Oxbridge Physics Mock Interview at Latymer

The idea of the mock interview is for us to have an Oxbridge-style interview with someone we’ve never met before. These took place at Latymer Upper School (on King’s Street), and my interviewer was from St Paul’s Girls’ School.

I went into the interview room and the first thing I was asked was why I wanted to apply to Oxford for Physics, at which point I explained that actually I was applying to Cambridge for Phys Nat Sci but due to an error I was down for Physics at Oxford. He said it was fine and didn’t actually let me explain why I wanted to apply for my course, and straight away asked me to differentiate a pretty standard quadratic. I did it and predicted the next question would be to do it from first principles (which it was). I got as far as the second line (writing Lim(Dx→0){the entire mess before it simplifies}) before he cut me off and asked me whether I knew about radioactive decay. I cautiously said yes, at which point he asked me to write down the equation, then derive it from first principles. I wrote down the ODE, separated variables and proved the formula. He then asked me what I knew about how calculus was conceived. I hadn’t gone to the Newton/Leibnitz Maths Soc lecture but I knew enough about the history (thank you Simon Singh!) to say that they had independently invented calculus at the same time. He asked me what Newton was researching at the time and I said gravity, and was about to go into detail at which point he asked me what I knew about Leibnitz. I confessed that I didn’t know much about him, and he said it’s fine – ‘he’s a mathematician – nobody really cares what they were researching’ (in case readers haven’t already worked it out, he was playing bad cop). He asked me why it’s impossible to say who was the first to invent calculus (which I at first misinterpreted and talked about the different notation which I was going to relate back to something but I now forget) to which I talked about research taking time and that they probably each took lots of time to formulate calculus, and it can’t just be proven who was first by who was the first to submit the paper. He implied it was really about fast communication and he asked whether I knew how research is now distributed. I talked about papers being published online (the arXiv logo jumped to mind though I didn’t mention it) at which point he asked me what scientific papers / magazines I read. I said New Scientist and Scientific American (I could have mentioned Physics/Chemistry Review etc. but I didn’t for some reason), and he asked me to talk about an interesting article I read recently. I started enthusing about this awesome article I’d read in Sci Am about semiclassical gravity – formulating QFT on the hyperbolic geometry of general relativity and possibly proving singularities cannot be formed. Before I could get to the crux of the issue (black stars, repulsive forces etc.) he asked me what I knew about black holes. I started talking about singularities and he asked what terminology I know concerning black holes. I said a list including accretion disks, Hawking radiation, event horizons. He asked me to define all of those. I defined the event horizon, then started talking about an effect which had nothing to do with Hawking radiation (axial plumes coming from the black hole, with an accompanying utterance about conservation of angular momentum and fast spinning) but saved myself just in time and said something about virtual particles being created and destroyed. I mentioned proving virtual particles with the Casimir Effect just before I got to the crux of Hawking Radiation, at which point he interrupted me again to explain the Casimir Effect. I said what I knew – something to do with an attraction between two metal sheets.

At approximately that point he said ‘that’s it’ and that I did fine. He explained he’d been playing [not his words] ‘bad cop’ (by then I’d worked out that either that was the case or he was just in a really bad mood because everything was behind schedule (!)) and that I reacted well under that. There’s a reason I’ve written all that in one paragraph – the interview felt exactly like one continuous rush of me going through almost every bit of classical (and some non-classical) physics I’ve ever come across in half an hour (it felt a lot shorter than that)! It felt a bit like some of the ‘Achilles and Tortoise’ recursion stories out of GEB by Hofstadter in that he kept cutting me off before I could finish one thing, but as it turned out that was the whole point.

At some point he also asked me about the difference between resistance and resistivity (object vs intrinsic material property) and I asked whether I should write the equation connecting them at which point he said ‘yes that might be nice’. He must really get a kick out of playing bad cop! He then asked what causes resistance and what happens to resistivity when you heat something – I drew the approximate structure of a metal and talked about electrons hitting metal cations, and that when temperature rises the cations vibrate more. He asked me to be clearer about ‘more’ – I said greater amplitude and hesitated on saying greater frequency trying to remember the SHM equation for energy (I thought I might have been being ‘browbeaten’ into assuming frequency would increase and in my panicked state I couldn’t remember properly!). I must have said something about SHM and he asked me what that was – I wrote the ODE and said what it meant in words (forgot to write it in x=(x0)sin(wt+phi) form), to which he said nothing and moved on. I can’t remember how that episode fitted in, so I left it out of the mega-paragraph.

Anyways overall, I almost hope my Cambridge interview ends up going like that. I feel I’m now more resistant to intimidating interviewers and have read relatively widely so an interview basically inviting me to talk about what I know about physics until I run out of breath and pass out on the floor (Calvin & Hobbes reference) would be pretty much perfect. He didn’t actually ask me to solve any physics problems, which was not what I was expecting, but hey.

UCL Lecture: Cosmic Rays, Neutrinos & Micro-Black Holes

Yesterday (16th October) I attended another of the weekly UCL science lectures. This week it was given by Dr Ryan Nichol from the Department of Physics and Astronomy at UCL. It was basically about practical particle physics, discussing experiments such as the LHC and the ANITA experiment (the one with hot air balloons flying over Antarctica). So here are my relatively brief impressions…

The first thing I noticed before the lecture started was the enormous turnout. In fact the lecture was moved from the usual Massey Lecture Theatre to the vastly larger Chemistry auditorium, and even so I ended up sitting on the steps. The audience was largely populated with schools, perhaps explaining the turnout. I also noticed the MIT-style blackboards adorning the front of the lecture theatre.

The talk started with a primer on high-energy physics. This was a pretty standard intro, putting familiar things on a log scale of size, quickly delving into some elementary particle and the ball-exchange explanation of repulsion and attraction in Quantum Field Theory (two people on boats throwing balls to each other), an explanation Feynman would not approve of considering his famous answer to the question ‘what makes two magnets attract’! QFT was elaborated upon slightly in terms of a brief description of the four gauge bosons.

He then moved onto cosmic rays. Apparently it was discovered there were more high-energy particles being detected than there ’should’ have been. In ~1910 Theodor Wulf attempted to detect a difference in muon detection between the top and bottom of the Eiffel Tower, but his instruments weren’t sensitive enough to record any difference. In 1912 Victor Hess did the same experiment, but using hot air balloons instead. As it turned out, as the balloon’s height increased, the radiation detected decreased owing to a decrease in detection of earth-produced radiation due to an increased amount of atmosphere between the balloon and the surface. But after a certain point, the detection rate actually increased, leading the scientists to conclude this excess radiation actually came from space. He also talked about the Pierre Auger Observatory in Argentina. This is a set-up spanning an enormous area consisting of a grid of particle detectors. If a shower occurs, several of these detectors will be hit at the same time. There are also four telescope stations which can, on a clear moonless night, actually ’see’ the fluorescence caused by the shower particles hitting air molecules (Cherenkov radiation?) and produce a pretty picture and model 3-D of the event. Dr Nichol was also at one point involved in ‘CREAM TEA’ which stands for ‘Cosmic Ray Extensive Area Mapping for Terrorism Evasion Application’. Supposedly this uses naturally occurring muons to map an area – detectors can build up a good picture of dense objects (like bombs) within an area by measuring scattered muons.

He then moved on to talking about neutrinos, invented in 1930 by Pauli to conserve energy. I knew they didn’t interact with much, but apparently the average neutrino travels through 53 light years of water before interacting! Luckily the sun produces 100 Bn neutrinos per cm² per second, and the few milligrams of ⁴⁰K in humans emits about 300 M neutrinos per second. I was pretty surprised by the sheer number of neutrinos being constantly produced – beta decay must be a big thing… He then talked about some neutrino experiments. He mentioned the MINOS experiment in which Fermilab fires a massive stream of neutrinos at Soudan (MN) in an attempt to detect a few. He also talked about the Super-Nemo experiment (interesting name…) which was created to discover whether neutrinos are their own antiparticles through the inspection of radioactive decays. Apparently theory has it that neutrinos can turn matter into antimatter (I’m guessing something to do with beta+ decay), so the discovery that neutrinos are their own antiparticles might help explain why the universe has more matter than antimatter.

The talk moved onto the less well-known field of micro-black holes. He didn’t actually say much about this except that most black holes are several hundred/thousand/million solar masses, but that it’s possible to create tiny ones of only several milligrams. Concerning the media scare about the LHC creating a black hole and eating the earth, he explained that only some exotic models allow collisions in the LHC to produce micro-black holes (which can be subsequently studied by measuring the Hawking radiation produced as they [very rapidly] evaporate), and only the most exotic models allow one such black hole to grow large enough to engulf the Earth. Thinking about it, 14 TeV (now reduced to something like 7 or 8 TeV) collisions are unlikely to do much harm considering the Earth is constantly being slammed into by 300 TeV particles from über-novae and other such awesome events. This actually reminded me of an interesting article I read in Scientific American (my preferred science magazine) which discussed formulating QFT on the hyperbolic geometry of general relativity (semiclassical gravity). Apparently as a star begins to collapse into a black hole, a force gets created which opposes this collapse which grows to infinity when the star tends from above to a certain radius. So according to this article, while singularities are theoretically possible, there is no way of going from a non-singularity to a singularity (a bit like travelling faster than light). So Black Holes are actually Black Stars. All very interesting stuff, though I just don’t know enough about the maths to really appreciate it myself. My only experiences of hyperbolic geometry are from a C4 programme about 10 years ago, and from reading GEB by Hofstadter. Not to mention QFT…

Finally, he talked about ANITA, a project he had recently worked on. I think someone came to Halley Soc recently to talk about ANITA, so this sounded pretty familiar. The idea was to fly around Antarctica in hot air balloons in the hope of detecting a Cherenkov cone of RF radiation produced when a neutrino decays in the ice. Apparently the battery box of ANITA had to be painted half black and half white to prevent overheating / freezing (since fans wouldn’t be very effective at low pressures at high altitudes), so they did an art contest for the best 1/2 black and 1/2 white design! Later they analysed their results and discovered no neutrinos, but did find they had detected 6 ultra-high energy cosmic ray air showers – the radiation was so intense that it actually bounced off the ice and was picked up by their detectors.

