The craft of writing software will not become obsolete. And the craft of using soft ware creatively is flourishing even more than the craft of writin… - Freeman Dyson

The expansion of life, moving out from Earth into its inheritance, is an even greater theme than the expansion of England across the Atlantic. As Hakluyt wrote that there is under our noses the great and ample country of Virginia, I am saying that there is under our noses the territory of nine planets, forty moons, ten thousand asteroids and a trillion comets.

The essence of Hilbert's program was to find a decision process that would operate on symbols in a purely mechanical fashion, without requiring any understanding of their meaning. Since mathematics was reduced to a collection of marks on paper, the decision process should concern itself only with the marks and not with the fallible human intuitions out of which the marks were reduced. In spite of the prolonged efforts of Hilbert and his disciples, the Entscheidungsproblem was never solved. Success was achieved only in highly restricted domains of mathematics, excluding all the deeper and more interesting concepts. Hilbert never gave up hope, but as the years went by his program became an exercise in formal logic having little connection with real mathematics. Finally, when Hilbert was seventy years old, Kurt Godel proved by a brilliant analysis that the Entscheindungsproblem as Hilbert formulated it cannot be solved.

Godel proved that in any formulation of mathematics, including the rules of ordinary arithmetic, a formal process for separating statements into true and false cannot exist. He proved the stronger result which is now known as Godel's theorem, that in any formalization of mathematics including the rules of ordinary arithmetic there are meaningful arithmetical statements that cannot be proved true or false. Godel's theorem shows conclusively that in pure mathematics reductionism does not work. To decide whether a mathematical statement is true, it is not sufficient to reduce the statement to marks on paper and to study the behavior of the marks. Except in trivial cases, you can decide the truth of a statement only by studying its meaning and its context in the larger world of mathematical ideas.

In contrast to Kuhn, Galison in his classic work Image and Logic, published in 1997, describes the history of particle physics as a history of tools rather than ideas. According to Image and Logic, the progress of science is tool-driven. The tools of particle physics are of two kinds, optical and electronic. The optical tools are devices such as cloud chambers, bubble chambers, and photographic emulsions, which display particle interactions visually by means of images. The images record the tracks of particles. An experienced experimenter can see at once from the image when a particle is doing something unexpected. Optical tools are more likely to lead to discoveries that are qualitatively new.

On the other hand, electronic tools are better for answering quantitative questions. Electronic detectors such as the Geiger counters that measure radioactivity in the cellars of old houses are based on logic. They are programmed to ask simple questions each time they detect a particle, and to record whether the answers to the questions are yes or no. They can detect particle collisions as at rates of millions per second, sort them into yes's and no's, and count the number that answered yes and the number that answered no. The history of particle physics may be divided into two periods, the earlier period ending about 1980 when optical detectors and images were dominant, and the later period when electronic detectors and logic were dominant. Before the transition, science advanced by making qualitative discoveries of new particles and new relationships between particles. After the transition, with the zoo of known particles more or less complete, the science advanced by measuring their interactions with greater and greater precision. In both periods, before and after the transition, tools were the driving force of progress.