This post is a continuation of "The Universe in Four Easy Operations." I apologize for the long delay everyone.

Qubits

Qubits are quantum mechanical analogs to classical bits discussed in the last post. Nuclear spins are often used as qubits in quantum computation. "Spin up" is conventionally represented by the symbol 0> and "spin down" is represented by 1>. These spins also correspond to waves. A wave moving counterclockwise is conventionally 0> and clockwise waves are 1>. -0> is 180 degrees out of phase from 0>.Superpositions of these waves also exist. 0> + 1> represents rotation around the axis perpendicular to the "up-down" axis. 0> - 1> is rotation around that same axis, except in the opposite direction.

The Double Slit Experiment

The double slit experiment can be performed with an electron beam, a screen with two slits that can be opened and closed, and a photographic plate to detect the impact of incoming electrons. When either of the slits are closed, the electrons behave like classical particles and pass through only the open slit. When both slits are opened an interference pattern appears on the photographic plate, as if the electrons passed through both slits at once, a wave-like behavior. When a photodetector is placed at one or both of the slits the interference pattern disappears, even when the experiment is performed with both slits open. The ability of the environment to remove the wave-like behavior of matter is known as decoherence. Decoherence localizes the position of macroscopic bodies through the many intereactions of such bodies with the environment. As a result, classical behaviour arises. The Heisenberg uncertainty principle applies to the waves-particle duality of quantum particles. The more accurately one can describe the speed of a particle the less can be known about its position, and vice versa. The same is true with the axes of nuclear spin.

Quantum Computation Operations and Entanglement

Applying a magnetic field to a nuclear spin changes the direction of the spin. The longer the field is applied to the spin, the more the direction of the spin is changed. Eventually the spin returns to its originally orientation. Applying the field for half the time it would take to return to the original orientation would displace the orientation of the spin by 180 degrees, applying the field for a quarter of the time would result in a spin 90 degrees out of phase, and so on. Qubit states are reversible in this manner, just as classical bits are reversible. Qubits can be correlated by performing controlled NOT operations just as classical bits can. However, one of the properties of quantum mechanics that would be counterintuitive from a classical perspective is that interacting qubits can create new bits of entropy. Suppose that a qubit is initially in the superposition 0> + 1>. A controlled NOT operation is performed which correlates a second qubit with the control, resulting in 00> + 11>. If the operation is reversed on either component, the qubit will be found to be in a random state. This is a disturbance of a quantum system due to measurement. If the operation is reversed on both components of the correlated superposition, the initial state of the qubit is restored. In other words, when the qubits were in the 00> + 11> superposition, they were in a known state which contained no bits of entropy. But each qubit on its own is in a random state, with one bit of entropy each. This is known as entanglement, and this is how new information is created in the universe. Seth Lloyd's book "Programming the Universe" contains a more detailed discussion of the these topics.

## Friday, November 16, 2007

## Tuesday, November 13, 2007

### The Universe in Four Easy Operations

In this post I would like to explain some examples of physical systems performing computation. Any possible logical expression can be formed from four basic operation: AND, OR, NOT, and COPY, a discovery due to George Boole. AND takes a string of input bits and outputs a 1 if and only if all the bits are 1s and outputs 0 otherwise. OR outputs a 0 if and only if all the input bits are 0s and outputs a 1 otherwise. NOT simply transforms the 0s in the input string to 1s and the 1s to 0s, and COPY just reproduces the input string. In principle, any possible computational process could be carried out by these four operations, though creating computer programs in this way would be very impractical.

Entropy and Energy

Entropy is a measure of the amount of energy in a system that can not do work, while free energy, or Gibbs energy, is a measure of the amount of useful energy in a system. Entropy can also be defined as the amount of information required to describe the states of atoms in a system. In other words physical systems register information. States of the system where entropy is high and free energy is low are very unorganized or random. A great deal of information is required to describe these states. States of a system where free energy is high and entropy is low are organized. Therefore less information is required to describe them. Entropy tends to increase over time (in fact, this is the physical quantity which gives directionality to the "arrow of time"). Seth Lloyd described the unorganized uncertainty of entropy as "infectious." However, the total energy and total information in a closed system is conserved. This same phenomenon can be observed with bits and logical operations. Consider a string of two bits. The value of the first bit is unknown and the value of the second bit is 0. This system has two possible states: 00 and 10. Now suppose that value of second bit is flipped to 1 if and only if the value of the first bit is 1, and is left alone otherwise. After the operation is applied, the string still has two possible values, either 00 or 11. We cannot predict which state the system will be in before the operation is applied. Although the values of both the first and second bits are now uncertain, the total number of possible system states is conserved. Thus entropy has increased while the total information contained in the system is conserved. I will discuss a quantum system registering information in my next post, "Information Ex Nihilo."

