I’ve said a number of things about good and evil at Overcoming Bias, and I decided to gather my comments together in one place. I’ve extracted the following quotes out of their surrounding context. The full original discussion can be found in Rationality Quotes 7 and Morality Is Overrated. Arguments similar to mine appear in The Moral Void.

Excerpts from Rationality Quotes 7

Robert Bruce Thompson: The simple fact is that non-violent means do not work against Evil. Gandhi’s non-violent resistance against the British occupiers had some effect because Britain was wrong, but not Evil. The same is true of the success of non-violent civil rights resistance against de jure racism. Most people, including those in power, knew that what was being done was wrong. But Evil is an entirely different beast. Gandhi would have gone to the ovens had he attempted non-violent resistance against the Nazis. When one encounters Evil, the only solution is violence, actual or threatened. That’s all Evil understands.

Me: I believe that this quote is not rational, because thinking of human relations in terms of “good” and “evil” is not rational. I prefer to think in terms of the iterated prisoners’ dilemma; in terms of cooperation and defection. If you frame a conflict in terms of “good” and “evil”, you quickly reach violence. If you frame it in terms of “cooperation” and “defection”, you may be able to negotiate a cooperative agreement. Violence may be necessary in certain situations, but it represents a suboptimal solution to conflict.

In a blog that is dedicated to overcoming bias, the term “evil” should only be used to point out the bias and irrationality that is encouraged by the concept of “evil”.

Some people believe that, “In an ideal world, disagreements would not exist”, and that “‘agreeing to disagree’ is a sign of mutual disrespect and contempt.” Others disagree. I believe that agreeing to disagree is a sign of respect and a practical necessity.

— xkcd

My argument for disagreement follows:

I have revised my blog comment policy. Here is the new item:

At any time, I may choose to limit the number of comments per reader per post to an arbitrary number, such as one or two. My intent is to maximize the diversity of comments. If you wish to have a discussion without my arbitrary restrictions, you are welcome to leave a brief comment with a link to your own blog, inviting readers to continue the discussion there.

I have been applying this policy all along, as some of you know, but I think it’s wise to make these things explicit. I know this policy will cost me some readers, and I accept that. I blog because I enjoy it, but I don’t enjoy long debates. I believe that most readers prefer to read a wide variety of comments, rather than a two-sided debate.

I admit that I cause debates, by sometimes making controversial claims, and then replying to comments that disagree with my claims. I know that my reply may make you think (perhaps quite rightly) that I misunderstood your first comment, but please let me assure you that I will also (most likely) misunderstand your second comment.

Convergent evolution is “the development of similar structures in distantly related organisms as a result of adapting to similar environments and/or strategies of life”. I’ve talked before about multiple independent simultaneous discovery and invention in science, technology, and art. I’ve mentioned that multiple discovery supports an evolutionary view of culture, but I haven’t really discussed why I believe this. The reason is that convergent evolution is the best explanation for multiple discovery.

Multiple invention in biology:

• Wings: birds, bats, bugs
• Spines: hedgehogs, porcupines
• More: Convergent evolution

Multiple discovery in science:

• Theory of evolution: Darwin, Wallace
• Calculus: Newton, Leibniz
• More: Multiple Discovery: The Pattern of Scientific Progress

Multiple invention in technology:

• Heavier-than-air flight: too many to list
• Radio: Tesla, Popov, Bose, Marconi
• More: Multiple Discovery: The Pattern of Scientific Progress

Multiple creation in art:

• Comet/Asteroid impact: Deep Impact (1998) and Armageddon (1998)
• Capote: Capote (2005) and Infamous (2006)
• More: List of films with similar themes and release dates

It is generally accepted that Darwinian evolution explains convergent evolution in biology. Darwinian evolution happens whenever we have three things: variation, heredity, and differential fitness. If different species are faced with similar environments, then it is not surprising that they often evolve similar mechanisms for survival in those environments.

However, there seems to be resistance to the view that Darwinian evolution explains convergent evolution in culture (e.g., science, technology, art). Perhaps this is because Darwinian evolution is often described as “random mutation plus selection”. We are reluctant to view human ingenuity as mere randomness, so we reject the application of Darwinian theory to culture. But Darwinian theory does not require randomness; it requires variation. The source of the variation can be random, but it is not necessary that it must be random.

