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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…
‘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…
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 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…
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…
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’…
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…
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…
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…