Entropy and Energy

Entropy is a measure of the amount of energy in a system that can not do work, while free energy, or Gibbs energy, is a measure of the amount of useful energy in a system. Entropy can also be defined as the amount of information required to describe the states of atoms in a system. In other words physical systems register information. States of the system where entropy is high and free energy is low are very unorganized or random. A great deal of information is required to describe these states. States of a system where free energy is high and entropy is low are organized. Therefore less information is required to describe them. Entropy tends to increase over time (in fact, this is the physical quantity which gives directionality to the "arrow of time"). Seth Lloyd described the unorganized uncertainty of entropy as "infectious." However, the total energy and total information in a closed system is conserved. This same phenomenon can be observed with bits and logical operations. Consider a string of two bits. The value of the first bit is unknown and the value of the second bit is 0. This system has two possible states: 00 and 10. Now suppose that value of second bit is flipped to 1 if and only if the value of the first bit is 1, and is left alone otherwise. After the operation is applied, the string still has two possible values, either 00 or 11. We cannot predict which state the system will be in before the operation is applied. Although the values of both the first and second bits are now uncertain, the total number of possible system states is conserved. Thus entropy has increased while the total information contained in the system is conserved. I will discuss a quantum system registering information in my next post, "Information Ex Nihilo."

## Sunday, November 11, 2007

### An Example of Newton's Genius

It's well known the Isaac Newton was among the greatest scientists, but I never truly appreciated the magnitude of his genius until I came across this anecdote in Richards Feynman's book QED. Newton noticed the light did not completely reflect from a glass surface as he expected. The difference was very subtle, as approximately 96% of the light did reflect. He thought of possible explanations for this, and imagined that there may be holes in the glass' surface that allowed light to pass through. He soon dismissed this idea when he realized that he could polish glass and that this did not seem to change the reflection properties of the material. Polishing the glass would smooth any holes on the surface, and Newton was at a loss to explain this phenomenon. This answer would have to wait more than two centuries for the development of quantum electrodynamics. According to Occam's razor, our hypotheses should be as simple as possible while still be a sufficiently detailed as an explanation. Nature does not lend itself to our intuitions, and a small deviation from our expected results can be very profound in any situation.

## Wednesday, November 7, 2007

### Some thoughts on the Morality of Human Enhancement

Following our initial inclinations unfortunately tends to be far from the best course of action in most situations. Many aspects of a wide variety of ethical systems pertain to restraining our base instincts. Indeed, this is one of the major functions of ethics in society. Attempts at human enhancement are often criticized as breaching our natural limits. Any modifications we may become able to make to our bodies and minds entail a complex set of issues, such as ensuring that any such changes are always voluntary and available to as many people as possible. However, efforts toward human enhancement carry a moral argument that is often overlooked. We generally agree that striving to become better versions of ourselves is a good thing. At least in democratic societies, we interact with each other under an implicit assumption that we are unique and valuable individuals, yet we still try to hone our talents, treat others more civilly, learn new skills etc. Would it not be morally valid for us to use our technology as an aid in becoming more the people we wish to be?

## Sunday, November 4, 2007

### The Novelty of Non-Anthropomorphic Reasoning

The first time I read a basic description of cognitive biases I laughed. Like the jokes of a good observational comic, they pointed out so many of my bad habits, and others that I didn't even know I had. I saw how a subtle change in perspective could instantly clarify some results of my decision-making that I once found baffling, and recognized the ridiculousness of many behaviors that I had always carried out thoughtlessly. On the other hand, part of the amusement I felt was from encountering a fascinating new idea. When I first began noticing the effect of these biases, it was almost as if I was thinking with a part of my mind that I had never used before. I had another similar experience when I first began considering possible artificial intelligences whose cognitive architectures are not based on our own. For example, the instinct to punch back if one is unexpectedly punched is actually a very complex and non-obvious response, however automatic it might seem. It's been said that a function of humor is to help assimilate unusual ideas or events into our minds. Perhaps laughing at yourself might help provide a gentle introduction to the serious business of resisting your own mental biases.

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