tag:blogger.com,1999:blog-172329042014-10-03T07:39:38.768+00:00The SplineCommentary on anything that interests meStephen Luttrellhttp://www.blogger.com/profile/11094835879740297834noreply@blogger.comBlogger73125tag:blogger.com,1999:blog-17232904.post-4588176067382322752012-05-09T10:58:00.001+00:002012-05-09T10:58:28.250+00:00Where have all my images gone?Very funny, Google! All of the images have disappeared from this blog.Stephen Luttrellhttp://www.blogger.com/profile/11094835879740297834noreply@blogger.com3tag:blogger.com,1999:blog-17232904.post-49999120149256422622011-07-22T01:26:00.001+00:002011-07-22T01:26:55.914+00:00Embedding a Computable Document in a Blogger PostPeeking at the source code in the Wolfram blog post <a href="http://blog.wolfram.com/2011/07/15/mathematica-qa-creating-movie-files/">here</a> has revealed to me how to embed CDF documents in Blogger posts, and here is the proof:<br /><br /><div class="WriCDF"><div style="margin: 0px auto; width: 450px;"><div id="A0a80e4147b724017e6b37e1ab7e8f9c5" style="background-color: #e8e8e8; border: 1px solid rgb(160, 160, 160); color: #333333; height: 300px; margin-bottom: 15px; text-align: center; width: 450px;"><noscript><br /> <p style="margin: 0; padding: 10px 10px 0">To view the full content of this page, please enable JavaScript in your browser. <br /> Learn more <a href="http://www.wolframalpha.com/jsMac.html">here</a>.</p> </noscript><br /><br /><div style="margin: 0px; padding: 10px;">To view this content, please install <em>Wolfram CDF Player</em>. You can install the free <em>CDF Player</em> <a href="http://demonstrations.wolfram.com/download-cdf-player.html" title="Wolfram CDF Player">here</a>.</div></div></div><script type="text/javascript">var cdf = new cdf_plugin(); cdf.addCDFObject("A0a80e4147b724017e6b37e1ab7e8f9c5", "http://blog.wolfram.com/data/uploads/2011/07/Animation11.cdf", 450, 300); </script></div>Stephen Luttrellnoreply@blogger.com6tag:blogger.com,1999:blog-17232904.post-6672119772515039492011-07-21T14:39:00.002+00:002011-07-22T00:05:18.373+00:00Computable Document FormatA post <a href="http://blog.wolfram.com/2011/07/21/launching-the-computable-document-format-cdf-dont-compress-the-idea-expand-the-medium/">Launching the Computable Document Format (CDF): Don’t Compress the Idea, Expand the Medium</a> at the Wolfram Blog explains why <a href="http://www.wolfram.com/cdf/">CDF</a> is so important, and it points to some nice <a href="http://www.wolfram.com/cdf/uses-examples/">examples</a> of its use. If you find that mapping your high-dimensional thoughts onto a 1-dimensional line (i.e. a traditional static document) destroys most of the information, then CDF is for you (i.e. an interactive dynamic document). I have always found that using <em><a href="http://www.wolfram.com/mathematica/">Mathematica</a></em> - the engine under CDF's hood - has given me an <em>enormous</em> advantage over my peers who used "A N Other Product", because it allows me to do <a href="http://en.wikipedia.org/wiki/Literate_programming">literate programming</a> and <em>lots</em> more in a unified way. However, I always ended up rewriting everything in traditional 1-dimensional style to communicate with other people - usually <em>not</em> very successfully. CDF changes the game because it allows me to present material in the natural form in which it was created in the first place. Not only that, the interactivity of CDF it makes it <em>much</em> easier for the reader to understand what you are saying/doing. My <a href="http://stephenluttrell.blogspot.com/2011/07/interactive-demonstrations-computable.html">previous post</a> contains some practise runs at using CDF, though I'm sure I will do better after I have studied the Wolfram's <a href="http://www.wolfram.com/cdf/uses-examples/">examples</a> of CDF use.<br /><br />What about long-term archiving of material? Will CDF be around in 10 (or 100) years? As far as I know, the only "complete" and "open" document format with a <em>long</em> track record is <a href="http://en.wikipedia.org/wiki/TeX">TeX</a>/<a href="http://en.wikipedia.org/wiki/LaTeX">LaTeX</a>, so that is my preferred choice to ensure my place on the "dusty shelf" in perpetuity. Sometimes, I even print things out on paper!Stephen Luttrellnoreply@blogger.com0tag:blogger.com,1999:blog-17232904.post-42790356658661038752011-07-19T18:20:00.003+00:002011-07-19T21:42:15.274+00:00Interactive Demonstrations - Computable Document Format<div><div><div><a href="http://www.wolfram.com/">Wolfram Research</a> supplies a free plug-in for viewing and interacting with online documents saved from <em>Mathematica</em> in Computable Document Format (CDF) - the plug-in can be downloaded from <a href="http://www.wolfram.com/cdf-player/">here</a>. I thought that I would try it out on a few of my interactive <em>Mathematica</em> demonstrations, and here are the (draft) results for you to enjoy:<br /><ol><li><a href="http://www.stephenluttrell.com/documents/topographic%20string.cdf">Topographic String</a>: This grows a 1-dimensional self-organising map, starting from 3 nodes and progressively inserting additional nodes. It is an implementation of the SOM training method that I published in 1988: "Self-organising multilayer topographic mappings", <em>Proceedings of 2nd International Conference on Neural Networks</em> (San Diego, USA), pp. I/93-I/100 - an online version is available <a href="http://www.stephenluttrell.com/papers/ieeenn88/ieeenn88.html">here</a>.</li><li><a href="http://www.stephenluttrell.com/documents/ising%20model.cdf">Ising Model</a>: This simulates a 2-dimensional Ising model, and it allows you to dynamically vary the clique factors for the 4 distinct types of 2-clique (i.e. N/S, E/W, NE/SW, SE/NW) to see how the Ising model behaves. It is an implementation of the Ising model simulations described in a report that I wrote in 1985: "The implications of Boltzmann-type machines for SAR data processing: a preliminary survey", <em>RSRE technical report</em>, 3815 - an online version is available <a href="http://www.stephenluttrell.com/papers/3815/3815.html">here</a>.</li><li><a href="http://www.stephenluttrell.com/documents/bz%20reaction.cdf">BZ Reaction</a>: This simulates the <a href="http://en.wikipedia.org/wiki/BZ_reaction">Belousov–Zhabotinsky reaction-diffusion system</a> - it's very pretty.</li><li><a href="http://www.stephenluttrell.com/documents/current%20algebra.cdf">Current Algebra</a>: This interactively computes commutators of products of current operators - it's a bit inflexible, but it shows some interesting <em>Mathematica</em> techniques in action.</li><li><a href="http://www.stephenluttrell.com/documents/IMO%202011.cdf">IMO 2011</a>: This is hot off the press in response to Terence Tao's <a href="http://polymathprojects.org/2011/07/19/minipolymath3-project-2011-imo/">Minipolymath3 project: 2011 IMO</a>, which plans to work on Q6 of the 2011 International Mathematics Olympiad. I have implemented an interactive version of Q6, so you can get an intuitive feel for the geometry involved. <strong>Update:</strong> I see that TT eventually decided to go with Q2 rather than Q6. Oh well, my interactive Q6 is fun to play with anyway.</li></ol></div></div></div>Stephen Luttrellnoreply@blogger.com0tag:blogger.com,1999:blog-17232904.post-78508944293993595442010-12-22T09:18:00.003+00:002010-12-22T09:27:00.846+00:00Some More Unpublished WorkHere are some more unpublished papers that I have uploaded to the <a href="http://arxiv.org/">arXiv</a>:<br /><ol><li><a href="http://arxiv.org/abs/1012.4126">Self-Organising Stochastic Encoders</a><br /><br />The processing of mega-dimensional data, such as images, scales linearly with image size only if fixed size processing windows are used. It would be very useful to be able to automate the process of sizing and interconnecting the processing windows. A stochastic encoder that is an extension of the standard Linde-Buzo-Gray vector quantiser, called a stochastic vector quantiser (SVQ), includes this required behaviour amongst its emergent properties, because it automatically splits the input space into statistically independent subspaces, which it then separately encodes. Various optimal SVQs have been obtained, both analytically and numerically. Analytic solutions which demonstrate how the input space is split into independent subspaces may be obtained when an SVQ is used to encode data that lives on a 2-torus (e.g. the superposition of a pair of uncorrelated sinusoids). Many numerical solutions have also been obtained, using both SVQs and chains of linked SVQs: (1) images of multiple independent targets (encoders for single targets emerge), (2) images of multiple correlated targets (various types of encoder for single and multiple targets emerge), (3) superpositions of various waveforms (encoders for the separate waveforms emerge - this is a type of independent component analysis (ICA)), (4) maternal and foetal ECGs (another example of ICA), (5) images of textures (orientation maps and dominance stripes emerge). Overall, SVQs exhibit a rich variety of self-organising behaviour, which effectively discovers the internal structure of the training data. This should have an immediate impact on "intelligent" computation, because it reduces the need for expert human intervention in the design of data processing algorithms.