The Q&A session afterwards didn’t seem as lively as normal, possibly due to the sheer size of the audience, but overall it was an interesting talk and I learnt about several cool experiments I’d never heard of before. I’m always quite interested in how there’s always lots of good theory in practical experiments (cf. my Imperial work experience – week 1, week 2), so it’s all good.

Afterwards we (the three of us from SPS who went) managed to spend 3 solid hours discussing physics and maths in the regular post-UCL-lecture pub ranging from things from the lecture, CERN and QM to Feynman, Galois, Turing and Boltzmann to Primer (my new favourite film), a suitable conclusion to the evening!

EDIT: Urgh that wasn’t brief at all. I should really stop doing this whole mega-post thing…

The Wavefunction of a Tossed Coin

This is actually my Science Essay Prize submission – here it is for you to read / scoff at…

The title is a reference to a famous article by Hawking and Hartle: ‘Wave Function of the Universe’ (2)

'Coin Toss'. Taken at 21:34 on 3 Aug 2009 at home using an ad-hoc strobe and a 1p coin. Camera: Fujifilm Finepix S5800 (DSLR); 1” exposure; F/3.5 aperture

The Quantum world, the world of the very small, is very different from the world we live in and are familiar with. In this world, the law of conservation of energy can be cheated for a short period of time owing to the time-energy relation to produce short-lived but vital ‘virtual photons’, and even the concept of probability has a quantum twist. This rather bizarre framework has however been enormously successful and has allowed physicists to make very accurate predictions of experiments’ results; it has never been shown to be incorrect or inaccurate. This seems to imply that, however different it may be from classical physics, quantum mechanics is correct. Yet it seems utterly inconceivable that such apparently opposing ideas are in fact both largely correct and thus identical on a macroscopic level, as evidence suggests, and that the correspondence principle, which states that Quantum Mechanics (QM) reduces to classical mechanics at high masses, is true. Classical mechanics provides a full description of a coin toss. Can QM make the same claim while keeping its predictions consistent with those of classical physics?

The Correspondence Principle

The most important relationship between the quantum mechanical description of this coin and its classical counterpart is embodied in the correspondence principle.

The Schrödinger equation is used principally to work with the energy of a system and is displayed here:

Where m corresponds to the mass of the system, E is a number whose possible values are the possible energies the system may take on, and Ψ(x) is a function of the position of the system (the wavefunction) whose square modulus is the probability density of the particle being at position x. In the example of the one-dimensional infinite square well in which a particle is trapped in a one-dimensional universe (such that V(x)≡0) with impassable ‘walls’ placed at 0 and l, it turns out that:

Ψ(x)=sin⁡Ax (In fact Ψ(x)=cos⁡Ax also works)

At both walls (at l and 0):
Ψ(x)=sin⁡Ax=0

So:
A=nπ/l (n=1,2,3…)

When Ψ(x)=sin⁡(nπ/l x) is plugged into the Schrödinger equation, one obtains:

This tells us that the greater the value of n, the more nodes the wavefunction has on the interval [0,l], so the more energy the system has.

Contrasting the shape of the graph of Ψ(x)²=sin²⁡Ax=sin²⁡(nπx/l) (a probability density plot) when n=1 (below, left) with that when n=50 (below, centre), one surmises the one corresponding more closely with what classical physics would predict (i.e. a constant probability density) is the case when n is high; when n is sufficiently high, the graph of Ψ(x)² can be faithfully approximated to a classical constant probability density (below, right) in which the particle can be anywhere along the line with equal probability.

Click to embiggenatrify

Thus as the energy of the system increases, the value of n rises and thus the correspondence between classical and quantum mechanics becomes closer.

Although this is a very specific example, wavefunctions tend to turn out to be trigonometric functions (such as sin⁡x, cos⁡x and e^ix) which are often the only eigenfunctions of the second differential operator in the Schrödinger equation, leading to the occurrence of a positive power of this naturally arising quantum number (n=1,2,3…) which increases with the number of nodes. One can use the periodicity of Ψ(x) to support the argument that this positive integer quantum number n exists for almost every wavefunction Ψ(x) (i.e. for almost every quantum system). So long as the system’s energy is over a certain limit known as the classical limit, it will have a sufficient number of nodes that it will behave effectively identically to a classical system; as its energy tends to infinity, its behaviour will tend to classical behaviour. Extending this concept, since the energy of the coin toss situation is so large relative to atomic energies (the kinetic energy of the entire coin while spinning is many orders of magnitude greater than that of a stream of particles about to collide at 99.9999991% the speed of light in the LHC), n is extremely large so the quantum description of the coin toss approximates extremely well, and in most respects identically, to its classical counterpart.

Ensemble Interpretation

At its heart, the interpretation states that the Quantum Mechanics is a statistical abstraction from reality: No single particle has a wavefunction; rather the wavefunction applies to a group, or ensemble, of classical particles and it merely describes their distribution. Although this interpretation is largely rejected on the grounds of the Young’s double slit experiment run using a light source that emits only one photon at a time in which an interference pattern still appears, it is an apt intuitive argument for the correspondence principle: the time evolution of the graph of position against probability for a single particle with a particular wavefunction is very similar to the that of position against an approximate measure of density of an ensemble of classical particles. Since in the example of a coin toss there are a large number of particles participating with similar wavefunctions, the distinction between a Quantum and a Classical approach to determining the behaviour of the experiment becomes merely academic and a matter of paradigm since both methods will yield very nearly identical results – whether every particle has a wavefunction or the entire system is considered collectively is no longer relevant to predicting the result of a coin toss.

Classical Probability: Coarse Graining

When a decision event occurs, there are several histories associated with it. For example in a simplified universe containing only one photon, a target, and a piece of card with two slits in it, when the photon ‘chooses’ whether to travel through the right or left slit in the Young’s double slit experiment before hitting the target, a history is created for each of the two possibilities: one for when the photon chooses the left slit and one for the right slit. In a more complicated universe containing several particles, every combination of ‘decisions’ the particles ‘make’ constitutes a different history: each possible history (containing complete information about every particle in the universe at every point in time) is a separate history according to quantum mechanics. These histories are known as fine-grained histories.

As I mentioned, the quantum version of probability is very different from its classical counterpart. Instead of assigning each fine-grained history a probability, Quantum Mechanics assigns pairs of fine-grained histories values. This value for a pair of histories A and B can be denoted by a function: D(A,B). The pair of histories can be a pair constituting of just one history, for example D(A,A), which would in fact be a number between zero and one and can be interpreted as the probability of history A occurring. However the function D follows the following rule:

D(A or B,A or B)=D(A,A)+D(B,B)+[D(A,B)+D(B,A)]

The last term, [D(A,B)+D(B,A)], is called the interference term between histories A and B and can have both positive, negative and zero values; if it is not zero, histories A and B interfere with each other, making it difficult, and sometimes impossible, to assign a probability to each separately.

The problem has now been implicitly stated: if interference makes it so difficult to assign probabilities to histories, what makes it possible to say that the probability of tossing ‘heads’ on an unbiased coin is ½; how can such a prohibitive concept of probability be reduced at large scales to classical probabilities?

The solution lies in an idea called coarse graining: histories are organised into sets. For example there might be the set of all histories in which Photon A travels through the left slit – all histories in which this event takes place are organised into a set. The purpose of this classification is to ignore all factors that do not matter to the critical situation by taking the set of all fine-grained histories which agree that the critical event occurs but may disagree on the goings-on in the rest of the universe. This allows the construction of a single coarse-grained history whose probability is:

D(A₁ or A₂ or A₃…,A₁ or A₂ or A₃…)

where A₁, A₂ etc. are all the different histories that make up this set. If all the fine-grained histories can be divided into sets such that each fine-grained history belongs to one and only one set, one obtains a set of mutually-exclusive coarse-grained histories. The result of all this is that, for two coarse-grained histories α and β consisting of fine-grained histories {A_i } and {B_i } respectively (where {A_i } stands for A₁,A₂,A₃,…), D(α,β)+D(β,α)—the interference term between α and β—is the sum of all the interference terms between pairs of fine-grained histories that belong to those two coarse-grained histories: the net interference between α and β is the sum of all the smaller interferences between {A_i } and {B_i }. This summation often leads to cancellation of positive and negative interference terms, leading to a near-zero interference term between α and β: D(α,α) and D(β,β)—the probabilities of α and β respectively—are very well-defined numbers, no longer dependent on interference terms, leading to independent probabilities of mutually-exclusive events. This collapse of D values into classical probabilities via coarse-graining is called decoherence, and statistically, the more fine-grained histories that are summed over, the closer to zero the net interference term becomes, and the more definite and independent the probabilities of coarse-grained histories become. Returning to the coin-toss example, since a huge number of particles interact with the coin’s faces, an enormous number of histories have to be summed over to obtain the two coarse-grained histories of the coin: heads or tails, leading to a near-zero interference term between the heads-up and tails-up histories: it can be said with much confidence that the probability of tossing heads is ½.

