Posted tagged ‘maths’

Zero to Infinity – connections are made

November 24, 2008

I was invited, by a friend, to attend the Zero to Infinity event at the Dana Centre South Kensington (Thursday 20th November 2008).

A quick look at the panellists and the topic for discussion sparked some interest with me. These panellists included:

Paul Prudence, generative artist
Eleanor Robson, historian of mathematics, University of Cambridge
Marcus du Sautoy, mathematician, University of Oxford
Jane Wess, curator, Science Museum
Facilitator: Rachel Thomas, Editor, Plus magazine

Panellists

From this list of names only one stood out to me and that was Marcus du Sautoy. I had recently viewed his documentary “The Story of MathsThe Language of the Universe” on the BBC (thanks for telling me about it Simon) and thought he was great at explaining math related theories in a friendly and an easy to understand way.

The four very different backgrounds of the panellists was great as it provided different views on the same subject. It was clear that different uses of the mathematical theories relating to infinite numbers, the idea of multiple infinities and whether the number zero is something real or abstract can allow for connections in different areas of practice and study.

Midway through the talk we were split into two groups to participate in a short workshop first off with Marcus du Sautoy. This was a brilliant and practical demonstration to help us understand how one infinity could be larger than another. Ok there were many things floating about such as how fractions and decimal numbers could be used to check against whole number and negative numbers and this was delving into scary territory for me – maths not being my forte. So these further explorations into different types of numbers, rational and irrational, and the stark statement from Du Sautoy that there are different types of mathematics just completely lost me. At one point I had to just accept that there are many possibilities out there in the universe numbers and mathematics are perceived and manipulated to prove various theories using various methods.

Even then, Du Sautoy’s enthusiasm made the workshop enjoyable. Even though there were, well lets say, some brains participating too who were determined to prove something by asking questions that could only really lead to a debate that the rest of us wouldn’t be able to keep up with, it was quite funny to see that not everyone had the same views. And I’m pretty sure one man was actually flirting with him and using his mathematical knowledge to impress him!

Anyway so the next workshop was more of a historical look at how the number zero came into existence and its early use by the ancient Babylonians who kept records of how many different types of cattle were collected and received for the king. This part of the workshop was overseen by Eleanor Robson of Cambridge University. She explained that the Babylonians used to make marks representing different numbers on chunks of clay. This allowed for the accounts to be preserved for thousands of years. An empty space basically represented a zero. Of course their idea of the number zero was used merely for counting that something was not there but not in the same way it is now used for example for negative numbers and calculations of the abstract kind.

Twelve German Jetons - The Science Museum

We also looked at some of the shapes included in a mid 17th century wooden learning box – based on the teachings and principles of Euclid’s geometry. These were original items from the Science Museum’s collection and explained to us by curator Jane Wess. The collection included abacuses from China, Japan and the West where the base numbers for counting were all different.

Euclid's geometry - wooden box of shapes from 17th century Abacuses

Having reached the last part of the evening we heard from Paul Prudence; a generative artist and Video Jockey (VJ) whose work was displayed on the screen in the room. The display was of moving tesselated digital imagery. These images were based on geometric forms relating to the theories we had been hearing about earlier in the evening and in the workshops.

View a video of his work here: http://www.transphormetic.com/2_talysis2/talysis01.htm>/a>

Fast Fourier Radials - A spectrographic visualisation of sound

http://www.transphormetic.com/12_FFradial/pics/02.jpg
Fast Fourier Radials

I was in awe. He had succeeded in creating digital work based on geometric shapes and from this were produced beautiful patterns. So obviously all of this started ringing bells in my head. I was thinking to myself ‘I need to ask this guy some questions and find out what processes he is involved in, what software, which techiniques, etc etc’. I was very curious. So I waited till most people had started dispersing after the talk and told him about the MA and why his work was of particular interest to me in relation to my project. He gave me some of his business cards and encouraged me to take as many as I wanted, as he had so many and each had a different image on the back (stills from his work). They were really cool so I took six 🙂

Talysis 2

http://www.transphormetic.com/2_talysis2/talysis05.htm
Talysis 2

I found a lot more information about Prudence’s work and recent project history on his website: http://www.transphormetic.com/

And I don’t think I could be any more amazed and slightly jealous. He uses Flash and ActionScript to write programs which then produce the patterns and some of them in real time!!! The use of algorithms and mathematics (written into the ActionScript) means that numbers can be used to produce 3d effects of shapes within certain spaces. These have boundaries in which the pattern might become curved along the outer curve of a sphere or within the inner curve and so producing both a convex and concave look with the shapes getting smaller or larger as they move along, further toward or away from the x axis. Ok I’m not sure if I explained this the right way.

