Stephen Wolfram

How should we tell AIs what we want? For the past few decades, the Wolfram Language has been developed as a computational communication language to provide a bridge between human goals and computational capabilities. The Wolfram Language is becoming a full symbolic discourse language that can capture the kinds of human intentions we find in laws and contracts. If we want to tell AIs to “be nice to humans,” how should we actually do that? This chapter first discusses how the development of symbolic discourse language can make it possible to express such ideas. It then considers how we might approach building an AI constitution that defines how we want AIs to act and what ethics they should follow. This chapter also discusses some of the fundamental issues around having a complete computational legal or ethical system.

"What is mathematics?" is a question that has been debated since antiquity. This book presents a groundbreaking and surprising answer to the question-showing through the concept of the physicalization of metamathematics how both mathematics and physics as experienced by humans can be seen to emerge from the unique underlying computational structure of the recently formulated ruliad. Written with Stephen Wolfram's characteristic expositional flair and richly illustrated with remarkable algorithmic diagrams, the book takes the reader on a unprecedented intellectual journey to the center of some of the deepest questions about mathematics and its nature-and points the way to a new understanding of the foundations and future of mathematics, taking a major step beyond ideas from Plato, Kant, Hilbert, Gödel and others.

This chapter explores some fundamental consequences of the correspondence between physical process and computations. Most physical questions may be answerable only through irreducible amounts of computation. Those that concern idealized limits of infinite time, volume, or numerical precision can require arbitrarily long computations, and so be considered formally undecidable. The behavior of a physical system may always be calculated by simulating explicitly each step in its evolution. Much of theoretical physics has, however, been concerned with devising shorter methods of calculation that reproduce the outcome without tracing each step. Computational irreducibility is common among the systems investigated in mathematics and computation theory, but it may well be the exception rather than the rule, since most physical questions may be answerable only through irreducible amounts of computation.

The most elementary way to think about Mathctrtati ca is as an enhance calculator — a calculator that does not only numerical computation but also algebraic computation and graphics. Matltcmatica can function much like a standard calt".1a- tor. you type in a question, you get back an answer. But Mat/tctttadca ga's turthcr I ue an ordinary calculator. You can type in questions that require answers that arc longer than a calculator can handle. For example, Matltcmatictt can giv; you thc numerical value of tr to a hundred decimal places, or the exact result for a numerical calculation as complicated as the result of 3)tI0, (m Fig. 1)