Zephyr’s Reviews > The Pattern on the Stone: The Simple Ideas that Make Computers Work > Status Update

No predictable technical breakthroughs in computers will help solve the traveling salesman problem, since even a computer a billion times faster will still be stumped by the addition of a few more cities.

The brain is a kind of computer, and thought is just a complex computation. Life is a complex chemical reaction. It takes nothing away from the wonder or value of human thought. Life and thought are both made all the more wonderful by the realization that they emerge from simple, understandable parts. I do not feel diminished by my kinship to Turing’s machine.

the physics of a neuron depends on quantum mechanics, just as the physics of a transistor does, but there is no evidence that neural processing takes place at the quantum mechanical level as opposed to the classical level; that is, there is no evidence that quantum
mechanics is necessary to explain human thought.

The bits in a quantum computer must remain entangled in order for the computation to work, but the smallest of disturbances—a passing cosmic ray, say, or possibly even the inherent noisiness of the vacuum itself—can destroy the entanglement. This loss of
entanglement, called decoherence, could turn out to be the Achilles heel of quantum mechanical computers.

A quantum computer would take advantage of entanglement. This is analagous to an atom being in many places at once: a bit that it is in many states (1 or 0) at once.

Atoms seem able to compute certain problems easily, such as how they stick together—problems that are very difficult to compute on a conventional computer. For instance, when two hydrogen atoms bind to an oxygen atom to form a water molecule, these atoms somehow “compute” that the angle between the two bonds should be 107 degrees. How can a single molecule be so much faster than a digital
computer?

A single subatomic particle exists everywhere at once, and we are
just more likely to observe such a particle at one place than at another. For most purposes, we can think of a particle as being where we observe it to be, but to explain all observed effects we have to acknowledge that the particle is in more than one place.

The only way we know how to achieve genuinely unpredictable effects is to rely on quantum mechanics. Unlike the classical physics of the roulette wheel, in which effects are determined by causes, quantum mechanics produces effects that are purely probabilistic. There is no way of predicting, for example, when a given uranium atom will decay into lead.

Statistically speaking, most mathematical functions are noncomputable. This is because any program can be specified in a finite number of bits, whereas specifying a function usually requires an infinite number of bits.

A roulette wheel is an example of what physicists call a chaotic system—a system in which a small change in the initial conditions (the throw, the mass of the ball, the diameter of the wheel, and so forth) can produce a large change in the state to which the system evolves (the resulting number). This notion of a chaotic system helps explain how a deterministic set of interactions can produce unpredictable results.