Another objection to applying Darwinian evolutionary theory to cultural change is the idea that most multiple discoveries are due to copying. It is true that direct copying happens, and that the later discoverer/inventor/creator may sometimes be dishonest about copying, but there are many historical cases where copying appears unlikely. Note that direct copying is not incompatible with evolution. For example, bacteria copy plasmids from one another.

We know that biological evolution generally happens in many small increments. Perhaps we resist the theory of Darwinian cultural evolution because it often seems that technology (for example) proceeds in sudden jumps. However, a close study of the history of any particular technology invariably shows a series of small, incremental developments. The apparent jumps are an illusion, caused by the way technology is adopted.

Do you accept convergent (Darwinian or neo-Darwinian) evolution as an appropriate theory for multiple invention in biology, yet reject it as an appropriate theory for multiple invention in culture? If so, why? (If you reject Darwinian evolution in biology, please don’t bother leaving any comments.)

In a previous post, I discussed the distinction between attributes and relations:

An attribute is a characteristic of an entity, whereas a relation is a connection between two or more entities. In logic, we can define an attribute as a predicate with one argument and a relation as a predicate with two or more arguments. The distinction between attributes and relations can be unclear. For example, the colour red may be seen as an attribute, RED(X), or a relation, REDDER_THAN(X, Y).

This leads to a distinction between attributional similarity and relational similarity. Two things, X and Y, are attributionally similar when the attributes of X are similar to the attributes of Y. Two pairs, A:B and C:D, are relationally similar when the relations between A and B are similar to the relations between C and D. I’ve been thinking about the rules that govern attributional and relational similarity.

Let A:B::C:D be the assertion that A:B and C:D are relationally similar. The expression A:B::C:D is usually read as “A is to B as C is to D”. This is called a proportional analogy. Aristotle knew that proportional analogies obey certain logical rules:

(1) A:B::C:D → B:A::D:C
(2) A:B::C:D → A:C::B:D

From (1) and (2), we can derive:

A:B::C:D → C:D::A:B

More recently, these rules have been studied by Yves Lepage and others. Rule (1) seems clear, but rule (2) is sometimes odd. It seems that rule (2) is reasonable when the items (A, B, C, and D) are all of the same general type, but it is less reasonable when they are different types:

uncle:aunt::brother:sister → aunt:uncle::sister:brother [same types: kin, rule (1)]
uncle:aunt::brother:sister → uncle:brother::aunt:sister [same types: kin, rule (2)]
dog:bark::cow:moo → bark:dog::moo:cow [different types, rule (1)]
dog:bark::cow:moo → dog:cow::bark:moo [different types, rule (2)]

Let X~Y be the assertion that X and Y are attributionally similar. When X and Y have a very high degree of attributional similarity, we call them synonyms. I have argued that attributional similarity can be reduced to relational similarity, but not vice versa. Here is one way to do the reduction:

(3) X~Y = (by definition) for all Z, X:Z::Y:Z

In other words, X and Y are attributionally similar when, for all Z, the relations between X and Z are similar to the relations between Y and Z. This definition of attributional similarity results in a score of 83.75% on the TOEFL synonyms. (The paper is about tensors, not similarity measures, so it does not explain that the tensor is computing similarity by using definition (3).) Rules (1) and (2) give us:

X:Z::Y:Z → Z:X::Z:Y → Z:Z::X:Y [assuming X, Y, and Z are the same type?]

Hence:

X~Y = for all Z, Z:Z::X:Y

Transitivity seems plausible for proportional analogies:

(4) A:B::C:D & A:B::E:F → C:D::E:F

Now we have a little theorem:

Theorem: A~C & A:B::C:D → B~D

Proof:

1. A~C [by assumption]
2. A:B::C:D [by assumption]
3. A:C::B:D [from 2 by rule (2)]
4. for all X, A:X::C:X [from 1 by definition (3)]
5. for all X, X:X::A:C [from 4 by rules (1) and (2)]
6. for all X, X:X::B:D [from 3 and 5 by rule (4)]
7. for all X, B:X::D:X [from 6 by rules (1) and (2)]
8. B~D [from 7 by definition (3); QED]

I’m not sure about the significance of this, but I thought it was worth writing down.