</li><br /><li><a href="http://arxiv.org/abs/1012.4173">A Self-Organising Neural Network for Processing Data from Multiple Sensors </a><br /><br />This paper shows how a folded Markov chain network can be applied to the problem of processing data from multiple sensors, with an emphasis on the special case of 2 sensors. It is necessary to design the network so that it can transform a high dimensional input vector into a posterior probability, for which purpose the partitioned mixture distribution network is ideally suited. The underlying theory is presented in detail, and a simple numerical simulation is given that shows the emergence of ocular dominance stripes.<br /><br /></li></ol>Stephen Luttrellnoreply@blogger.com0tag:blogger.com,1999:blog-17232904.post-34919456152755802602010-12-17T01:20:00.005+00:002010-12-17T01:48:24.996+00:00Some Unpublished Work<p>I have decided to upload some of my unpublished work to the <a href="http://arxiv.org/">arXiv</a>:</p><ol><li><a href="http://arxiv.org/abs/1012.3656">Adaptive Cluster Expansion (ACE): A Multilayer Network for Estimating Probability Density Functions</a><br /><br />We derive an adaptive hierarchical method of estimating high dimensional probability density functions. We call this method of density estimation the "adaptive cluster expansion" or ACE for short. We present an application of this approach, based on a multilayer topographic mapping network, that adaptively estimates the joint probability density function of the pixel values of an image, and presents this result as a "probability image". We apply this to the problem of identifying statistically anomalous regions in otherwise statistically homogeneous images.</li><br /><li><a href="http://arxiv.org/abs/1012.3705">Stochastic Vector Quantisers</a><br /><br />In this paper a stochastic generalisation of the standard Linde-Buzo-Gray (LBG) approach to vector quantiser (VQ) design is presented, in which the encoder is implemented as the sampling of a vector of code indices from a probability distribution derived from the input vector, and the decoder is implemented as a superposition of reconstruction vectors, and the stochastic VQ is optimised using a minimum mean Euclidean reconstruction distortion criterion, as in the LBG case. Numerical simulations are used to demonstrate how this leads to self-organisation of the stochastic VQ, where different stochastically sampled code indices become associated with different input subspaces. This property may be used to automate the process of splitting high-dimensional input vectors into low-dimensional blocks before encoding them.</li><br /><li><a href="http://arxiv.org/abs/1012.3724">The Development of Dominance Stripes and Orientation Maps in a Self-Organising Visual Cortex Network (VICON)</a><br /><br />A self-organising neural network is presented that is based on a rigorous Bayesian analysis of the information contained in individual neural firing events. This leads to a visual cortex network (VICON) that has many of the properties emerge when a mammalian visual cortex is exposed to data arriving from two imaging sensors (i.e. the two retinae), such as dominance stripes and orientation maps.</li></ol>Stephen Luttrellnoreply@blogger.com0tag:blogger.com,1999:blog-17232904.post-11675417396747752852010-12-08T02:15:00.001+00:002010-12-08T02:16:31.276+00:00Yawn, stretch, ...It's time to wake things up again ...Stephen Luttrellnoreply@blogger.com1tag:blogger.com,1999:blog-17232904.post-39291800166193292472008-11-28T18:55:00.006+00:002008-11-28T19:54:33.673+00:00Second Life for Virtual ConferencesContinuing the theme I blogged about recently (see <a href="http://stephenluttrell.blogspot.com/2008/11/second-life-for-science-and-scholarship.html">Second Life for Science and Scholarship</a>), here is an example of a virtual conference that will be held in Second Life:<br /><br /><a href="http://www3.imperial.ac.uk/earthscienceandengineering/research/climateconference08">Virtual Conference on Climate Change and CO<sub>2</sub> Storage</a><br /><br />The organisers of this particular conference have an interest in getting the conference delegates to the "venue" with the minimum of travelling, so organising a virtual conference is the obvious choice.<br /><br />The trend towards having virtual conferences is in its early stages, but there will be a lot more of this sort of thing in the future. There are many conferences that you would <i>like</i> to attend in person, but which would involve a lot of travelling/expense/fatigue/etc so you don't bother going. I can think of <i>many</i> annual conferences that fall into this category for me, but then I <i>hate</i> travelling. Perhaps there could be some sort of <i>hybrid</i> real/virtual conference to allow such people to attend conferences that would otherwise be difficult to attend. Of course, a <i>purely</i> virtual conference would be much easier to organise, and would present a very low barrier to attendance.<br /><br />Currently, the main inhibiting factors working against the adoption of virtual conferences are unfamiliarity with the possibilities offered by the virtual medium, low quality of virtual reality compared to real reality, lack of communication cues that are only available in interactions between real humans, and so on. I would have thought that all of these inhibitors would reduce with time, so virtual conferencing will inevitably take off sooner or later.<br /><br />The so-called "conference call", where multiple participants connect their telephones to have a multiway conversation (if it works at all!), will seem positively archaic in comparison with virtual reality.Stephen Luttrellnoreply@blogger.com3tag:blogger.com,1999:blog-17232904.post-62913067179212209042008-11-19T11:16:00.013+00:002008-12-02T11:45:44.182+00:00Mathematica 7<a href="http://blog.wolfram.com/2008/11/18/surprise-mathematica-70-released-today/"><i>Mathematica</i> 7 is released today</a>, and its new features are summarised <a href="http://www.wolfram.com/products/mathematica/newin7/">here</a>. Hang on! I haven't yet mastered all of the new features that were added in <i>Mathematica</i> 6 (see <a href="http://www.wolfram.com/products/mathematica/newin6/">here</a>).<br /><br />The <i>Mathematica</i> "universe" is growing so large that I find that there is a dynamic equilibrium between the things that I learn about it and the things that I forget, so I can never hold it all simultaneously in my head. I wonder if <i>anybody</i> understands it all.<br /><br />Anyway, for those of you who don't already know, <i>Mathematica</i> is a "tool of thought" that raises your consciousness to levels that you didn't think were possible. But it <i>does</i> require a lot of practise to become a master of this art.<br /><br /><strong>Update (20 November 2008):</strong> Something that caught my eye in the list of new features of <i>Mathematica</i> 7 was "Multicore parallelism standard with zero configuration on all versions of <i>Mathematica</i>" (see <a href="http://www.wolfram.com/products/mathematica/newin7/content/BuiltInParallelComputing/">here</a>). What this means is that when you run <i>Mathematica</i> 7 on a multicore computer (these days, all new computers are multicore) it can parallelise across the cores. In the basic version of <i>Mathematica</i> 7 you can have a maximum of 4 cores running in parallel (see <a href="http://www.wolfram.com/news/m7.html">here</a>), which allows you to have 1 master and 3 slave processes, which gives a useful degree of parallelism straight out of the box. This parallel processing capability will be very useful when applied to the image processing capabilities of <i>Mathematica</i> 7 (see <a href="http://www.wolfram.com/products/mathematica/newin7/content/BuiltInImageProcessing/">here</a>).