continuous – that is it goes through smooth, infinitesimally gradual transitions, and has no discontinuities or “jumps”.  But in reality the word is rarely used outside of Star Trek and mathematics.  The continuum I will write about is not the space-time continuum, but the real numbers,\mathbb{R}.  In my post onp-adic numbers, I mentioned that completeness is an important mathematical attribute for a space of numbers to possess.  The notion of continuity is even more fundamental, and people often refer to mathematics as having 2 distinct branches: continuous mathematics, and discrete – or discontinuous – mathematics.

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