Hagan’s Seminal Paper “THE MATHEMATICAL TRANSFORMATION OF GROWTH AND FORM”
April 19th, 2006 | No Comments »I have referenced on a number of occasions a paper by Brian Hagan (”THE MATHEMATICAL TRANSFORMATION OF GROWTH AND FORM: TRANFERRING THE WAVE-PARTICLE DUALITY FROM PHYSICS TO BIOLOGY AND PROPOSING WAVE INTERACTION AS A KEY DETERMINANT OF BIOLOGICAL STRUCTURE”, Medical Hypotheses, 6, 559-609, 1980). I do not believe that this very prescient paper has received the attention that it deserves. I highly recommend reading it!
Hagan was certainly among the first proposing that vision involves a Fourier transformation process. I will quote from that section (p.594) of his paper:
“The human eye has been seen by some investigators as a device for producing a Fourier transform of an object and of recovering the transform for presentation to the brain ( ref.Ochs). This recovery of the transform reproduces the object with which we are familiar, in contrast to the appearance of the intermediate or one-step stage with which we are less familiar (Figure 15)”
(The Ochs reference - “Is Fourier Analysis Performed by the Visual System or by the Investigator”, J. Opt. Soc. of Amer. 1979 - introduces the thought but goes on to say very little that is explanatory or substantive)
(Figure 15 is a usual diagram that I have often discussed diagramming the focal (or Fourier) and image planes of a converging lens).
Hagan goes further:
“There is no reason to doubt the existence in biological systems of a multiude of Fourier transforming devices which do not recover the image as the eye does, but leave it at the one-step intermediate or transform stage. Edges, holes, slits, reglar grids or any other type of discontinuity are examples of lensless agents wich can act as operators to form one-step Fourier transforms of objects (Figure..)”
This is an extraordinary proposal about which I will have more to say shortly.
GCH
