Notes for the Lifebox, the Seashell, and the Soul - Rudy Rucker

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Notes for The Lifebox, the Seashell, and the Soul, by Rudy Rucker Fredkin’s Billiard Ball Computer In the 1970s, the computer scientist Edward Fredkin gave a theoretical proof that, if you idealize away all of the real-world crud, you can make a universal computer from billiard balls bouncing around on a sufficiently large table. At the time this seemed like a surprising result, but by now it’s beginning to seem likely that almost all of the physical systems we encounter are universal, just as they are. Now, in reality, you can’t actually build a Fredkin-style billiard ball computer, for the balls’ large-scale motions will quickly display the slight inaccuracies in your starting conditions, not to mention the influences of effects as small as gravitational forces from your body as you walk around the table observing the experiment. The system won’t behave in the repeatable digital fashion that you’d planned. It’s not realistic to expect the motions of ordinary objects to behave like a digital computer. We live in an irredeemably analog world. But Fredkin’s proof-in-principle encourages us to believe some form of Wolfram’s Principle of Computational Equivalence, which claims that essentially all physical systems embody universal computations fully rich enough to emulate anything that happens inside an electronic machine. Schrödinger’s Wave Equation I’m not going to try and explain Schrödinger’s Wave Equation in detail, but I do feel I owe you a few comments. • Since a system’s wave function ψ(x) changes with time, we write it as ψ(x, t). • We put an arrow over the x to indicate that this symbol stands in for an arbitrarily long list of state variables • Multiplying by i on the left corresponds to a ninety-degree rotation of phase. • h is a the tiny number called Planck’s constant. • The quotient with the two backwards sixes means “the change with respect to time”. • The H on the right is the so-called Hamiltonian operator, which corresponds to the total energy of the system. In practice it’s difficult or even impossible to write out a precise formula for a complicated system’s Hamiltonian operator ⎯ which fact tends to limit the real-world usefulness of Schrödinger’s Wave Equation. Randomness When you measure a system, its wave function undergoes an abrupt change ⎯ sometimes called the collapse of the wave function. The resulting simplified wave function is called an eigenstate of the measurement. The particular measurement eigenstate is picked wholly at random, although in accordance with probabilities that can be calculated from the pre-collapse wave function. Regarding the randomness of quantum mechanics, where would the randomness come in? One might say that the world contains two kinds of computation: the computation of quantum mechanical physics and the computation of classical physics. Each of these is deterministic, but there is an unavoidable element of randomness in switching from the p. 58
Notes for The Lifebox, the Seashell, and the Soul, by Rudy Rucker quantum mechanical view to the classical. Dumping on Entanglement Entanglement is a popular topic for quantum mechanical mystery-mongering. But it’s easy to read too much into it. If you heat a large flat pan of water, steam bubbles will appear at the same time on opposite sides of the pan. This doesn’t necessarily mean that there’s a magical faster-than-light entanglement between distant pairs of bubbles. It can simply mean that the bubbles are the result of a lower-level common cause. Unfinished Summary of Chapter Two • Physical computations involve very many states, and we speak of them as analog. Although mathematics speaks of infinite ranges of real numbers, its enough to think of analog computations as involving very many possible values. • A physical computation is usually unrepeatable. • A computation can incorporate quantum indeterminacy and still have a definite rule. Human language and the hierarchy of programming languages. By way of making automatism seem reasonable, I show how programmers have worked out a hierarchy of languages in order to bridge the gap between bytes and reality, and I explain some of the ways in which the real world can be simulated by software. There are layers upon layers of languages used for controlling computers. The lowerlevel languages are more closely related to the machine, while the higher-level languages are more abstract, more appropriate for describing human thoughts. Human language itself includes low-level and high-level features. Let’s clarify the distinction by saying a bit about human language before we talk about the languages of the machines. One of the first things a child learns is names for simple body sensations. Cold, wet, hungry, tired. And the names of objects. Mommy, hand, water, bed, sun. And simple verbs. See, stand, walk, cry. Slowly the child learns to make a few simple sentences. Occasionally I’ve lived in a foreign country and made conversation in my hosts’ language. When doing this, I often think a game of Lotto that my children had. The game consisted of a hundred pairs of glossy square cards, each card blank on one side and with a color photo of some object on the other side. Mommy, hand, water, bed, sun. Clumsily talking a foreign language is like having a pocketful of the Lotto squares and handing them to someone one by one. Tomorrow sun swim eat sausage. By contrast, when you gracefully speak your native language, it’s like singing or dancing. The ideas just flow out. And if you happen to be speaking with a close friend or a loved one, the language even begins to feel like telepathy. Your thoughts jump back and forth. Describing a conversation between two lovers in one of his books, Vladimir Nabokov writes something like, “We had one of those conversations in which the words leave no trace of memory. It was like a duet in an opera, the emotions riding on wings of song.” Before starting in on programming languages, I need to mention a distinction between p. 59
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Notes for the Lifebox, the Seashell, and the Soul - Rudy Rucker

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