Heres what he’s got in the biography section of his site which pretty much sums up his skills quite impressively:

Artist and real-time visual performer working with computational and visual feedback systems and video. Uses VVVV, Flash & processed Digital Video. Lecturer on visual music and syneasthetic art.

Researcher and writer at Dataisnature.

Freelance Interaction Designer and ActionScript Developer. Authoring chapters in a few books relating to computational design with Actionscript.

http://www.transphormetic.com/bio.htm

I’m glad to see a clear example of how a contemporary approach using the latest in technology and programming skills can be made the most of in order to produce something that connects all the ideas that are bought to light in the subject of geometry, shapes, and space (more specifically numbers and their connection to the theories of science and physics of the universe). I mentioned in an earlier post that it was hard to make the connections between the different subject areas as they could become very diverse and branch off into their own projects all together. But this is a great example to show that it is possible to make those connections apparent in one piece.

I feel inspired and have a positive feeling about achieving something great, as a result of this project. God willing 🙂

Don Relyea – artist

October 11, 2008

I’ve just found this site a sort of online portfolio of work by Don Relyea. http://www.donrelyea.com/

Some of Relyea’s art projects focus on the use of a few basic geometric shapes. The combination of these shapes and the vibrant colours produces some interesting pieces. I really like them and think it is striking enough to make the viewer want to dismantle all the geometric components and examine them as individual parts.

The still image above is a view of what you would see once you have generated the design as the user (click the image to have a go). Relyea uses Shockwave applets to present his work. It is usually in the form of an interactive project and requires the user to take an initial action. For examle when the user clicks on the red blank box the design quickly starts printing itself from the top left corner all the way around the box in a clockwise spiralling motion until the whole box is covered with the pattern.

Relyea has variations of these pieces – some even allowing you to choose the combination of colours and the randomness of the generation of pattern. See the Space Filling Curve Art Generator

The technical background to his work is explained on his site. Here is an excerpt from the Artist Information page:

Relyea’s tools are script editing windows and compilers. Relyea’s schooling in traditional printmaking (under Lawrence Scholder) left him with a strong consideration for the process of image creation. Relyea loosely defines new digital processes by creating works manually first, he then transforms the processes into programming routines with parameters. The parameters can be dynamic data from the network, mathematical algorithms or number generators. The routines are repeated with parameter variations to generate designs of similar aesthetic quality.

I think I might try contacting him and ask him a few questions about his work and how much of it he considers to be influenced by the world of geometry. hmm wonder if he’ll reply – will keep you posted.

Identifying a line of inquiry – which one?

October 11, 2008

On my way to uni on Wednesday I decided that maybe it would be a good idea to formulate my ideas and project aims and objectives as best I could. I started writing notes most of the journey and, as it had been about a week since I had fully concentrated on summing up my project in such a way, I think it helped to make it more structured in my head. I was able to sum up the links a bit better than before. This is what I came up with in relation to the two key words ‘Shapes’ and ‘Space’ being components of a possible working title:

The first two words are key as they sum up the elements that the areas of research I will be looking at are anchored by. In other words you can always relate the subject areas, I am interested in, back to one of these words if not both.

We usually think of shapes as pre-defined areas of outlined space that have specific names. We’ll grow up knowing that these named shapes have properties that allow the shapes to be classed within certain gropus of shapes too. So a square is made of of 4 right angles at each corner and 4 sides. A triangle with three sides and of various angles and combinations of these.

But can a shape alway be defined? And should it be defined? And how about those shapes which have properties or characteristics that are overlooked? And which characteristics should we look more closely at because they’ve been overlooked in the past?

The second key word is space. My use of the word implies many senses of space including the mathematical and the scientific (these I believe overlap in some sense), as well as the physical, perceptual and conceptual. I cannot restrict my meaning at this point. I have no reason to restrict until I have conducted more research and found a reason to do so.

