odd number

I’ve just signed up for a new course, Applications in Probability.

The word “probability” has a contrary provenance. Wikipedia says:

According to Richard Jeffrey, “Before the middle of the seventeenth century, the term ‘probable’ (Latin probabilis) meant approvable, and was applied in that sense, univocally, to opinion and to action. A probable action or opinion was one such as sensible people would undertake or hold, in the circumstances.

The most obvious example of chance as the subject of a piece of work is Duchamp’s Three Standard Stoppages: three one metre long threads are dropped onto pieces of cloth, which are then chopped up according to where the threads have fallen. Duchamp wrote the instructions of the work’s making on the side of the box – the process of its creation was as important as the resulting artefact. Maybe it’s not a readymade, but an unreadymade.

Any work that incorporates real-world processes is invoking chance – but not necessarily in the plain sense of randomness, or as a subject in itself. If there is something as obvious as the roll of dice, then it’s about unlocking and making visible the natural processes which are the subject.

Process art employs natural forces, and its practitioners seem to have a passing interest in chance and serendipity.

Generative art uses randomness, often as a seed for the algorithmic process, either at the start or within each iteration. But I don’t think chance is (normally) its subject – rather, it’s a conveniently available unspecified event to be exploited.

Chance sits at a particular meeting point between knowledge and ignorance. We can say something quantitive about an outcome, especially over a long period of time if it involves repeating the same event. If it’s equally likely outcomes, then this quantity can be worked out by counting (the theoretical approach). Or we can establish the probability of outcomes from empirical observation, and accumulation of data.

But if we need probability, then we either can’t have knowledge of all the factors contributing to an outcome, or there are simply too many factors to calculate effectively. Probability and chance are admissions of failure – we don’t know what’s going to happen, but we can say how many times something might happen as opposed to not.

Whatever, it’s apparent that predictions and their relationship to outcomes are at the heart of human interests, from gambling to the enlivening possibility of failure in a performance. I’m unsure of its validity as an area of artistic exploration though. Maybe it’s simply a tool to be employed.

I went to Abu Dhabi recently. Here’s the view looking from the flat where we were staying:

The light changed all the time – so the detail on the buildings in the distance came and went.

Here’s one from the public beach – a slightly more careful approach:

Image used under terms of GDFL (1)

Exhibition in the Emirates Palace, Abu Dhabi, visited 24th December 2008 – plans for Saadiyat Island.

Currently this is an island containing little to speak of, in a country which half a century ago was very little but desert. If the plans come to fruition, visiting aliens will cast their large eyes around the planet, and naturally home in on this cluster of sci-fi buildings. Its inherent quality is sheer ambition of scale and speed of construction, unhindered by existing context.

Any art commissioned must be international by nature – there’s not a large quantity made locally. It is culture divorced from geography.

While art is often rooted in money, particularly in newspapers, it is at least normally seen as having separate value outside of that money (rightly or wrongly). Such cognitive dissonance may be unnecessary here.

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December 5th 2008 -Richard Serra at the Gagosian Gallery, Kings Cross, London.

• there is something playful about people disappearing and reappearing. Is this a slow climbing frame for adults?
• people have to negotiate their way around one another in the maze-like structure
• gallery attendants are very watchful, sometimes following you into a structure. This can become a game as you work out how long it takes them to appear
• difficult to gain a mental picture of the large, spiralled maze sculpture. Disorientation part of the experience
• many viewers employed tourist reactions to the sheer phenomenon and went into photography mode
• there is something inherently unusual in seeing such large slabs and curves of steel outside of their normal functional architectural role. Normally they’re doing something.

Apply the nice Chain Rule: to where:

and

then

and

so by the Chain Rule:

Differentiation is, for me, where understanding of what’s going on slips into a mess of tools, symbols and formulas. The grapher application helps greatly with this – after doing the necessary mental gymnastics, it’s useful to see the relationship between the derivation and the original. Here’s and its derivative . You can see the latter changing nicely with the former.

The material I’m revising introduces differentiation from its bare definition, calculating the gradient between two different points on a smooth function, then making those points arbitrarily close from the quotient:

Then there’s lots of nice reasoning to find results for different functions, with new techniques enabling further discoveries. For example, here’s the logic for the sine function:

If and is more than zero, and , after collecting like terms we end up with:

it can be shown (using geometric and algebraic arguments) that:

and

which ends up with:

leaving

Thursday 31st September – Cildo Meireles at the Tate Modern. Brazilian conceptual artist.

