Conceptual and Technological Revolutions

There are two kind s of scientific revolutions, those d riven by new tools and those d riven by new concepts. Thomas K uhn in his famous book, The Structure of Scientific Revolutions, talked almost exclusively about concepts and hard ly at all about tools. His id ea of a scientific revolution is based on a single example, the revolution in theoretical physics that occurred in the 1920s with the advent of quantum mechanics. This was a prime example of a concept-d riven revolution. K uhn's book...

 The Universe as a Simulation

‘Duh huh! That’s putting it mildly!’ Zinda purses her lips. ‘There are two problems, really. The first is that we can’t solve any hard problems. Not really. Anything that’s NP-complete. The Travelling Salesman. Pac-Man. They are all the same. All too hard. Even if we had a computer the size of the Universe! It drives the Sobornost crazy. We don’t mind it so much: that’s what makes most games fun. And we have quantum shortcuts for some special cases, like coordination. And for ...

 Hawking's Equation

awking has written down an equation which looks rather like Planck's equation. Hawking's equation is S = kA, where S is the entropy of a black hole, A is the area of its surface, and k is a constant which I call Hawking's constant. Entropy means roughly the same thing as the heat capacity of an object. It is measured in units of calories per degree. A is measured in square centimeters. Hawking's equation says that entropy is really the same thing as area. The exchange rate between area and en...

 Plank's Constant

In the year 1900 Max Planck wrote down an equation, E = hv, where E is the energy of a light wave, v is its frequency, and h is a constant which we now call Planck's constant. Planck's equation was the beginning of quantum theory. It said that energy and {22} frequency are the same thing measured in different units. Energy is measured in ergs and frequency in cycles. Planck's constant gives you the rate of exchange for converting frequency into energy, namely, 6 × 10–27 ergs per cycle. B...

 The Two Tables

I have settled down to the task of writing these lectures and have drawn up my chairs to my two tables. Two tables! Yes; there are duplicates of every object about me—two tables, two chairs, two pens.... One of them has been familiar to me from earliest years. It is a commonplace object of that environment which I call the world. How shall I describe it? It has extension; it is comparatively permanent; it is coloured; above all it is substantial. By substantial I do not mean that it does n...

 The Mathematical Image

The proof is elegant and the result profound. Still, it is typical mathematics; so, it’s a good example to reflect upon. In doing so, we will begin to see the elements of the mathematical image, the standard conception of what mathematics is. Let’s begin a list of some commonly accepted aspects. By ‘commonly accepted’ I mean that they would be accepted by most working mathematicians, by most educated people, and probably by most philosophers of mathematics, as well. In listing them as...

 Metaphor for the Uncertainty Principle

There is a slightly flawed yet very satisfying physical argument that gives some heuristic understanding of the uncertainty principle. Quantum mechanics endows all particles with a wavelike behavior, and waves have one striking property: they are disturbed only when they encounter objects larger than their wavelength (the distance between successive crests). You have only to observe water waves in the ocean to see this behavior explicitly. A pebble protruding from the surface of the water wil...

 Scientists Create and Thrive in a Stable Civilization

I take a different view of science as a method; to me, it enters the human spirit more directly. Therefore I have studied quite another achievement: that of making a human society work. As a set of discoveries and devices, science has mastered nature; but it has been able to do so only because its values, which derive from its method, have formed those who practice it into a living, stable and incorruptible society. Here is a community where everyone has been free to enter, to speak his mind,...

 The Bogo-Sort Algorithm for Creating Universes

A spectacular variant of bogo-sort has been proposed which has the interesting property that, if the Many Worlds interpretation of quantum mechanics is true, it can sort an arbitrarily large array in linear time. (In the Many-Worlds model, the result of any quantum action is to split the universe-before into a sheaf of universes-after, one for each possible way the state vector can collapse; in any one of the universes-after the result appears random.) The steps are: 1. Permute the array rand...