What about white space? Is it real? Does it mean something to everyone? What is it’s role? Is it intentional? Should it be identified in more places?

An area of study that connects to this idea of space around shapes (and here I wonder – is this space not then a shape too?) is that of Geometry. These shapes are formed from vertices (easier to think of as dots in an invisible grid of any size). These vertices may then be connected with a line from one to another. these lines will be joint in such a way to form a shape. Various shapes are then placed together to form a larger formation. They could arguably be described as a system of shapes. This system could be called a pattern. these patterns can then become quite complex and due to their placement, repetition and possibly the ability to tesselate them – they can be endless and seem to go on for infinity.

One of my biggest aims in my project is to look into the history of Geometry – how it was developed and how it has been used over the centuries (more specifically in art work).

Then there is the branching off of Geometry in nature. I think this is a highly important and interesting subject to delve into. Not only because it entails many mysteries and brings into question the secrets of the Universe. But also because there is a tie with religion and sprirituality which is something that I can relate to on a personal level. Believing in God means that when I see the beauty of nature and proofs of perfection in nature (such as the way the body works and the structures and symmetry in plants and flowers to name a couple) I link it to Divine Creation. This is another aspect I would like to look into further. Especially as belief in this isn’t restricted to just one religion.

Geometry allows for the representation of space in 2d, 3d and even 4d and beyond:

Science.ca - Donald (H. S. M.) Coxeter, Pure and Applied Mathematics

4. Hypercube: If you pull a cube into the fourth dimension you get a hypercube. Eight cubes make a hypercube. The figure you see here cannot exist in the real world, which only has three-dimensional space. It is a projection of a four-dimensional object onto two dimensions, just as the cube before it is a projection from three-dimensional space to the two-dimensional flat surface of the paper.

5. Regular polytope: If you keep pulling the hypercube into higher and higher dimensions you get a polytope. Coxeter is famous for his work on regular polytopes. When they involve coordinates made of complex numbers they are called complex polytopes.

http://www.science.ca/scientists/scientistprofile.php?pID=5&pg=1

These main topics then branch off into other areas but are still anchored by the main theme of shapes, space and I guess now geometry too. By always having my main question along the lines of ‘ the place of geometry in the world around us’ I will have something to refer back to. Is that what I am looking at? Am I any closer to finding the answer? Am I looking into something that is relevant or have a veered off too far down a small cobbled street?

Outcomes for project: My background has been predominantly in expressing some form of communication and his has been mostly interactive. I would like to continue this by producing work that compels the user/viewer to become involved with it. I believe that the most interactively creative works are those that captivate the viewer and involve them within a process. This can be in many forms such as when using sensors to trigger some kind of behaviour or change in the work (lighting, sounds etc). This could be on an abstract level too where triggering thoughts and movements in people and influencing these is enough of a form of interaction. Only that this can be more difficult to measure.

However, my interpretation of an interactive work would be using multimedia as a possible option. My work has always been either viewable of a computer screen (short video clips), graphics, websites. Or viewable on some form of small physical and traditional media such as paper or canvas. I would really like to create some sort of installation to take my experience and work to the next level or beyond for this project. This installation would be my blank slate. Possibly like a box or container that allows a person to fully submerge themselves within it – literally or mentally. The key is for it to be thought provoking. I would want the person to question their surroundings, the purpose of the installation and investigate it too. Possibly manipulate their thoughts by pre-determining the factors the could influence their senses and perceptions related to the space around them.

And that is the end of my notes from my journey to Uni. Yes I am one of those people who can write loads of notes whilst travelling on the tube/bus/camel 🙂

We had a sort of informal feedback session after one of the Critical Framework lecture where we were required to write in one sentence what our project was about. I knew it would be a bit crazy to even attempt this so I decided to use the key words to form almost a sentence. I came up with ‘Shapes and space – the place of these and geometry in the world around us’ using my notes from the journey in. It could be the closest I’ve got to a working title yet so I just let that be discussed in the group.

After some discussion with Andy (course leader) and some feedback and questions from fellow students it would seem that perhaps I should narrow my field of research down a tad bit so that I can concentrate on finding the niche in which my project would excel. Something no one else is questioning, expressing or even addressing. Or maybe they will have but I’ll be doing it from a different angle? a unique p.o.v?

Only time will tell.