Free The Wild by David Zindell

difficult than the straightforward mapping through such spaces. But in the Vild, piloting a lightship never remains easy or simple. Soon, in less than a moment, he entered a disorienting shear space, the kind of topological nightmare that the pilots sometimes call a Danladi inversion. Now the veils of the manifold were a bright azure, fading almost instantly to a pale turquoise, and then brightening again to an emerald green. The space all around him was like a strangely viewed painting in which figure and ground kept shifting into focus, forward and back, light and dark, inside and out. It was beautiful, in a way, but dangerous too, and so he was glad when this particular space began to break apart and branch out into a more or less normal decision tree. All pilots would wish that the manifold held nothing more complicated than such trees, where all decisions take on the simplest form: maximize/minimize, left/right, inside/outside, yes/no. So simple was this tree that Danlo had a moment to build up a proof array of the Zassenhaus Butterfly Lemma of the Jordan-Holder Theorem. (That is to say, that any two composition series of a group G are isomorphic.) He took the time to reconsider this proof of ancient algebra because he had a notion of how it might be used in an escape mapping if he should ever be so unlucky as to enter an infinite tree.
    It is one of life's ironies that most of what we fear never comes to pass, while many dangers – even killing dangers – will steal upon us by surprise. During all his time as a pilot, Danlo was to face no infinite trees. But then, just as he was leisurely defining the homomorphism, phi, the branch of the tree holding up his lightship suddenly snapped – this is how it seemed – and he was hurled into a rare and quite deadly torison space, of a kind that Lord Ricardo Lavi had once discovered on one of the first journeys toward the Vild. Suddenly, he was again very aware of colours. There were the quick violets of space suddenly folding, and the r-dimensional Betti numbers appearing as ruby, auburn, and chrome red. There were flashes of scarlet, as if all the other colours might momentarily catch on fire and fall past the threshold of finite folding into an infinite and blazing crimson. Space itself was twisting like a snowworm in a strong man's hands, writhing and popping and twisting until it suddenly burst in an opening of violet into violet and began folding in upon itself. Now, for Danlo, there was true peril, danger inside of danger. Now – for a moment that might last no longer than half a beat of his heart – he floated in the pit of his ship, sweating and breathing deeply, and thought as quickly as it is possible for a man to think. He had little fear of death, but even so he dreaded being trapped alive inside a collapsing torison space. His dread was a red-purple colour, the colour of a blood tick squeezed between finger and thumb. He took no notice of this colour, however, nor did he give care or thought to himself. All his awareness – his racing mathematical mind and every strand of his will to live – spread out over the space before him. There were dark tunnels that kleined back and through themselves, impossibly complex, impossible to map through. There was the very fabric of the manifold itself, lavender like a fabulist's robes, infolding upon itself through shades of amethyst, magenta, and deep purple, the one and true purple that might well be the quintessential colour that underlay all others. Everywhere, the manifold was falling in on itself like dark violet flowers blossoming backward in time, folding up petal inside petal, always infolding toward that lightless singularity where the number of folds falls off to infinity. He might never have mapped free from such a space, but then he chanced to remember a certain colour. In truth, he willed himself to summon up a perfect blue-black hue that suffused his mind the way that the night fills the late evening sky.