The National Curriculum requires schools to teach not computer science but ICT – a strange hybrid of desktop-publishing lessons and Microsoft tutorials. While Word and Excel are useful vocational skills, they are never going to equip anybody for a career in video games or visual effects. Computer science is different. It is a vital, analytical discipline, and a system of logical thinking that is as relevant to the modern world as physics, chemistry or biology. Computer science is to ICT what writing is to reading. It is the difference between making an application and using one. It is the combination of computer programming skills and creativity by which world-changing companies such as Google, Facebook, Twitter and Zynga are built. Indeed, in a world where computers define so much of how society works, I would argue that computer science is “essential knowledge” for the 21st century.
Title: Can apparent superluminal neutrino speeds be explained as a quantum weak measurement?
Authors: M V Berry, N Brunner, S Popescu & P Shukla
Published: November 11 2011, J.Phys.A 44 492001
Abstract: Probably not.
“I have been asked whether a student can bring her kindle into an open book exam, as she has e-copies of the relevant set texts. Logically I’d be worried about saying no, as it isn’t unreasonable for a student to buy set books in e versions. However, there are clearly problems in controlling what else might be on the kindle.”
Rather than consider how Kindles might affect the present system of open book exams (now about 40 years old) we might consider how Kindles (and, perhaps, Google) might affect how and what we examine. It is possible that an open book exam, under time pressures, might incorporate an internet search as part of its testing, with the requirement to reference findings as appropriate. Limiting the role of technology could be seen as rather like Canute.
In my opinion, the new technology makes obsolete the very concept of standardised and controlled assessment because anything which can be standardised can be much better done by a computer. For example, there is software — easily available on the Internet — which not just solves standard school and undergraduate level algebraic, trigonometric, logarithmic, differential equations, it produces a complete step-by-step verbal write-up of the solution, with a detailed explanation of every step; if the user wishes, more mundane symbolic rearrangements could be kept hidden, or, on the contrary, unrolled.
However, the solution to the challenges of new technology had been known for at least 70 years now, and used in educational establishments working at the cutting edge of technological progress of their time, say, in physics and mathematics university departments involved in training of researchers and engineers for the Manhattan project in the USA, and in similar establishments in Russia. This solution was an open book public oral examination, where a candidate was allowed (and actually encouraged) to consult books and records of his choice, while examiners reserved the right to ask any question — and many, if not most, statements were distinctively non-standard. Also, it was at examiners’ discretion to decide whether the candidate had to answer particular question on the spot or given a couple of hours for thinking. If the Internet existed in 1940-s, it would be instantly and painlessly adopted into the open book examination procedure.
Of course, such examinations are not allowed under the current legal framework which regulates British univerisites. But this is a sign of a real technological change: it does not necessarily fit in the existing legal set-ups.
On page 6 of this NYT article, search for words “my mathematical training”.
Magazine Preview: On the Ropes with Herman Cain
By T. A. FRANK
The end of the Cain campaign has been at hand for months. And yet the end doesn’t arrive. And the end isn’t about to arrive now either.
With thanks to muriel.
A book picked at random off a shelf in the library of Mathematisches Forschungsinstitut Oberwolfach and opened at a random page revealed a little gem, a paper by Pierre Ageron Logic without self-deductibility, in: Logica Universalis (J.-Y. Beziau, ed.), Birkhauser, Basel – Boston -Berlin, 2007, pp. 87-93.
The “law of self-deductibility” is a simple principle “if A, then A” which expresses the reflexivity of entailment; apparently, its formulation can be traced back to Stoic philosophers. Pierre Ageron comments that
Self-deductibility has a paradoxical status. It seems so obvious that, unlike the law of exluded middle [...] it has hardly ever a matter of controversy [...]. Also it seems of no use whatsoerver in the mathematical practice and totally sterile in terms of deductive power.
However, then Pierre Ageron points out that Charles Pierce in hisAlgebra of Logic (1885)
mentions in passing quite a remarkable interpretation of the law of self-deductibility. Pierce referes to it as the “first icon of algebra” and argues that it “justifies our continuing to hold what we have held, though we may, for instance, forget how we were originally justified in holding it”. This clearly suggests that self-deductibility works as an amnesia principle: once some statement is proved, it allows us to forget how it was proved. In mathematical practice, it is obviously a good thing that we can continue to trust our old theorems even if we are unable to reconstruct their proofs.
In my book, I briefly discuss Timothy Gowers‘ observation that, in his opinion, a “comprehensible” proof is not necessarily the shortest one, but a proof of small width. Here, width measures how much you must hold in your head at any one time. Alternatively, imagine that you write a detailed proof on a blackboard, carefully referring to all intermediate steps.
However, if you know that a certain formula or lemma will never be used again, you erase it and re-use the space. A “small width” proof is a proof which never expands beyond one (small) blackboard. In other words, a “comprehensible” proof is a proof produced by a systematic application of the “amnesia principle” and the humblest of all tautologies, “if A then A”.
[Imported from my old and now defunct blog]
Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. One goes into the ﬁrst room, and it’s dark, completely dark. One stumbles around bumping into the furniture, and gradually, you learn where each piece of furniture is, and ﬁnally, after six months or so, you ﬁnd the light switch. You turn it on, and suddenly, it’s all illuminated. You can see exactly where you were.
[With thanks to Thomas Riepe]