Saturday, 6 April 2013

What are inheritance and copying?

Copying is one of the foundational principles of universal Darwinism. The others main ideas involved are: variation, selection, and cumulative adaptation.

"Inheritance" and "copying" are basic concepts, which I often just assume that people understand. However, a lot of ink has been spilled over the issue of what they mean. In particular, whenever I use the term "copying" in this context, there's often someone who objects to my usage, claiming that the word "copying" implies high fidelity. Some of the confusion in the area stems from using the terminology of replication - which really does have implications of high-fidelity copying - in everyday use.

Sylvain Magne recently claimed that the issue of high-fidelity copying is "one of the major challenges that memetics is facing". I've written about he issue of high-fidelity copying before. I don't think it is a particularly complex or difficult issue. Surely it is only a challenge to memetics in the eyes of its critics.

However, I do think that a proper approach to universal Darwinism should define what it means when it talks about "copying", "inheritance" or "reproduction". So, this post will do precisely that:

"Copying" is an ordinary dictionary word - but if you look at dictionaries and popular definitions of the term, they are often completely useless for technical work. Look at Wikipedia, for an example of the muddle surrounding the term.

I think the best way to define "copying" for technical work is using concepts from information theory and the theory of causality. Information theory was pioneered by Claude Shannon, and the theory of causality was pioneered by Judea Pearl.

To say that A has copied from B makes two main claims:

  • That A has become more similar to B in some respect;
  • That the increased similarity between A and B was caused by A's influence on B.
The first claim is simpler - A and B have increased their Shannon mutual information associated with some measurable aspect or trait.

The second claim is more complex - since it involves the idea of causality. Causality is a difficult concept:

We usually think we know that causes come before events that they cause - and not the other way around. However, we also know that the laws of physics exhibit microscopic reversibility. This means that either causality has to do with large scale thermodynamics and increases in entropy - or our conventional conception of the past causing the future is wrong. Physicists are generally more comfortable with the latter notion. For example Feynman diagrams feature particles that travel backwards in time. This just shows that causality is a more complex topic than it may - at first - appear to be.

I'm mostly just going to defer to Judea Pearl's book when it comes to explaining what "causality" means. However, I will make a few comments:

The idea that B copied from A can be dealt with scientifically. The main hypotheses that can account for increased similarity between A and B are:

  1. B has become more similar to A because of causal influences from A;
  2. A has become more similar to B because of causal influences from B;
  3. B has become more similar to A because of causal influences from C.
  4. B has become more similar to A by chance;
These are all scientific hypotheses that make predictions. The first hypothesis suggests that changes in A might have been been copied into B. If you can repeat the experiment, change A, and then see that B copies that change, then this counts as evidence against hypotheses 2 and 3. Dawkins (2004) proposes precisely this test, saying:

For an operational criterion for whether an entity is a true replicator, ask what is the fate of blemishes in entities of this class.
If you repeat such an experiment on multiple occasions - and if the results are consistent - that counts as evidence against hypothesis 4.

Sometimes you can't rerun the experiment - e.g. because it involves a unique historical event. However you can usually model or simulate it - and then apply the same process to the model.

There are sometimes other ways of exploring the issue of whether A copied from B. For example, you can look for possible Cs, which A and B both copied from. Or you can look at how and when A and B previously interacted.

These two ideas - Shannon mutual information and causality - are the main concepts you need to put the ideas of inheritance and copying on a firm theoretical footing - for use in Universal Darwinism.

The 2008 paper In defence of generalized Darwinism makes the same point as follows:

A number of authors have developed and refined the definition of a replicator. An emerging consensus argues that replication involves a causal relationship between two or more entities, where there is substantial similarity between the original and replicated entities, and where information concerning adaptive solutions to survival problems is passed from one set of entities to another (Sterelny et al. 1996; Godfrey-Smith 2000; Sperber 2000). The definitional characteristics of causality, similarity and information transfer are common to these accounts.
There's no reason to introduce the concept of high-fidelity copying - unless you want to get into the issue of the conditions required for cumulative adaptive evolution.

1 comment:

  1. Hello Tim.

    First of all, I am really glad to see my name cited in your blog. It gives me a warm feeling of belonging. Reflecting on memetics feels sometimes like a rather lonesome endeavor.

    So thanks a lot for taking the time to react to my article. Your criticism can only help me move forward.

    Note that my articles are still a work in progress and are, or will, be amended in the future.

    So, let me try and respond quickly.

    I think understand clearly your issues with high fidelity, and I actually had the same issues with it myself. In fact, my point was to try and account for the apparent incompatibility between a high fidelity replicator model and the apparent low fidelity of cultural inheritance.

    It is true that, to me, the concept of replicator implies high fidelity. More than that actually, it implies perfect fidelity, from a purely theoretical point.

    So how could I reconciliate both worlds ? This is where my "relative fidelity" comes in. I have basicaly made the concept of fidelity relative (although I actually don't use the word "fidelity" in my article). This relativity allows to have replicators which, from the outside seem to have a low fidelity, but from a certain perspective keep a very high fidelity. This is thanks to a change of perspective and fuzzy logic.

    In a way, I am saying that high fidelity is not necessary at all but it is still compatible with a high fidelity replicator model because there is a point of view from which things appear to have high fidelity.

    I am afraid I might not have managed to get my point across clearly, but is it more clear now ?
    Maybe I should explain more why the replicator idea implies high fidelity ?