This post was partly inspired by a blog post by Gustavo Lacerda. Suppose we have:

A = me
B = my lover
C = my lover’s past lovers
D = my lover’s past lovers’ lovers

Then A~C & A:B::C:D → B~D. If I am similar to my lover’s past lovers (A~C) and I am attracted by my lover like my lover’s past lovers are attracted by my lover’s past lovers’ lovers (A:B::C:D), then my lover should be similar to my lover’s past lovers’ lovers (B~D). Thus I am likely to be attracted by my lover’s past lovers’ lovers.

I believe that similarity is a matter of degree, but the above discussion assumes that it is binary (true/false).

Contemplating the comments on my last post, I began thinking about Ockham’s Razor versus Darwinian Evolution. Both of them can be used as heuristics or algorithms for creation, invention, and discovery. In 1964, Ray Solomonoff proposed A Formal Theory of Inductive Inference (Parts I and II). His theory is an Ockhamian algorithm for searching through the space of computer programs. It inspired Gold’s language identification in the limit and Kolmogorov complexity. On the other hand, genetic programming is an evolutionary algorithm for searching through the space of computer programs. It is interesting to compare these two approaches to searching in program space.

In Solomonoff’s 1964 approach, each program is treated as a black box. This is inefficient, because the knowledge that is gained from evaluating one program cannot be applied when evaluating another program. On the other hand, genetic programming combines pieces from programs to create new programs. The knowledge that is gained from past programs is used in the construction of new programs. Thus we should expect this Darwinian algorithm for searching in program space to perform better than an Ockhamian algorithm for searching in program space. In fact, genetic programming has some impressive successes. As far as I know, Ockhamian algorithms for searching in program space have not achieved anything this impressive. (Let me know if I’m wrong.)

I looked in the index of Peter Grünwald’s The Minimum Description Length Principle and in the index of Marcus Hutter’s Universal Artificial Intelligence, and I found Solomonoff and Kolmogorov, of course, but there was no mention of genetic programming or John Koza. I looked in the index of Koza’s Genetic Programming, and there was no mention of Solomonoff or Kolmogorov, but Chaitin is mentioned. Most interestingly, Ray Solomonoff has a 2006 paper, Machine Learning - Past and Future, in which he talks about his research in Genetic Programming:

Genetic Programming is my second area of recent research. Koza’s Genetic Programming system has been able to solve many difficult problems of very varied kinds.

Solomonoff was born in 1926. There’s a lesson for us young people.

Ockham’s razor is the principle that entities must not be multiplied beyond necessity. There are many different interpretations of Ockham’s razor. For me, the idea that simplicity is a guide to truth is the core of Ockham’s razor.

For any set of observations, there are an infinite number of theories that can fit the observations, with varying degrees of accuracy. For any set of data points, there are an infinite number of curves that fit the points, exactly or approximately. We don’t usually pick the theory with the highest accuracy (in general, there are infinitely many theories that are perfectly accurate); instead, we pick the theory that best balances accuracy and simplicity. Why? Because simplicity is a guide to truth. That is, the theory that best balances accuracy and simplicity is the theory that will make the most reliable predictions about future observations.

My PhD thesis was, in essence, about Ockham’s razor. For a period of about a decade, extending from my late undergraduate years to my early postdoctoral years, it would be fair to say that I was obsessed with Ockham’s razor. I was convinced that it was the key to understanding how we acquire knowledge about the world. I no longer believe in Ockham’s razor.

There are various ways to make Ockham’s razor more precise, such as Bayesian inference, minimum description length, minimum message length, Kolmogorov complexity, and data compression. My own approach was to reduce simplicity to stability. That is, we should prefer simpler theories because they are more stable, more resistant to noise in the data. This approach is closely related to the Akaike information criterion and the bias/variance dilemma.

For some time, I was satisfied with bias/variance as a justification for Ockham’s razor. The papers that awoke me from my dogmatic slumber were Cullen Schaffer’s “A conservation law for generalization performance” and “Overfitting avoidance as bias“. The subsequent No Free Lunch theorems and Webb’s “Further experimental evidence against the utility of Occam’s razor” further persuaded me that Ockham’s razor is dull.

It is notoriously difficult to explain the No Free Lunch theorems informally. I think of the theorems in terms of Hume and Kant. The NFL theorems show that there is no a priori reason to prefer any one theory to another. If you don’t make any assumptions about the world (i.e., the universe, the environment, the particular dataset that you are analyzing), then you can’t make any claims about the reliability of your predictions.

