Great question. No, we do not define FI this way. We infer FI from recurrence, and this is usually a valid inference.
Rather, the chances of having the same mutations arising in multiple independent cancers overlap is very low, by random chance alone. I’ve even shown how to estimate the amount of information in common too. These common mutations are called “reccurent” in cancer genomics. In evolutionary terminology, they are homoplastic, or convergent, mutations. In light of the very low likelihood by random chance, at this point, ID makes a the design inference.
However, the design inference does not appear justified in this context, unless someone wants to argue that God is guiding the development of cancer. So this appears to be a clear false positive of the design detection mathematics of ID.
As scientists, that isn’t the whole story. We still want to know how such a low likelihood event takes place. We need to have a good explanation for how this mutual information, these recurrent mutations, arose. The best explanation is that the cancers have common mutations because they both have the same cancer “function.” Cancer genomes, after all, have the same function. Remembering that genotype often causes phenotype, we rationally conclude that the common mutations are those that are causing the cancer phenotype-function. So, therefore, we infer that recurrent mutations are drivers mutations that cause the cancer function.
Is this inference entirely accurate? Without knowing the details it should be obvious the answer is “no”. For every rule in biology there are exceptions. I’m not going to get into that here though. This is usually a valid inference. Nonetheless, it parallels how Durston, Dembski, and Marks define FI. (1) Gather examples of entities with a function, (2) compute their mutual information.
True. What they do, however, is just assume:
- life must have very high FI,
- the only source of FI is intelligence.
Durston has improved a small bit on this by actually trying to measure FI. However, he misunderstands how to compute FI, associating it with the wrong type of MI. I’ll show that visually in a moment. So he fails at this basic computation in the end, but ID is trying to engage the data. They just do not have enough working knowledge of information theory to even see for themselves when they are in error.
So what can cause high mutual information? It very much depends on the what type of mutual information we are talking about. We can grant a few possibilities.
- Intelligence, we can presume is a technical possibility.
- Common history / Common ancestry (common starting point before mutation added)
- Common mutational distributions and mechanisms (neutral evolution).
- Common selective pressures (best explanation for most of cancer FI).
- Complex interactions between all of the above.
All these can produce high MI in the right contexts. Of most importance is #2, common history. It turns this explains the vast majority of the MI we see in biology, and because ID is non-commital or opposed to common descent, they are blind to how this affects their calculations. In the case of cancer, if we remove 6 billion bits of mutual information from shared history, the remaining amount is probably FI, and mostly caused by common selective pressures (i.e. natural selection). It is however just a tiny tiny fraction of the total amount MI between two cancer genomes.
The key point is that there is absolutely zero justification for the belief that FI is a unique signature of minds. Zero. What Dembski (and for example @EricMH) is an end run around the hard work of untangling the contributions of all these mechanisms to MI. Instead, they declare that if there is MI, it must be intelligence. Zero justification. Zero tests. Zero demonstration.
This comes out strikingly in Durston’s work. He computes FI wrong, by using a MI that does not take common ancestry into account. He just assumes that all MI must be produced by a mind, and never actually does a coherent simulation of DNA evolution. If he did, and then applied some clear thinking, he would find out that common history explains MI as he computes just fine.
The reason why is because he computes FI incorrectly, by equating it with the wrong type of MI. What we really want is the mutual information computed like this, excluding everything caused by common history:
FI = (C_1 \cap C_2) \setminus G, which correspond to the tiny overlap here (about 60-350 bits, not drawn to scale):
They, however make the mistake of computing FI this way instead, lumping common history as also caused by common function (about 6 billion bits here, and not to scale):
FI = (C_1 \cap C_2) , which corresponds to the overlap here. In our example of cancer genomes, the FI would be computed at about 6 billion bits. As you can see, that equivocation between different types of MI wildly overestimates FI by neglecting the contribution of common shared history.
I want to emphasize, from my interactions with Durston and other ID advocates, I do not think this is dishonesty. They appear to have been blinded by their polemic goals, and self-reinforcing echo chamber. Because most people are lost in the Byzantine derivations of mathematics in general, and information theory of ID proponents too, it is hard for people to break in and enter the conversation with them. They just do not have any practical experience in applying information theory. So it is not surprising that they are making errors here.