The Perils of Modern Living

Posted in Poetry, The Universe and Stuff with tags , , , on July 15, 2011 by telescoper

Well up above the tropostrata
There is a region stark and stellar
Where, on a streak of anti-matter
Lived Dr. Edward Anti-Teller.

Remote from Fusion’s origin,
He lived unguessed and unawares
With all his antikith and kin,
And kept macassars on his chairs.

One morning, idling by the sea,
He spied a tin of monstrous girth
That bore three letters: A. E. C.
Out stepped a visitor from Earth.

Then, shouting gladly o’er the sands,
Met two who in their alien ways
Were like as lentils. Their right hands
Clasped, and the rest was gamma rays.

by Prof. Harold P. Furth (1930-2002)

Buzzwords (via The Upturned Microscope)

Posted in Uncategorized with tags , , , , , , , , , on July 15, 2011 by telescoper

This wouldn’t be so funny if it weren’t so true…

Buzzwords (Click on image to enlarge) See more comics … Read More

via The Upturned Microscope

A Diving Bell Problem

Posted in Cute Problems with tags , on July 14, 2011 by telescoper

You will have noticed that, in recent weeks, I’ve been posting divers physics problems on here. They seem to be quite popular so I thought I’d try another, which I found this morning in an old A-level physics textbook:

A diving bell of internal volume 6 m3 is lowered into a freshwater lake until the volume of the contained air is 4 m3. The height of a water barometer at the surface is 10 m. Assume that the temperature of the air in the bell does not change as the bell is lowered.

Columbo’s Blind Date

Posted in Columbo with tags on July 14, 2011 by telescoper

Some years ago, back in Beeston days, my friend and former student Rockhee tried to arrange a blind date for Columbo. I’ve just rediscovered these photographs of the event. I don’t think it was a success.

Come, Night

Posted in Poetry with tags , on July 13, 2011 by telescoper

Come, night; come, Romeo; come, thou day in night;
For thou wilt lie upon the wings of night
Whiter than new snow on a raven’s back.
Come, gentle night, come, loving, black-brow’d night,
Give me my Romeo; and, when he shall die,
Take him and cut him out in little stars,
And he will make the face of heaven so fine
That all the world will be in love with night
And pay no worship to the garish sun.

From Romeo and Juliet, Act III Scene 2, by William Shakespeare.

Astronomy Look-alikes, No. 59

Posted in Astronomy Lookalikes with tags , , , , , on July 13, 2011 by telescoper

It’s not widely known that the painstaking detective work done by Penzias and Wilson in confirming the extraterrestrial
origin of the excess noise that they measured, and eventually understood to be evidence of the cosmic microwave background radiation, was actually the original inspiration for the 1970s British television police drama, The Sweeney.

The Inflatable PostDoc! (via The Upturned Microscope)

Posted in Uncategorized with tags , , , , , , , , , on July 12, 2011 by telescoper

I hope they’ve patented this idea, because it could be worth a fortune, although I hasten to add it shouldn’t be used as a sex toy.

The Inflatable PostDoc! (Click on image to enlarge) From the people that brought you The PostDoc Trailer! See more comics … Read More

via The Upturned Microscope

Cardiff News

Posted in Education, Politics with tags , , , , , on July 12, 2011 by telescoper

It’s been a while since I’ve blogged about local affairs, but the emergence of three items of news in the past few days has given me an opportunity to remedy that.

First, and hot off the press this morning, is the news that Cardiff University has at last decided who its next Vice-Chancellor will be after the incumbent,  David Grant, retires next year. The lucky winner is Professor Colin Riordan, who is currently Vice-Chancellor of the University of Essex (which apparently exists). His background is in the humanities, and his speciality post-war German literature. Since his previous institution doesn’t have a Physics Department, we’re probably  safe for a few years until he finds out Cardiff has one and decides to close it.

