THE RELATIONSHIP BETWEEN MATHEMATICS AND MYSTICISM OF THE GOLDEN MEAN THROUGH HISTORY

1992 ◽  
pp. 33-65 ◽  
Author(s):  
Jay Kappraff
Keyword(s):  
2020 ◽  
Vol 15 (2) ◽  
pp. 309-326 ◽  
Author(s):  
Vincent Ng ◽  
Louis Tay

A seemingly universal lesson is that anything taken to its extreme is detrimental. Indeed, there has been growing interest in testing this idea within psychology. These studies have often been framed in terms of Aristotle’s doctrine of the golden mean or the idea that virtue lies between the vices of deficiency and excess. Recent explicit reviews of this hypothesis in the psychological literature have led to the paradoxical conclusion that one can have too much virtue (i.e., the too-much-of-a-good-thing effect) despite virtue being identified by the golden mean. We argue in this article that this conclusion is due to a reductionist account of virtues in psychology and the resultant measurement of virtues as general dispositional tendencies in behavior. We review philosophical theory on the golden mean to show that the relationship between virtue and relevant behavior is fundamentally about situation-specific optimality. Using schematic models, we contrast the former measurement approach against the latter to explain the too-much-of-a-good-thing effect and further demonstrate why virtues cannot be properly measured as general tendencies in behavior. We conclude with methodological implications of our theory-informed approach to virtue measurement for research design, evaluation, and conceptualization.


Author(s):  
Lovemore Mamombe

The proportiones perfectus law states that σ_x^y=(x+√(x^2+4y))/2 is a proportione perfectus if 1≤y≤x such that for an arbitrary positive integer , there exists an integer sequence defined simultaneously by the quasigeometric relation h_(n+1)=round(σ_x^y h_n ),n≥1 and the arithmetic relation h_(n+2)=〖xh〗_(n+1)+〖yh〗_n,n≥1.        When x=y=1 σ_x^y  is the golden mean. When x=2,y=1,σ_x^y  is the silver mean. In previous works we introduced the theory of number genetics – a framework of logic within which the golden section is studied. In this work we apply the concept to all proportiones perfectus. Let  be defined as above. Furthermore, let h1 satisfy {█(round(h_1/(σ_x^y ))=w@round(wσ_x^y)≠h_1 ). ┤Now let H'nbe Hn  with h1=1 Again let  be defined as  A robust universal computing machine is herein developed for the purpose of establishing the relationship  h_i=g_(n+i-1)±h_i^',i,n≥1,  which relationship is key to the logic protocol. It is clear therefore that this system of logic presents  as the building block of every  (including itself) within a particular σ_x^y regime. Clearly number genetics takes central place in the proportiones perfectus theory.


1967 ◽  
Vol 31 ◽  
pp. 239-251 ◽  
Author(s):  
F. J. Kerr

A review is given of information on the galactic-centre region obtained from recent observations of the 21-cm line from neutral hydrogen, the 18-cm group of OH lines, a hydrogen recombination line at 6 cm wavelength, and the continuum emission from ionized hydrogen.Both inward and outward motions are important in this region, in addition to rotation. Several types of observation indicate the presence of material in features inclined to the galactic plane. The relationship between the H and OH concentrations is not yet clear, but a rough picture of the central region can be proposed.


Paleobiology ◽  
1980 ◽  
Vol 6 (02) ◽  
pp. 146-160 ◽  
Author(s):  
William A. Oliver

The Mesozoic-Cenozoic coral Order Scleractinia has been suggested to have originated or evolved (1) by direct descent from the Paleozoic Order Rugosa or (2) by the development of a skeleton in members of one of the anemone groups that probably have existed throughout Phanerozoic time. In spite of much work on the subject, advocates of the direct descent hypothesis have failed to find convincing evidence of this relationship. Critical points are:(1) Rugosan septal insertion is serial; Scleractinian insertion is cyclic; no intermediate stages have been demonstrated. Apparent intermediates are Scleractinia having bilateral cyclic insertion or teratological Rugosa.(2) There is convincing evidence that the skeletons of many Rugosa were calcitic and none are known to be or to have been aragonitic. In contrast, the skeletons of all living Scleractinia are aragonitic and there is evidence that fossil Scleractinia were aragonitic also. The mineralogic difference is almost certainly due to intrinsic biologic factors.(3) No early Triassic corals of either group are known. This fact is not compelling (by itself) but is important in connection with points 1 and 2, because, given direct descent, both changes took place during this only stage in the history of the two groups in which there are no known corals.