Classic Mistakes: Misinterpretations

Common misinterpretations of the implications of the postulates tend to make QM sound more unbelievable and divergent from classical physics than it really is. For example a famous example often quoted when explaining QM is Schrödinger’s Cat. This is a thought experiment invented by Erwin Schrödinger in which a truly random (unpredictable) process produces a Boolean (yes/no) output which determines the fate of a cat contained in a sealed box. If the output is ‘no’, poison is released into the box and the poor animal perishes; if the output is ‘yes’, no poison is released and the cat remains alive. The concept Schrödinger was attempting to communicate by producing this analogy is that of superposition: in the story of the cat, after the cat’s fate has been determined and appropriate actions effected but before the box has been opened and the ‘aliveness’ of the cat observed, the cat is in a superposition of being dead and alive: while classical physics would state that the cat is either dead or alive, quantum physics would assert that the cat is in a curious state of being neither dead nor alive but in some half-way state, and only when the box is opened does the cat decide its ‘aliveness’. My personal opinion is that this is a brilliant analogy and can be a great help in explaining quantum superposition. Unfortunately the analogy is far too often taken literally, leading many to believe that in such a situation the cat really would be neither dead nor alive. As Gell-Mann pointed out in his book The Quark and the Jaguar (1), the cat frequently interacts with air particles inside the box which in turn interact with the box which in turn interacts with the rest of the universe; since a large number of particles are involved the two outcomes (living cat vs dead cat) decohere leading to a more or less classical situation in which the cat is either dead or alive: by the time the cat is observed, the wavefunction has already collapsed and the cat’s ‘aliveness’ is completely classical.

The idea that ‘anything can happen because of Quantum Mechanics’ is another myth. It is to some extent true, but often abominably misinterpreted by unthinking readers, perhaps a situation exacerbated by episodes of The Big Bang Theory and chapters of The Hitchhiker’s Guide to the Galaxy in which references to this idea are made through jokes and invented technology such as the improbability drive without making clear the true nature of the numbers behind these events happening. The probability of a familiar object visible to the naked eye such as a coin spontaneously appearing on Earth within a person’s lifetime is probably smaller than the probability of someone winning the lottery every time for the entirety of his/her lifespan (which itself is in the order of about 10^(-105) ). It is in fact so unlikely that it is, in all practical sense, impossible (an argument often used, and bizarrely often rejected, to support the case against God).

So what about the coin?

In conclusion, the quantum mechanical description of a tossed coin is identical to its classical counterpart. The probability of obtaining heads is the same in both models; the coin spins and is affected by the air in the same way in both models; in neither model is it possible for the coin simply to disappear in mid-air: the coin never has strange quantum-mechanical properties such as superposition or ill-defined probabilities. By obeying the correspondence principle, QM completely describes classical mechanics and in theory, everything previously explainable and predictable by classical mechanics with regards to a coin toss can be fully explained and predicted by quantum mechanics.

Bibliography

1. Gell-Mann, Murray. The Quark and the Jaguar. s.l. : Abacus, 1995.
2. Wave function of the Universe. Hawking, Stephen and James, Hartle. s.l. : Physics Review, 1983.
3. Hawking, Stephen. A Brief History of Time. s.l. : BCA, 1996.
4. Gillespie, Daniel. A Quantum Mechanics Primer. s.l. : International Textbook Company Limited, 1973.
5. Ballentine, Leslie. Quantum mechanics: a modern development. s.l. : World Scientific Publishing Co Pte Ltd, 1998.
6. Gribbin, John. Q is for Quantum. s.l. : Simon & Schuster, 2000.

Quantum Computing Work Experience – Week 2

Today concludes another fantastic week working at Imperial. This post will probably be a lot less massive than the previous one owing to time constraints (I’ve just come back from several exhausting hours of rock climbing at the Westway and Google Calendar tells me I have my driving theory test at some point in the near future).

Firstly, some pics to support stuff from my last post.

The entire table looks like this - I can understand why everything needs to be realigned and tweaked every 15 minutes for the experiment to work! The two blue lasers are I think the main cooling lasers, pumping from the ground to the high energy levels of Ca+.

This is a used Cu O-ring (actually called a gasket) - you can easily see where the knife edge bit into the Cu making a vacuum seal

A top view of the laser setup. You can see the diffraction grating (with an arrow drawn on it) and the connections to the piezo behind it. Click to embiggen.

Equipment

Tantalum Oven

This is the equipment used to produce neutral atoms which are to be ionised.

The oven is suspended between the two electrodes by a Ta wire. The Cu foil is there for a test run of the oven - if it works we should be able to see a spattering of grey Ca on the Cu.

This is the plate on which the entire experiment (ion trap, oven and all) will sit. It will get inserted into one of the holes in the central 6-way cross can.

When I first heard they were going to use an oven, for some reason I imagined some sort of miniature baking oven that somehow emits atoms when turned on! The actual oven is actually a tiny 1cm long tube of tantalum (Ta), sealed at one end by essentially squashing the end, with a tiny hole in the middle of the tube. Ca shavings are stuffed into the open end before the oven is closed, again by squashing. The whole oven is attached by a piece of Ta wire to two electrical contacts across which a potential is applied. The Ta conducts current and heats up, acting as a heating filament. The Ca heats up and the most energetic atoms spit out of the hole (the process is basically evaporating the Ca at very low pressure and high temperature).

I asked why Ta is used – presumably Tungsten (W) has virtually the same properties in that it heats up when current flows through it, and since W is the metal of choice in light bulbs, presumably it’s cheaper? Apparently W can indeed be used; for such applications the criteria for metals are that they are UHV-suitable (don’t trap/adsorb other molecules/atoms on/to their surface which subsequently outgas, ruining Ultra-High Vacuums) and won’t melt at high temperatures. However Ta is normally more suitable than W because it’s more malleable (whereas W is very springy) and can be easily spot-welded (to stick the wire onto the oven). However thoriated W is better than Ta as an electron source since the thorium gives it a much lower workfunction, allowing more electrons to pop out for the same energy input.

Vacuum Pumps

In my previous post about this work experience I omitted some detail on the pumping that I learnt this week. As it turns out, the actual pumping requires three pumps. The first is a roughing pump, to get the pressure down to a very rough vacuum (~10^-2 mbar). Here they were using a rotary vane pump:

This image was nicked from wiki

Essentially as the off-centre internal cylinder turns, the vanes get longer / shorter accordingly such that the pressure at the input is always getting lower and at the output it’s always getting higher, forcing the air out of the output. The principle is essentially PV conservation.

The second stage is a turbo pump which is basically an electrical version of the intake fan of a jet engine. It spins extremely quickly (so quickly that it requires a low pressure to operate lest it smash itself to pieces) and the idea is that it spins so quickly that any molecule that hits a spinning blade hits the part of it such that it gets kicked outwards, away from the vacuum. This gets the pressure down to about 10^-5 mbar. The final stage of course the ion pump.

When air is pumped out the can sits in an oven - the idea is to heat up anything that can outgas while pumping, making it outgas more, thus getting rid of 'outgassable' stuff

Wavelength Tuning using Iodine

There are several ways of tuning wavelength (I wrote something about the cavity method – setting up a standing wave – in my previous post), but I found this way of doing it particularly interesting. Like all other elements, iodine has a certain absorption spectrum, a feature used in star spectroscopy to determine elemental composition. But instead of doing what astronomers do (measure wavelengths to identify elements), here we were using a known map of iodine’s spectrum to tune the wavelength: light shining through the iodine has a certain attenuation which is dependent on the wavelength (owing to electron energy levels). By shifting the wavelength around using a piezoelectric it is possible to obtain a local iodine absorption spectrum (wavelength against intensity). By comparing this local spectrum with an ‘atlas’ – iodine’s spectrum for a large range of wavelengths, it is possible to locate the local spectrum within this atlas, thus identifying the wavelength. Apparently a narrow band of local spectrum is sufficient to identify a unique location in the atlas: there are no ‘repeats’. Whether this is non-repeating property is specific to iodine (hence its use) I’m not sure; the isotope used is radioactive so there must be some really good reason to want to use it!

Techniques and Procedures

Saturated Absorption Spectroscopy

All atoms radiate photons. However in a cloud of atoms these photons are affected by the Doppler shift owing to the random movement of the atoms, and a graph of frequency against intensity (basically a spectrum) shows an underlying distribution for this radiation. However the interesting bit of spectroscopy occurs on the surface of this curve, in the form of ‘ripples’ on the underlying curve’s surface. While a human can normally see the ripples roughly by eye, the underlying curve gets in the way of accuracy.

The solution is a method of somehow obtaining the underlying distribution without the ripples using lasers and subtracting this curve from the spectrum, resulting in a graph of just the ripples. I’m still clueless as to precisely how this works / is performed since I didn’t personally bear witness to the process (I heard something about matching lorentz curves to points but that was probably more to do with analysis of the ripples rather than the process of saturated absorption spectroscopy) so it looks like some wiki-ing is called for.

Walking the beam

This isn’t some physicist’s attempt to be a pirate and getting the words muddled; it’s actually a rather clever (though extremely time-consuming) method of aligning a laser beam. Bascially the ideal situation is a laser beam passes precisely through two points. This is very difficult to achieve with just one stand so a setup with mirrors is necessary. Here are several different failed attempts at diagram-ifying the thing:

The dotted lines were added by me to show where the beam will go

At each of the two points the beam needs to go through an adjustable iris is placed (think circular doors in sci-fi films), and mirrors alpha and beta (making up the periscope) can be adjusted so the beam’s height (h) and angle of elevation (e) can be adjusted more or less independently. Then the following two-step process is iterated until the beam is almost exactly where it needs to be.