In machine learning, the NFL theorems are explained in terms of inductive bias. Note that inductive bias is distinct from statistical bias, which is the kind of bias involved in the bias/variance dilemma. Inductive bias is anything that is used to select a unique theory from the set of all theories, other than fit of the theory to the training data. In the words of Tom Mitchell, inductive bias is “a means of selecting between competing hypotheses that utilizes criteria beyond those strictly encapsulated in the training data”. The NFL theorems show that there is no way to avoid inductive bias, and there is no way to justify one inductive bias over another, without making assumptions about the world.

The lesson I draw from this is that, instead of asking how to measure the complexity/simplicity of a theory, we should ask which inductive biases tend to work well in this particular universe in which we find ourselves. Simplicity is just one more example of an inductive bias, and there is no reason to prefer it to any other inductive bias, unless empirical evidence supports its value. Webb’s experiments suggest that simplicity is not a particularly good bias for our world. The success of support vector machines, on the other hand, suggests that maximum margin is a good bias for our world.

In my experience with machine learning algorithms, on a wide variety of problems, the choice of features in the feature vectors is far more important than the choice of learning algorithm. That is, the most important issue is representation, and the inductive bias due to a given representation. When applying decision tree induction to chess endgame classification, Quinlan reported that the most difficult part of the problem was finding the right features to represent the data. The initial attempt was a feature vector with 64 elements, one for each square of the board. This low-level representation was useless. The final features were much higher-level. This kind of experience is rarely written down, but it is often discussed informally, in hallways at machine learning conferences, for example. I believe that it is not fruitful to think of the representation problem in terms of Ockham’s razor.

I have nothing against Bayesian inference, for example. It is often a useful tool. But there are those who seem to believe that all problems can be solved using a Bayesian approach. I disagree. You can’t apply Bayesian inference until you figure out how to represent the problem. But figuring out how to represent the problem is 95% of the work. By the time you have the representation right, the tool that you use to finish the remaining 5% is not terribly important.

What is evolution? There are three main components to evolution: variation, heredity, and differential fitness. The best definition I have seen is in Robert Brandon’s Concepts and Methods in Evolutionary Biology:

The following three statements are crucial components of the Darwinian (or neo-Darwinian) theory of evolution:

1. Variation: There is (significant) variation in morphological, physiological and behavioral traits among members of a species.
2. Heredity: Some traits are heritable so that individuals resemble their relations more than they resemble unrelated individuals and, in particular, offspring resemble their parents.
3. Differential Fitness: Different variants (or different types of organisms) leave different numbers of offspring in immediate or remote generations.

Of course life evolves, but evolution inevitably happens whenever we have these three things: variation, heredity, and differential fitness. Thus life is not the only thing that evolves.

Culture evolves:

• Cultural Evolution (Stanford Encyclopedia of Philosophy)
• Memetics
• Cultural Selection Theory
• Dual Inheritance Theory

Science evolves:

• Evolutionary Epistemology
• The Heroic Theory of Scientific Development
• Without Miracles: Universal Selection Theory and the Second Darwinian Revolution
• Incremental Doubt

Technology evolves:

• Simultaneous Invention
• The Evolution of Technology

Language evolves:

• Evolutionary Linguistics
• The Symbolic Species

Art evolves:

• The Evolution of Movies
• Does Beauty Build Adapted Minds?
• Literary Study and Evolutionary Theory: A Review Essay
• Literary Darwinism
• The Literary Animal

Ethics evolves:

• A Scientific Approach to Morals and Ethics
• The Evolution of Cooperation
• Genetic and Cultural Evolution of Cooperation
• The Complexity of Cooperation

Evolution evolves:

• Unbounded Evolutionary Versatility
• Increasing Evolvability
• The Evidence of Progress
• Baldwin Effect

Universes evolve:

• The Life of the Cosmos
• Evolution of the Universe by natural selection?
• Fecund Universes
• A Universe of Universes

It seems safe to say that significant discovery, really creative thinking, does not occur with regard to problems about which the thinker is lukewarm.
— Mary Henle

There seems to be a growing consensus that genius is all about hard work; really hard work, for at least a decade. What can motivate that kind of sustained effort? The answer must be passion. If you care very deeply about a certain thing (e.g., science, art, sports), you will be motivated to work hard at it for decades, and, with a bit of luck, you may eventually be blessed with the label “genius” (although you probably don’t really care about that particular blessing).

