"Go exploring, I think."
He touched Yatima's shoulder. "Good luck, then."
Paolo closed his eyes, and followed the Transmuters.
Yatima felt a wave of grief wash over ver, but Paolo was right; other versions had lived for him, nothing had been lost.
And as the grief decayed into loneliness, Yatima was tempted to apply the same logic. Vis' own clones must have done everything ve was contemplating, and more, long ago.
That wasn't enough, though. There were still some discoveries ve needed to make for verself.
Yatima surveyed the sky of this universe one last time, then jumped to the copy of the Truth Mines ve'd carried all the way from Konishi.
To play out everything ve was, to be complete, ve had to find the invariants of consciousness: the parameters of vis mind that had remained unchanged all the way from orphan psychoblast to stranded explorer.
Yatima looked around the jewel-studded tunnel, and sensed the gestalt tags of axioms and definitions radiating from the walls. Everything else from vis life in the home universe had been diluted into insignificance by the scale of their journey, but this timeless world still made perfect sense. In the end, there was only mathematics.
Ve began to review the simple concepts nearby—open sets, connectedness, continuity—waking old memories, resurrecting ossified symbols. It would be a long, hard journey to the coal face, but this time there'd he no distractions.
GLOSSARY
Address: A string of bits that specifies a source or destination for data, such as a file in a library, a camera on a satellite, or a location in a scape. Different addresses can be of different lengths, and the same data can have multiple addresses.
Boson: All elementary particles can be classified as either bosons or fermions; the bosons include photons and gluons. The quantum wave function for two or more identical bosons is unchanged if any two particles are swapped, and the wave function for a single boson is unchanged if the particle is rotated by 360 degrees. Bosons have a spin which is an integer multiple of the fundamental unit of angular momentum. In Kozuch Theory, all these properties arise from the topology of the particle's wormhole.
Citizen: Conscious software which has been granted a set of inalienable rights in a particular polis. These rights vary from polis to polis, but always include inviolability, a pro rata share of processing power, and unimpeded access to public data.
Coalition of Polises: (1) The community of all polis citizens. (2) The physical computer network which comprises all polises.
CST: Coalition Standard Time. A system of specifying internal time used across the Coalition of Polises. CST is measured in "tau" elapsed since the system was adopted on 1 January 2065 UT; the equivalent in real time of 1 tau varies as polis hardware is improved.
Cypherclerk: A structure within Konishi citizens which handles encryption and decryption tasks, including the authentication of claims of identity. See also signature.
Delta: The base unit of all scape addresses. The usual height for a citizen's icon is two delta. Multiples and fractions of a delta can be specified, and there is no universal smallest or largest distance. Pluraclass="underline" delta.
Dream ape: A biological descendant of a group of exuberants who engineered-out their own language facilities.
Embedding: A way of fitting one manifold into another, larger one as an aid to visualizing its properties. For example, some 2-dimensional manifolds can be embedded as a surface in 3-dimensional Euclidean space (a sphere, a torus, a Mobius strip), while others (such as Klein's bottle) can only be embedded in 4-dimensional space. The size and shape of the surface are properties of the embedding, not of the manifold itself—so a sphere and an ellipsoid are two different embeddings of exactly the same manifold—but a particular embedding in Euclidean space can he used to supplement a manifold with the geometrical concepts needed to make it into a Riemannian space.
Euclidean space: The Euclidean space of N dimension, is a natural generalization of the 2-dimensional Euclidean plane, where the square of the total distance between two points is the sum of the squares of their separation in each of the N dimensions. The Euclidean spaces are simple examples of the more general idea of a Riemannian space.
Exoself: Non-conscious software that mediates between a citizen and the polis operating system.
Exuberant: A flesher whose genes have been modified.
Fermion: All elementary particles can be classified as either bosons or fermions; the fermions include electrons and quarks, and composites of three quarks like protons and neutrons. The quantum wave function for two or more identical fermions reverses phase if any two particles are swapped; this leads to the Pauli exclusion principle, which gives a zero probability for two fermions being in exactly the same state. The wave function of a single fermion reverses phase if the particle is rotated by 360 degrees, and is only restored exactly by two full rotations. Fermions have a spin which is an odd-integer multiple of half the fundamental unit of angular momentum. In Kozuch Theory, all these properties arise from the topology of the particle's wormhole.
Fiber bundle: A fiber bundle is a manifold (the "total space") plus some scheme for projecting it onto a second manifold of lower dimension (the "base space"). For example, the surface of a torus is a two-dimensional manifold, but if every longitudinal circle is reduced to a point, that projects the torus onto a single, equatorial circle, a one-dimensional manifold. The set of points in the total space that is projected onto any given point of the base space is called the "fiber" of that point (e.g. one of the longitudinal circles of the torus). The fibers need not he identical from point to point, but if they are, their general form is called the standard fiber of the bundle. So, a torus is a fiber bundle with a circle as its base space, and another circle as its standard fiber. In classical Kozuch Theory, the universe is a fiber bundle with four-dimensional space-time as its base space, and a six-dimensional sphere as its standard fiber.
Field: A six-bit segment of a mind seed, comprising a single instruction code in the Shaper programming language.
First generation: Those citizens or gleisners who have been scanned from flesh, as opposed to those created by psychogenesis.
Flesher: Any biological descendant of Homo sapiens. Those with genetic modifications are known as exuberants; those with only natural genes are known as statics.
Forum: A public scape.
Geodesic: A path of zero intrinsic curvature in a Riemannian space. If the Riemannian space is a surface embedded in Euclidean space, the geodesics are either straight lines in the external space, or they curve in a direction perpendicular to the surface. For example, a great circle on a sphere is a geodesic—because so far as inhabitants of the sphere are concerned, a great circle "curved" only in an abstract dimension which is perpendicular to the surface's two dimensions.
Gestalt: (1) A data format which encompasses both images, and "tags" conveying miscellaneous information. (2) A visual language based on inflections of flesher-shaped icons; an enlarged version of pre-Introdus communication through facial expressions, gestures, etc.