<br /><br /><strong>Update (24 November 2008):</strong> It just keeps getting better! Running <i>Mathematica</i> on your own personal super-computer (for a reasonable cost, that is) will be reality not that far in the future judging by the following announcements: <ul><li><a href="http://www.nvidia.com/object/io_1227010734073.html"><i>Mathematica</i> Users Get 100x Performance Boost From NVIDIA CUDA</a></li><li><a href="http://www.eweek.com/c/a/IT-Infrastructure/Nvidia-Details-Personal-Supercomputer-Design-Based-on-Tesla-GPU/">Nvidia Details 'Personal Supercomputer' Design Based on Tesla GPU</a></li></ul><strong>Update (2 December 2008):</strong> Some gratuitous showing off of the image processing capabilities of <i>Mathematica</i> 7 has been published at <a href="http://blog.wolfram.com/2008/12/01/the-incredible-convenience-of-mathematica-image-processing/">The Incredible Convenience of <i>Mathematica</i> Image Processing</a> on the Wolfram blog.Stephen Luttrellnoreply@blogger.com2tag:blogger.com,1999:blog-17232904.post-6412622763439309262008-11-13T15:07:00.002+00:002008-11-13T15:14:01.179+00:00The Multiverse<a href="http://discovermagazine.com">Discover Magazine</a> has published a very useful article on the <a href="http://en.wikipedia.org/wiki/Multiverse">multiverse</a> entitled <a href="http://discovermagazine.com/2008/dec/10-sciences-alternative-to-an-intelligent-creator">Science's Alternative to an Intelligent Creator: the Multiverse Theory</a>. The article is entirely non-technical, but it is well written and it shows how the various aspects of physics which are relevant to cosmology are interrelated. It is a good read that I would recommend to anyone who is interested in the big picture.Stephen Luttrellnoreply@blogger.com0tag:blogger.com,1999:blog-17232904.post-30706914185327557402008-11-08T11:09:00.003+00:002008-11-08T11:47:17.512+00:00Adopt a Book<a href="http://www.bl.uk/">The British Library</a> has set up an <a href="http://www.bl.uk/adoptabook">Adopt a Book</a> scheme in which you select a book to "adopt", provided you make a donation in support of the British Library's book conservation programme.<br /><br />The <a href="http://adoptabook.bl.uk/mall/infopageviewer.cfm/BritishLibraryAdoptABook/Giftlevelsandbenefits">benefits</a> of adopting a book are tied to the size of your donation, and a cumulative list is as follows:<br /><br />£25+: An attractive personalised certificate recording the beneficiary’s name and details of the book<br />£75+: A voucher for a public tour of the British Library for two people<br />£150+: A bookplate containing your personal dedication added to the book<br />£250+: An invitation for two people for special behind-the-scenes tour of the conservation studios, including the chance to ‘meet’ your book<br />£500+: The addition of the your name on the Adopt a Book Benefactor List in the British Library, and acknowledgement in the Annual Report<br />£1,000: If you would like to adopt a book which doesn’t appear on the list, we can offer a ‘choose your own book’ option for gifts of £1,000 or more. You will also enjoy all of the benefits listed above.<br /><br />Amongst the 200 books that are currently available for adoption are some of your favourites, ranging from the profound "Philosopiae Naturalis Principia Mathematica" (3rd edition, 1739) by Sir Isaac Newton, to the tedious "A Law Dictionary" (1839) by John Bouvier. They even offer a list of gift ideas for Christmas which includes (for the children) "Alice's Adventures in Wonderland" (1908) by Lewis Carroll and "Aesop's Fables" (1666) by Aesop, and the venerable (take one average-sized cow, and stew it for a week) "Mrs Beeton’s Family Cookery and Housekeeping Book" (1907) by Mrs Beeton.Stephen Luttrellnoreply@blogger.com0tag:blogger.com,1999:blog-17232904.post-64313954692790748092008-11-07T17:00:00.006+00:002008-11-07T17:19:29.670+00:00Proof by ComputerThe <a href="http://www.ams.org/notices">Notices of the American Mathematical Society</a> has published <a href="http://www.ams.org/notices/200811/">A Special Issue on Formal Proof</a> in mathematics, which is freely available online. There is a report on this by <a href="http://www.physorg.com/">PhysOrg</a> at <a href="http://www.physorg.com/news145200777.html">Proof by computer: Harnessing the power of computers to verify mathematical proofs</a>.<br /><br />There are 4 articles in the Special Issue:<br /><br /><ol><li>Formal Proof, by Thomas Hales</li><li>Formal Proof - The Four-Colour Theorem, by Georges Gonthier</li><li>Formal Proof - Theory and Practice, by John Harrison</li><li>Formal Proof - Getting Started, by Freek Wiedijk</li></ol>The last paragraph of "Formal Proof - Getting Started" reads as:<br /><br /><blockquote><span style="font-size:85%;">However, having mathematics become utterly reliable might not be the primary reason that eventually formal mathematics will be used by most mathematicians. Formalisation of mathematics can be a very rewarding activity in its own right. It combines the pleasure of computer programming (craftsmanship, and the computer doing things for you), with that of mathematics (pure mind, and absolute certainty). People who do not like programming or who do not like mathematics probably will not like formalisation. However, for people who like both, formalisation is the best thing there is.</span></blockquote>Clearly, formalisation is "geek heaven"!<br /><br />The Wikipedia page on <a href="http://en.wikipedia.org/wiki/Formal_proof">Formal Proof</a> is a useful place to start learning the basic concepts. Informally, the idea of "formal proof" is that you replace error-prone human mathematicians by error-free computers, which are then used to expand each step of a (human-generated) proof all the way down to the fundamental axioms of mathematics. Naturally, this leads to extremely verbose formal proofs, but computers are ideally suited to handling this verbosity, and the advantage for us humans is that we can ensure that our proofs are error-free, because they have been checked by computer in every detail. Of course, we might have neither the time nor the inclination to fully "understand" the details of these proofs.<br /><br />The following is a verbatim copy of the main part of a posting of mine <a href="http://acenetica.blogspot.com/2006/08/burden-of-proof.html">Burden of Proof</a> that I wrote over 2 years ago on my <a href="http://acenetica.blogspot.com/">ACEnetica</a> blog. It is very relevant to the issue of "formal proof" which is why I have included it here.<br /><blockquote><span style="font-size:85%;">My own view on this issue is that a computer generated proof has <em>exactly</em> the same status as a human generated proof. The difference is only one of the degree of assistance provided to the brain of the human to help with the generation of the proof. A totally unassisted human would have to somehow do the whole proof mentally, which severely limits the length of proofs that are accessible. A human with the typical assistance that is allowed in an examination room (i.e. pen and paper) has the luxury of at least being able to write things down, which allows <em>much</em> longer proofs to be reliably generated. The mechanics of generating a proof then reduce to using well-defined rules to manipulate symbolic expressions, where pen and paper are used as a medium for representing these symbols, and the rules are implemented in the human brain.<br /><br />The degree of assistence in generating a proof can be taken one stage further by using a computer to implement some or all of the rules for manipulating the symbolic expressions, rather than implementing all of the rules in the human brain. This seems to be a fairly radical step to take, because hitherto the only part of the proof that was "outside" the human brain was its "dumb" representation using pen and paper, whereas the "clever" bit involving the implementation of rules to manipulate this representation was "inside" the human brain.<br /><br />Let us consider what these rules of manipulation actually are. Effectively, they define a procedure for taking an initial expression constructed out of symbols, and repeatedly operating on it using the rules to eventually generate the required final expression. The cleverness is in the <em>construction</em> of the set of rules, which is where a human is the best source of the cleverness needed to create the rules. There is <em>no</em> cleverness in the repeated <em>application</em> of these rules; all that is required is that their application is done <em>reliably</em>, which is where a computer is the best approach, especially if the proof has many steps.