The Margolus-Levitin Theorem, the Beckenstein Bound, and Computronium

Computronium is a proposed form of matter that is optimized for computation. The speed of the fastest possible computer can be calculated by the Margolus-Levitin theorem, which states that that rate is (E * 4) / h, where E is the amount of energy available to the system in joules (the maximum value is E = mc^2, where m is mass in kilograms and c is the speed of light, 3 *10^8 m/s) and h is Planck's constant, which is approximately 6.626 * 10^-34 J * s. The units of the result are operations per second. The maximum possible memory capacity of a computer is related to the Beckenstein bound, which is the maximum amount of information that a given region of space can contain. This equals one bit per 4 square Planck lengths (a Planck length is approximately 1.616 * 10^-35 meters. This means that one kilogram of computronium taking up a volume of one liter could perform 10^51 operations per second and store 10^31 bits. For comparison, the world's fastest computer can currently perform 10^15 operations per second and a typical large hard drive can store one terabyte (approximately 10^13 bits). Processing speeds and memory capacities are currently doubling about every 12 and 15 months, respectively. If these trends continue, the maximum possible storage density will be reached around the year 2080 and the fastest possible computing speed will be reached around 2200. The Margolus-Levitin theorem also implies that computation speed is inversly proportional to entropy. On a tangentially related note, there is an interesting post on the generally obstructive effect of disorder on intelligent processes at Tom McCabe's blog.

Happy Holidays

For over a century humanity has searched the skies for signs of other intelligent civilizations. In fact, Nikola Tesla designed an early radio for specifically this purpose. That search has found nothing but a black silence spanning 13.7 billion lights years in every direction. No other known place in this inconceivably huge expanse is there creatures that we can call friends. I hope that everyone, myself included, keeps this fact in mind as we interact with others. Life and mind seem to be vanishingly scarce resources. May we be grateful for every day that we experience them.

A Summary of Social Biases

Here's a non-exhaustive list of social biases and some thoughts on how they interact.

Biases related to self estimation

egocentric bias- The tendency to give ourselves more credit for positive outcomes than a neutral observer would when engaging in an activity with others.

self-serving bias- Then tendency to credit ourselves for successes and attribute failures to outside causes, or in other words, having an external locus of control. This is often combined with egocentric bias.

over-confidence bias- The tendency to over-estimate our own competence. More specifically, the Dunning-Kruger effect is when someone believes that they are making valid choices even after experiencing negative outcomes. For reasons I can't easily comprehend Dunning and Kruger won a 2000 Ig Noble for a paper they published on this topic, especially in light of the fact that winners that year included a comparative study of the tastiness of Costa Rican tad poles.

illusion of control- The tendency for individuals to believe that they can control events which are in fact beyond their control.

Group biases

Reactance- The tendency to do the opposite of what one is instructed to do by others because of the perception that they are trying to restrict one's freedom. Clever marketers have created an industry tailored to non-conformist teenagers by exploiting this bias i.e. "the rebel sell".

deformation professionnelle- the tendency to examine issues from the viewpoint of one's profession only and neglect other perspectives.

bandwagon effect- the tendency to hold beliefs simply because they are popular.

notional bias- the belief that the views of one's culture are natural law.

status quo bias- the tendency to favor certain circumstances simply because they are familiar.

system justification- defending current circumstances to the point of being detrimental to one's own interests. This can act in tandem with status quo bias and the bandwagon effect.

ingroup bias- the tendency to behave more favorably to people who are perceived to be members of one's own group.

stereotyping- the tendency to attribute traits to someone simply because they are a member of a certain group.

outgroup homogeneity bias- The belief that the members of one's own group are more varied than members of other groups. "All [insert ethnic group that the speaker is not a member of here] look alike." Stereotyping, ingroup bias, and outgroup homogeneity bias are contributing factors in racist beliefs.

Social interaction biases

halo effect- the tendency to believe that people are generally good or bad because of one observed superficial positive or negative trait. The great importance assigned to first impressions is a result of this bias.

false consensus effect- the belief that others agree with us more than they actually do.

illusion of asymetric insight- the belief that we know others better than they know us.

illusion of transparency- the tendency to over-estimate the ability of others to know us. This results in blaming mis-communications on others rather than believing that we were not clear. This is one that I definitely need to work on.

projection bias- the assumption that other's share our beliefs. This can act in tandem with the illusion of transparency and the false consensus effect.

trait ascription bias- the tendency to believe that we are more unpredictable than others.

actor-observer bias- the tendency to attribute our own actions to our situation and the actions of others to their personalities. This is a particularly nasty one in my opinion. It can cause serious distortions of our moral judgments.

It seems that a recurring theme in social interaction biases is that we tend to believe that we have a richer internal thought life than others. Keeping this error in mind can not only help us behave more rationally, but also help us to be more friendly.

Information Ex Nihilo

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.

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."

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.

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?

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.

Hello

Hi everyone. My name is Matt Duing. I'm an college student. I'll be blogging about my general interests, with a focus on science and technology and, in particular, futurism, but also anything else that might be on my mind at the time. I will try to post several times per week. I am new at this, and I intend to post on a near-daily basis once I learn the ropes. Feedback and discussion are welcome. If you believe that anything that I write is in error, please do not hesitate to point it out. I will try to produce the best content I can and I hope that this will be a learning experience for both myself and my readers. I look forword to sharing my thoughts with you all, and I hope you enjoy.