Anyway, Professor Riordan became a Vice Chancellor for the first time at the age of 48, which is the same age I am now. Maybe I should be climbing aboard the gravy train? I hear there’s a vacancy as Vice Chancellor at the University of Essex. I would apply, but I fear I have all the wrong vices…

That brings me to yesterday’s news that Cardiff University, along with all the proper most other universities in Wales, is to charge annual tuition fees of, you guessed it, £9K. This is despite recent reports that the Higher Education Funding Council for Wales (HEFCW) was set to refuse permission to set such high fees. I always thought it was inevitable that Welsh universities would want to charge as much as possible to bring funding levels closer to those in England, but it remains to be seen what effect the new regime will have on student recruitment.  The £9K level is substantially higher than the Welsh Assembly Government’s initial estimate of £7K so it also remains to be seen what the implications are for the WAG budget. We live in interesting times…

However, not wishing to end on a down note, I’ll finish by passing on a bit of up-beat news. Apparently – according to the esteemed National Geographic Magazine – Cardiff is one of the top ten places in the world to visit in 2011, coming in at Number 6 in  this rigorously compiled and totally objective league table. I’m usually a bit skeptical about such things, but who could possibly disagree with the ranking?

1. Muskoka Orange County, Ontario, Canada
2. Patagonia, Argentina
3. San Juan Islands, Washington
4. Minneapolis, Minnesota
5. Glacier Bay National Park, Alaska
6. Cardiff, Wales
7. Stockholm Archipelago Sweden
8. Azores, Portugal
9. Roatan, Honduras
10. Istria, Croatia

Hang on a minute. Minneapolis? At Number 4?

A Simple Problem in Statistical Physics

Posted in Cute Problems with tags , , , , on July 11, 2011 by telescoper

In physics we often have to resort to computer simulations in which continuously varying quantities are modelled on a discrete lattice. We also have recourse from time to time to model physical properties of a system as random quantities with some associated probability distribution. The following problem came up in a conversation recently, and I think it’s rather cute so thought I’d post it here.

Consider a regular three-dimensional Cartesian grid, at each vertex of which is defined a continuous variable x which varies from site to site with the same probability distribution function F(x) at each location. The value of x at any vertex can be assumed to be statistically independent of the others.

Now define a local maximum of the fluctuating field defined on the lattice to be a point at which the value of x is higher than the value at all surrounding points, defined so that in D dimensions there are 3^{D}-1 neighbours.

What is the probability that an arbitrarily-chosen point is a local maximum?

Solution

Well, the most popular answer is in fact the correct one but I’m quite surprised that a majority got it wrong! Like many probability-based questions there are quick ways of solving this, but I’m going to give the laborious way because I think it’s quite instructive (and because I’m a bit slow).

Pick a point arbitrarily. The probability that the associated value lies between x and x+dx is f(x)dx, where f(x)=dF(x)/dx is the probability density function. According to the question there are 3^3-1=26 neighbours of this point. The probability that all of these are less than x isF(x)\times F(x)\times \ldots F(x) 26 times, i.e. [F(x)]^{26}  becauses they are independent. Note that this is a continuous variable so the probability of any two values being equal is zero. The probability of the chosen point being a local maximum with a given value of x is therefore f(x)dx\times [F(x)]^{26}. The probability of it being a local maximum with any value of x is obtained by integrating this expression over all allowed values of x, i.e. \int f(x) dx [F(x)]^{26} . But the integrand can be re-written

\int f(x) dx [F(x)]^{26} = \int dF \times F^{26} = \frac{1}{27} \int d\left(F^{27}\right) = \frac{1}{27},

because  F=1 at the upper limit of integration and F=0  at the bottom.

So you don’t need to know the form of F(x) – but the calculation does rely on it being a continuous distribution.

This long-winded method demonstrates the applicability of the product rule and the process of marginalising over variables, but the answer should tell you a much quicker way of getting there.  The central point and the 26 neighbours constitute a set of 27 points. The probability that any particular one is the largest of the set is just 1/27, as each is equally likely to be the largest. This goes for the central value too, hence the answer.

 

Not Now, Voyager

Posted in The Universe and Stuff with tags , , , , , , on July 10, 2011 by telescoper

Last week I found myself a bit perplexed by the frenzy of twitter angst surrounding the last ever launch of the Space Shuttle. It’s not the first time something like this has happened. I’ve often felt like there must be something wrong with me for not getting agitated over such things. After Altantis returns to Earth in a couple of weeks’ time she will be taken out of service and, for the foreseeable future, America will no longer have the ability to put humans into orbit. This does mark the end of an era, of course, but is it really something to get all upset about?