1. Open B completely, close A so it becomes a tiny hole, and adjust the laser so it goes through A using mirror alpha
2. Open A, close B so it becomes a tiny hole, and adjust the laser until it goes through B using mirror beta.

Illustrations of the steps are as follows:

For some reason it reminded me of numerical analysis / Newton Raphson type things – constantly optimising and getting closer and closer to perfection yet never reaching it. GL’s cobweb illustration of numerical analysis seemed particularly similar to this situation. Anyways while I quite like how it works, walking the beam does start to lose its novelty after doing it for a couple of hours…

Scanning Tunnelling Microscopy

Danny also explained some awesome stuff on this and how it works. Basically the idea of STM is to use quantum tunnelling calculations to make a map of a surface. A probe is held (say at +5V) very near a surface (grounded), and owing to quantum tunnelling, a certain current flows between the probe and the surface. This current is proportional to exp(-l) (or something like that) so it is possible to measure l to a very high degree of accuracy. As the probe is scanned across the surface, a matrix of measurements of l against (x,y) can be created, thus mapping the topology of the surface. This mapping can in fact be so accurate that it can pinpoint individual atoms sticking out from / adsorbed to an otherwise flat surface.

Conclusion

The last two weeks have been nothing short of awesome. I’ve learnt (and sometimes noted down) many new things on every one of the last ten working days and I’ve recounted here and in last week’s post merely a handful of the more interesting bits and pieces. I even solved an apparently insurmountable practical problem thus moving the entire scientific community forwards! I mean … I came up with a (pretty good) solution to unscrewing a stuck nut… Many thanks to Danny Segal for giving me such a wonderful opportunity.

There is one thing I still can’t work out though:

Quantum Computing Work Experience – Week 1

5W Green Laser used for pumping Titanium-Sapphire Laser

I’ve been looking forward to this for quite some time – two weeks of work experience in a lab at Imperial College working with some PhD students with an ultimate goal of making some progress towards the construction of a quantum computer that doesn’t take tens of man-hours to perform each calculation. After a week I feel I’ve learnt a lot about formal lab work and large-scale experiments (*slightly* different from the 20-minute assessed practicals from AS!) and about the general physics and concepts behind some of the experiments and equipment – I’ve been (not so) conscientiously filling pages of my notebook with messy notes and cryptic diagrams so hopefully some of the stuff I write here will make some vague sense and not quite directly contradict truth.

There are also several interesting bits and pieces lying around the place. There’s an enormous Newton’s Cradle in which each ball looks like it could be heavy enough to be a ship’s anchor. There are also enormous capacitors lying around everywhere for the people working on high-density fluxes.

Capacitor banks lying around

The Building

The Physics / Maths / Computer Science part of Imperial is somewhat bizzarre – from what I gather it consists basically of two adjacent buildings which were built at different times and were haphazardly connected together by knocking down bits of walls. Unfortunately the actual floor levels are out of alignment and the floor heights are also different, which means there’s a crazy staircase joining the two buildings together and floors 6 and 7 in one of the buildings had to be rechristened 6 and 6M for the sake of keeping the numbering consistent with the lifts. There are also only connections on certain floors of each building so it’s possible to leave the Blackett Lab on the bottom floor, go up one level and be confronted with a solid-looking wall where the connection should be. As if things aren’t crazy enough, there’s a set of lifts placed almost exactly at the junction (so to speak) between the two buildings, making it really confusing to navigate the whole 3D maze. It’s pretty good fun actually!

The Lab and Equipment

Optics

I was quite surprised when I first saw the lab – I was expecting a Leonard Hofstadter style lab (as seen on The Big Bang Theory) but actually quantum computing with ions (ions therefore being the main focus of most of the projects which I’ll come to later) involves a fairly large amount of optics work, so each of two adjacent, connected labs I was working in has an optical table as its centrepiece littered with lasers and ridiculously complicated setups of mirrors and lenses which have been tuned very accurately to direct laser beams into tiny optical fibres and whatnot. Speaking of accuracy, the setups are so sensitive to small shifts that they need to be tuned almost constantly. The PhD students told me they detect a lot more drift during the daytime when other experiments are going on in other labs which release radio waves and traffic is rumbling overhead (despite being two floors below ground level and over a block away from a small road) than at night when there is less activity.

The equipment is also sensitive to tiny temperature fluctuations. Most of the lasers are basically diode lasers:

It’s a fairly standard laser setup in which electrons and holes come together in the depleted region between n and p type semiconductors and then either wait for a nanosecond or so before annihilating and releasing a photon (spontaneous emission) or get hit by a photon, resulting in stimulated emission. What was experimentally interesting was that the cavity length in fact determines the wavelength of the laser owing to the fact that a standing wave needs to be created which ‘fits’ exactly in the cavity (a whole number of half-wavelengths need to fit in the cavity) and this is sensitive to temperature. So each laser box has four BNC sockets: one for providing the laser with electricity, one for a thermistor which is hooked up to a feedback loop system which regulates temperature using a Peltier junction heat pump (which occupies another socket on the laser), and one for a piece of Piezo (placed on the diffraction grating) which can change width depending on the voltage across it (or maybe current through it, or something) thus allowing the cavity length to be adjusted, though my suggestion to manipulate the piezo in the feedback loop to compensate for temperature changes would fail since the temperature-dependent expansion of the cavity is several orders of magnitude greater than anything the piezo can correct. When I heard that I was pretty astonished the laser cavity had to be adjusted to such an exact length – several orders of magnitude more exact than the expansion of a bit of metal when raised by a few degrees. The entire laser is covered by a thick black piece of foam to protect it from temperature fluctuations in the room.

Electromagnets

It was pretty cool to find out that I was to be working in the same room as a 2.5 Tesla electromagnet! Ion trapping, as I will also come to later, involves not only charge and potential fields but also magnetic fields, so the Penning Trap the researchers there were using was sitting inside an enormous superconducting electromagnet.

The superconducting electromagnet uses liquid He to keep cool – as a sidenote I asked why they (and CERN) use cool superconductors (more expensive liquid He) instead of the more recently discovered crazy warm ones (cheap liquid N₂); the reason is because above a certain current, superconductors end up failing and develop some resistance causing heat to be produced resulting in a quench (the He boils off, expands to something like 15x its volume and the whole can explodes in a fit of freezing fury), and the cool superconductors can carry a much higher current before this happens, allowing more powerful electromagnets. Of course this comes at a very high cost. As can be seen from the diagram, the He (at ~4K) is shielded from room temperature by a layer of liquid N₂ (at a balmy ~77K). The He needs to be replaced about once every couple of months, while the N₂ is replaced about twice a week. The superconducting coil, power supply and cables are eventually going to have 80A coursing through them – a truly formidable current!

Refilling with N2

N2 is very cold!

Apparently the way they get the electromagnet to start conducting current is to simply arrange the coil in a loop – they can’t expose the 4K superconductor to air, so it is necessary to induce the current in the superconducting coil. Once this is done, the power supply can be switched off and the current in the superconductor just keeps going round (owing to the lack of resistance), allowing a very strong noise-less magnetic flux to be produced (the flux’s precision is something like 10^-6%)

Vacuums

This was particularly new to me. I’d never worked with 2.5 Tesla or 5W lasers before, but while I’ve come across magnets and lasers in experiments, I’ve never really observed experiments involving vacuums before (apart from the bell-ringing-in-a-jar/gerbil-squeaking-in-a-jar one to show sound doesn’t travel well through a near-vacuum). There’s a lot of novel (to me) and interesting experimental stuff that goes on here.

Basically the idea of creating a seal when joining two flanges together is to use a copper O-ring. Each flange has a ‘knife edge’ (90° very sharp edge) and when they’re pressed together with a Cu O-ring in between, the knife edges cut into the soft Cu; thus the Cu itself becomes the seal.

While flicking through Inward Bound by Abraham Pais (recommended by CAPS) I read about various attempts at making a good vacuum pump. Modern technology has come a long way since the mercury-filled jar, and now creating a very good vacuum is a multi-stage process. First all the equipment is cleaned thoroughly – for some reason fats and oils from people’s hands (for example) are disastrous for a vacuum so everything needs to be wiped squeaky clean with something like acetone or isopropanol. Then everything is sat on the optical table which has a source of clean dust-free air on the ceiling which constantly blows on the equipment, keeping dust off and constantly cleaning it of bits of dust that have settled. Then everything is put together using gloves, nuts, bolts, Cu O-rings and *a lot* of effort (believe me, putting flanges on sideways while stopping the Cu O-ring from slipping out is infinitely more difficult than measuring SHM of a cork in a tub of water – reference to AS practical; one of the researchers also described putting He into the cannister having first cooled it sufficiently to stop everything boiling off immediately as a dark art rather than a science). The air is pumped out using a conventional pump until the pressure inside is something like 10^-6 millibars, at which point an ion pump is turned on to essentially evacuate the remaining air molecule by molecule. The pump essentially ionises the gases inside the chamber and use charged plates to attract them out. The final result is a very good vacuum.

The Projects

Photon Ionisation

There was a MSC researcher from Germany sharing the lab with the PhD students from Imperial, and he was working on a different method of ionisation. The supervising prof, Dr Danny Segal (a reader in Quantum Optics), explained that the previous approach to getting ions was to use a ’splat gun’ approach – basically a stream of neutral atoms from an oven hits a stream of electrons from an electron gun, and those electrons will tend to knock out some electrons from the stream of particles, resulting in a few ions. This has a few problems: lots of atoms never get ionised so end up getting deposited on the side of the chamber, screwing up the shape of the potential well in the ion trap; lots of electrons end up floating around in the chamber and get deposited on insulators, again causing irregularities in charge distribution.

