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I was thinking about how to make my lectures more interesting. However, I have decided not to follow the lead of Ramil Buenaventura… |
In my class you see me rapping, singing, dancing on the tables—I even made a music video about math to grab their attention.
Buenaventura
But then if it works…
Link
US-based Filipino teacher cited for making algebra cool
 The working rebuilt bombe at Bletchley Park Image courtesy of Wikipeda. |
Mathematicians from the Polish Cipher Bureau, Marian Rejewski, Jerzy Różycki and Henryk Zygalski broke the German Enigma cipher machine codes in the 1930’s. |
Working with engineers from the AVA Radio Manufacturing Company, they built the “Bomba”, which was the first machine to break Enigma codes. By working with a commercially available version of the Enigma machine, they laid down the mathematical foundations that were essential for the British work at Bletchley Park in breaking the German military codes. In particular Alan Turing helped develop the British version of the Bomba and the story from here is well-known.
The efforts of Rejewski, Różycki and Zygalski are far less well-known and were never really appreciated in their lifetimes. There is a small memorial at Bletchley Park in honour of these three.
In August 2014 the Institute of Electrical and Electronics Engineers (IEEE), as part of their Milestones commemorations have honoured Rejewski, Różycki and Zygalski with a plaque outside the Institute of Mathematics of the Polish Academy of sciences. I was lucky enough to be present at the unavailing ceremony which was hosted by IEEE President Prof. J. Roberto B. de Marca. There were several diplomats and representatives from the Polish military. Janina Sylwestrzak, the daughter of Marian Rejewski, was also present and gave a short speech (in Polish of course).
The Rejewski, Różycki and Zygalski memorial stone.
The plaque reads as follows;
You can find out more about the Polish work on breaking the Enigma codes by following the links below.
Links
Milestones:First Breaking of Enigma Code by the Team of Polish Cipher Bureau, 1932-1939 IEEE website.
The Breaking of Enigma by the Polish Mathematicians, Virtual Bletchley Park.
Poland’s overlooked Enigma codebreakers, BBC News.
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scientists from South Korea have converted cigarette butts into a high-performing material that could be used to coat the electrodes of supercapacitors [1]. |
The material is produces via the heat treatment of used cigarette butts in a nitrogen rich environment.
The article states that the processed cigarette filter material stored a higher amount of electrical energy than commercially available carbon. Also the material stored more energy than the more experimental materials graphene and carbon nanotubes.
If the process can be made economically viable then this process could be used to ecologically recycle cigarette butts.
Reference
[1] Minzae Lee, Gil-Pyo Kim, Hyeon Don Song, Soomin Park and Jongheop Yi, Preparation of energy storage material derived from a used cigarette filter for a supercapacitor electrode, 2014 Nanotechnology 25 345601.
Link
Cigarette butts offer energy storage solution IOP News
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Researchers at the University of Sussex have published their research on how horses communicate [1]. It seems that they use their swiveling ears to aid in communication. |
Talking to someone who is not a scientist, but has lots of experience of working with horses, said that the horse riding community knew this already. However, a scientific study was needed as anecdotal evidence is not enough.
That said, this was known about for donkey’s years*!
*Non-native speakers may find this link useful.
Link
Horses’ mobile ears are ‘communication tool’ BBC News
Reference
Jennifer Wathan & Karen McComb, The eyes and ears are visual indicators of attention in domestic horses, Current Biology , Volume 24, Issue 15, 4 August 2014, Pages R677–R679.
As you can imagine as a mathematician, the bigger and harder the equations the happier I am. Not really, we look for pattens and elegance rather than just difficult equations, though of course difficult equations can be elegant and contain a lot of interesting structure.
Anyway, scientists now have an equation for happiness and here it is
Taken from [1].
Now we just need to apply some calculus to find the maxima (local or global I’m not fussy) and find out just how happy a mathematician can be!
Reference
[1] Robb B. Rutledge, Nikolina Skandali, Peter Dayan, and Raymond J. Dolan, A computational and neural model of momentary subjective well-being, PNAS 2014 : 1407535111v1-201407535.
Link
Equation ‘can predict momentary happiness’ BBC News
I have again been playing with some random walks, using the same method as here. This time I used 1000000 iterations and added some colour.
Below are random walks, on the plane (not a lattice) for which step size gets (on average) smaller and smaller with each step. I pick the step size using the Maxwell-Boltzman distribution (with a =1) and a suitable scaling which depends on the iteration parameter. I the add a opacity depending on how many times the points are visited: bright white means a lot, while grey means not many and black never.
Once again, these images are rather for artistic purposes than scientific purposes.
Dalek-like robots are being employed to clean the wards of a North Wales hospital.
Robomen being lead by a Dalek. Image by the BBC.
One of my friends (who shall remain nameless) was worried about robots taking over the world. His nightmares will only get worse!
A member of the cleaning staff at Glan Clwyd hospital in Bodelwyddan. Image by the BBC.
Link
Robot cleaners used cut hospital infection in north Wales
Below are random walks on the plane (not a lattice) for which step size gets (on average) smaller and smaller with each step. I pick the step size using the Maxwell-Boltzman distribution (with a =1) and a suitable scaling which depends on the iteration parameter. I the add a opacity depending on how many times the points are visited: bright white means a lot, while grey means not many and black never.
I may play with these further, but they make some interesting pattens. We have approximate self-similarity and so these patterns have fractal-like properties. Anyway, enjoy….
These images were created for artistic rather than scientific reasons. That said, random walks are have been applied to many fields including ecology, economics, psychology, computer science, physics, chemistry, and biology.
Probably the most famous application of a random walk is to Brownian motion, which describes the trajectory of a tiny particle diffusing in a fluid. I have no idea if there is anything scientific in these images, but I would not be surprised if for small step sizes we have approximately Brownian motion. However, I would need to think a lot more about this before making concrete statements.
Another IFS that my wife and I created. Not sure what to call this one!
The above is an IFS fractal that resembles a fern. Maybe not as good as Barnsley’s fern , but mine was generated using two affine transformations and not the four as used by Barnsley. It is a nice image and I am happy with it.