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Historical representation of Galileo’s pendulum depends on the dominant mode of rationality and its strategic suppression of the body. I have already analyzed in the second chapter Koyré’s dry and strictly textual representation of Galileo’s pendulum as typical for the ways in which we know Galileo’s pendulum today. The main aspect of this representation is formal knowledge of a pendulum itself as a discursive sign disassociated from the knowing body. Schematic images of the pendulum, with mathematical formulas and tables of numbers in an abstract space that cannot be touched, made, or performed by a human hand, commonly dominate the space of scientific texts and textbooks today. Thus our knowledge gleaned from these pages remains textual, disembodied , and sexualized. In other words, our knowledge today is rooted in the Christian and Neoplatonic discourse of abstract pleasures, which were appropriated by the seventeenth-century scientist’s subjectivity and disassociated from the body as a matter of personal ethics and of scientific method. Let me proceed with the exposition of the formal structure of Galileo’s pendulum. The dawn of classical physics begins with Galileo’s formulation of the law of free fall. This law claims that the acceleration of a falling body (S) is constant and stands in proportion to the squares of elapsed time (T): S = T2 . The revolutionary significance of this law, according to Kuhn, is the radical change it caused in the perception of the world.1 Since Aristotle, it was assumed that motion in free fall is constant and is a function of the weight of a descending object: heavier objects fall faster than lighter. Renaissance physicists revised this view but still maintained its consistency with sensual perception.2 They claimed that motion in free fall is a function of height; namely, that objects falling from a higher point will drop with more speed than objects from a lower height.3 The relationship between weight and motion and between space and motion is easily and intuitively comprehended. It makes sense to bodily experience that a hundred-pound lead ball will touch 115 F I V E T h e F o r m a l S t r u c t u r e o f G a l i l e o ’ s Pe n d u l u m the ground before a feather will if both are released from the same height and at the same time, or that a dime dropped on one’s head from one foot above will have a different speed than if dropped from the Sears tower. In light of this common-sense comprehension, it appears that speed is a function of weight and/or height. But Galileo’s law of free fall challenges this. “Motion in space,” for Galileo, may have a biased observation that hides a deeper truth about physical reality. “Motion in space” is only a symptom of an essentially temporal reality4 in which free fall is a function of time. Time, as an abstract concept, cannot be directly experienced but only indirectly expressed by mathematics. To know and explain physical reality one therefore has to see and think in mathematical terms. Nature, according to Galileo, is written in a mathematical language.5 Probably the law’s most far-reaching consequence for the future of “classical” and “modern” physics is the realization that time conforms to natural numbers and geometric figures.6 Since motion, velocity, acceleration, and space are temporal categories, it follows that they too must conform to the rules of mathematics. Ironically, Galileo initially believed that nature can never conform to the ideal order of mathematics—only to find himself inventing mathematical physics.7 Once he acknowledged the important role of mathematics in physics, the world of objects became mathematically analyzable , the physical order mathematically reconstructible, the relations of things inferred in ideal terms by axioms and theorems, and these mathematically constructed relations were quantified by measuring.8 The realization is that space traversed through equal time units increases regularly, that is, acceleration increases constantly as do the squares of these units: A falling object descends 16 feet in the first second and 64 feet in the second second. Sixty-four is 4 x 16 feet of acceleration in the second second, meaning that the acceleration increases as does the square of the second time unit, 22 = 4, and so on.9 The rule for the acceleration of a falling body when friction is eliminated, is given in the time...

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