<br /><br />Use a human to <em>define</em> the rules of manipulation, and use a computer to <em>implement</em> these rules. This approach seems to me to be entirely uncontroversial, and it is exactly how computer generated proofs are done. Note that software bugs in the computer part of the proof are dealt with in an <em>analogous</em> way to "software" bugs in human part of the proof, i.e. try a variety of approaches on a variety of platforms.</span></blockquote>Stephen Luttrellnoreply@blogger.com0tag:blogger.com,1999:blog-17232904.post-38510742094380910822008-11-03T18:45:00.004+00:002012-05-16T17:06:26.822+00:00Second Life for Science and Scholarship<div align="center"><iframe allowFullScreen='true' webkitallowfullscreen='true' mozallowfullscreen='true' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dwyW8JnbCtcX5kcn5soGCzahAUG_fmEUxpu4u3_dU9eqhhsupXFfNBRYATwhCzNCYpCkXUdtxZMWag' class='b-hbp-video b-uploaded' FRAMEBORDER='0' /></div><div style="text-align: center;">Demonstration of a <a href="http://en.wikipedia.org/wiki/Lorenz_attractor">Lorenz Attractor</a> in <a href="http://secondlife.com/">Second Life</a>.</div><br />I created the little video above as a simple example of how you can implement a dynamical 3D model in Second Life. All you need to do make a rudimentary demonstration of a Lorenz attractor is to create a set of particles in SL, and to embed a script inside each of the particles to tell it how to move according to the equations that govern the Lorenz attractor. The simulation itself is then automatically carried out by the SL virtual reality engine, whilst you move your virtual camera around the simulated Lorenz attractor in order to film a demonstration. That's all there is to creating the rather basic video that I posted above.<br /><br />Some additional points: <br /><ol><li>Each particle's motion leaves behind it a trail of "hot embers" that gradually cools off yellow/orange/red until it vanishes. This traces out the Lorenz attractor so we can easily see it.</li><li>In this example I moved the camera <i>manually</i> rather than by scripting its motion, so the camera motion is rather clumsy.</li><li>I had planned to include a voice-over commentary, but found that <i>all</i> my attention was needed just to operate my mouse and keyboard, so all you can hear is the occasional mouse-click.</li><li>The background scenery is <i>not</i> actually relevant to this demonstration, which I performed in a small corner of my cliff-top land holding in Second Life. But maybe you can see a few objects of interest in the background.</li><li>The almost invisible translucent motion in the background is an animated movie that I am displaying on a large screen I built in SL. More to come later on this...</li></ol>That leads me onto the main subject of this posting.<br /><br /><a href="http://www.astro.caltech.edu/~george/">George Djorgovski</a>, Professor of Astronomy at Caltech, has a <a href="http://cosmicvariance.com/2008/11/03/guest-post-george-djorgovski-a-new-world-overture/">guest post at Cosmic Variance</a> in which he vividly describes his experiences in using the virtual world <a href="http://secondlife.com/">Second Life</a> for science and scholarship. To those who think that SL is just a game he offers the following advice:<br /><blockquote><span style="font-size: 85%;">Judging by my own experience, there is no way that you can really understand all this just by reading or listening; you have to try it. It is a fundamentally visceral, as well as an intellectual experience. It is as if you have never seen a bicycle, let alone ridden one, and someone was showing you pictures of people having a good time biking around, and telling you what a fun it is. Please keep that in mind. You gotta try it, then judge for yourself.</span></blockquote>On the quality of the virtual experience he writes:<br /><blockquote><span style="font-size: 85%;">What really surprised me; knocked my virtual socks off, so to speak; is the subjective quality of the interpersonal interaction. Even with the still relatively primitive graphics, the same old flat screen and keyboard, and a limited avatar functionality, it is <i>almost</i> as viscerally convincing as a real life interaction and conversation. Somehow, our minds and perceptive systems interpolate over all of the imperfections, and it really clicks. I cannot explain it; it has to be experienced; it is not a rational, but a subjective phenomenon. It is much better than any video- or teleconferencing system I have tried, and like most of you, I have suffered through many of those. As a communication device, this is already a killer app. Going back to the good old email and Web feels flat and lame.</span></blockquote>On the use of SL for science and scholarship he writes:<br /><blockquote><span style="font-size: 85%;">So the first major scholarly use of [virtual worlds] is as a communication, interaction, and collaboration venue. This includes individual, group, or collaboration meetings, seminars, or even full-blown conferences. You can interact with your colleagues as if they were in the same room, and yet they may be half way around the world.</span></blockquote>And he writes much more about how virtual worlds in general (and Second Life in particular) are a key technology in the future of science and scholarship. Commentary, such as this by George Djorgovski, on the serious (rather than gaming) use of Second Life is to be welcomed.<br /><br />I never have travelled well, typically arriving at conferences totally knackered and not recovering for days, so I look forward to <i>virtual</i> meetings becoming the norm, at least for short meetings, that is. Also, I have a highly visual way of explaining science (to myself <i>and</i> to others), so I look forward to building illustrative 3D dynamical models in SL. I think a key technology that is missing here is ready access to a higher-level set of tools for building and scripting such models in SL, at least that is what I see as being the main thing that is slowing down my progress in using SL.<br /><br />This is only the start of what is to come...Stephen Luttrellnoreply@blogger.com1tag:blogger.com,1999:blog-17232904.post-33011376206219741692008-10-25T15:14:00.007+00:002008-10-25T15:58:19.307+00:00Martin Gardner Mathematical LibraryI have just received a flyer from the <a href="http://www.cambridge.org/">Cambridge University Press</a> advertising <a href="http://www.cambridge.org/martingardner">The New Martin Gardner Mathematical Library</a>. Of course, the name <a href="http://en.wikipedia.org/wiki/Martin_gardner">Martin Gardner</a> immediately attracted my attention (isn't it <i>so</i> useful to have a widely recognised name?), because I immediately thought of his excellent <a href="http://en.wikipedia.org/wiki/Mathematical_game">Mathematical Games</a> column that used to appear in <a href="http://en.wikipedia.org/wiki/Scientific_American">Scientific American</a>. It says <a href="http://en.wikipedia.org/wiki/Martin_gardner">here</a> that his column stopped being published in 1981 - was it <i>that</i> long ago?<br /><br />Anyway I clicked through to The New Martin Gardner Mathematical Library to discover that it is exactly what I thought it might be, i.e. an updated version of his Mathematical Games column. The library is described thus:<br /><br /><blockquote><span style="font-size:85%;">The books based on Martin Gardner's enormously popular Scientific American columns and puzzles continue to challenge and fascinate readers. In these new editions, the author, in consultation with experts, has written updates to all the chapters, including new game variations, new mathematical proofs, and connections to recent developments and discoveries. New diagrams and illustrations have been added and old ones improved, and the bibliographies have been greatly expanded throughout.