The German MSC researcher was working on using photons to create these ions – a much more tenuous stream of neutral particles is projected into a beam of photons which, via the photoelectric effect, knock out electrons creating ions. This should have a higher rate of ionisation leaving fewer ‘waste’ atoms sticking to the inside, and the number of photoelectrons knocking around the chamber should be much lower than the number of electrons being shot from the electron gun. I suggested the photons might knock electrons off other bits of the apparatus, again screwing up the flux; apparently this should happen infrequently enough to allow a reasonably controllable flux, though some researchers using a Paul trap (involving an oscillating EM field) apparently detected ionisation using photons of the wrong frequency for direct ionisation leading them to believe electrons were being knocked from the apparatus and these, accelerated by the oscillating field, slammed into atoms causing ionisation.

Anyways the setup was more or less thus (a picture is worth a thousand words):

The way to ionise these Ca atoms is to first use a laser to excite the atoms – push some electrons up to a higher energy level. The UV LED then does the actual ionisation from that energy level. The picture above is of a half-finished setup (optics haven’t been sorted out yet and there are two unsealed flanges).

Laser cooling

GSM/KPZ gave us an article in class last year about laser cooling (‘Cool things to do with lasers’, Ifan G Hughes et al 2007), and it turns out it’s useful for Quantum Computing – a jittery ion is presumably pretty bad for physicists who want a stable wavefunction. Well, here’s the setup.

Click to embiggen

It’s in fact mostly about using lasers to manipulate electron energy levels in a Ca⁺ ion:

The Ca⁺ ion has an energy level electrons can fall down to (RHS of diagram) where they would stay for quite long before falling back down which is undesirable considering the cooling involves shuttling electrons between the leftmost levels (in the diagram). So four red lasers are required to pump those back up to the top energy level.

QED

I’m not really sure what’s going on in this experiment but basically, since QED is only significant at high charges (something like that), the researchers go to GSI to conduct this research. The idea at GSI is to slam super-high energy ions through a gold foil which apparently strips them of all electrons. Different ions are separated via a very similar system to how a mass spec works.

Some Other Physics-ey Stuff

Ion Trapping

There are of course lots of different methods of trapping ions – I mentioned one in my post about the UCL antimatter lecture. Apparently it’s provable from Maxwell’s equations that it is impossible to create a static 3-dimensional potential well to trap ions, so there are currently two main methods: using a purely electromagnetic system (using either some feedback system to wobble the ions towards the centre of the trap or a constantly oscillating field like in a Paul trap), or to use magnets:

A cation is sitting at the bottom of a potential well in the z direction. It is surrounded in the xy plane by oppositely charged plates. As it is attracted to the plates, the z-directional magnetic field causes it to move in a circular motion (as seen in cloud / bubble chambers to determine momenta of ejected charged particles), represented on the diagram by ‘micro OOO’. The charge on the plates are then somehow tuned to make the large-scale motion of the particle resemble a circle and so it eventually loops back on itself, so its path shape looks like what is labelled in the diagram as ‘tuned, get O’

The Ca⁺ Ion

The actual quantum computation to be done with the Ca⁺ ion (not a typo: just one +; this isn’t chemistry!) involves electron energy levels. An electron can be in one of two energy levels, and that is the qubit. In Ca⁺ there are two more or less independent distinct situations in which an electron can be in one of two energy levels, allowing two qubits to be encoded into one ion.

The use of this isn’t only to cram more qubits into fewer ions (I read a research group somewhere is making base-5 ‘qudits’ using microwaves and superconducting things) but also to allow easier entanglement – since both qubits are in the same ion it’s supposedly easier to make them interfere in a predictable manner, which allows a quantum NOT gate to be set up which is critical to quantum computing; supposedly only two research groups in the world have managed to get this quantum NOT gate to work.

Ion hopping

The biggest limitation apart from the sheer fiddly-ness and slowness of everything in the quantum computing world is the fact that it’s impossible to put more than about 8 ions in one trap before they start screwing up each others’ wavefunctions. The PhD researchers had previously been working on a solution to this problem that the theorists came up with – getting the ions to hop around in the trap, thus manipulating each ion more or less individually. This has already been done using Paul traps (I think) but the researchers here were trying to use Penning traps and show they are in fact better for quantum computing (or at least can do the same things as Paul traps).

Overall

There’s a lot more I would say if I had the time but as with all blog posts, you’ve got to stop somewhere. But overall I’ve never done modern practical physics before (at UCL we looked at some particle traces on the computers which is the closest I’ve really got so far) so this is a pretty damn amazing experience for me, hence the mega-post.

Introducing: the world's smallest allen key!

Aerospace Challenge Finals at Cranfield

Last week I was in Cranfield participating in the Aerospace Challenge Finals. The challenge this year was to come up with a design for a device to drop humanitarian aid accurately (within 20 metres of a target) from 3000 metres up. Our idea managed to make it to the finals which turned out to be a week of lectures on general aerospace engineering, activities and flying! Photos are here.

Flying

Each person got two flying experiences, both of which included some time piloting the aircraft: about 10-20 minutes in a helicopter and about half an hour in a fixed-wing plane.

My first flying experience was with a small Robinson helicopter, which can only really be described as terrifyingly, exhilaratingly awesome. The pilot managed the take-off which was one of the most breathtaking experiences I’ve ever had – in a helicopter you’re literally sitting in a big transparent flying bubble with the engine behind you, so the view and experience is truly amazing as the land falls away beneath you… I later took over and found control extremely difficult – even a tiny movement of the stick causes the vehicle to tilt violently in that direction making a beginner like me very prone to overcorrection leading to a serious case of increasing-amplitude SHM! The actual stick is situated between the pilot and the copilot and a rotating handle is stuck on the end allowing dual control, so my rather flailing and uncontrolled flight was abruptly and expertly rectified when the pilot took control (though not before I turned and prepared to land by erratically lurching towards a patch of grass). The pilot then demonstrated some cool things one can do with a helicopter including skid landing and take-off, going backwards and sideways while spinning etc.

Here you can see how control over steering is shared between pilot (me) and real pilot (instructor)

The next day I got in a PA28 – my first fixed-wing experience. The pilot had to go through an enormous list of things to check before taking off and explained a little about what she was doing (mostly checking the engine could rev at certain RPMs and wouldn’t give out in certain situations, flicking on and off various lights and calibrating [and pointing at] instruments). The runway was also ridiculously long so she didn’t even bother with flaps for takeoff. This was much easier to fly than the helicopter and the dials and instruments in the cockpit didn’t obscure the view as much I had inferred they would from MS Flight Sim’s portrayal. I did a few rather ginger turns and pitch adjustments before relinquishing control back to the pilot who then demonstrated some steep banks, a stall (which sounded dangerous and seemed to imply the engine cutting out) and a dive (which was extremely cool). Later that week Matthew and I were inspired enough to ask about possible places to get flying instruction – flying has always been one of those things I’ve wanted to learn but I’ve always ended up not having enough time or money to start…

Here the instructor is doing a steep bank. She even did a pretty steep dive totally relaxed and with that pen in her hand!

Me flying the PA28!

Activities

The week started with some group leadership exercises which consisted of attempting to place 30 cards in the correct pattern (easy) and work out the shape and colour of two missing shapes while blindfolded (hard) – both were much more enjoyable than I had expected from that genre of exercises.

The first engineering challenge we were given was an egg-drop challenge – the idea was to construct a package which will protect an egg from a drop of 4 metres. We were given limited materials and each material had a price; the idea was to make the cheapest package that doesn’t crack the egg. Our attempt turned out to be the most epic non-fail in history – literally seconds before the end of the construction phase we managed to pop two balloons which made us completely change our plan and in the last few seconds and in great haste we crammed stuff into a crumple zone and added a parachute … and it somehow worked and turned out to be the cheapest package (if wastage is deducted)! I guess that really proves the KISS principle: Keep It Simple Stupid.

The second engineering challenge was along similar lines – dropping aid – though it was from a more macro perspective. The game was called ‘airlift’ and sold by Elite – the idea was to plan an air route through several African villages which uses the least fuel, while dropping packages of aid which we had to construct out of wooden blocks, paper and tape while making sure everything fits in the cargo hold. The first thing I pointed out when time started was that both problems were NP-complete: the packing problem was almost exactly the same as the knapsack problem and the route planning was basically the Travelling Salesman problem with fuel added in as a factor. In other words we had to be either very good at intuitive problem solving or somehow get lucky. As it turned out, as perhaps a combination of the two, we somehow managed to come up with both the the optimum packing configuration as well as the best route, and finished literally as the final buzzer went – not bad!

The rest of the week was dotted with things like paper plane competitions (which included an awesome flying paper ring which seems impossible when you first see it fly), a game of (actual) CTF and some sports.

Lectures

Over the week there were daily lectures. Much as I would love to discuss them all here in depth I haven’t got that much time / space and besides most people aren’t as interested as I am in the effect of negative angles of attack… But I’ll go a little into some of the most interesting lectures.