I find myself agreeing with the Guardian editorial, which I’ve taken the liberty of copying here:

Fewer than 600 people have been admitted an exclusive club: space travel. Now, with the last flight of the space shuttle under way, the membership list is harder to join than ever. When Yuri Gagarin orbited the earth, half a century ago, and when astronauts landed on the moon eight years later, it would have been inconceivable to think of a time when manned space flight began to slip from the present to the past. But America, at least for the moment, no longer has the capacity to send people into space. In terms of national pride, this may be a failure. In terms of scientific advancement, it may not matter that much at all. Deep space exploration – using robot probes – is a very different and more useful thing than the expensive and unreliable effort to send human beings into low earth orbit, no further from Cape Canaveral than New York. The shuttle has been an icon of its age, but its human passengers – however brave and skilled – have made their flights as much to show the world what America could do as for any particular and necessary purpose. Even the International Space Station, extraordinary though it is, could operate without a human presence, its experiments automated. The only good argument for sending people into space is the simple daring of it – the need, as Star Trek used to claim, “to boldly go where no man has gone before”. Visit Mars, by all means – but there is little to be gained by sending astronauts to orbit this planet, not all that far above our heads.

For me, the most remarkable thing about the Space Shuttle is how matter-of-fact it has become. It’s rather like Concorde, which was an engineering marvel that people would drop everything and gawp at when it  first appeared, but which soon became a part of everyday life. Technology is inevitably like that – what seemed remarkable twenty years ago is now pretty commonplace.

I had similar feelings a couple of  years ago, when Planck and Herschel were launched. Of course I was extremely nervous then , because many of my colleagues had invested so much time and effort in these missions. However, watching the behaviour of the mission control staff at ESA during the launch it struck me how routine it all was for them. It’s a great achievement, I think, to take something so complex and turn it into an everyday operation.

Incidentally, it always strikes me as curious that people use the phrase “rocket science” to define something incredibly difficult. In fact rocket science is extremely simple: the energy source is one of the simplest chemical reactions possible, and the path of the rocket is a straightforward consequence of Newton’s laws of motion. It’s turning this simple science into working technology where the difficulties lie, and it’s a powerful testament to the brilliance of the engineers working in the space programme that workable solutions have been found and implemented in working systems.

So now the era of the Shuttle has passed, what next? Should America (and Europe, for that matter) be aiming to send people to Mars? Should manned spaceflight resume at all?

Different people will answer these questions in different ways. Speaking purely from a scientific point of view I would say that manned space exploration just isn’t cost effective. But going to Mars isn’t really about science; going to the Moon wasn’t either. It’s partly an issue of national pride – note how loss of the Shuttle programme has effectively ended America’s dominance in space, and how keenly that has been felt by many US commentators.

Others argue that manned space flight inspires people to become scientists, and should be done for that reason. I can’t speak for anyone but myself, and I’m sure there will be many who disagree with me, but it wasn’t the Apollo missions that inspired me to become a scientist. When I was a kid I found the footage of people jumping around on the Moon rather boring, to be honest. What inspired me was the excellent science education I received at School. And just think how many physics teachers you could train for the cost of, e.g. the ESA Aurora program…

Another argument is “because it’s there” or, as Walt Whitman put it,

THE untold want, by life and land ne’er granted,
Now, Voyager, sail thou forth, to seek and find.

As a species we have an urge to set challenges for ourselves, whether by asking difficult questions, by designing and building difficult devices, or by attempting difficult journeys – sometimes all three! This is our nature and we shouldn’t shy away from it. But we should also recognize that “going there” is just one of the ways in which we can explore the cosmos. Modern telescopes can see almost to the visible edge of the Universe, the Large Hadron Collider can probe scales much smaller than the nucleus of an atom. I worry sometimes that the political lobbying for manned space flight often seems to be arguing that it should be funded by taking money from other, more fundamental, scientific investigations. Astronomers and particle physcisists are explorers too, and they also inspire. Don’t they?