Theoretical mathematical results have often little immediate practical application and in some cases initially can seem obvious. Still they usually are not obvious as such since it is quite different to imagine that a result holds true, and to prove it mathematically in a rigorous way. Moreover such a proof often helps explaining the reasons of the result and its possible applications.
Very recently a theoretical (mathematical) results in Machine Learning (the current main version of Artificial Intelligence) has been announced: the paper can be found in Nature here and a comment here .
Learnability can be defined as the ability to make predictions about a large data set by sampling a small number of data points. This is what usually Machine Learning does. The mathematical result is that, in general, this problem is ‘undecidable’, that is it is impossible to prove that it always exists a limited sampling set which allows to ‘learn’ (for example to always recognise a cat in an image from a sample of a limited number of cat’s images). Mathematicians have proven that Learnability is related to fundamental mathematical problems going back to Cantor’s set theory, the work of Gödel and Alan Turing, and it is related to the theory of compressibility of information.
This result poses some theoretical limits on what Machine Learning can ever achieve, even if it does not seem to have any immediate practical consequence.
I am still interested in developements in the area of Quantum phenomena which can be used in ICT and in particular in ICT Security. Recently there have been quite a few announcements of interest. Here are a some of them:
- A scientific paper proposes on a new way of generating Quantum Random Number, that is ‘real random numbers’ (whatever that means) by using every day technology like the camera of our smart phone; this does not mean that the smart phone camera is enough to produce real random numbers (for the moment you still need a computer to process the data produced by it) but it is a sign that the technology is providing us with tools of unprecedented power, and soon our smart phone will be enough for a good many things;
- New developments in Quantum Cryptography (se here and here for details) would make it easier to implement Quantum Cryptography in practice; this is nice, even if it does not changes dramatically the current status and relevance of Quantum Cryptography;
- Another article (see here for a comment) leaves me instead quite puzzled: either I don’t understand it or there is something fundamentally flawed in the argument otherwise it will look like it is possible to obtain quantum effects in classical physics, which is just what it is not.
The Hubble Tarantula Treasury Project has just released some amazing pictures (see here and here with more technical details) of the Tarantula Nebula with more than 800.000 baby and young stars. Worth a look.
I have been following at a distance since a few years the development of Quantum Computers. One of the more controversial approaches to Quantum Computing is the one proposed by D-Wave. D-Wave is also the only company which claims to have a specialized version of Quantum Computer ready to sell, and actually they did sell at least one Quantum Computer to a consortium made by Google, NASA, and the Universities Space Research Association.
What it is not yet clear is if it is really a Quantum computer, and even if it is, if it gives any advantages with respect to traditional computers. There are quite some different opinions about this, and this IEEE Spectrum article tries to understand where we stand now.
At the 2013 Moriond Conference, CERN has released more data indicating that the particle discovered last year is really a Higgs boson, and it looks more like the Standard Model particle we studied in text books, see here for CERN announcement.
The ATLAS experiment has also published here some very nice animated plots which show how the measured events slowly build up statistics which give the above mentioned results.
I have just written a short essay entitled Physics, Mathematical Models and Human Intuition (the title should say it all) drawing on my previous job as researcher and professor in elementary particle physics.
Since it is a little too long for a blog entry (just 4 pages) you can download it here.
(You can also check my website for most of my recent papers.)
It has just been published here a paper by Ross Anderson and Robert Brady on Quantum Computing, Quantum Cryptography and Quantum Mechanics.
I personally know some of the people mentioned in the paper and who worked for many years on these aspects of fundamental Quantum Mechanics and Particle Physics. Without discussing the details of the theory proposed in this paper, I think that some comments can be useful since I worked in research in theoretical physics for a good part of my life.
It is true that the Bell’s inequalities and the EPR paradox have been and are the cause of many debates in fundamental theoretical physics, beginning with Einstein’s reject of these concepts. I believe that today there is enough experimental evidence that on this point Einstein was wrong and the Bell’s inequalities are violated. In other words, I believe that Quantum Mechanics is a valid description of elementary physics at the Quantum scale. We know very well that (non-relativistic) Quantum Mechanics does not work eg. at very high energy scales like the ones probed by the CERN experiments which led recently to the discover of the Higgs particle.
We know very well that there is a lot that we do not understand yet in Particle Physics. This could mean that Quantum Computing could be harder than what we expect due to our ignorance of some new (quantum) physics.
But I disagree with Ross Anderson this time since I do not believe that Classical Mechanics can explain this kind of phenomena nor that it can show that the theory of Quantum Cryptography is flawed (implementing Quantum Cryptography in practice is a completely different story).