Diffusion Processes with Hidden States from ... - FU Berlin, FB MI

1 Motivationmere model.In the appendix is presented an example, in order to show the extraordinary relationship betweenobservation and theory in the natural sciences on the one hand and the interrelation between modelsand theories on the other hand (see section A.1 on page 99).We see here an example for the modeling that grounds on observation (Tycho Brahe) which led tothe laws of planetary motion (Johannes Kepler) and later to the formulation of probably the firstscientific theory of mankind by Isaac Newton, from which earlier formulated models such as theplanetary motion model of Kepler and others can be derived.The motivation of this thesis is the decent ambition to take into account some observation and onthe basis of this observation to set up a model that hopefully broadens our view of the consideredphenomenon. Maybe this will help us in the future to understand the whole process in the senseof something like a theory, although the process herein is so complex that we can not possess thecertainty to reach this ambition but hope will not leave us.The phenomenon in consideration is the first stage of the process which is taking place in the eyeand converts the light into an electrical signal. It is nothing less than the process which finallyafter numerous steps leads to vision.When it was pointed out at the beginning of this motivation chapter that we own the desire tounderstand the world that surrounds us, then vision is maybe the most important gift that we havereceived from nature, in order to reach this understanding. It is our vision that let us see the worldbefore interpretation and model building, based on what we see, is taking place in our brains. Forthis reason vision is the gate to our consciousness, as anatomically the retina, where the conversionof light information into electrical information is taking place, is the gate to our brain.The history of theories on the visual sense is dating back from the Greek philosophers like Platoand Aristotle, and it was finally Kepler who, grounding on the works of middle ages Arabianscientists, established a model for the process of seeing which is the basis for our today’s understandingof the visual sense. In his work ”Dioptrice” from 1611 Kepler constituted optics as anarea of science. In this and in earlier works he condemned ancient associations that describedvision through the thesis that rays extinguish from the eye and comprehend the considered object.Moreover light rays extinguish from every point of an object into all directions of space and reachfor instance also through the pupil the inner eye.Today it is of great importance and motivation to understand vision even deeper, to understandthe single sub elements, which are finally leading to visual sense. To begin this ambition, anintroduction will be given to the visual transduction process as a whole and the first stage of thisprocess in particular in the next chapter.For modeling this and other processes in biology, we have a priceless advantage compared toour scientific ancestors. Today we possess both enormous experimental and theoretical tools enablingus to reach such heights of knowledge about nature that our ancestors may never have beendreamed of.Experimentally we are able to make visible such events and processes that are laying in the tinyworld of the microcosm down to the range of nanometers, and on the other side we have telescopes,enabling us to see events and processes up to 10 billion light years away from the earth.2