John Pickering is a sculptor who, like a modern-day alchemist, hews his works from a pure mathematical formula, the Inversion Principle MP_MQ = MR2. He conjugates a numerical sequence, then casts its form in space. The sculptures that emerge are in one sense magical, set firmly within the architectural tradition of the visionary form. Yet, because of the mathematical rigour that underpins them, they are also already rational, engineered, potent and buildable. The Inversion Principle steps outside the conventions of the artist's monograph by considering, on an equal level, the meticulous process of making the work and the finished forms themselves. It discusses their engineering implications and the inspirations behind them (ranging from Naum Gabo and space satellites to Stockhausen). George Liaropoulos-Legendre is an architect and teacher. He is the author of ijp: The Book of Surfaces (AA Publications, 2003). Chris Wise is co-founder and director of Expedition Engineering, London. In 1998 he was awarded the distinction of Royal Designer for Industry by the Royal Society of Arts, only the second structural engineer to be honoured in this way. 'MP_MQ = MR2. What does this strange algebra actually define? For a man who makes 3d objects, his choice of this 2d equation is odd. It means that, before he can make anything, Pickering has to map it onto the third dimension to give it [its] mass, volume and shape. Only then can he, and we, consider the maths from outside, from any direction. The equation itself defines an infinite number of possibilities, but it doesn't define all the world's possibilities. (I guess this is the attraction.) It generates either an infinite number of points, or a line, or perhaps the area bounded by the line. Yet when we look at his work it becomes clear that Pickering doesn't actually represent the equation directly but instead makes a jig on which to hold the answer - it is up to us as observers to construct the gossamer mathematical surface ourselves. And from this observation flows the need for another layer of structure altogether: the framework to hold the envelope. Here Pickering has been forced to be rational and to make choices. At a practical level he has to choose only a small proportion of all the possible points to use as the basis for his models. But in defining the rhythm of the supporting framework he has found that he has to give his objects a Corbusian language, separating the enclosure from the structure which defines and supports it. If you discuss this with him, he recognizes it and his eyes twinkle as he says "Well, I wondered if they could actually be used as architecture?". Now there's a question. And at a purely physical level, the answer has to be "yes".'