Fly by Wire (FBW)

The problem for a long time had been that when going sufficiently quickly, adjusting the controls from the cockpit was really quite hard work – the air going past has so much momentum and the mass flow rate is so high that to change its direction by (for example) adjusting the ailerons requires a lot of force. To make things worse, at supersonic speeds a shock cone is developed (some awesome videos of this are on Youtube) – if this touches the aileron the stick can be wrenched out of the pilot’s hand. Some of these controls were partially solved by making the stick adjust small tabs in the wing instead of the entire aileron, reducing the force required to steer, and by making controls non-reversible (force on the aileron doesn’t affect the flying stick). There are of course some problems with these such as lack of ‘feel’ of the controls. So recently manual stick-aileron transmission was replaced with an electronic motor which receives instructions from the cockpit and adjusts the ailerons itself. Not only does this take all the strain off the pilot, but it also allows a computer to neutralise bad judgements on the part of the pilot such as initiating a sharp dive at 50 feet, implemented by a feedback mechanism from the aircraft to the computer. It also simplifies the cockpit – instead of filling the area with controls, dials an instruments, a computer screen with a joystick and throttle suffices to fly a FBW plane. I asked whether, since FBW significantly reduces the pilot’s direct control over the aircraft, FBW might actually make complicated manouevres more unsafe or indeed completely impossible. John Farley, who was giving the talk, said that, from his vast experience, pilots, however experienced, cannot really be trusted to fly planes safely all the time, and in fact he would feel safer trusting a computer’s judgement and letting a computer do such manouevres than a pilot. That talk also proves that a Boeing 747 probably has non-reversible controls so that scene in Snakes on a Plane (I think it was that film) in which the pilot asked the co-pilot to help pull back on the stick very hard was probably a load of rubbish. Not that you needed to be told that.

Basic Aerodynamics

One of the interesting things from this talk was the reasoning for why helicopters don’t go fast. There is always one part of the rotor going forwards, and if the helicopter moves forwards sufficiently quickly that part of the rotor travels at supersonic speeds generating a shockwave that could rip apart the rotor. In addition, even at lower speeds, there is an imbalance between the airspeed of the fowards-going part and backwards-going part of the rotor meaning a gimbal has to change the angle of attack of the blade depending on which way it’s going: the angle of attack of the rearwards-going blade has to increase to increase lift on that side otherwise the helicopter would just roll over. Of course, there is a maximum angle of attack this blade can be set to before it stalls which is about 20°. This limits the helicopter’s speed at subsonic speeds.

An RAF Hawk landed at the airstrip for us - here is the pilot demonstrating how the entire tailplane rotates

Automation and the future

This was probably the most interesting talk of the week; unfortunately it was cut short for us owing to a jetstream flight. Apparently currently pilots of Euro Fighters get sensor fused info presented to them in the form of advice as to what to do and they simply act upon that, which means half the time the plane is telling the pilot what to do: it is telling the pilot how to control it: semi-automation. Even in commercial aircraft a system called TCAS (Traffic Collision Avoidance System) senses other aircraft and advises the pilot on how to manoeuvre. There is clearly room for improvement: unmanned aerial vehicles are coming. This of course led to the whole humans v computers discussion but for every example of a pilot doing something heroic and saving the plane, there are several examples in which pilots screwed up and computers would have saved lives – Chris Roberts, the speaker, asked whether it *really* is desirable to have a pilot flying the plane, and whether the problem of pilots becoming de-skilled from letting the autopilot take over really is such a problem after all. I also found it very interesting and surprising that currently many landings of commercial aircraft are performed by the autopilot in low-visibility situations.

Anyways overall it was a fantastic week. Whatever the results of the competition turn out to be, I for one got a lot out of six days in Cranfield. I learnt a lot, made some friends, made some good contacts in the industry, and had some great fun relaxing in the English countryside!

Walking in the English countryside

Antimatter Lecture at UCL

On Friday (24 April) I attended an open lecture at UCL on antimatter (“Antimatter in the Laboratory and beyond”). The lecturer was Dr Dan Murtagh from the Department of Physics and Astronomy, UCL, who is currently working on antimatter. The talk was split up into several main areas: the prediction of antimatter, creating, harnessing and detecting it, and applications for it, both current and future. My memory is poor and I only wrote down bits that I thought were interesting / useful to me, so I shan’t attempt to give a comprehensive summary; rather I’ll just put into a coherent and legible form my scribbles.

Discovery

Antimatter was originally proposed by Paul Dirac as it came out of his equations. Originally he thought the antimatter equivalent of an electron would be like a proton and therefore have the same mass; eventually the positron was discovered by someone who noticed what seemed like a positively charged electron in his bubble chamber (a rudimentary particle detector). Thus was antimatter born.

Detection of Positrons

Positrons are created from Sodium-22, an artificial isotope which for some reason is only produced in one place in the world (somewhere in South Africa), and is also in relatively high demand owing to increased research on it. The situation appears to have some money-making potential… But anyway, when the positron stream is created, the positrons have mostly far too high an energy to be useful. So, like in nuclear power plants, a moderator is used in an attempt to slow down the positrons.

Moderators (mostly made out of tungsten) tend to have several problems. Positrons go into the metal and interact with matter, presumably mostly via EM forces, and can end up doing one of four things: they can end up coming back out the way they came as ‘thermal positrons’ (whatever they are; not very useful); they might get stuck in a hole where a tungsten ion is absent and end up annihilating, creating gamma photons (useless); they could come out the other side and somehow have gained energy or not lost enough (useless) or they might lose sufficient energy to be useful in most experiments (useful). Once they come out the other side they follow a complicated path through some apparatus as illustrated, guided by magnetic forces in a very similar way to the LHC.

(click to enlarge)

Essentially the positrons get channelled through various filters to clean up the beam (most of the process consists of getting rid of electrons) which itself ends up in a gas cell where various detection instruments (ion detectors, positron detectors and photonmultiplier tubes).

Positron Interactions

Positrons interact with normal matter in three different ways:

Positron Impact Annihilation

In other words:

This is however a rare occurrence – it requires a positron to occupy the exact same position as an electron and the probability of this happening makes annihilation almost negligible.

Positronium Ionisation

In other words:

A positronium is essentially a Hydrogen atom in which the proton is replaced with a positron – it’s an electron-positron pair. It has an average life of 143ns before the pair annihilates. Fortunately (from what I inferred) most positronium ‘atoms’ are moving fast enough to be relativistic, so scientists have just about enough time experiment with them, and, as discussed later, even in the Ps’ frame of reference, 143ns is enough time to do chemistry.

Speaking of atoms, there is some research called ATHENA taking place at CERN to attempt to create anti-hydrogen: an anti-proton/positron pair, an experiment which was discussed to some depth in the questions and which made another appearance when the lecturer was discussing traps.

The third interaction is impact ionisation, when the positron knocks the electron out of orbit:

Harnessing Positrons

As an aside, I was discussing the possibility of work experience at Imperial with a reader in Quantum Optics, and he showed me round the lab. As it turns out, his PhD students were/are also working on ion traps, though instead of with antimatter with entangled ions.

Anyway, onto positron traps. As it turns out, the method for trapping them involves cylinders held at different voltages. As shown in the diagram, the trap consists of a series of cylinders laid end-to-end, held at different voltages. The positrons are repelled by the walls of the cylinders by different amounts. Since E = QV, the positrons will be at lowest energy (preferred) when the cylinder voltage is 1V. An energy diagram is shown below the schematic showing clearly how positrons get trapped. The voltages shown are arbitrary and are there just to give an idea…

These traps are very effective but unfortunately occupy a substantial amount of room, thus are unfeasible for antimatter storage.

Returning to ATHENA, their method of creating anti-Hydrogen consists of using ion traps. Using a potential diagram, the idea is to trap anti-protons and anti-positrons in the same place. Positrons chase low potential while anti-protons chase high potential.

So positrons are being pulled up, trapped by the underside of the potential curve, while anti-protons are being pulled down, trapped by the top of the curve. Eventually the two types of particles interact to form anti-hydrogen. Unfortunately the anti-atoms produced are higly excited and since they are neutral, cannot be trapped by electro-magnetic means and end up hitting the side of the apparatus where they annihilate.

Uses of Antimatter

PET scanners (Positron Emission Tomography) bombard the subject with positrons (essentially like beta-plus radioactivity) and when annihilation takes place, the photons can be detected with gamma-ray detectors. It’s apparently used for detecting cancer and beta-plus emitters can be bonded to sugars which is also apparently useful. This strikes me as a somewhat dangerous procedure – bombarding a patient’s brain with beta-plus ionising radiation which itself produces enough gamma radiation to be imaged.

A futuristic and probably impractical use involves using antimatter as rocket fuel, something NASA are working on. And rather than producing antimatter, the rockets would need an antimatter harvester in the form of a massive satellite with rings of 30Km diameter positioned near Saturn’s rings which uses strong magnetic fields to gather antimatter. It all sounds rather … unlikely.

Questions

Anti-proton production involves colliding protons (a 2GeV beam) with metal which results in pair production, producing a proton/anti-proton pair.

I wondered how antimatter is supposed to interact with gravity. What I thought (as a sort of wild guess) was that if the Feynman model of antimatter as matter going backwards in time is correct, antimatter should attract itself going backwards in time, thus be observed by us as repelling itself going forwards in time. There’s also a theory that it doesn’t interact at all. As it turns out, a research group at CERN fired a (very long) anti-proton beam and found antimatter does indeed fall towards the earth; antimatter is attracted by matter.

I had read in the New Scientist about how lasers work – the interaction of electrons with holes and subsequent production of positronium which ends up annihilating if a photon passes releasing a coherent photon (stimulated emission). Apparently some scientists have managed to stabilise that Ps, turning it into ‘excitons’ which have a much longer life. I asked if this may be a potential form of storage. Since positronium is like an atom, it has a first ionisation energy (of about 6.8eV) which means if it were possible to somehow store Ps it would probably be feasible as positronium storage.

