All great designs are driven by a motivator. A single or series of entities prompt the

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1 The Driving Force: Mathematics or the Universe? All great designs are driven by a motivator. A single or series of entities prompt the development of the design, shaping and influencing the end product. An individual, a tool, a simple idea all serve as potential motivators. Now, extend the argument by likening this motivator-design concept to mathematics and the universe. Individuals began studying mathematics in terms of what was already known within the universe, thus assigning the universe to the role of motivator with mathematics serving as its design canvas. However, passing time prompted a transition in thought, suggesting that mathematics served as the motivator for the progress of the universe. The Babylonians, Egyptians, and Indians were some of the earliest civilizations to contribute to the history of mathematics. They relied principally on methods of induction, conducting experiments with a preference for concrete solutions. Babylonian and Egyptian mathematics was prompted largely by a need to survey plots of settled land for agricultural and taxation purposes. i Body parts such as the palm and forearm were used as tools of measurement for land and buildings, and written numbers were expressed as pictures of common items. ii The former measurement method was most likely adopted for convenience sake, however, the latter choice signifies a deeper implication. One can speculate that the pictorial method was chosen to function as a visual aid for comprehension purposes. For instance, the lotus plant was chosen to represent the thousands, as seen in Figure 1. Figure 1: Ancient Egyptian Numerals. Each value is represented by a picture of an object found in the physical world. ii

2 The choice of the lotus plant is perhaps attributed to the nature of its abundance. Thus, the Ancient Egyptians see the symbol and associate it with a thousand, possessing an inherent understanding of the quantity behind the value. Relating a mathematical representation to the physical universe helped promote understanding and clarity by establishing a link between the unfamiliar and familiar, respectively. The Ancient Greeks served a prominent role in the development of early mathematical concepts. Thalus of Miletus, notable Greek philosopher and mathematician, had a simple motivation. As described by Aristotle, to Thalus the primary question was not what do we know, but how do we know it. 1iii Thalus of Miletus is credited with devising a way to determine the height of a pyramid by comparing the length of its shadow to that of another vertical object at the same instant. His discovery is illustrated in Figure 2. iv Figure 2: Determining the Height of a Pyramid. Thalus corresponded the length of each entity's shadow with each entity's height to determine the height of the pyramid. Certain accounts of Thalus discovery indicate that he used methods of induction to arrive at his conclusion, namely by measuring the shadow of the object at the time when a body and its shadow are equal in length. 2v However, Thalus is credited by others as employing deductive 1 Aristotle. 384 BC 322 BC. [extraction information in end notes] 2 Pliny the Elder. 23 AD 79 AD. [extraction information in end notes]

3 methods, able to state the height of a pyramid without trouble or the assistance of any instrument. 3v The latter accounts are an early indication of a transition in thinking - relying not on experimentation, but rather, on known mathematical principles to dictate discoveries. This deductive reasoning, in turn, set the basis for geometrical proofs. Thus, conclusions about the characteristics of an entity were drawn based on geometrical principles. The roles of unfamiliar and familiar are gradually shifting, and mathematics has stepped up to serve as the driving force of understanding of the universe. Plato s contributions to the mathematical and philosophical worlds can be summarized as Platonism. Platonism is a form of realism that is partially derived from Pythagorean philosophy or geometry, as known today. vi Geometrical proofs were said to be inarguable and eternal, independent of the actions of human beings. vii Plato s assertions imply that mathematics was the beginning and served as the foundation on which the universe was built. Neither humans nor divine powers altered the natural form of mathematics but rather used, and currently use, it as a tool. This is further supported by Plato s claim, the creator god uses mathematics to fashion the world. 4viii Platonism influence fed into the modern notion of the Universe Ensemble. ix Coined by Max Tegmark, the Universal Ensemble Theory proposes that all mathematical entities possess a physical counterpart. ix By extension, each entity assignment prompts a heightened understanding of the physical world. The swapped roles of familiar and unfamiliar further solidifies mathematics new role as the driving force of the universe. 3 Plutarch. 45 AD-120 AD. [extraction information in end notes] 4 Plato. Classical Athens. [extraction information in end notes]

4 Assessing familiarity is integral in assigning the roles of motivator and design. The dawn of mathematics prompted individuals to employ the universe as the source of understanding. However, as time passed and they became more in tune with the mathematical world, and arguably less so with the physical one, the source of understanding switched. This begs the question Is one role more dominant than the other? The influential nature of the motivator argues for itself, but the mere existence of the design is required for the motivator to even serve a purpose. Perhaps mathematics is the tool required for the universe to function, but the universe serves as the vessel for mathematics to take form. The two entities never served with varying levels of intensity, but rather, were always equally codependent and coexistent. The transition in roles is noted and apparent but at all times were equally as significant. i Sumerian/Babylonian Mathematics - The Story of Mathematics. (n.d.). Retrieved September 5, 2016, from ii "Egyptian Mathematics - The Story of Mathematics. (n.d.). Retrieved September 4, 2016, from iii Ji, Shanyu. Thales, the Originator of the Deductive Method. History of Mathematics, Math 4388, 1 September 2016, University of Houston, Houston, TX. Lecture. iv Michon, G. (n.d.). Ancient Answers Gérard P. Michon, Ph.D. Retrieved September 7, 2016, from v Thales of Miletus. Retrieved September 6, 2016, from vi Plato. (Retrieved September 6, 2016, from idealism.htm

5 vii Internet Encyclopedia of Philosophy. Retrieved September 5, 2016, from viii Ji, Shanyu. Plato and His Academy. History of Mathematics, Math 4388, 5 September 2016, University of Houston, Houston, TX. Lecture. ix Tegmark, M. Is the theory of everything merely the ultimate ensemble theory? Retrieved September 4, 2016, from

Math Number 842 Professor R. Roybal MATH History of Mathematics 24th October, Project 1 - Proofs

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