Question

4. Suppose that there is a mathematical pattern that allows one to comprehend the order of...

4. Suppose that there is a mathematical pattern that allows one to comprehend the order of the universe. How would that impact the question of free will and determinism?

5. Are the concepts of free will and determinism mutually exclusive? (or using a term from the course, disjoint)

6. Patterns are used everywhere in this film. For instance the spiral pattern in the coffee creamer, the slinky, smoke, shells and plants. In Chapter 1 of our text, we looked for hidden patterns in number sequences, and (briefly) discussed the Fibonacci sequence and the Golden Ratio, both of which have been (reliably) related to some patterns in nature. How far can this be extended? To life, to the universe? Can this concept be generalized? Is this belief an underlying assumption that makes us study mathematics?

7. Men (or women) risks their minds in pursuit of a dangerous obsession. Is the character of Max (in Pi) a fictionalization of Cantor or Godel (or Boltzmann or Turing for that matter) as described in “Dangerous Knowledge”? Why and/or why not.

8. It has been said that “one problem of mathematics is that you can’t prove it (or even accept it) except on its own terms”. To what extent does this apply to the understanding of this film?

9. How much real math is actually in this film? There is certainly some, the Fibonacci sequence and the Golden Ratio, but there is also lost of numerology. Does this count as mathematics? In your opinion, how much math is really in the film?

10. Aronofsky (the director) used the “hip hop pill montage” to signify the start of each of Max’s migraine headaches. In the montage, extreme camera angles, drastic contrasts in lighting and strange music to create a manic atmosphere until the migraine headache attack is over. The director repeats the same sequence even though the hallucinations are different. Does the pattern, which give the viewer a sense of familiarity with the attacks, work well, or since each attack is unique, would it be better to make each scene different?



Homework Answers

Answer #1

4.

A mathematical model can be developed to comprehend the order of the universe. The "Theory of Everything" is such a similar idea pursued by theoretical physicists, where they try to find an equation which unifies everything.

However, whether or not free exists is debatable and depends completely on the accuracy of the potential mathematical model. For example, the existence of free-will will make the model more complicated with several more possibilities and occurrences. The model could be a complex algebraic structure with several operations defined on it.

Else if the free will is non-existant and deterministic, the before the development of the model, we need to investigate the direction of flow of events and the definite causes for them.

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