</span> </blockquote>The web page looks unfinished, but it gives at least some of the titles that will be in the library, which I list below with links that I have added for convenience:<br /><br />1. <a href="http://en.wikipedia.org/wiki/Hexaflexagon">Hexaflexagons</a>, <a href="http://en.wikipedia.org/wiki/Monty_Hall_problem">Probability Paradoxes</a> [I have linked to the Monty Hall problem as an example of this genre], and the <a href="http://en.wikipedia.org/wiki/Tower_of_Hanoi">Tower of Hanoi</a><br />2. <a href="http://en.wikipedia.org/wiki/Origami">Origami</a>, <a href="http://en.wikipedia.org/wiki/Eleusis_(game)">Eleusis</a>, and the <a href="http://en.wikipedia.org/wiki/Soma_cube">Soma Cube</a><br />3. <a href="http://en.wikipedia.org/wiki/Sphere_packing">Sphere Packing</a>, <a href="http://en.wikipedia.org/wiki/Lewis_Carroll">Lewis Carroll</a>, and <a href="http://en.wikipedia.org/wiki/Reversi">Reversi</a><br /><br />It looks like the sort of good stuff that will provoke those familiar mental gymnastics of yore.Stephen Luttrellnoreply@blogger.com0tag:blogger.com,1999:blog-17232904.post-12635332499604035722008-10-23T13:15:00.012+00:002008-10-24T11:32:19.414+00:00Many Worlds Theory<a href="http://www.pbs.org/wgbh/nova/">Nova</a> has a nice collection of information <a href="http://www.pbs.org/wgbh/nova/manyworlds/">here</a> about <a href="http://en.wikipedia.org/wiki/Hugh_Everett">Hugh Everett</a>'s so-called <a href="http://en.wikipedia.org/wiki/Many_worlds_theory">Many Worlds Theory</a> of quantum mechanics. The package includes a <a href="http://www.pbs.org/wgbh/nova/manyworlds/orig-02.html">letter</a> from Everett to <a href="http://en.wikipedia.org/wiki/Bryce_DeWitt">Bryce DeWitt</a> explaining the basic concepts underlying his theory, and the published version of <a href="http://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf">Everett's PhD dissertation</a>. It's fascinating stuff that I highly recommend.<br /><br />For a long time I have had an affinity for Everett's theory, but I didn't find out about Everett's work until long after I had discovered "Many Worlds Theory" for myself whilst doing my PhD work (circa 1980) in high energy particle physics. The reasoning that led me to this theory was to try to see the world from the "point of view" of a simple QM system (e.g. a fundamental particle), and to then work upwards in complexity towards ever larger QM systems.<br /><br />The only way a fundamental particle can "see" the world is to exchange particles with it, and QM does this by progressively applying (the infinitesimal version of) the evolution operator exp(i H t), which is a unitary operator that rotates the system state (e.g. scattering/creating/annihilating particles) in a norm-preserving way (i.e. probability conserving). This leads to a QM description of the world in which there are physical processes going on "in parallel", where all the alternative processes that can be generated by exp(i H t) actually <i>do</i> occur simultaneously. QM (<i>unlike</i> classical physics) automatically does parallel processing at each and every point of space-time, which is where the processing power of a <a href="http://en.wikipedia.org/wiki/Quantum_computer">quantum computer</a> comes from.<br /><br />Working upwards towards larger QM systems involves no change in the theory (that we know of, that is) because the evolution operator exp(i H t) can be applied to <i>any</i> state no matter how complicated it is. There is no system "size" above which the physics is fundamentally different from what is already known to be correct at the level of elementary particles. This includes the use of effective degrees of freedom, because these are still governed by the underlying exp(i H t) although many of the details are usually hidden from view; I reserve the right to revise my opinion here having now seen the paper <a href="http://arxiv.org/abs/0809.0151">More Really is Different</a>.<br /><br />Carried on to physically large system sizes (e.g. human brains), this line of reasoning inevitably leads to a "Many Worlds Theory" point of view, where it is QM all the way up from the bottom to the top. We are <i>inside</i> a QM universe, <i>not</i> outside it looking in.<br /><br />I need <i>direct</i> experimental evidence for "non-QM physics" (i.e. evidence that exp(i H t) is <i>not</i> the whole story) in order to discard my assumption that it is QM all the way from bottom to top. Isn't that the way science should normally be done (I innocently ask), where you preserve the status quo until experimental evidence contradicts it? <br /><br />Circa 1980 I was on the receiving end of a lot of criticism from physicists around me, but in the interests of self-preservation I then decided to keep quiet about my contrarian thoughts on QM. It was only many years after completing my PhD (and moving to another research field outside QM, but continuing to think about QM) that I finally realised that I had not been the first person to think of these ideas. Duh!Stephen Luttrellnoreply@blogger.com0tag:blogger.com,1999:blog-17232904.post-83044840794803872892008-10-13T15:01:00.009+00:002012-05-16T16:53:17.426+00:00Virtual Forbidden City<a href="http://en.wikipedia.org/wiki/Ibm">IBM</a> and <a href="http://en.wikipedia.org/wiki/Palace_Museum">Palace Museum</a> announce the opening of the Forbidden City Virtual World celebrating 600 years of Chinese culture (see <a href="http://www.marketwatch.com/news/story/ibm-palace-museum-announce-opening/story.aspx?guid=%7B1A543A62-4D7E-46BA-92B5-133A69C6CFB8%7D&dist=hppr">here</a>). The <a href="http://www.virtualforbiddencity.org/">Virtual Forbidden City</a> website says:<br /><br /><blockquote><em>The Virtual Forbidden City is a 3-dimensional virtual world where visitors from around the world can experience the Forbidden City in Beijing. You can explore the magnificient palace as it was during the Qing dynasty, which ruled from 1644 until 1912, the end of the Imperial period in China.</em></blockquote><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-q59kmW4lBoQ/T7PbaZ8jd0I/AAAAAAAAAH8/ByzQ1ijZEf8/s1600/Virtual+Forbidden+City.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="187" src="http://2.bp.blogspot.com/-q59kmW4lBoQ/T7PbaZ8jd0I/AAAAAAAAAH8/ByzQ1ijZEf8/s320/Virtual+Forbidden+City.jpg" width="320" /></a></div><br />The image above shows a location that I "photographed" on my first visit to the Virtual Forbidden City. There is <em>much</em> more than can be seen in this single photograph.<br /><br />This is not a fully featured virtual world (e.g. <a href="http://secondlife.com/">Second Life</a>), but it is good enough for visiting and familiarising yourself with the Forbidden City. This virtual reconstruction of the Forbidden City has been done quite carefully. The in-world objects have been "painted" with textures that appear to have been derived from photographs of their real-world counterparts, which adds to the realism. This is quite hard work to do properly, especially for irregularly shaped objects, as I have found when creating virtual copies of real-world objects in Second Life.Stephen Luttrellnoreply@blogger.com0tag:blogger.com,1999:blog-17232904.post-39834942059324693912008-09-26T11:05:00.007+00:002008-09-26T16:07:46.927+00:00Sustainable Energy - without the hot air<a href="http://www.inference.phy.cam.ac.uk/mackay/">David MacKay</a> (Professor of Natural Philosophy, Department of Physics, University of Cambridge) has just finished writing his book <a href="http://www.withouthotair.com/">Sustainable Energy - without the hot air</a>. The online version of the book is free.<br /><br />You can learn what the purpose of the book is from this extract quoted from the book's preface:<br /><br /><blockquote><span style="font-size:85%;">I’m concerned about cutting UK emissions of twaddle – twaddle about sustainable energy. Everyone says getting off fossil fuels is important, and we’re all encouraged to “make a difference,” but many of the things that allegedly make a difference don’t add up.<br /><br />Twaddle emissions are high at the moment because people get emotional (for example about wind farms or nuclear power) and no-one talks about numbers. Or if they do mention numbers, they select them to sound big, to make an impression, and to score points in arguments, rather than to aid thoughtful discussion.<br /><br />This is a straight-talking book about the numbers. The aim is to guide the reader around the claptrap to actions that really make a difference and to policies that add up.