Information

Meireles spread ideas, statements and the art itself through use of existing mechanisms, such as banknotes, recycled coke bottles and the classified pages of newspapers. The choice of the system itself carries meaning (“Yankees go home!” on the bottles). The world around becomes the space for the art to work in.Babel (2001) is a tower of radios. Each one is a different model, tuned to different frequencies. Instead of being an overwhelming wall of noise, the many fuse into a single experience – you have to lean close to hear individual voices. It exposes a broad range of the electromagnetic radio spectrum, to be heard as a single thing.In Eureka/Blindhotland (1970-5) there are many spheres, which you are encouraged to pick up. Each is a different weight, from 500 grams to 1500 grams, but all are visually identical.Glovetrotter (1991) is also composed of spheres, but this time each is a different type. A steel mesh has been draped over all, concealing their identity, but not the scale.

Measuring space

The first room is full of precise works on graph paper, where repeated, systematically joined points create clearly defined volumes. This moves on to proposals/instructions for conceptual works, also drawn on graph paper, many of which concern different forms of measurement. For example, a work is proposed where Meireles will canoe around the North Pole, becoming a day younger on each circumnavigation. Maps feature heavily, fundamentally being the lines which delineate borders between countries.Fontes (1992/2008) is a brightly lit room full of tape measures hung from the ceiling, creating a forest in which visitors can lose themselves. There are spiral paths through the measures, which can be walked through – but becoming progressively narrower towards the middle of the room, and then imperceptible. Having followed the spiral, you are disorientated, and wanting to leave, it is very difficult to tell if you are pushing through the tapes in a straight line. When out, you are confronted with walls packed with clocks – each of which has a non-uniform distribution of time, with the 12,3,6 and 9 placed at varying points around the dial.

Circular momentum is one of those things that I whizzed through in studying – but all the really crucial stuff is packed into a page I read too fast (there was a whole book to read too…)

If you can see this Flash movie, then click on it to set the point circulating away. You will be able to see the green velocity vector perpendicular to that of the point, and a tiny red acceleration vector pointing in the opposition direction (it would be bigger if the dot went faster).

If the position of a point is described as the following vector:

is the angle of the line joining the point to (0,0) with the positive x-axis, with being a constant, and being time. When is constant, we have uniform circular motion.

The angular speed of the point is (in radians).

The vector for the point can be differentiated:

The magnitude of the velocity vector is

which gives a velocity vector perpendicular to the position vector, and tangential to the circle.

Differentiating the velocity vector gives an acceleration vector which is in the opposite direction to the position vector:

The magnitude of the acceleration vector is

While the maths of this is all logical, I have to admit to still finding it tricky to intuitively understand the meaning of the velocity and acceleration vectors. But the first time I read this material, it was the meaning of the angular speed which I missed. The normal understanding of speed is as a linear property, and it’s a subtle leap to think of it in radians.

I’m doing an Open University degree in Computing and Mathematical Sciences. Completion of next year’s module will earn the last 30 points for the qualification.

The problem is that the course has varied its focus each year on either maths or computing. I’ve done little maths for the last two years – last year was Software Engineering, the year before was Developing Internet Applications. Preceding that wasGraphs, Networks and Design, which was challenging and lovely, but involved maths of a particular flavour. The upshot: the last time I worked hard at maths learning was 2005, and that was a struggle at the time.

Much of maths involves building on strong foundations, and thinking about things in the appropriately accurate, unambiguous manner. It is possible to march ahead through an accumulation of poorly understood precepts – enough at least to get high marks in assignments and exams.

The plan is to look over the ground that’s been covered – but this time, to make it familiar territory, rather than viewing it from a window at high speed. This may reveal a direction for next year’s journey, and even provide enough momentum to create a trajectory. It will most likely involve dawdling around some of the simpler areas of the landscape.

Latex:

Code: [tex ]\frac12 < \left\lfloor \mathrm{mod} \left( \left\lfloor \frac{y}{17}\right\rfloor 2^{-17\lfloor x\rfloor -\mathrm{mod}(\lfloor y\rfloor , 17)},2\right)\right\rfloor[ /tex]

WP Math Pub:
[pmath](a^2+b^2)=a^2+2ab+b^2[/pmath]

Code: \[pmath \](a^2+b^2)=a^2+2ab+b^2[ /pmath]

WP Math Pub looks nicer, but LaTex seems the standard, offering more portability in the future. MathML is probably the most accessible, but is dependent on browser support and looks cumbersome.

I made two changes to wp-latexrender:

1. PHP 5 interprets formfeed characters differently, meaning that \formulabox ends up outputting ormulabox, which ends up on screen. Fixed by amending the wrap_formula function in class.latexrender.php to use single quotes
2. Changed latex.php so that img tags are xhtml compliant