A fractal fern

June 30th, 2014 by ajb


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.

America has Roswell, Great Britan has Rendlesham Forst, Poland has Emilcin

June 28th, 2014 by ajb

On the 10th of May 1978 Jan Wolski, a local farmer, reportedly hand a close encounter of the Polish kind.

The claim is that Pan Wolski, who was 71 at the time, while out driving his horse-drawn cart near the small village of Emilcin, Poland was jumped on by two aliens. The description of these aliens is similar to the well-known grey alien, but a little greener.

They took him to their craft which is depicted below;


Once on board he was de-robed and thoroughly probed!

The story at the time did not course much of a stir. The only other witness was a six year-old boy and of course Polish farmers like vodka!

To commemorate the strange events of that day, in 2005 a memorial was constructed in Emilcin. The plaque reads “On 10 May 1978 in Emilcin a UFO object landed. The truth will astonish us in the future”.

ufo statue

I tried to convince my wife that we should see this monument, I think it is cool and a bit wacky!

You can find out more about the Polish abduction by following the link below.

Emilcin Abduction Wikipedia

Turing’s Birthday

June 23rd, 2014 by ajb
Turing Everybody reading this post should be aware that today is Alan Turning’s birthday. He was born on the 23th June 1912.

I say everyone reading this should be aware of this fact as Turing is considered the farther of theoretical computer science.

Memorial at Manchester
Turing was involved in the development of the Manchester computers, which were the first series of stored-program electronic computers. They were developed during the 30-year period between 1947 and 1977 by a small team at the University of Manchester.

Near the Sackville street buildings of the University of Manchester there is a memorial. The plaque reads as follows;


I won’t say much about the way he was treated, different times and so different ways of thinking. You can find out more via the link below.

Alan Turing: the enigma

On to infinity: a peice of art

June 21st, 2014 by ajb


This is another piece of mathematical art my wife and I created. I call it “On to infinity”.

Newton to appear at a pub in Cardiff!

June 20th, 2014 by ajb
Newton As part of this year’s Cardiff Science Festival the Institute of Physics has organised for Prof. Mike Edmunds to perform his one man play about Sir Isaac Newton at Porter’s Bar in Cardiff on Wednesday, 16 July 2014 from 18:30 to 20:00.

This event is completely FREE, but spaces are limited. Please follow the link below for more details.

Sir Isaac remembers…

Take care with units!

June 14th, 2014 by ajb
maths One of the common problems that A-level physics students have is being slack with units and powers of 10. Often they neglect to include units in their final answers or are out by factors of 10, sometimes many factors of 10.

The BBC News Magazine has collected 10 such instances in the real word and not just in the homework of physics students.

The key message here must be take care with units and exponents!

Paying £300,000 instead of £3,000, and other mix-ups BBC News Magazine.

Back to school for me

June 14th, 2014 by ajb
classroom At the end of this month I will be attending a summer school “Introduction to the geometry of jet spaces and nonlinear differential equations” in Wisła, Beskid Mountains, Poland. The school is being organised by the Baltic Institute of Mathematics.

The summer school will consist of lectures by Joseph Krasil’shchik and Alexander Verbovetsky​, both of whom are world leading experts in the theory and application of jets to differential equations.

The period of the summer school is the 29th of June till the 6th of July.

Introduction to the geometry of jet spaces and nonlinear differential equations

Cardiff Science Festival 2014

June 12th, 2014 by ajb
flag of wales Cardiff Science Festival 2014 is nearly here and will from run from the 14th to the 20th July at various locations across Cardiff.

Events include hands on workshops, live demonstrations, talks, discussion forums, performances, lectures, debates, exhibitions, guided tours and panel discussions.

To find out more details follow the link below.

Cardiff Science Festival

On curves and jets of curves on supermanifolds

May 28th, 2014 by ajb
My work on curves and higher tangent bundles on supermanifolds has now been published as “On curves and jets of curves on supermanifolds“, Archivum mathematicum, Volume 50 (2014), No. 2.

In this paper we examine a natural concept of a curve on a supermanifold and the subsequent notion of the jet of a curve. We then tackle the question of geometrically defining the higher order tangent bundles of a supermanifold. Finally we make a quick comparison with the notion of a curve presented here are other common notions found in the literature.

The main idea was to try to follow the classical definitions of a curve, jets of curves at a point and the geometric or kinematic definition of higher tangent bundles. One of the complications in the superworld is that supermanifolds are not just set theoretical objects. To overcome this the more categorical set-up of the “functor of points” and “internal Homs” is needed.

I posted a little about this before here.

Einstein Relatively Simple by Egdall

May 18th, 2014 by ajb

Both special and general relativity have a reputation for being very complicated theories to understand. While it is true that one needs some mathematical machinery to really master these theories, Egdall does a great job in showing that it is possible with a bare minimum of high school mathematics to get an appreciation of the main ideas.

Edgall does not completely stay away from some mathematics, though as it is isolated somewhat from the main text, the mathematically shy should not be scared away from this book. The style is lighthearted and is full of thought experiments illustrated by short entertaining stories.

The author does an excellent job in highlighting the main features of special and general relativity in a way suitable for the lay reader to understand. Moreover, the development of the theory is presented in a chronological/historical context by trying to describe Einstein’s trail of thought and how he was influenced by the various problems with physics found in the late 1800′s. We get a good overview of Einstein the man from this book.

However, like all popular science books, there are the odd statements like “…the photon’s perspective” and “..spacetime curvature has energy” which any physicist will question. That said, I do consider the book well-written, entertaining and a useful introduction to the ideas of relativity for the lay person.

The book is divided into two chapters, an appendix with more mathematical details and a rather extensive list of notes with sources. Part I deals with special relativity describing the initial development of the theory starting from the conflict between classical mechanics and electromagnetic theory. The strange consequences of Einstein’s special relativity including the idea of space-time, time dilation, length contraction and his famous equation E=mc^2 are discussed.

Part II introduces us to general relativity which is the most accurate theory of gravity know to science. The fundamental idea is that gravity should be viewed as space-time curvature and some of the consequences of this are discussed in this book. Some aspects of modern cosmology and the big bang theory are also briefly discussed.

Note: This book is based on lay courses in modern physics Edgall teaches at Lifelong Learning Institutes at several universities in South Florida.

Paperback: 300 pages
Publisher: World Scientific Publishing Company (February 24, 2014)
Language: English
ISBN-10: 9814525596
ISBN-13: 978-9814525596

Einstein Relatively Simple