People tend to link genius with IQ, but I think this is misguided. I suspect that IQ scores are closely connected to personality. There seems to be some weak evidence to support this hypothesis. IQ tests typically involve a certain kind of puzzle solving, and it seems to me that the people who do particularly well on IQ tests are those who have the kind of personality that enjoys puzzle solving. And the people who make IQ tests are also people who enjoy puzzle solving, and who believe that puzzle solving is an important and valuable ability (i.e., they are passionate about puzzle solving, interpreted in a very general sense). Essentially, an IQ test measures the overlap between the passions of the test taker and the passions of the test maker.

(Disclaimer: I have very little scientific evidence to support the wild conjectures in the preceding paragraph. I enjoy puzzles, in a general sense, such as the puzzle of life.)

Ideally, teachers would focus on one single thing: getting their students really, deeply excited about the subject of the course. Everything else, the students can do on their own. If you don’t know how to do research, but there is a research question that really excites you, then you will figure out how to do research.

(This post was inspired by discussion with Daniel Lemire.)

People like to say that a certain book “changed their life”: The quoted phrase “book that changed my life” gets 61,000 hits on Google. I have some favourite books, but can I honestly say that one of them significantly changed my life? It seems more likely that my life has been influenced by the gestalt of the books I have read; perhaps any individual book could have been skipped without much impact on my life. For the last few years, most of my professional reading has been journal and conference papers, rather than books. Also, there are books that I think are extremely important, such as Axelrod’s The Evolution of Cooperation, yet they have not had any impact on my research, so far. If a reader cannot point to some tangible outcome from reading a book, then the reader may be overestimating the personal impact of the book. Pondering these thoughts, I decided to try to track the major decision points that led to my current research project, to try to recall what books (or papers or lectures) most influenced my decisions.

1. Deciding to do research in AI: I was a teenager when I decided that I wanted to do research in AI. There were several digressions (e.g., a PhD in philosophy), but I eventually became an AI researcher. Science fiction was a major influence on this decision. I don’t think I can pin the credit (or blame) on any individual author or book, but A.E. van Vogt’s short story Fulfillment stands out in my memory (in the collection The Far-Out Worlds of Van Vogt). I can see that it also had a big impact on Damien Broderick, since the opening sentence of Transcension comes from Fulfillment. I should also mention Asimov’s short story, The Last Question. As a teenager, I was quite troubled by entropy.

2. Deciding to specialize in machine learning: As a PhD student, my interest in AI was rekindled by Machine Learning: An Artificial Intelligence Approach (Volume I and Volume II). These books pulled me away from philosophy and back to computer science. They also led me to specialize in machine learning.

3. Deciding to focus on machine learning applied to semantics: In 1997, I attended a lecture by Geoffrey Hinton, on Unsupervised Neural Networks. He convinced me that I should learn more about unsupervised learning and that I should read A Solution to Plato’s Problem (Landauer and Dumais, 1997). Hinton was clearly very impressed by Landauer and Dumais, and so was I. This paper has had a major influence on my research.

4. Deciding to focus on analogy-making: Michael Littman invited me to try to apply machine learning techniques to SAT analogy questions. Around the same time, I was reading Where Mathematics Comes From (Lakoff and Núñez). Later, I read Metaphors We Live By (Lakoff and Johnson). These two books convinced me that analogy-making was central to cognition, and the SAT analogy questions gave me a tool that I could use to guide my research. Michael and I viewed the SAT analogy questions as analogous to the TOEFL questions that were used by Landauer and Dumais (1997). We were both directly influenced by A Solution to Plato’s Problem.

5. Deciding to attempt to emulate the Structure Mapping Engine without hand-coded representations: My current project is most influenced by (1) The structure-mapping engine: Algorithm and examples, (2) High-Level Perception, Representation, and Analogy: A Critique of Artificial Intelligence Methodology, and (3) Structure-Mapping vs. High-level Perception: The Mistaken Fight Over The Explanation of Analogy. The first paper describes a symbolic approach to analogy-making, the Structure Mapping Engine (SME). The second paper argues that SME is flawed, because it relies on hand-coded representations, instead of accepting raw data as input. The third paper argues that the first two papers are not really in conflict: It may be possible to enhance the SME so that it can use raw data instead of hand-coded representations. My current research is inspired by ideas from these three papers.

What books (or papers or lectures) changed your life (or research)?