I find myself looking for a job…

January 22, 2011

I have a weird collection of skills. Mathematics, talking about mathematics, art, making…

I am certainly missing opportunities, maybe because few know the skill set even exists! So its time to advertise myself. Perhaps you are looking for someone who can…

  • Do mathematics at a research level, especially:
    • Geometry, understanding the spaces we live in and more exotic ones.
    • Tilings and patterns.
    • History and culture of Mathematics
  • Talk maths in public.
  • Teach (and be creative at it)
  • Program
  • Use computer manufacturing tools, Laser cutters, 3d printers, 3/5/n-axis routers.
  • Make Art and do Design

You need more evidence? I guess that makes sense. More details are below. If you still need to know more get in touch. I can provide references! (edmund.harriss at mathematicians.org.uk)

More details and evidence…

Mathematics: The heart of what I do, I have been an academic mathematician since getting my PhD from Imperial College in 2004. I have written papers, and been invited far and wide to talk about my work. See my CV for the gory details.

Geometry, Tilings and Patterns: I have a very strong understanding of the space we live in (and more exotic spaces). As this is a mathematical understanding I also have the tools to make this concrete, putting it into the equations and other things that computers can play with. My mathematical research has looked at tilings and patterns. Especially substitution tilings a sort of scaling symmetry, I probably know as much about the Penrose tiling than anyone else alive or dead!

History of Mathematics: It is mostly an amateur interest, though I nearly started a PhD with David Fowler before beginning one on tilings. I also think about the role of mathematics as a subject in the world and its relationship to art.

Talking maths in public: You can understand what I have to say without specialist training! I have explained the beauty and wonder of mathematics from the sacred halls of the Royal Society to primary schools. You can even hear me on the radio (and of course read this blog!). Or dive into the geekiness of prime birthdays.

Teaching: I want to teach people to actually think mathematically, not just get the rules that can be followed to a right answer, and have had success with it. Of course I can teach a traditional maths course and these are often necessary to get the bulk of material across, however I have also worked with more innovative courses. That is why I came to Arkansas. I wanted to teach MATH 2033 the conspiracy or mathematics course designed to corrupt people into the subject by giving a glimpse of  undecidability, game theory, 4 dimensional geometry, hyperbolic geometry, topology, codes, sphere packings… The students then have to come up with their own projects and, as could be expected often get incredibly creative.

3d cog spirographs

Art and Design: I can make pretty pictures, normally using maths. I am on the board of the new Art and Science masters at Central St Martins school of Art in London, and designed the screens for the new Mathematics Learning Centre at Imperial College London. I can do graphic design in 2d and make models and render them in 3d. I can use all the standard software, Adobe Illustrator and Photoshop, Rhino 3d (especially with Grasshopper) etc.

Making: I make things, normally focussing on explaining mathematics. I even have my own Laser cutter! I designed some larger versions of the hexayurt, a simple building made, without waste from 12 sheets of plywood or other materials. I am currently working with the FabLab at the architecture school here at the University of Arkansas, and am writing software to drive their 5-axis router.


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Posted by gelada

Carnival of Mathematics #65

May 7, 2010

Consider two numbers i,j with no common factors, and take the sum of their squares i^2+j^2:

In many cases the result is a prime, twice a prime, a prime power, or twice a prime power . Consider the others, shown in red. We have  65 = 1^2 +8^2 = 4^2 +7^2, 85=2^2+9^2=6^2+7^2, 130=9^2+7^2 and 145=8^2+9^2. Expanding our search however we can also find that 130 = 11^3+3^2 and 145=12^2+1^2. All numbers in this table that do not have the forms described therefore also occur more than once in the table. In fact every number that can be represented in exactly one way as the sum of two squares is a prime, twice a prime, a prime power, or twice a prime power . This makes 1 an idoneal number, suitable number or ideoneal number. More generally this is a number D such that any number that has a unique representation as i^2+D j^2 (where i^2 and D j^2 are coprime) is the now familiar list: a prime, a prime power, or twice a prime power.  These numbers were studied by Euler who said:

An outstanding paradox stands upon this, for although the idoneal numbers are shaped and proceed according to a certain law, the multitude of which however are not infinite yet are extended even onto 65 terms, concern- ing this paradox I have recorded so far no more of this type in the succession which has been observed; yet neither on the other hand has it been permit- ted by me to make firm a finite number of terms, except that after the 65th term, which is 1848, none thereafter have been bestowed, even though I have continued the examination up to 10000 and beyond.

So it brings me great pleasure to announce the 65th maths carnival.

