Joined: May 2002
Evidently Berlinski is engaging in debates at http://www.talkreason.org.
Here is a letter I wrote:
Dr. Berlinski writes,
In my Commentary essay of December 2002, I observed that Nilsson and Pelger provided no justification for their claim that precisely 1829 one percent steps were sufficient to transform an initial light-sensitive patch into an eye whose geometry was comparable to that of an aquatic organism.
There are two points of importance that must be stressed. In the first place, Nilsson and Pelger have made an historically important claim, most notably in view of Darwin’s own concern that his theory somehow accommodate the development of organs of extreme perfection. And in the second place, the claim that 1829 one percent steps are required to complete their proposed transformation represents the very heart of their paper and so its argument.
Berlinski then go on to criticize Nilsson and Pelger for not providing the excruciating detail of each calculation for how they arrived at the 1829 steps.
But the procedure really is trivial. Nilsson and Pelger needed to calculate the number of 1% steps so that they had some approximate quantification of how much morphological change was required. They made no claim to this being "precise" as Berlinksi claims above.
Here is how N-P did their calculations:
In order to quantify the amount of morphological change, N-P constructed graphical models of various stages in the process (Figure 2) and decided to calculate the number of 1%-change steps in-between each stage. As an example, it takes 70 1% steps in order for a structure to double in length (due to the compounding of change -- think compound interest -- it takes only 70 steps rather than 100 in order for doubling to occur). They admit that there is some subjectivity in deciding *how* to measure morphological change, but they decide on the following as simple measures:
- length of straight structures
- "arc length of curved structures"
- "height and width of voluminous structures"
- changes in radius of curvature use the arc length of the inside and outside of the curved structure
- changes in lens refractive index above the starting point of 1.34
With this method they came up with 1829 1% morphological steps for the evolutionary sequence. They note that in actual evolution, some of the changes could happen simultaneously (e.g., lense development and aperture narrowing could occur together), but because they are being pessimistic, they restrict the steps to happen in series.
Note that only *after* this measurement of morphological change has been made, do they move on to calculating how long it might take for a population to undergo this amount of change. This can be discussed elsewhere.
What, may I ask Berlinski, is so mysterious and dubious about calculating the change in length or width of something?