</span></blockquote>Nice one! I would recommend this book to anyone who wants to base their knowledge about sustainable energy on science rather than hot air.Stephen Luttrellnoreply@blogger.com0tag:blogger.com,1999:blog-17232904.post-62823018246130582832008-09-24T18:53:00.005+00:002008-09-24T19:14:08.814+00:00Methane Bubbles in the Arctic Bathtub<a href="http://www.independent.co.uk/">The Independent</a> has an alarming report on a <a href="http://www.independent.co.uk/environment/climate-change/exclusive-the-methane-time-bomb-938932.html">potential methane time bomb</a>. The sub-sea deposits of methane beneath the Arctic are beginning to bubble to the surface as the region warms up and the ice retreats. <a href="http://en.wikipedia.org/wiki/Methane">Methane</a> is a very potent greenhouse gas, and its past release from deposits has been suggested as the cause of abrupt changes in the past global climate. If these observations are confirmed, and if there is found to be a positive feedback loop driving the effect, then it would be rather bad news for the projected rate of <a href="http://en.wikipedia.org/wiki/Climate_change">climate change</a>.Stephen Luttrellnoreply@blogger.com0tag:blogger.com,1999:blog-17232904.post-5723439143648358082008-09-18T17:07:00.009+00:002008-09-20T12:37:50.711+00:002008 Dirac Medal - Institute of PhysicsThe <a href="http://www.iop.org/">Institute of Physics</a> has awarded its <a href="http://www.iop.org/activity/awards/Gold_medals/The_Dirac_Medal_of_the_Institute_of_Physics/Dirac_medal_recipients/page_29099.html">2008 Dirac medal</a> to <a href="http://www.phy.cam.ac.uk/people/webberb.php">Bryan Webber</a> who was my PhD supervisor at the <a href="http://www.phy.cam.ac.uk/">Cavendish Laboratory</a> circa 1980.<br /><br />Congratulations!<br /><br />The brief version of the citation is:<br /><br /><blockquote><span style="font-size:85%;">For his pioneering work in understanding and applying quantum chromodynamics (QCD), the theory of the strong interaction which is one of the three fundamental forces of Nature.</span></blockquote>The full citation is:<br /><br /><blockquote><span style="font-size:85%;">The Dirac medal of the Institute of Physics for outstanding contributions to theoretical, mathematical and computational physics has been awarded to Professor Bryan R. Webber, Professor of Theoretical Physics at the University of Cambridge, for his pioneering work in understanding and applying quantum chromodynamics (QCD), the theory of the strong interaction which is one of the three fundamental forces of Nature.<br /><br />The strong force is felt by quarks, the constituents of protons and neutrons, and is carried by gluons which themselves interact via the strong force. To verify that the theory is correct requires being able to make accurate predictions of its consequences in particle physics experiments. Since the interactions are complex, this represents a formidable challenge.<br /><br />Professor Webber is recognised worldwide as having a profound understanding of QCD - from which he has derived key practical numerical tools for extracting quantitative information from high-precision experimental data. Over the past 20 years, these tools have been used in high-energy experiments around the world, for example, in the Large Electron-Positron Collider at CERN.<br /><br />Webber proposed a number of successful models that show what happens during high-energy particle collisions, for example, the break-up of quarks into jets of other particles. He developed powerful algorithmic approaches that not only allow much more accurate interpretation of particle events but also provide theoretical insights into the complexities of QCD. His work led to the theoretical consolidation of QCD, as recognised by the ensuing award of the Nobel Prize to the originators of the theory.<br /><br />Recently, Webber performed ground-breaking work on the phenomenology associated with the kind of physics that will be explored in the very high energy proton-proton collisions shortly to begin at the Large Hadron Collider at CERN. Professor Webber’s contributions to our understanding of the fundamental properties of matter have been invaluable, as revealed by the large number of citations of his published research.</span></blockquote>I notice that the winner of the 2008 Dirac Medal (Institute of Physics) appeared in <a href="http://en.wikipedia.org/w/index.php?title=Dirac_Prize&diff=163105140&oldid=155780225">Wikipedia on 8th October 2007</a>, so this blog posting of mine brings year-old news to you. My apologies for this oversight.<br /><br />I also notice on <a href="http://en.wikipedia.org/w/index.php?title=Dirac_Prize">Wikipedia</a> that the winner of the 1987 Dirac Medal (Institute of Physics) was Stephen Hawking, who was my brother Julian's PhD supervisor, so we are now <i>both</i> "descended" from Dirac Medallists.Stephen Luttrellnoreply@blogger.com0tag:blogger.com,1999:blog-17232904.post-84964403721200533192008-09-09T19:30:00.007+00:002012-05-16T16:48:15.146+00:00Luttrell Psalter<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-3ESmvnTVlgg/T7PaOOMyRpI/AAAAAAAAAHs/uRGfX3ep7Kg/s1600/Luttrell+Psalter.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://4.bp.blogspot.com/-3ESmvnTVlgg/T7PaOOMyRpI/AAAAAAAAAHs/uRGfX3ep7Kg/s320/Luttrell+Psalter.jpg" width="240" /></a></div><br />I've just got around to looking at a book that I bought in early 2007. The photo shows the front cover of the book, which immediately suggests the reason that I bought it. It is 36cm high by 25cm wide, it is 7.5cm thick, it weighs over 5kg, and it is by far the largest book that I possess.<br /><br />It is a facsimile copy of the <a href="http://en.wikipedia.org/wiki/Luttrell_Psalter">Luttrell Psalter</a>, which was written and illuminated during the second quarter of the 14th century, and is famed as a source of pictorial information about everyday life during the Middle Ages. A small sample of this can be seen in the photo above.<br /><br />The original project to create the Luttrell Psalter was very expensive in both time and money. It was commissioned by <a href="http://en.wikipedia.org/wiki/Geoffrey_Luttrell">Sir Geoffrey Luttrell</a> who ensured that an image of him and his family appeared in the book, which guaranteed that his name would never be forgotten, as no doubt he intended.<br /><br />The Luttrell Psalter will be a great source of pictures for me to write about in this blog.Stephen Luttrellnoreply@blogger.com10tag:blogger.com,1999:blog-17232904.post-50595380249601922352008-09-04T13:13:00.007+00:002012-05-16T16:49:52.426+00:00Scientific Linux - navigation blockedI was browsing the <a href="http://www.scientific-computing.com/">Scientific Computing World</a> article <a href="http://www.scientific-computing.com/features/feature.php?feature_id=207">A Universe of Data</a> on the computing resources at <a href="http://public.web.cern.ch/Public/Welcome.html">CERN</a>, when my attention was caught by mention of a version of Linux that I had not heard of before called Scientific Linux. What's so special about that? So I duly Googled the string "Scientific Linux" and the top hit was www.scientificlinux.org described as:<br /><br /><em>Scientific Linux - Welcome to Scientific Linux (SL) - 13:58Is a Linux release put together by Fermilab, CERN, and various other labs and universities around the world ready tuned for experimenters.<br />www.scientificlinux.org/ - 26k - Cached - Similar pages - Note this</em><br /><br />So I then followed the <a href="http://www.scientificlinux.org/">www.scientificlinux.org</a> link to get this:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-dz1Uinae6Lc/T7PakE8Kl-I/AAAAAAAAAH0/MgyfULyUGDI/s1600/Scientific+Linux.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="260" src="http://3.bp.blogspot.com/-dz1Uinae6Lc/T7PakE8Kl-I/AAAAAAAAAH0/MgyfULyUGDI/s400/Scientific+Linux.gif" width="400" /></a></div><br />I have <em>never</em> seen this sort of warning before, and I do a <em>lot</em> of internet browsing. I didn't explore any further because unexpected things on the internet always spook me, and by playing very safe I have managed to avoid all the nasty problems that I regularly hear about from other people.<br /><br />I am reasonably sure that the problem is a trivial misconfiguration of the www.scientificlinux.org site, rather than a malicious attempt by Internet Explorer to try to prevent people from visiting this particular site. Surely, it couldn't be the case that a www.scientificlinux.org is so self-righteous that they shoo away Internet Explorer users? Or am I just being paranoid?Stephen Luttrellnoreply@blogger.com2tag:blogger.com,1999:blog-17232904.post-4342472964461153642008-08-24T14:51:00.004+00:002008-08-24T16:13:27.023+00:00Dropping the BatonThere seem to have been rather a lot of dropped batons in the relay races at the Olympics (e.g. see <a href="http://www.independent.co.uk/sport/olympics/athletics/us-relay-team-drop-baton-904703.html">here</a>).