The seasons are related to the relation of the sun relative to the axis of the earth, and at the equator the daily rhythm of day and night is exactly 12 h, and varies north and south from there, while the seasonal variation, which disappears at the equator picks up on both sides until one has maximum variation at the poles. In northern and southern regions the sine (or cosine) curves would be shifted up or down relative to the line. Day and night, for example, have to do with the amount of sunlight daily which could be so portrayed, though once one has passed the "no sunlight" point one would have to think of darkness, I suppose, which is a bit of a strain. It is not obvious to me that all of these periodic regularities are best portrayed this way, but in general they can be so portrayed. Commenting on Whitehead’s use of periodic functions in expressing events like day and night, the seasons as well as tides, Ian Winchester writes: “Both sines and cosines can be portrayed as an undulating line above and below passing regularly through a straight line, usually a horizontal one. But this would have been impossible, unless mathematicians had already worked out in the abstract the various abstract ideas which cluster round the notions of periodicity … Then, under the influence of the newly discovered mathematical science of the analysis of functions, it broadened out into the study of the simple abstract periodic functions which these ratios exemplify” (p. Later, when writing of the development of science in the 16th and 17th centuries (1953), he states that: “The birth of modern physics depended upon the application of the abstract idea of periodicity to a variety of concrete instances. The concept of a periodic function is Whitehead ( 1958a, b) preferred method of expressing these formal abstractions on the basis of “a sum of sines … called the ‘harmonic analysis’ of the function … process of gradual approximation” capable of analyzing such events as the relationship between “the tide-generating influences of one ‘period’ to the height of the tide at any instant” (pp. Whitehead himself (1958) calls attention to the importance of spatial intuitions despite their logical independence from the mathematical science of geometry (pp. ![]() Desmet goes further, arguing that, “his ultimate drive was … to unify the mathematical structures underlying the analogical reasonings that constitute the art of physics, an art which his Cambridge training impressed on him” ( 2010b, p. The emergence of mathematics involves the direct pattern recognition that is proper to our sense perception … is inseparably tied to our feeling of space, and because our space-intuition is so essential an aid to the study of geometry, it seems as if geometry cannot be part of pure mathematics” ( 2010a, p. As Ronny Desmet points out: “According to Whitehead, mathematics is the study of relational structures or patterns. Hardy remarked that “A mathematician, like a painter or a poet, is a maker of patterns … The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful the ideas, like the colours or the words, must fit together in a harmonious way. For a critique of Newton’s attempt to exclude hypotheses from “experimental philosophy,” see Carey ( 2012). ![]() Thus any account of meaning that limits thought to the empirical is bound to break down just as it approaches the metaphysical” (p. Winchester ( 2000) observes that Whitehead was engaging in a critique of the limitations of the empirical or scientific method: “Because of the omnipresence of the metaphysical there are limits to the employment of the empirical method here. We can never catch the actual world taking a holiday from their sway” (p. ![]() While metaphysical first principles can always be questioned, they are open to human experience: “There is no first principle which is in itself unknowable, not to be captured by a flash of insight … The elucidation of immediate experience is the sole justification for any thought and the starting point for thought is the analytic observation of components of this experience.” As a result, “metaphysical first principles can never fail of exemplification. In Process and Reality (1929a), he reasserted that it is the “general success” of first principles, not their “peculiar certainty or initial clarity,” which is the goal of rational thought, since “even in mathematics the statement of the ultimate logical principles is beset with difficulties, as yet insuperable” (p. At the same time, Whitehead recognized that in practice science advances despite imprecise calculations and laws that are open to question-“so, after all, our inaccurate laws may be good enough” (1958, p.
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