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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How conkers created Israel, cats cause wars, and painkillers are bad for religion

November 22, 2010

I’ve recently been reading a book called Chaos, by James Gleick.  It is a nice, easy-to-read overview of chaos theory in all its forms.  Chaos theory is not really a proper mathematical field, more of an ideology, which has applications in all walks of life.   The phrase seems to be bandied about less these days, perhaps because the ideas have become so accepted that it is no longer considered a theory, but just “how things are”.  It takes the form of turbulence, entropy and unpredictability; it has great influence on the weather, the traffic, the stock markets…indeed it is hard to imagine how science worked before the notion of chaos.  As one physicist in the book puts it:

“Relativity eliminated the Newtonian illusion of absolute space and time; quantum theory eliminated the Newtonian dream of a controllable measurement process; and chaos eliminates the Laplacian fantasy of deterministic predicability”.

Poor physicists! Always having their work eliminated by something or other.  Luckily this doesn’t happen in mathematics.  Chaos in mathematics is studied in the form of dynamical systems,  in which small perturbations in initial conditions can have a dramatic long-term effect.  This sensitivity is known in popular culture as the “butterfly effect”, from a paper by Edward Lorenz – a pioneer of chaos theory – titled: Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?

Lorenz was  a meteorologist, and first noticed chaotic effects whilst running weather simulations.  Weather is notoriously chaotic (see, for example, long-term forecasts by the Met Office for evidence of this), and one day, whilst trying to restart a simulation where he had left off, he fed in data which had been output from the middle of a previous session.  He noticed that the outcome was wildly different from his previous results, a consequence of the computer having rounded his output to what he had thought was an insignificantly fewer number of decimal points.    Gleick goes into weather patterns in some depth, as well as delving into such interesting topics as the fractal – and by implication, infinite – nature of coastlines (the closer you get the more little “bays” there are), and the chaotic behaviour a human heart displays while fibrillating (basically what a defibrillator does is to reset a chaotic system with a massive jolt of electricity).*

But I am not actually going to talk about chaos theory today.  Well, not quite.  Instead I am going to share a few odd and interesting freakonomics-style chains of events I’ve learnt about recently.  They all involve seemingly insignificant things – conkers, diclofenac and a cat parasite, to be precise  – which have (arguably) had a huge impact on world events.   In that sense you could possibly claim that this was some kind of chaos in practice.  But that would be quite a tenuous way to try and link it with what I’ve written so far, so I won’t.

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