Geometria holochroicznego oka trylobita a problemy uniformitaryzmu w geologii -
Abstract
GEOMETRY OF THE HOLOCHROIC EYE OF TRILOBITE AND THE PROBLEM OF UNIFORMITARISM IN GEOLOGY
Summary
The Geikie's phrase "the present is the key to the past" presents in the most popular form the basic assumption of geological sciences - the principle of uniformitarianism. Although uniformitarianism means different things to different scientists it is widely accepted the laws that describe nature's behavior today also described it in the past, i.e. the natural laws are invariant in time and space. This paper concerns with holochroal trilobite eyes and their geometrical properties in relation to natural laws. The holochroal trilobite eyes are a fossil analog of a compound eyes of crustaceans. They comprise a nearly spherical aggregate of identical structural units called ommatidia. Visual mechanism of trilobites obeyed mosaic-vision theory. According to the theory entire image formed in compound eyes is composed of a mosaic of reports from the indivdual ommatidia. Each ommatidium is sensitive to light entering at a small angle to its axis only. In the simplest form the quality of vision is a function of ommatidium lens dimension (D), ommatidia angular separation Φ, and eye surface curvature (R). The task of an eye is to give the best possible vision image. So the real size of lenses is a compromise between two contradictory factors: small lens diameter gives good vision quality (small interommatidial angle) and poor vision acquity (large diffraction), while large lens diameter acts contrarily. In optimal case, values of ommatidia angular separation and diffraction angle should be proportional. Coefficient of linear proportionality depends on light intensity. All calculations are based on diffraction theory using wavelength of sun light. According to black body radiation laws (valid also for the Sun!) a wavelength of a maximum radiation energy depends on the temperature of the body only. Value of D2/R, so called "eye parameter", is characterstic for given eye. Among recent deep sea crustaceans the value of ("eye parameter") is greater than 3. Similar value is expected for holochroal eyes of trilobites. Calculated "eye parameter" values for early Phanerozoic trilobites are in fair conformity with predicted ones. It suggests that wavelength, and consequently Sun surface temperature in early Phanerozoicum were the same as present ones. It is in agreement with astronomical hypothesis. Moreover, it gives rise to an assumption that the diffraction and black body radiation laws in palaeozoicum were as valid as they are nowadays. It attests not only a qualitatively but also quantitatively the uniformitarianism hypothesis in geology.
Summary
The Geikie's phrase "the present is the key to the past" presents in the most popular form the basic assumption of geological sciences - the principle of uniformitarianism. Although uniformitarianism means different things to different scientists it is widely accepted the laws that describe nature's behavior today also described it in the past, i.e. the natural laws are invariant in time and space. This paper concerns with holochroal trilobite eyes and their geometrical properties in relation to natural laws. The holochroal trilobite eyes are a fossil analog of a compound eyes of crustaceans. They comprise a nearly spherical aggregate of identical structural units called ommatidia. Visual mechanism of trilobites obeyed mosaic-vision theory. According to the theory entire image formed in compound eyes is composed of a mosaic of reports from the indivdual ommatidia. Each ommatidium is sensitive to light entering at a small angle to its axis only. In the simplest form the quality of vision is a function of ommatidium lens dimension (D), ommatidia angular separation Φ, and eye surface curvature (R). The task of an eye is to give the best possible vision image. So the real size of lenses is a compromise between two contradictory factors: small lens diameter gives good vision quality (small interommatidial angle) and poor vision acquity (large diffraction), while large lens diameter acts contrarily. In optimal case, values of ommatidia angular separation and diffraction angle should be proportional. Coefficient of linear proportionality depends on light intensity. All calculations are based on diffraction theory using wavelength of sun light. According to black body radiation laws (valid also for the Sun!) a wavelength of a maximum radiation energy depends on the temperature of the body only. Value of D2/R, so called "eye parameter", is characterstic for given eye. Among recent deep sea crustaceans the value of ("eye parameter") is greater than 3. Similar value is expected for holochroal eyes of trilobites. Calculated "eye parameter" values for early Phanerozoic trilobites are in fair conformity with predicted ones. It suggests that wavelength, and consequently Sun surface temperature in early Phanerozoicum were the same as present ones. It is in agreement with astronomical hypothesis. Moreover, it gives rise to an assumption that the diffraction and black body radiation laws in palaeozoicum were as valid as they are nowadays. It attests not only a qualitatively but also quantitatively the uniformitarianism hypothesis in geology.