2020 ◽  
Vol 43 ◽  
Author(s):  
Thomas Parr

Abstract This commentary focuses upon the relationship between two themes in the target article: the ways in which a Markov blanket may be defined and the role of precision and salience in mediating the interactions between what is internal and external to a system. These each rest upon the different perspectives we might take while “choosing” a Markov blanket.


2019 ◽  
Vol 42 ◽  
Author(s):  
Paul Benjamin Badcock ◽  
Axel Constant ◽  
Maxwell James Désormeau Ramstead

Abstract Cognitive Gadgets offers a new, convincing perspective on the origins of our distinctive cognitive faculties, coupled with a clear, innovative research program. Although we broadly endorse Heyes’ ideas, we raise some concerns about her characterisation of evolutionary psychology and the relationship between biology and culture, before discussing the potential fruits of examining cognitive gadgets through the lens of active inference.


Author(s):  
Robert M. Glaeser

It is well known that a large flux of electrons must pass through a specimen in order to obtain a high resolution image while a smaller particle flux is satisfactory for a low resolution image. The minimum particle flux that is required depends upon the contrast in the image and the signal-to-noise (S/N) ratio at which the data are considered acceptable. For a given S/N associated with statistical fluxtuations, the relationship between contrast and “counting statistics” is s131_eqn1, where C = contrast; r2 is the area of a picture element corresponding to the resolution, r; N is the number of electrons incident per unit area of the specimen; f is the fraction of electrons that contribute to formation of the image, relative to the total number of electrons incident upon the object.


Author(s):  
D. F. Blake ◽  
L. F. Allard ◽  
D. R. Peacor

Echinodermata is a phylum of marine invertebrates which has been extant since Cambrian time (c.a. 500 m.y. before the present). Modern examples of echinoderms include sea urchins, sea stars, and sea lilies (crinoids). The endoskeletons of echinoderms are composed of plates or ossicles (Fig. 1) which are with few exceptions, porous, single crystals of high-magnesian calcite. Despite their single crystal nature, fracture surfaces do not exhibit the near-perfect {10.4} cleavage characteristic of inorganic calcite. This paradoxical mix of biogenic and inorganic features has prompted much recent work on echinoderm skeletal crystallography. Furthermore, fossil echinoderm hard parts comprise a volumetrically significant portion of some marine limestones sequences. The ultrastructural and microchemical characterization of modern skeletal material should lend insight into: 1). The nature of the biogenic processes involved, for example, the relationship of Mg heterogeneity to morphological and structural features in modern echinoderm material, and 2). The nature of the diagenetic changes undergone by their ancient, fossilized counterparts. In this study, high resolution TEM (HRTEM), high voltage TEM (HVTEM), and STEM microanalysis are used to characterize tha ultrastructural and microchemical composition of skeletal elements of the modern crinoid Neocrinus blakei.


Author(s):  
M.J. Murphy ◽  
R.R. Price ◽  
J.C. Sloman

The in vitro human tumor cloning assay originally described by Salmon and Hamburger has been applied recently to the investigation of differential anti-tumor drug sensitivities over a broad range of human neoplasms. A major problem in the acceptance of this technique has been the question of the relationship between the cultured cells and the original patient tumor, i.e., whether the colonies that develop derive from the neoplasm or from some other cell type within the initial cell population. A study of the ultrastructural morphology of the cultured cells vs. patient tumor has therefore been undertaken to resolve this question. Direct correlation was assured by division of a common tumor mass at surgical resection, one biopsy being fixed for TEM studies, the second being rapidly transported to the laboratory for culture.


Author(s):  
T. G. Naymik

Three techniques were incorporated for drying clay-rich specimens: air-drying, freeze-drying and critical point drying. In air-drying, the specimens were set out for several days to dry or were placed in an oven (80°F) for several hours. The freeze-dried specimens were frozen by immersion in liquid nitrogen or in isopentane at near liquid nitrogen temperature and then were immediately placed in the freeze-dry vacuum chamber. The critical point specimens were molded in agar immediately after sampling. When the agar had set up the dehydration series, water-alcohol-amyl acetate-CO2 was carried out. The objectives were to compare the fabric plasmas (clays and precipitates), fabricskeletons (quartz grains) and the relationship between them for each drying technique. The three drying methods are not only applicable to the study of treated soils, but can be incorporated into all SEM clay soil studies.


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