Hard
Simulation Argument Feasibility
Analyze the probability and feasibility of the Simulation Hypothesis.
Provide a rigorous theoretical analysis of the Simulation Hypothesis. Discuss the trilemma presented by Nick Bostrom, evaluate the computational requirements required to simulate a universe indistinguishable from reality, and argue whether statistical probability favors us living in a base reality or a simulation.
Hard
Many-Worlds Interpretation Analysis
Explore the implications of the Many-Worlds Interpretation of quantum mechanics.
Explain the Many-Worlds Interpretation (MWI) of quantum mechanics without collapse of the wavefunction. Compare and contrast it with the Copenhagen interpretation, specifically addressing the problem of definite outcomes and the ontological status of the 'branching' worlds.
Medium
Post-Scarcity Economic Models
Design a theoretical economic framework for a post-scarcity society.
Theorize the fundamental structure of an economy in a post-scarcity society where physical goods and energy are virtually unlimited. How are resources allocated if price mechanisms are obsolete? Discuss the role of non-material currencies such as reputation, social capital, or time.
Hard
Maxwell's Demon Entropy Paradox
Resolve the theoretical paradox of Maxwell's Demon regarding the Second Law of Thermodynamics.
Explain the thought experiment known as Maxwell's Demon. Analyze how this being appears to violate the Second Law of Thermodynamics by decreasing entropy without work. Provide a detailed resolution to the paradox that incorporates information theory and Landauer's principle.
Hard
Implications of Gödel's Incompleteness Theorems
Discuss the impact of Gödel's theorems on the foundations of mathematics.
Describe Gödel's First and Second Incompleteness Theorems. Discuss their profound implications for the limits of axiomatic systems and Hilbert's Program. Can all mathematical truth be captured by a formal system, or are there inherent limits to what can be proven?
Medium
Sapir-Whorf Hypothesis Evaluation
Evaluate the strong and weak versions of linguistic relativity.
Compare and contrast the strong (linguistic determinism) and weak (linguistic relativity) versions of the Sapir-Whorf hypothesis. Provide examples of how language structure might influence cognitive processes such as color perception, spatial orientation, or gender association.
Medium
Orthogonality Thesis in AI
Examine the relationship between intelligence and final goals in artificial agents.
Define and analyze the Orthogonality Thesis which suggests that high intelligence does not imply any specific final goal. Discuss the implications of this thesis for AI safety, specifically focusing on the difficulty of aligning a superintelligent AI with human values without constraining its capabilities.
Medium
Coase Theorem and Externalities
Analyze the theoretical conditions required for the Coase Theorem to hold.
Explain the Coase Theorem regarding the efficiency of private bargaining in the presence of externalities, regardless of the initial allocation of property rights. Identify the critical theoretical assumptions (zero transaction costs, well-defined property rights) and discuss why the theorem often fails in real-world applications.
Medium
Rawls' Veil of Ignorance
Apply the veil of ignorance to modern social justice issues.
Elaborate on John Rawls' concept of the 'original position' and the 'veil of ignorance.' Apply this thought experiment to a contemporary policy issue (e.g., wealth tax or healthcare access). Determine what principles of justice rational agents would choose if they did not know their place in society.
advanced
The Simulation Argument
Explore the probabilistic arguments regarding whether we live in a computer simulation.
Elaborate on Nick Bostrom's Simulation Argument. Discuss the trilemma: civilizations go extinct before reaching post-human stage, civilizations have no interest in running simulations, or we are almost certainly living in a simulation. Analyze the statistical probabilities and the implications for reality.
medium
The P vs NP Problem
Discuss one of the most important open problems in computer science.
Explain the P vs NP problem in detail. Define complexity classes P and NP. Provide examples of problems in P (e.g., sorting) and NP-complete problems (e.g., traveling salesman). Discuss the implications if P were equal to NP versus if they are distinct.
medium
Nash Equilibrium in Non-Cooperative Games
Analyze the concept of Nash Equilibrium within game theory.
Define the Nash Equilibrium. Explain how it represents a state where no player can benefit by changing strategies while other players keep theirs unchanged. Provide a concrete example using the Prisoner's Dilemma to illustrate the concept.
hard
Fundamentals of String Theory
Theoretical framework in which point-like particles are replaced by one-dimensional objects.
Provide an overview of String Theory. Explain the transition from standard model particles to vibrating strings. Discuss the requirement of extra dimensions (10 or 11) and how different vibration modes correspond to different particles.
easy
Act vs Rule Utilitarianism
Compare and contrast two major branches of utilitarian ethical theory.
Define Utilitarianism broadly as maximizing utility. Contrast Act Utilitarianism (assessing each act individually) with Rule Utilitarianism (following rules that generally maximize utility). Provide a scenario where these two approaches yield different moral conclusions.
medium
Cantor's Infinities
Explore the concept of different sizes of infinity.
Explain Georg Cantor's diagonal argument. Describe how he proved that the set of real numbers is uncountably infinite, strictly larger than the set of natural numbers. Discuss the concept of cardinality and the continuum hypothesis.