There were quite a lot of questions and it all ended up as a big discussion about ‘anti-chemistry’ (a research group at Riverside, CA are investigating that) and the possibility of antimatter galaxies.

All in all, the talk was, to me at least, highly interesting and thought-provoking. My friend had advised me that most of the actual talks, since they are public and pre-university students are in the audience, tend to be relatively non-mathematical and simple (and I was horrified at first when he declared E=mc² was to be the only equation in the talk); but I felt that the talk itself probed the subject quite deeply and the experimental side was very new to most of us. And of course, the questions were an invaluable part of the experience.

๏̯͡๏﴿

British Informatics Olympiad Finals at Cambridge

I’ve just got back from the British Informatics Olympiad finals (they chose the top 14 in the country to take this – I was an experimental error) which took place at Trinity College in Cambridge. Despite a fairly epic fail, I thought the weekend was quite productive and I’ve definitely acquired better skills from the only formal or otherwise training in programming the contestants were (strongly) encouraged to undertake. More photos can be found on my Flickr photostream.

Night shot of housing

As always with such activities, the people there shared many interests, and since programming is (at St Paul’s anyway) an interest few people take vaguely seriously, it was a particularly unique weekend for me in that I could talk about Dijkstra’s Algorithm without getting suspicious sideways glances and a general awkward diffusion of human density away from myself… Pretty much all the people there were doing double Maths and were very much into it, and even at a school like St Paul’s one probably wouldn’t be able to mention the Collatz Conjecture and have every person in the room nod and begin elucidating their own hypotheses on where the proof will (if ever) eventually come from (e.g. graph theory, number theory, computing etc). One of the people who had a big hand in organising and managing the whole affair (Tom), seemed to know a great deal about Physics, Maths and computing and the night before the olympiad he and a few of us had a long argument about string theory, something unheard of even in Physics lessons at school. Tom also seemed to know my maths teacher from helping him set ridiculously hard BMO questions at some point in the past (I think I can just about forgive him for doing that). The atmosphere was also quite singular since geek humour actually worked, and maths and physics jokes got a higher laugh:groan ratio than usual; though I couldn’t help facepalming when, while collecting in papers, Tom remarked ‘all your papers are belong to us’.

I think I probably did get quite a bit out of this whole experience. Since being invited to the finals I’ve been constantly prodded to complete USACO training challenges which are combined with a form of structured training / algorithmic tutorial thing which gives users formal training of algorithms. This training is actually the only time I’ve ever been ‘trained’ in programming and I’d been sort of making things up on the fly since I started programming (in visual basic…) back in Colet Court – I didn’t actually know what a greedy algorithm was until this year, and my understanding of even what algorithms are was still sketchy when I took the BIO for the second time (last year). So by going through a beginners through intermediate algorithms training course was definitely useful for me and I now approach problems more analytically rather than just trying to convince a compiler to automatically do what I would personally do if faced with a problem (no, not give up straight away and watch a film instead). I have to say though that despite its utility I acquired a few bad habits from it. Since for each assignment infinite attempts are allowed, I tend not to actually test programs against anything other than sample data and submit it, hoping something that can solve a specific case will probably work with all other cases. Inevitably it tends not to work first time and rather than sitting down and debugging it, I take the test data and just try to make the program work for that by doing silly things like making loops slightly longer or incrementing variables by 1 randomly. USACO helpfully also provides the full answers for test data. I have to say though that the grading system on USACO is impressive – after you submit a solution the backend code automatically compiles and runs the program for each test case and grades its answer. Inspired, I’ve now got something vaguely similar set up on my Debian server (albeit requiring both FTP and SSH connections to sort of do everything manually).

Another thing I’ve always wanted to do was learn C++ as every linux package seems to require compilation with g++, so C/C++ seems to be the language to learn. Since the BIO Finals required code in C/C++ or Delphi (that nobody used, surprise surprise) I was forced to learn a new language, and after discovering the awesomeness of pointers, I have an incentive to endure the confusion and use some really cool programming features (at the risk of corrupting random critical data in the system memory).

And as always with a visit to Cambridge, I got to see more of the college and living quarters. I have to say, the Corpus rooms were more spacious though assuming a specific comparison is representative of a more general comparison would be displeasing to my stats teacher.

And of course since the BIO is sponsored by Lionhead Studios (gaming company) we got to meet a representative and should find obtaining work experience there much easier.

So anyway, here’s what I remember from the itinerary:

Day 1
Erroll and I arrived at Trinity only to be told we had to be at the porters of Burrell College on Grange Road, which is somehow related to Trinity. After a bit of a trek we arrived, Pauline-style, fashionably late. We were shown our rooms, were provided with food and were shown the computer rooms where we got used to our environments. It was actually a very simple question on summing squares repeatedly (up to 2^63 times) – all we had to do was notice there was a repeating sequence – but the unfamiliar environment and unfamiliar method of file input (fscanf in <stdio> as opposed to fin >> in <fstream>) made me do all sorts of stupid things. I think after three months of USACO challenges in C++ I think I still prefer C# / Java as languages. Perhaps it’s got something to do with compilers (my 2003 MS C++ compiler at home goes kaput randomly).

Day 2
The brain uses an insane amount of energy when working hard and doing olympiads was even suggested (as a joke) as a means of weight loss. For this reason an awesome breakfast was bestowed upon us, consisting of baconey, eggy, toastey goodness. The morning papers were both written, the first being on Turing Machines and the second on emotion/sentiment detection in text. This was actually probably the most enjoyable part of the contest – the questions on turing machines were a bit like a mix of maths, logic and electronis (involving truth table like things and train track systems etc). It was also the only bit I could actually seem vaguely competent doing – an education in maths and electronics probably helped me.

The afternoon was when the hardcore competitioning kicked in with a whopping five-hour paper consisting of four questions (the best people completed two questions). I’ll talk about those later, but I failed quite epically, only managing to write a program to solve a question for about half the test data. It also transpired I’d spent all my time on the hardest question, and that although I saw immediately an algorithm that Dr Forster said worked, my implementation was total crap. Later that evening I managed to think up a linear time program to solve the same problem which when I mentioned it the next morning was apparently the best solution Dr Forster had thought of. I still blame C++

After the olympiad I attempted to take some night photography with a tripod which is apparently banned. Oops. We all then went to dinner at Ask and got quite stuffed up before being asked to eat more in the chill room afterwards.

Day 3
Today was mostly free time in which Erroll, I and another person we met spent our 2 hours of free time pulling newspaper, broadband adverts and IR spectra printouts out of a pool table in an attempt to get the balls out. Our efforts included using mobile phones as endoscopes to get a better view of the inside of the machine, using wire coat hangers as hooks to reach the newspaper and peering inside the machine to aid our end. We were eventually thwarted as we concluded our over-zealous table tilting had resulted in the balls falling out of the mechanism entirely and ending up unretrievably on the bottom of the table. For future reference: pool table lock picking doesn’t work with coat hanger wires.

After an inventive method of going round (in three dimensions) a gate without a keycard I and a few others got to the main Trinity college. The tension was apparently high as they announced the IoI competitors though I didn’t notice; my expectations were clearly low as I had just organised three weeks’ work experience with Microsoft at the same time as the finals. What was nice though was that we got very cool 4GB memory sticks with ‘British Informatics Olympiad’ on them, and we were issued with compulsory free games and ‘Introduction to Algorithms’. I already had the book and had in fact brought it to the contest in order to seem vaguely intelligent with no real intention of looking at it.

My room

The questions

I’ve put thumbnails of scans – click to enlarge. I cut out my retarded scribblings.

Desperate Measures

This is the one I half did, and also the hardest. You’re given a cross section of a polygon and are supposed to divide it into triangles using only given vertices. In the question the polygon is the cross section of a cave tunnel…

My initial (and apparently correct) thought was to cut off all the bits sticking out of the polygon (i.e. turn them into triangles and ignore the outside points) and end up with a convex polygon and subsequently just a triangle in the middle; sort of repeatedly going round the polygon chopping off bits. My second (and apparently better) thought was to go from left to right joining up points, an algorithm that runs in linear time.

River

This is apparently the easiest question: a river (= straight line) of up to length 2^31 kilometres (the unit was some amusing invented thing but I can’t remember what it was) can be split up in one of up to 1000 (=n) ways into n unequal segments (= up to 1000 different sections using up to 1000 different partitions). The question was to split it into n segments so that each different segment is a segment described in a different partition and there’s no overlap of partitions. OK that’s a crap explanation – the scan does it better.

I didn’t actually look at this which is a pity – it was the easiest. When I looked at it before going to bed that night I managed to come up with an algo straight away which would have worked in O(n^2 ish) – the biggest case would have taken about a second to run. Pity I saw 2^31 and immediately moved on when actually doing the competition.

All work and no play

The scan says it all. It was a really annoying question because I started working on it about an hour before the end. I wrote an efficient O(n) algo for finding how many ways there are of making n in such a way, had an amazing pascal’s triangle/combinatorics thing going, and was about to write it when I realised it all got screwed up by the blocks only going up to 10. Unable to repair my program, my final submission only worked up to n=10 (needs to work up to n=64). I might also have forgotten to change the output method from console to file output. Meh.

Spies

I couldn’t think of an efficient way of doing this (not even in the evening though I was very sleepy by then) and am certainly not going to attempt it again until I have lots of free time, i.e. summer. This was the second hardest.

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Particle Physics Lectures at UCL

I’ve just got back from a particle Physics Masterclass at UCL. Here’s a brief outline of what we did and what I thought.

