When examining the medical doctrines of previous empires, they reveal the influence of religion, societal attitudes, and the historical context that influenced the scholars that penned them. The advancements during the Islamic Golden age can be seen in the field of medicine, which had the Greco-Roman medical corpus as their foundation and the source of the theory of the four humors and anatomical beliefs. This paper will analyze the effect of cultural, societal, and historical influences on the medical doctrines of Muslim medieval physicians in the Golden Age and the works of the Roman physician Galen, and demonstrate how these effects result in similarities and differences in medical practice and the understanding of disease and anatomy. Due to translation efforts that were supported by religious views on the accumulation of knowledge and the efforts of the Abbasid empire, resultant acceptance of the theory of the four humors and anatomical doctrines is observed in the treatment and perception of disease, which would consist of this paper's focus on surgery, diet therapy and associations with nature. However, with further analysis of the extent of this acceptance and the findings in the Islamic medical doctrines, the differences in experimental methods, religious interpretations, and cultural attitudes shows a deviation from the Galenic tradition, with the second set of the paper's focus being human dissection, cause of disease, and experimentation. The purpose of this research is to demonstrate the impact of religion, societal attitudes, culture and the accepted paradigm on the practice of medicine and the study of anatomy, and what would cause a challenge against the legacy of Galen.
The coffee cup system can be simplified and modeled by a cart-and-pendulum system. Bazzi et al. and Maurice et al. present two different cart-and-pendulum systems to represent the coffee cup system [1],[2]. The purpose of this project was to build upon these systems and to gain a better understanding of the coffee cup system and to determine where chaos existed within the system. The honors thesis team first worked with their senior design group to develop a mathematical model for the cart-and-pendulum system based on the Bazzi and Maurice papers [1],[2]. This system was analyzed and then built upon by the honors thesis team to build a cart-and-two-pendulum model to represent the coffee cup system more accurately.
Analysis of the single pendulum model showed that there exists a low frequency region where the pendulum and the cart remain in phase with each other and a high frequency region where the cart and pendulum have a π phase difference between them. The transition point of the low and high frequency region is determined by the resonant frequency of the pendulum. The analysis of the two-pendulum system also confirmed this result and revealed that differences in length between the pendulum cause the pendulums to transition to the high frequency regions at separate frequency. The pendulums have different resonance frequencies and transition into the high frequency region based on their own resonant frequency. This causes a range of frequencies where the pendulums are out of phase from each other. After both pendulums have transitioned, they remain in phase with each other and out of phase from the cart.
However, if the length of the pendulum is decreased too much, the system starts to exhibit chaotic behavior. The short pendulum starts to act in a chaotic manner and the phase relationship between the pendulums and the carts is no longer maintained. Since the pendulum length represents the distance between the particle of coffee and the top of the cup, this implies that coffee near the top of the cup would cause the system to act chaotically. Further analysis would be needed to determine the reason why the length affects the system in this way.