<br /><br />It set me thinking about where I might have seen this sort of thing happening elsewhere, and I realised that dropping the baton is like annihilating the vacuum state.<br /><br />How so?<br /><br />The simplest possible algebra that one can use to model the process of baton-passing goes like this:<br /><br /><i>a</i><sup>†</sup> increments (by 1) the number of hands holding the baton<br /><i>a</i> decrements (by 1) the number of hands holding the baton<br /><br />|0> is the "vacuum" state where the baton has <i>one</i> hand holding it<br /><i>a</i><sup>†</sup>|0> is the state where the baton has <i>two</i> hands holding it<br /><br /><i>a</i>|0> = 0 is the annihilation of the vacuum where the baton has <i>zero</i> hands holding it, i.e. a state from which there is no way to recover<br /><br />Note that it is important to define the vacuum state as corresponding to <i>one</i> (rather than <i>zero</i>) hand holding the baton, otherwise the algebra (i.e. annihilation of the vacuum) doesn't correctly model the dropping of the baton. Thus the counting of hands holding the baton is really a measure of how many <i>excess</i> hands are holding the baton, because the case of <i>one</i> hand is actually the ground (or vacuum) state in a relay race.<br /><br />Most of the time the state is |0>, and during a <i>successful</i> handover of the baton it passes through the transition state <i>a</i><sup>†</sup>|0>, after which it returns to the state |0>. However, during an <i>unsuccessful</i> handover of the baton it goes to the state <i>a</i>|0> which is 0, where the vacuum has been annihilated.<br /><br />Successful handover: <i>a</i> <i>a</i><sup>†</sup>|0> = |0><br />Unsuccessful handover: <i>a</i><sup>†</sup><i>a</i>|0> = 0<br /><br />The order in which the <i>a</i> and <i>a</i><sup>†</sup> operations are applied is important, and is neatly summarised by how their commutator <i>a</i> <i>a</i><sup>†</sup> - <i>a</i><sup>†</sup><i>a</i> acts on |0> (take the difference of the above equations).<br /><br />(<i>a</i> <i>a</i><sup>†</sup> - <i>a</i><sup>†</sup><i>a</i>)|0> = |0><br /><br />A stronger form of this result is the <i>operator</i> relation<br /><br /><i>a</i> <i>a</i><sup>†</sup> - <i>a</i><sup>†</sup><i>a</i> = 1<br /><br />This relation takes note of the fact that there are <i>n</i> ways of applying <i>a</i> to the state (<i>a</i><sup>†</sup>)<sup><i>n</i></sup> |0> (i.e. choose from 1 of <i>n</i> excess hands to decrement by 1 the number of excess hands holding the baton), but there is only 1 way of applying <i>a</i><sup>†</sup> to the state (<i>a</i><sup>†</sup>)<sup><i>n</i></sup> |0>. The case <i>n</i>=0 is when the vacuum gets annihilated by application of <i>a</i>.<br /><br />The Olympic athletes who dropped the baton were the victims of <i>a</i> <i>a</i><sup>†</sup> - <i>a</i><sup>†</sup><i>a</i> = 1 (rather than 0). I wonder whether they saw it that way.Stephen Luttrellnoreply@blogger.com0tag:blogger.com,1999:blog-17232904.post-25398359408436866902008-08-24T13:42:00.005+00:002008-08-25T17:38:18.807+00:00Ethel the Aardvark Goes Quantity SurveyingHere is some Sunday afternoon entertainment.<br /><br />There was a "cheese shop sketch" <i>before</i> the famous <a href="http://en.wikipedia.org/wiki/Cheese_Shop_sketch">Cheese Shop Sketch</a> that we all remember. I was reminded about it whilst browsing the Wikipedia entry for <a href="http://en.wikipedia.org/wiki/Marty_Feldman">Marty Feldman</a>.<br /><br />Here it is (text copied from <a href="http://www.inprint.co.uk/thebookguide/bookshop-skit.htm">here</a>). The customer is played by Marty Feldman and the shop assistant by John Cleese.<br /><br /><b>Assistant:</b> Good morning, sir. <br /><b>Customer:</b> Good morning. Can you help me? Do you have a copy of 'Thirty Days In the Samarkand Desert with a Spoon' by A.E.J. Elliott? <br /><b>Assistant:</b> Um ... well, we haven't got it in stock, sir. <br /><b>Customer:</b> Never mind. How about 'A Hundred and One Ways to Start a Monsoon'? <br /><b>Assistant:</b> ... By ... ? <br /><b>Customer:</b> An Indian gentleman whose name eludes me for the moment. <br /><b>Assistant:</b> I'm sorry, I don't know the book, sir. <br /><b>Customer:</b> Not to worry, not to worry. Can you help me with 'David Copperfield'? <br /><b>Assistant:</b> Ah, yes. Dickens ... <br /><b>Customer:</b> No. <br /><b>Assistant:</b> ... I beg your pardon? <br /><b>Customer:</b> No, Edmund Wells. <br /><b>Assistant:</b> ... I think you'll find Charles Dickens wrote 'David Copperfield', sir. <br /><b>Customer:</b> No, Charles Dickens wrote 'David Copperfield' with two 'p's. This is 'David Coperfield' with one 'p' by Edmund Wells. <br /><b>Assistant:</b> <i>(a little sharply)</i> Well in that case we don't have it. <br /><b>Customer:</b> Funny, you've got a lot of books here. <br /><b>Assistant:</b> We do have quite a lot of books here, yes, but we don't have David Coperfield' with one 'p' by Edmund Wells. We only have 'David Copperfield' with two 'p's by Charles Dickens. <br /><b>Customer:</b> Pity - it's more thorough than the Dickens. <br /><b>Assistant:</b> More thorough? <br /><b>Customer:</b> Yes ... I wonder if it's worth having a look through all your 'David Copperfields'... <br /><b>Assistant:</b> I'm quite sure all our 'David Copperfields' have two 'p's. <br /><b>Customer:</b> Probably, but the first edition by Edmund Wells also had two 'p's. It was after that they ran into copyright difficulties. <br /><b>Assistant:</b> No, I can assure you that all our 'David Copperfields' with two 'p's are by Charles Dickens. <br /><b>Customer:</b> How about 'Grate Expectations? <br /><b>Assistant:</b> Ah yes, we have that ... <br /><i>He goes to fetch it and returns to the counter.</i> <br /><b>Customer:</b> ... That's 'G-r-a-t-e Expectations', also by Edmund Wells. <br /><b>Assistant:</b> I see. In that case, we don't have it. We don't have anything by Edmund Wells, actually - he's not very popular. <br /><b>Customer:</b> Not 'Knickerless Nickleby'? That's K-n-i-c-k-e-r <br /><b>Assistant:</b> No! <br /><b>Customer:</b> Or 'Quristmas Quarol 'with a Q? <br /><b>Assistant:</b> No, definitely ... not. <br /><b>Customer:</b> Sorry to trouble you. <br /><b>Assistant:</b> Not at all. <br /><b>Customer:</b> I wonder if you have a copy of 'Rarnaby Budge'? <br /><b>Assistant:</b> <i>(rather loudly)</i> No, as I say, we're right out of Edmund Wells. <br /><b>Customer:</b> No, not Edmund Wells - Charles Dikkens. <br /><b>Assistant:</b> Charles Dickens? <br /><b>Customer:</b> Yes. <br /><b>Assistant:</b> You mean 'Barnaby Rudge'. <br /><b>Customer:</b> No, 'Rarnaby Budge' by Charles Dikkens ... that's Dikkens with two 'k's, the well-known Dutch author. <br /><b>Assistant:</b> No, no - we don't have 'Rarnaby Budge' by Charles Dikkens with two 'k's the well-known Dutch author, and perhaps to save time I should add right away that we don't have 'Carnaby Fudge' by Daries Tikkens, nor 'Stickwick Stapers' by Miles Pikkens with four Ms and a silent Q, why don't you try the chemist? <br /><b>Customer:</b> I did. They sent me here. <br /><b>Assistant:</b> <i>(making a mental note)</i> ... Did they? <br /><b>Customer:</b> I wonder if you have ... 'The Amazing Adventures of Captain Gladys Stoat-Pamphlet and her Intrepid Spaniel Stig among the Giant Pygmies of Corsica', Volume Two. <br /><b>Assistant:</b> No, we don't have that one. Well, I mustn't keep you standing around all day .. <br /><b>Customer:</b> I wonder if ... <br /><b>Assistant:</b> No, no, we haven't got it. I'm closing for lunch now anyway. <br /><i>The assistant moves rapidly away from the counter.</i><br /><b>Customer:</b> ... But I thought I saw it over there. <br /><i>The assistant checks and turns slowly.</i><br /><b>Assistant:</b> ... What? <br /><b>Customer:</b> Over there. <br /><i>He indicates a bookshelf.</i><br /><b>Customer:</b> 'Olsen's Standard Book of British Birds'. <br /><b>Assistant:</b> <i>(very suspiciously)</i> 'Olsen's Standard Book of British Birds'? <br /><b>Customer:</b> Yes. <br /><b>Assistant:</b> ... 0-l-s-e-n? <br /><b>Customer:</b> Yes! <br /><b>Assistant:</b> B-i-r-d-s? <br /><b>Customer:</b> Yes! <br /><b>Assistant:</b> Well, we do have that one, yes. <br /><i>He goes and takes the book off a shelf.