Kinetic Gas Theory
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We discuss evolution and game theory, and introduce the concept of evolutionary stability. We ask what kinds of strategies are evolutionarily stable, and how this idea from biology relates to concepts from economics like domination and Nash equilibrium.
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The lecture begins with a review of the loop-the-loop problem. Professor Shankar then reviews basic terminology in relation to work, kinetic energy and potential energy. He then goes on to define the Work-Energy Theorem. Finally, the Law of Conservation of Energy is discussed and demonstrated with specific examples.
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Rotating Rigid Bodies, Moments of Inertia, Parallel Axis and Perpendicular Axis Theorem. The moment of inertia for a rigid body around an axis of rotation is introduced, and related to its rotational kinetic energy. Flywheels can be used to store energy. Planets and stars have spin rotational kinetic energy, and the Crab Nebula pulsar is presented as a spectacular example.
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Part 1 - The Good Citizen: Aristotle believes the purpose of politics is to promote and cultivate the virtue of its citizens. The telos or goal of the state and political community is the “good life”. And those citizens who contribute most to the purpose of the community are the ones who should be most rewarded. But how do we know the purpose of a community or a practice? Aristotle’s theory of justice leads to a contemporary debate about g...more
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We continue our discussion of mixed strategies. First we discuss the payoff to a mixed strategy, pointing out that it must be a weighed average of the payoffs to the pure strategies used in the mix. We note a consequence of this: if a mixed strategy is a best response, then all the pure strategies in the mix must themselves be best responses and hence indifferent. We use this idea to find mixed-strategy Nash equilibria in a game within a g...more
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Dr. Daniel Dennett presents the philosophical importance of Darwin's theory of evolution. The lecture is concluded with a panel discussion with Hank Greely and Chris Bobonich.
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This is the first of a series of lectures on relativity. The lecture begins with a historical overview and goes into problems that aim to describe a single event as seen by two independent observers. Maxwell's theory, as well as the Galilean and Lorentz transformations are also discussed.
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In the first half of the lecture, we consider the chain-store paradox. We discuss how to build the idea of reputation into game theory; in particular, in setting like this where a threat or promise would otherwise not be credible. The key idea is that players may not be completely certain about other players' payoffs or even their rationality. In the second half of the lecture, we stage a duel, a game of pre-emption. The key strategic ques...more
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We introduce Game Theory by playing a game. We organize the game into players, their strategies, and their goals or payoffs; and we learn that we should decide what our goals are before we make choices. With some plausible payoffs, our game is a prisoners' dilemma. We learn that we should never choose a dominated strategy; but that rational play by rational players can lead to bad outcomes. We discuss some prisoners' dilemmas in the real w...more
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Professor McBride expands on the recently introduced concept of the wave function by illustrating the relationship of the magnitude of the curvature of the wave function to the kinetic energy of the system, as well as the relationship of the square of the wave function to the electron probability density. The requirement that the wave function not diverge in areas of negative kinetic energy leads to only certain energies being allowed, a p...more
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This lecture introduces students to two broad theories of how the mind relates to the body. Dualism is the ubiquitous and intuitive feeling that our conscious mind is separate from our physical bodies, whereas Materialism is the idea that all of our mental states are caused by physical states of the brain. This lecture reviews arguments explaining why materialism has become the predominant theory of mind in psychology. This discussion is f...more
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