After a number of technical difficulties involving the projector, the morning programme began. Interestingly, two of the lecturers were using Macs and the lecturer on distributed computing was running Linux with what looked like a GNOME desktop. Sadly for Linux supporters like me, it subsequently crashed apparently owing to the wifi (so cafe wireless at school isn’t that bad after all), after which he either did a really fast XP install or dual booted to XP.

1100 The LHC, ATLAS @ CERN

Dr Mario Campanelli, a researcher at CERN as I understand from his intro, gave us a brief talk on the LHC and the detectors. We got a brief description of the various different particles and a run-down on how precisely aligned the LHC’s parts had to be (0.1mm), leading to its being underground; why singularities produced in it weren’t going to swallow the earth and KILL US ALL (black holes would quickly evaporate in a puff of radiation), and besides cosmic rays hitting the Earth’s atmosphere create such singularities all the time – we’d be long gone by now if those were the Earth-swallowing type of black hole; the setup of the tubes; and a bit on how the detectors work. There was a lot specifically about CERN that I didn’t know before and that hadn’t been mentioned so I think we all found this particularly interesting.

He also said as a sidenote that apparently CERN would have closed over winter anyway owing to electricity costs, so the schedule wasn’t as badly set back by the ‘minor’ ‘meltdown’ (i.e. like 27 Kelvin) as the media make it out to be. Or maybe that’s his CERN researcher pride speaking

1200 Search for neutrinos in Antarctica

We were then told about the tremendous difficulties faced by scientists attempting to find neutrinos. When neutrinos interact with matter they form a cone of Čerenkov radiation consisting of blue light and radio waves projected in the shape of a cone caused (as I understand) by charged particles moving faster than the speed of light in the given medium. The research brought the scientists to the icy region of Antarctica, attempting to detect radio transmissions caused by neutrinos interacting with ice which carries radio waves well. The search went from water to ice to salt as media for neutrinos to interact with, and as yet neutrinos have never been detected except from two occasions: our sun and a supernova in 1987 (or thereabouts).

1230 Distributed Computing

This was more or less about how to process the 5 PB of data emerging from the LHC while in operation. The talk touched on supercomputers, showing us pics of CRAY supercomputers from ye olden dayes and more modern cloud computing centres. The capacity of distributed computing is enormous, as demonstrated by projects such as SETI@HOME and Folding@HOME.

After lunch:

1430 Hands-on

This consisted firstly of looking at simulated data from realistic particle collider experiments. We used Atlantis (software) and data from ATLAS (i.e. looking at particle traces and detector readings and unintelligible graphs of logs of angles against logs of other angles in some crazy units against GeV) and learnt to recognise different types of W and Z particle decays. I personally thought it was quite exciting and certainly eye-opening to be using the same software as researchers at CERN are using to analyse their data. However, realistic as the graphs and charts seemed and authentic-looking as they were, we successfully identified a Higgs Boson trace which the lecturers did not seem at all surprised about. Realistic indeed…

The day concluded with a video conference with some research labs in the US. As with all video conferences, the quality left something to be desired, but it was interesting if a little disheartening to watch the other side rip apart our conclusions from data and ridicule us as inefficient British people! In the end we ended up discussing in some depth differences in education systems between the US and the UK (apparently they start at 7:30 and finish at 2pm but were envious of our almost 2hr lunch breaks) before the sound quality totally disintegrated and nothing was left but an IRC channel!

Overall, I certainly got something out of the day. Although we didn’t really discover all that much new in terms of the theory behind particle Physics thanks to fairly thorough AS teaching, there was a lot I learnt about the practical side of particle colliders and detectors. More importantly, lunch was quite sublime (surprisingly so for pub food).

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John Polkinghorne at St Paul’s

John Polkinghorne's signature on The God Delusion

On Friday, Halley Soc welcomed Dr John Polkinghorne to St Paul’s to talk on how science and religion work together. Lest this post turn into an enormous dissertation I will attempt to digress as little as possible from what he said, and merely restate some of his main arguments (the things that I wrote down) and explain why I think he’s wrong. All quotations are paraphrased since I didn’t write down every word he said. Apologies if I’ve misinterpreted some of the things he said.

He began by stating that religion is a search for truth, and that both science and religion rely to an extent on belief:

Both science and religion are a search for truth, and both rely on motivated belief

In my opinion, while science is a genuine search for truth, religion is in many cases the opposite. Looking at evidence, God seems to be no more than a convenient gap-filler for what humans do not know. When Pasteur turned up, disease was no longer a manifestation of God’s wrath but merely the action of millions of tiny microbes, and was treated with medicine instead of prayer. On the subject of belief, while science relies on believing measurements made by humans and machines, religion relies mostly on what a book full of contradictions is interpreted to say – which seems to be just about everything.

He subsequently said something about religion being a human version of science:

Science treats humans as objects. Humans are obviously not objects, thus need something else: religion

I think humans are objects. Just because we classify ourselves as intelligent life with complex emotions, we are governed by exactly the same laws as everything else. Emotions are simply manifestations of neurones firing and hormones and chemicals being released in the body (I’m no biologist but I’m pretty sure it’s something along those lines). However complicated the brain is, I believe there’s nothing to separate the mind from the brain than a different paradigm – fundamentally the mind is a function of the state of the brain. Humans are objects after all. Saying they are different things are a bit like saying the Newtonian paradigm contradicts the Hamiltonian one.

He used this argument to create an argument about beauty, specifically music:

When we hear music, we hear its beauty, and can appreciate that. This implies there is something other than science, and we call this other thing God

As above, beauty and emotions relating to it are merely functions of the brain, abstractions relating to certain neurones firing. Beauty is not an inherent part of the universe – we merely interpret it to be.

He then said that science and religion help each other:

Science helps religion by telling the world how the world works, about truth

‘Truth’ is the exact word he used (I wrote it down enclosed in quotation marks). If science tells religion the truth, his first statement must be false: religion can’t be told the truth and come up with it at the same time. More importantly and indeed disturbingly, he insists that religion can explain evolution:

God made the world so that creatures can evolve: rather than making homo sapiens with five fingers he created a world in which life can make itself. Life evolved from a ready-made world

Apparently it is more likely that we are living in a computer simulation than in a ‘real’ world (c.f. several New Scientist articles). So God is a computer programmer with a genetic algorithm. In a way I can believe that, after reading the articles. There’s still no justification for practising religion though – merely believing in a probability of there being a form of ‘god’, and only tenuously.

He then said Newton is proof of God:

Evolution cannot explain Isaac Newton: there is absolutely no evolutionary benefit for humans to be able to understand the cosmos

I think he’s made a mistake here. Of course there’s no evolutionary benefit for the ability to understand the universe and invent calculus, just as there’s no evolutionary benefit for a dolphin to be able to jump through hoops (I’m not intentionally comparing Newton to a dolphin). What allowed Newton to discover his laws was his intelligence and a high degree of intuition, undeniably qualities beneficial to an animal; qualities which enable it to survive better.

He fell back again to a beauty argument:

Science and Maths are beautiful: Mathematical equations and the way everything fits together is just so beautiful that it cannot exist without God. Quoting Wigner, ‘Mathematics is so unreasonably effective’. God must have made it that way

Personally I think there are three good reasons why science and maths yield such beautiful equations. The first is statistics. It is statistically likely that there will exist some beautiful equations, and some not so beautiful ones. Beautiful ones include e^iπ+1=0. Not so beautiful ones include the quadratic formula, or indeed the quartic formula. The second reason is that science and maths are based on very simple rules which can themselves be described as beautiful. Simplicity of certain solutions and results stem from the fact that the basis is fundamentally simple – there are many hidden fundamental underlying patterns interspersed throughout the sciences, which means you tend to end up with something quite nice. The third reason is that aesthetics are a human invention. Beauty doesn’t really exist – humans just assign that quality to certain things. So saying beauty proves god is circular: “God made man to invent beauty to prove God”.

The last part of his talk involved a well-known argument for intelligent design:

Life as we know it can’t exist without the parameters of our universe.

I have all sorts of objections to this and could get into the anthropic principle and keep going forever. He said ‘life as we know it’, citing specifically carbon-based life. He also said if those parameters were tweaked just slightly, we couldn’t exist. It’s possible though that a radical change in one or more of the parameters might still yield intelligent life. Who knows, that life might not even need photons.

Someone asked a question about the multiverse theory, a popular method to get round this problem. He replied that this is too speculative an idea. I asked whether he thought, if the idea of multiple universes (a part of many theories such as M-theory and the many-worlds interpretation of Quantum Mechanics) was too speculative, that God is too speculative. He said something about there being evidence for God and none for multiple universes. I asked him what he thought of David Deutsch’s idea that quantum computing is evidence for the many-worlds interpretation of quantum mechanics as the computing power is too great to come from one universe. His reply:

I think it’s perverse for David Deutsch to say such a thing. All you need is the Copenhagen interpretation

So multiple universes are ridiculous to even consider, but God is; and spooky action at a distance is fine?

Many things he said contradict things I believe and conclusions I have come up with. I remain no more convinced that religion is worth practising and that God exists. Furthermore, after all this argument why theology in general is maybe a good idea, he became specifically Anglican, a branch of religion that requires him to believe all sorts of ridiculous assertions made by the bible. He said he has his reasons but wasn’t prepared to delve into them with the little time that he had. My suspicion is that he and I will never agree. But to commemorate the occasion (a famous person coming to St Paul’s), I managed to get his signature on my copy of Richard Dawkins’ The God Delusion in which he is (probably) referred to as a crackpot (image is at top of post, and on my Flickr photostream). Score…

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