From Euler there is only one place to go, the debate over who are the greatest mathematicians. There were a couple of posts on this topic. Euler made it into a post by Alex Bellos justifying his selections for a previous top ten article in the Times. Tanya Khovanova, however did leave Euler out, but this was understandable, she was looking at living mathematicians. To keep debate rumbling, I will add my top five favourite mathematicians. The ones whose work has most inspired me personally. In historical order they are, Archimedes, Gottfried Leibniz, Felix Klein, John Conway and Tim Gowers.

Having started with a little pure mathematics, the rest of this carnival focuses on the links between mathematics and other things.

Art and Circles

One of my favourite links is of course mathematics and art and that is well represented. The wonderful Math Monday post on the Make blog, showed how to whittle knots and links, and several others played with images from parts of circles, spirographs and a circle puzzle. If you prefer to sit back and just watch GrrlScientist on Living the Scientific Life shows a beatiful maths and nature movie, that has gone viral, though it does have a little too much of the over-hyped golden ratio.

Logic and Computer Programs

One of the darks arts of programming is the creation of Quines, programs that can output their own source code (without cheating). Metaspring develop this idea to show how it can be extended to form the heart of the deep results of Kurt Gödel.  Computers are also of use for more practical things, but to do this we often need to make approximations, for example of the normal distribution.  Code can also provide elegant ways to construct mathematical objects, such as a collection of algorithms to make a matrix with a single 1.

Maps and Calculation

Before computers a whole world of charts to do calculation were developed. Dead Reckonings shows the example of Lallemand’s Hexagonal charts helping ships to determine precise directions from a magnetic compass. Modern mathematics can also help us think about how to navigate our world. Dave Richeson in Division by zero, uses the similarity between topological and topographic to explore this.

You would not expect…

The favourite line of the maths evangelist is that “maths is everywhere”, I am not sure if I go that far, but it certainly turns up in some unusual places. Just a mon looks at the mathematics of the premier league. Even a chiropractor can find uses for mathematics, though lets hope it is use, not abuse, like the BCA’s famous take on the British legal system.

Education

All links between mathematics and other things require people who can understand and apply the mathematical ideas. The great Terrance Tao gives some ideas on games that help you develop this mathematical thinking. From Let’s Play Math, you can even have a bit of fun with calculus.

Elections

To finish on a topical note, I was writing this carnival as I watched the British election. With the hung parilament and the discussions now going on the electoral system itself is coming under question. What does a mathematician think of this? Tim Gowers has some interesting comments.

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Posted by gelada

Finding Ada: Alicia Stott Boole

March 24, 2010

View inside the shadow of the 120-cell.

March the 24th is the birthday of Ada King, Countess of Lovelace. An icon for mathematicians and computer scientists as the first programmer. She developed algorithms that could be run on Babbage‘s analytical engine. For more on the history and relationship between Babbage and Lovelace and some exciting comic adventures twisted round it take a look at 2d goggles.

Ada is also one of the most iconic women in the history of science, so to celibrate that and all the other women who have helped develop science and technology we have “Finding Ada” today. For that I would like to remember a woman whose contribution was not just ahead of its time, it was out of this world: Alicia Boole Stott.

Alicia’s contribution was an intuition that few others have achieved. Though we claim to be able to see in 3d our eyes actually only see two dimensional images. It takes some clever processing in the brain to build a 3d world out of that. In fact even quite simple questions in 3d can be very hard to imagine. For example take the intersection of three cylinders at right angles. What shape is created? I recommend thinking about this for a while before clicking the link! Another problem, that I will not give the answer to, concerns cubes: How can I pass one cube through a small cube without touching or crossing the sides?

I hope that this convinces that seeing 3d is already a hard problem. Alicia did one better. She could almost see 4d. This is not the idea of 4d being 3d space and time. That is really 3+1 d, although it can be useful it also has some problems. For example I cannot have intuition of a rotation that puls the time dimension into the 3 spacial dimensions. Alicia’s intution was for four spacial dimensions. She was able to show that just as there are only 5 regular polyhedra in 3d (tetrahedron, cube, octahedron, dodecahedron and icosahedron) there are 6 regular shapes in 4d. She named them polytopes, a name we still use today. The shapes are:

  • The 5-cell, this has 5 tetrahedra as its 3d faces.
  • The Tesseract or 8-cell, the 4d cube, with 8 cubes as faces. The 3d net of which was used by Salvador Dali in Corpus Hypercubus.
  • The 16-cell, which has 16 tetrahedra as faces.
  • The 24-cell, with its 24 octahedra
  • The 120-cell with 120 dodecahedra
  • The 600-cell, containing a massive 600 tetrahedra.

It is very hard to imagine these shapes but there are two ways that we can bring them back to 3d. The first worked on by Stott-Boole is to take 3d cuts. Without using a computer (it is a lot easier to use an abstract method, once a shape is described) she was able to construct models of 3d sections of all six regular polytopes.

A 3d slice through a 4d stellated polytope made from wood. There are some animations here.

