Title Author Date

James Downard Curtis, Tom Sep 08, 2003

David Berlinski writes "... there is no indication in their paper that the calculations had been given to the Proceedings of the Royal Society of London, nor in the ten years since the publication of their paper have Nilsson and Pelger ever made their calculations available in any public format whatsoever. With this in mind I entertained the hypothesis – I did not nothing more – that Nilsson and Pelger had not performed those calculations for the full range of their sequence, but had instead undertaken calculations for a handful of points and completed their sequence by extrapolation. Whether this is what they did, I wrote, was something that I did not know."

He seems to have underestimated the force of his prose. In fact he wrote:
"Moreover, Nilsson and Pelger do not calculate the visual acuity of any structure, and certainly not over the full 1,829 steps of their sequence. They suggest that various calculations have been made, but they do not show how they were made or tell us where they might be found. At the very best, they have made such calculations for a handful of data points, and then joined those points by a continuous curve."

and:
"As I have already observed, the number 363,992 is derived from the number 80,129,540, which is derived from the number 1,829-which in turn is derived from nothing at all."

In fact, Nilsson and Pelger are very clear where the 1,819 steps come from, and very clear about the source of their calculations. Figure 1 (page 54) of their article consists of three graphs. The first shows increase of spatial resolution as the light sensitive patch invaginates (model sequence steps 1 to 3). The text commenting on this graph refers us to Nilsson 1990 for further details.

The second graph shows improvement of detectable resolution as the appature narrows when pit depth equals diameter (model sequence steps 3 to 6). The text cites two papers and the equation used to calculate this (and, I believe, the previous) graph.

The third graph plots increase of optical resolution as the refractive index of the lense increases. Again the text cites the source of the equations used (Fletcher et al. 1954).

So though figure three only plots the optical performance of the first seven model eyes, the performance of the continuos range of intermediate eyes has been previously plotted in figure 1.

Finaly, had Berlinski been in doubt as to the treatment of the subject, or the exact source of the various figures, he need only have written one of the authors and asked. As Berlinski has written to Nilsson on a related matter, such an enquiry would only be polite before making accusations of fraud.

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Title Author Date

James Downard Curtis, Tom Sep 08, 2003

Further to my previous message, here is the complete list of the 1829 steps as sent to me by Dan -E. Nilsson. I apologise for the loss of formating.

type of change start end 1% steps sum 1% steps
Stage 1 to 2 176
corneal width (curve) 46.5 46.5 0
corneal thickness 3.35 10.1 110
upper retinal surface width 46.6 47.2 1
lower retinal surface width 46.6 51.2 9
upper pigment surface width 46.6 53.9 14
lower pigment surface width 46.6 58.0 21

Stage 2 to 3 362
corneal width (curve) 46.5 46.5 0
corneal thickness 10.1 25.8 94
upper retinal surface width 47.2 75.6 47
lower retinal surface width 51.2 85.9 52
upper pigment surface width 53.9 97.7 59
lower pigment surface width 58.0 108.9 63

Stage 3 to 4 270
corneal width (curve) 46.5 40.2 15
corneal thickness 25.8 37.0 36
upper retinal surface width 75.6 130.6 54
lower retinal surface width 85.9 143.9 51
upper pigment surface width 97.7 145.6 40
lower pigment surface width 108.9 158.7 37

Stage 4 to 5 225
corneal width (curve) 40.2 29.5 31
corneal thickness 37.0 43.7 16
retinal surface width 137.2 202.3 39
pigment surface width 152.1 208.6 31

Stage 5 to 6 192
corneal width (curve) 29.5 37.2 23
corneal thickness 43.7 46.6 6
central refractive index increase from 1.35 0.010 0.060 180

Stage 6 to 7 308
corneal width (curve) 37.2 55.4 40
corneal thickness 46.6 42.3 9
iris width 4.76 11.99 92
retinal surface width 202.3 132.1 42
pigment surface width 208.6 143.7 37
central refractive index increase from 1.35 0.060 0.090 41
lens width 28.4 21.9 26
lens height 24.0 20.2 17

Stage 7 to 8 296
corneal width (curve) 55.4 60 8
corneal thickness 42.3 30.7 32
iris width 11.99 15.88 28
retinal surface width 132.1 72.6 60
pigment surface width 143.7 82.6 55
central refractive index increase from 1.35 0.090 0.180 70
lens width 21.9 16.7 27
lens height 20.2 16.7 19

Grand total 1829

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