Nature is the embodiment of science and mathematics. From Valentine's grouse to Thomasina leaf to human interactions, mathematics transcends the confines of simple numbers and symbols to create models that work to explain the universe. Yet, paradoxically, the most constant form of nature is its unpredictability. In his work Arcadia, Tom Stoppard examines this puzzle: he demonstrates that amidst the rigid structure of patterns and equations, there are unavoidable variables that create chaos that prevents us from fully predicting the future or recreating the past. Through the coexistence of disorder and order in the work, Stoppard incorporates deterministic chaos theory into iterated algorithms to represent the limits of human knowledge. Say no to plagiarism. Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an original essay The laws of Newtonian mechanics dictate a rigid, predetermined structure of the universe. Since an atom lacks many variables in its behavior in space and time, Thomasina states that if you “stop each atom in its position and direction,” then you can obtain a “formula for all the future” (5). So, in the absence of noise or errors, the universe follows Newton's laws; there is a single formula that calculates and returns the exact state of the atom at any time with absolute certainty. The future and the past can be determined. However, aspects of everyday life, “ordinary-sized things,” are susceptible to the “noise” of nature; while attempting to develop a universal formula for sage-grouse population changes, Valentine struggles because “the actual data is messy” (46). The algorithm he wants to acquire is too simple; tries to predict the sage grouse population for a specific moment in time. However, the algorithm can be influenced by a number of natural variables, such as “interference” from “foxes” or “weather” (45). Foxes can decrease the population by half a year, while one rainy season can double it the next. The population of sage grouse at a given time deviates from the expected value of the algorithm and cannot be predicted exactly. Although natural variables may follow the patterns of determinism, each variable follows its own formula; the culmination of these formulas creates uncertainties in the algorithm that destroy the essence of its structure and patterns, creating an unsolvable nonlinear equation. Therefore, Valentine “cannot keep tabs on everything” and his algorithm only needs to provide an extrapolation and generalized estimate of the partridge population each year (46). It can never predict the actual value of the sage grouse population at a specific point in time. In contrast to Valentine's search for an algorithm for nature's grouse population, Thomasina uses her own iterated algorithm to produce her apple leaf. As he plots each point of his equation, he “never knows where to expect the next point” (47). Each recursion results in an unpredictable position for the point. However, over time, after thousands of iterations, he would begin to notice an expanding pattern of the leaf's fractal. Despite the fractal patterns, Thomasina will never know where the next point will be; the patterns can only give her a guess, but the truth will always be unknown. Furthermore, due to the unpredictability of the points, the iterated algorithm can only create patterns that produce the shape of the leaf, but Thomasina will never be able to obtain the complete image and representation of the leaf itself. According to Valentine, models create only a “mathematical object,” which obeys a strict pattern and law (47). Natural leaves.