The second method, that in some ways can be more instructive is to take the 3d shadow. Just a the sun casts a 2d shadow of an object in 3d, a light in will cast a shadow of a 4d object on a 3d surface. If you want to glimpse the fourth dimension for yourself. The best way to do it is to build one of these for yourself. This is quite easy thanks to the magic of zometool (and shown at the start of this post). If you want to know more about the life of Boole-Stott, there is an excellent short biography in Theory and history of geometric models by Irene Polo-Blanco.  There is also lots more on 4d geometry at How do shapes fill space?. Finally you can play with the shapes themselves and their rotations in Jenn3d and SceneScreen, both open source projects.

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Posted by gelada

LMS internet communication 2

January 3, 2010

As promised here is a draft of my article on ideas for the LMS and using the internet for society communication. Please comment!

Currently the LMS has two main mean of communication. The first is the newsletter and the second the website. It has already been mentioned many times that the website is in need of a redesign. I will therefore concentrate on the options available for more general communication. In a way the modern version of the newsletter, however some of the ideas here might inform decisions on the redesigned website.

What options are available?

The first option is RSS/web feeds. Using these people can subscribe to the stories from the LMS and then let the system take over. The stories would then come in automatically mixed with their other news in the reader. If this is set up as a blog people will have the ability to comment back on stories and announcements. The futurelms blog has shown that their are people willing to engage in this manner, and have good comments to make.

The second option to consider is twitter. This is a new system and has been the subject of plenty of hype. The important thing to realise is that although much that travels over twitter is meaningless noise people can choose what they follow. It is thus reasonably easy to find the signal. It is thus a system that has attracted a large number of people who are worth following and talking to (whatever your definitions of those). I would single out in particular Lord Drayson (@lorddrayson) the Science minister who has used the system well, getting feedback and reacting to the concerns of scientists as well as simply broadcasting his messages. This engagement, as an example, generated a debate on science journalism between him and Ben Goldacre.

The final option are wikis. These obviously take their lead from the wikipedia. Essentially they provide a means for a community to jointly create web pages.

How can the LMS use these?

I want to start with a general comment. Whatever options the LMS decides to follow two things will be necessary for success (unfortunately they are not sufficient). The first is to commit to the system, with the suggestions below I will give some of idea of what this means. The second is to make the system as open as possible. If there are problems with spam inappropriate content etc, then these can be dealt with at the time, but trying to address all possible problem can easily create an unworkable system.

Another general comment is that all the communication should consider the entire community of mathematicians and maths related people in the UK. This will have a positive effect on membership as it will make the importance and role of the LMS clearer to everyone.

A blog for LMS news is the first, obvious option. In many ways this will take over from the newsletter (I will discuss that further below). This will enable news to come out in a more timely fashion (the newsletter can be a long way behind due to the constraints of printing and a monthly schedule). It will also allow comments in response to articles. As I mentioned above this would need commitment. There should be a dialogue, not just a broadcast. It would be important for the commentators on the blog to feel that their views are listened to, and regular responses to comments are therefore essential.

Taking the dialogue a step further would give the LMS an active twitter feed. Again this should not be considered a broadcast. This could be a way to get opinion and feedback from a variety of people both within and outside the LMS. Watching replies and responding would therefore be essential.

A final, and more radical step would be to open up the process of creating policy. This is where a wiki can come in. In draft form policy documents can be freely edited and discussed. Anyone with an interest in the topic can therefore express their view. This is something that might need to be restricted to members alone. Obviously the final document would be the work of council or the committee involved, however this would draw more people into the descision making process and allow the society to tap as much available expertise as possible, not just the (admittedly great) expertise of those who can commit themselves full time to council.

Going slightly beyond the idea of communication within the LMS the world is currently lacking good computer based news streams for mathematics. This is something that the LMS is perfectly positioned to provide. The stream could be a mix of simple links to important papers or events combined with the occasional specifically written article. Members of the LMS would form a natural pool to write these! It would of course help if they could be given some level of LMS blessing as a publication. The systems for dialogue (twitter and blogs) would give an excellent basis for this as people could put forward the stories that they felt were important.

How to implement this?

I have said above that commitment is an important part of these ideas. Unfortunately as it is the nature of things this does cost money. Some of the money is already spent. Their are people involved in writing the articles and gathering news for the newsletter for example. Some more money can be found by stopping the newsletter itself. The cost of printing and distribution can therefore be put into maintaining the online presence. This step will of course leave some people out of the loop as not everyone is using online newsfeeds. A half-way house option would be to produce the newsletter as an email (or pdf). This would be made up of the stories and events that had been posted during the last month. With a little investment in programming it could even be automated.

2 Comments | General, Main Article, Mathematics | Tagged: , , , , , , | Permalink
Posted by gelada

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