How Singular? How singular is the Singularity? Will it happen in an instant? Lets consider again the derivation of the word. In mathematics a singularity is a value that is beyond any limit - in essence, infinity. The Singularity as we have discussed it in this book, does not achieve infinite levels of computation, memory, as any other other measurable attribute. But it certainly achieves vast levels of all these qualities, including intelligence. With the reverse engineering of the human brain we will be able to apply the parallel, self-organizing, chaotic, algorithms of human intelligence to enormously powerful computational substrates. This intelligence will then be in a position to improve its own design, both hardware and software, in a rapidly accelerating iterative process.

Revision of the classic text in the field, adding two new chapters and thoroughly updating all others. The original structure is retained, and the book continues to serve as a combined text/reference.

A "skillful and literate" ( New York Times Book Review ) biography of the persecuted genius who helped create the modern computer. To solve one of the great mathematical problems of his day, Alan Turing proposed an imaginary computer. Then, attempting to break a Nazi code during World War II, he successfully designed and built one, thus ensuring the Allied victory. Turing became a champion of artificial intelligence, but his work was cut short. As an openly gay man at a time when homosexuality was illegal in England, he was convicted and forced to undergo a humiliating "treatment" that may have led to his suicide. With a novelist's sensitivity, David Leavitt portrays Turing in all his humanity?his eccentricities, his brilliance, his fatal candor?and elegantly explains his work and its implications.

Internationally honored for brilliant achievements throughout his career, author of Cybernetics, ExProdigy, and the essay God and Golem, Inc., which won the National Book Award in 1964, Norbert Wiener was no ordinary mathematician. With the ability to understand how things worked or might work at a very deep level, he linked his own mathematics to engineering and provided basic ideas for the design of all sorts of inventions, from radar to communications networks to computers to artificial limbs. Wiener had an abiding concern about the ethics guiding applications of theories he and other scientists developed. Years after he died, the manuscript for this book was discovered among his papers. The world of science has changed greatly since Wiener's day, and much of the change has been in the direction he warned against. Now published for the first time, this book can be read as a salutary corrective from the past and a chance to rethink the components of an environment that encourages inventiveness.Wiener provides an engagingly written insider's understanding of the history of discovery and invention, emphasizing the historical circumstances that foster innovations and allow their application. His message is that truly original ideas cannot be produced on an assembly line, and that their consequences are often felt only at distant times and places. The intellectual and technological environment has to be right before the idea can blossom. The best course for society is to encourage the best minds to pursue the most interesting topics, and to reward them for the insights they produce. Wiener's comments on the problem of secrecy and the importance of the "free-lance" scientist are particularly pertinent today. Steve Heims provides a brief history of Wiener's literary output and reviews his contributions to the field of invention and discovery. In addition, Heims suggests significant ways in which Wiener's ideas still apply to dilemmas facing the scientific and engineering communities of the 1990s.

THE old saying that small causes give rise to great effects has been confirmed more than once in the history of physics. For, very frequently, inconspicuous differences be- tween theory and experiment (which did not, however, escape the vigilant eye of the investigator) have become starting- points of new and important researches. Out of the well-known Michelson-Morley experiment, which, in spite of the application of the most powerful methods of exact optical measurement, failed to show an influence of the earth's movement on the propagation of light as was predicted by classical theory, there arose the great structure of Einstein's Theory of Eelativity. In the same way the trifling difference between the measured and calculated values of black-body radiation gave rise to the Quantum Theory which, formulated by Max Planck, was destined to revolutionise in the course of time almost all departments of physics. The quantum theory is yet comparatively young. It is therefore not surprising that we are confronted with an unfinished theory still in process of development which, changing constantly in many directions, must often destroy what it has built up a short time before. But under such circumstances as these, in which the theory is continually deriving new nourishment from a fresh stream of ideas and suggestions, there is a peculiar fascination in attempting to review the life-history of the quantum theory to the present time and in disclosing the kernel which will certainly out- last changes of form, 1 CHAPTER I The Origin of the Quantum Hypothesis § I. Black-Body Radiation and its Realisation in Practice THE Quantum Theory &st saw light in 1900. When, in the years immediately preceding (1897-1899), Lummer and Pringsheim made their fundamental measurements ' of black-body radiation at the Beichsanstalt, they could ba.ve had no premonition that their careful experiments would become the starting-point of a revolution such as has seldom occurred in physics. In the field of heat radiation chief interest at that time was centred in the radiation of a black body (briefly called " black- body " radiation), that is, of a body which absorbs completely all radiation which falls on it and which thus reflects, trans- mits, and scatters 2 none. We may shortly call to mind the following facts. It is known that any body at a given temperature sends out energy in the form of radiation into the surrounding space. This radiation is not energy in a single simple form but is made up of a number of single radiations of different colours, i.e. of different wave-lengths X or of different frequencies s v. In other words, it forms in general a spectrum in which radiations of all frequencies between v = and v = oo are represented. Further, these radiations are present in varying " intensities." We define this term thus. Consider the radiation emitted from unit surface of the body per second in a certain direction ; break it up spectrally and cut out of the spectrum a small frequency interval dv such that it contains all frequencies between v and V + dv. The energy of radiation E^ thus sliced out (namely, the emissivity of the body for the frequency v)