</i><br /><b>Customer:</b> ... The expurgated version, of course. <br /><b>Assistant:</b> ... I'm sorry, I didn't quite catch that. <br /><b>Customer:</b> The expurgated version. <br /><b>Assistant:</b> The expurgated version of 'Olsen's Standard Book of British Birds'? <br /><b>Customer:</b> Yes. The one without the gannet. <br /><b>Assistant:</b> The one without the gannet?! They've all got the gannet it's a standard bird, the gannet, it's in all the books. <br /><b>Customer:</b> Well I don't like them. They've got long nasty beaks! And they wet their nests. <br /><b>Assistant:</b> But ... but you can't expect them to produce a special edition for gannet-haters! <br /><b>Customer:</b> I'm sorry, I specially want the one without the gannet. <br /><i>The assistant is speechless.</i><br /><b>Assistant:</b> All right! <br /><i>He suddenly tears out the relevant page.</i> <br /><b>Assistant:</b> Anything else? <br /><b>Customer:</b> Well, I'm not too keen on robins. <br /><b>Assistant:</b> Right! Robins, robins ... <br /><i>He tears that one out too and slams the book on the counter.</i><br /><b>Assistant:</b> No gannets, no robins - there's your book! <br /><b>Customer:</b> I can't buy that. It's torn. <br /><b>Assistant:</b> ... So it is! He tosses it into the bin. <br /><b>Customer:</b> I wonder if you've got ... <br /><b>Assistant:</b> Go on! Ask me another. <br /><b>Customer:</b> How about 'Biggles Combs his Hair'? <br /><b>Assistant:</b> No, no, we haven't got that one, funny. Try me again. <br /><b>Customer:</b> 'The Gospel According to Charlie Drake'? <br /><b>Assistant:</b> No ... <br /><b>Customer:</b> Have you got 'Ethel the Aardvark Goes Quantity-Surveying'? <br /><b>Assistant:</b> No, no, we haven't ... which one? <br /><b>Customer:</b> 'Ethel the Aardvark Goes Quantity-Surveying'. <br /><b>Assistant:</b> 'Ethel the Aardvark'?! I've seen it! We've got it!! <br /><i>He dashes to a bookshelf, finds it, and holds it up triumphantly.</i><br /><b>Assistant:</b> Here! Here!!! 'Ethel the Aardvark Goes Quantity Surveying'. Now - buy it! <br /><i>He slams it on the desk. The customer stares in horror!</i><br /><b>Customer:</b> ... I haven't got enough money on me. <br /><b>Assistant:</b> <i>(quickly)</i> I'll take a deposit! <br /><b>Customer:</b> I haven't got any money on me. <br /><b>Assistant:</b> I'll take a cheque! <br /><b>Customer:</b> I haven't got a cheque book! <br /><b>Assistant:</b> It's all right, I've got a blank one! <br /><b>Customer:</b> I don't have a bank account!! <br /><b>Assistant:</b> ... All right!! I'll buy it for You! <br /><i>He rings the purchase up and pays for it himself. He gives the change to the customer.</i><br /><b>Assistant:</b> There we are, there's your change - that's for the taxi home ... <br /><b>Customer:</b> Wait! Wait! Wait! <br /><b>Assistant:</b> What? What? What?!!! <br /><b>Customer:</b> ... I can't read ... <br /><b>Assistant:</b> Right! Sit!! ... <br /><i>He sits the customer down on his knees and starts to read aloud.</i><br /><b>Assistant:</b> 'Ethel the Aardvark was trotting down the lane one lovely summer day, trottety-trottety-trot, when she saw a nice Quantity-Surveyor ...Stephen Luttrellnoreply@blogger.com3tag:blogger.com,1999:blog-17232904.post-60069973952398608992008-08-24T11:10:00.008+00:002012-05-16T16:21:01.525+00:00Twerp Bollickagh - the website<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-SwezOfKshg0/T7PTsicId7I/AAAAAAAAAGw/8JZXLRw6ie8/s1600/Twerp+Bollickagh+(website).gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="271" src="http://1.bp.blogspot.com/-SwezOfKshg0/T7PTsicId7I/AAAAAAAAAGw/8JZXLRw6ie8/s400/Twerp+Bollickagh+(website).gif" width="400" /></a></div>Stephen Luttrellnoreply@blogger.com2tag:blogger.com,1999:blog-17232904.post-58648862127349250882008-08-15T18:02:00.006+00:002008-08-15T21:47:22.911+00:00Twerp BollickaghIt could be the title of a journal!<br /><br />I suspect that many of the experimentally accurate theoretical "predictions" given in a "Grand Unified Theory" that is available online (search for the string "The calculated relations between the lepton masses") were arrived at by exhaustive numerology, i.e. by searching through a large number of simple expressions to find the ones that gave the required results. Then a "proof" of each of these results was reverse-engineered using pseudo-physical explanations rather than using rigorous maths.<br /><br />Let me show you an example of what I mean.<br /><br />This "GUT" gives some simple expressions for various mass ratios. There is even an expression for the ratio of the neutron mass to the electron mass, which depends <i>only</i> on the electomagnetic coupling strength (i.e. fine structure constant) and <i>not</i> on the strong interaction strength. How do the quarks and gluons in the neutron know how to interact in order to give this amazing result?<br /><br />The expression given by this "GUT" for the muon to electron mass ratio (i.e. mμ/me) is<br /><br />(α^(-2) / 2π)^(2/3) (1 + 2π α^2 / 2) / (1 + α/2)<br /><br />which produces a value 206.76828 that closely corresponds to the experimentally observed value 206.76827.<br /><br />Let's see whether it is possible to "derive" this result by an exhaustive search of all simple expressions of this general type. The parameterisation that I will use is the most general form that is suggested by the mass ratio quoted above<br /><br />f[{a1, a2, a3, a4}, {b1, b2, b3, b4}, {c1, c2, c3, c4}, {d1, d2, d3, d4}, α]] =<br />(a1/a2)^(a3/a4) (α)^(b1/b2) (2π α^2)^(b3/b4) (1 + (c1/c2)(α) + (c3/c4)(2π α^2)) / (1+ (d1/d2)(α) + (d3/d4)(2π α^2))<br /><br />where all of the parameters are integers which are grouped in pairs to form rational fractions. To compute numerical results I inserted specific values for these parameters (avoiding singular cases), I use α=0.00729735, and a target mass ratio mμ/me=206.76827.<br /><br />I then computed f[{a1, a2, a3, a4}, {b1, b2, b3, b4}, {c1, c2, c3, c4}, {d1, d2, d3, <br /> d4}, α]] for all parameter values in the following small ranges (I have been rather cavalier and restricted the ranges to save time):<br />{a1, 1, 2}, {a2, 1, 2}, {a3, 1, 3}, {a4, 1, 3},<br />{b1, 0, -3, -1}, {b2, 1, 3}, {b3, 0, -3, -1}, {b4, 1, 3},<br />{c1, 0, 2}, {c2, 1, 2}, {c3, 0, 2}, {c4, 1, 2},<br />{d1, 0, 2}, {d2, 1, 2}, {d3, 0, 2}, {d4, 1, 2}<br />There is some repetition of trial solutions here, but this doesn't matter.<br /><br />I then selected from this large set of trial solutions all of the cases that predicted a value for mμ/me that lay within 0.01 of the target value, and here they are (in decreasing order of goodness of fit) with the prediction errors shown in square brackets:<br /><br />(1/(2π α^2))^(2/3) (1 + π α^2) / (1 + α/2) [0.0000110213]<br />(1/(2π α^2))^(2/3) (1 + 2π α^2) / (1 + α/2 + π α^2) [0.000130968]<br />(1/(2π α^2))^(2/3) (1 + α/2 + π α^2) / (1 + α) [0.00261802]<br />(1/(2π α^2))^(2/3) (1 + α/2 + 2π α^2) / (1 + α + π α^2) [0.0027371]<br /><br />The best fit solution at the top of this list is the same as the one given by the "GUT".<br /><br />What do we conclude from this little exercise?<br /><br />It is <i>really</i> easy to do exhaustive searches to find best-fit solutions. The above fit works as well as it does because it starts with two different quantities (α) and (2π α^2) (where π is <i>not</i> a rational fraction), and combines them in various ways using lots of rational fractions to tailor the combination, which then leads to a dense set of candidate solutions from which the best-fit solution can then be picked.<br /><br />Unless you happened to pick the physically correct parametric form to search over (<a href="http://en.wikipedia.org/wiki/Balmer_series">Balmer</a> got lucky with atomic spectra, but that is not to be used as a justification for this approach), then there is <i>no physical significance</i> to solutions that are obtained in this way. If you hedge your bets by searching over a large set of parametric forms, then you will almost certainly find many solutions that have a good fit to the target value, but this doesn't guarantee that any of them is physically significant. Interestingly, a related problem occurs in the context of the <a href="http://en.wikipedia.org/wiki/String_theory_landscape">Landscape</a>.<br /><br />The approach used in this "GUT" is numerology, pure and simple. Of course, I only <i>suspect</i> that this is the way that the above expression for mμ/me was "derived"; I can't <i>prove</i> that this is the case.Stephen Luttrellnoreply@blogger.com0