5.5 Computability of Quantum Morality

5.5.1     Classical Morality is Not Computable

We now prove that classical morality is not computable under certain well-defined conditions and assumptions, like the way other complex or abstract concepts, like classical consciousness or classical intelligence, have been shown to be non-computable. The key challenge lies in formalizing morality into a computable framework and then identifying why classical computational models cannot capture this fully.

Let’s proceed with a general structure to show how classical morality might be proven to be non-computable:

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5.5.1.1      Define Classical Morality

Before we can prove that classical morality is not computable, we need to rigorously define what we mean by morality in a classical setting. This definition should be reducible to a formal model so that we can analyze it through computational complexity theory.

Morality can be thought of as a system of rules, judgments, and principles that guide human decisions and actions. However, to approach it computationally, we must represent moral principles and decision-making in a formal mathematical framework.

For the purposes of this proof, we could adopt a rule-based moral system, where actions and consequences are assessed according to a set of moral rules or norms.

Classical Morality Model

Let’s define classical morality as a function M(x), where:

• x represents a moral dilemma or decision context (a set of inputs describing actions, consequences, agents, etc.).

• M(x) is the corresponding moral judgment or outcome (e.g., whether an action is right or wrong according to the rules).

5.5.1.2       Define Classical Kolmogorov Complexity for Morality

Once we have a formal definition of morality, we can represent the complexity of this moral function using Kolmogorov complexity. Kolmogorov complexity measures the length of the shortest description (program) required to compute a function or solve a problem.

Kolmogorov Complexity of Morality
The classical Kolmogorov complexity C(M(x)) of the moral function M(x) is the length of the shortest classical program p that computes M(x) on a classical Turing machine.

If we can show that no classical algorithm can compute all possible moral judgments M(x) efficiently (or in some cases, at all), then we can argue that classical morality is non-computable.

5.5.1.3      Prove Classical Morality is Not Computable

Now, we attempt to show that there is no classical algorithm that can compute M(x) in general, and that classical morality is therefore non-computable. We can approach this proof by contradiction, similar to the proof techniques used to show non-computability of certain problems in theoretical computer science.

Theorem 15: Classical Morality is Non-Computable

Assumption
Assume there exists a classical computable moral function M(x), which can compute the correct moral judgment for any moral dilemma x.

Proof

1. Universality of Morality:

   • The set of possible moral dilemmas x is extremely large, as morality involves evaluating complex contexts, emotions, relationships, consequences, and long-term effects. There are potentially infinite combinations of moral situations.

   • For any moral rule or system to be complete, it would have to be able to handle all moral dilemmas, no matter how novel, complex, or emotionally nuanced.

2. Complexity of Moral Decisions:

   • Moral dilemmas often involve conflicting principles (e.g., justice vs. mercy, freedom vs. safety). Resolving these conflicts requires understanding context, subjective experience, and the long-term impact of actions.

   • To compute the correct moral judgment, the function M(x) would need to evaluate all possible consequences of actions over time, and assess them against conflicting moral rules.

   • This introduces a combinatorial explosion in the number of evaluations required to compute the correct moral decision for any given dilemma.

3. Uncomputability from Self-Reference

   • Following a technique similar to Gödel’s incompleteness theorem or Turing’s halting problem, we can construct a self-referential moral dilemma that leads to a paradox.

   • Consider a moral rule system that must evaluate whether it is moral to follow its own rules in a given situation. This creates a self-referential loop, where the system must evaluate its own validity.

   • Similar to Turing’s halting problem, this kind of self-reference creates an incomputable loop, because the system would need to infinitely evaluate itself to resolve the dilemma. Therefore, no classical program can fully compute the correct moral outcome for all dilemmas.

4. The Reverse-Logic Loop

   • Assume that the moral function M(x) is computable. This means that for every dilemma x, there is a program that can compute the correct moral judgment M(x).

   • By choosing certain moral dilemmas (such as the self-referential one described above), we can show that this would lead to a contradiction: the program would need to evaluate infinite moral consequences or its own validity.

   • Hence, no classical program can compute M(x) for all possible moral dilemmas, meaning classical morality is not computable.

Conclusion
Since classical morality cannot resolve all moral dilemmas through a classical computable function, classical morality is non-computable. ∎

5.5.1.4      Limitations and Discussion

• Context and Subjectivity: Morality often depends on context, subjective interpretation, and human experience, which makes it difficult to capture in rigid, rule-based systems. This is one reason why classical computation struggles with such tasks.

• Quantum Morality: Although classical morality might be non-computable, it is possible that quantum morality (analogous to quantum consciousness or quantum intelligence) could be computable. A quantum system could represent multiple moral states simultaneously (superposition), resolve conflicts (entanglement), and explore the moral solution space more efficiently (quantum parallelism).

• Moral Uncertainty: Even if morality were computable, there is moral uncertainty due to differing ethical frameworks (e.g., utilitarianism vs. deontology), which could make it impossible for any single algorithm to definitively compute a moral outcome.

5.5.1.5       Extending to Other Moral Frameworks

While this proof assumes a rule-based moral system, it could be extended to other moral frameworks, such as:

• Consequentialism: The challenge of computing all possible consequences makes it non-computable.

• Deontology: Handling complex rules and conflicting duties may lead to similar incomputability.

• Virtue Ethics: Evaluating subjective virtues, which are abstract and context-dependent, also presents computational difficulties.

In summary, classical morality is non-computable because it involves complex, subjective, and self-referential reasoning that cannot be captured by classical algorithms.

5.5.2    The Proof of “Quantum Morality is Computable”

The concept of "quantum morality" is an exciting extension of ideas like quantum consciousness, quantum intelligence, and quantum emotion. While morality is complex and multidimensional, there are ethical theories and mathematical frameworks in classical settings that can potentially be generalized to explore quantum morality.

5.5.2.1      Classical Models of Human Morality

Moral Decision-Making as Optimization

Morality is often modeled as a form of decision-making, where choices are evaluated based on certain ethical rules or principles. For example, in utilitarianism, the goal is to maximize overall utility, which can be framed as an optimization problem:

5.5.2.4    Conclusion

While there is no existing mathematical framework for quantum morality, we can draw inspiration from classical moral models, quantum game theory, quantum decision theory, and quantum information theory. By developing the appropriate formalism, we can explore how quantum computers might process moral decisions, potentially leading to theorems like those for quantum consciousness, intelligence, and creativity.

Mathematical expressions of quantum moral states, quantum moral evolution, and quantum moral entropy provide a foundation for proving whether quantum morality is computable.

5.5.2     Brief Explanation of Why Quantum Morality Is Computable While Classical Morality is Not

The computability of quantum morality versus the non-computability of classical morality stems from the fundamental differences between classical and quantum computation, particularly in how quantum computers can handle superposition, entanglement, and parallelism—features that classical computers lack. Here’s a concise explanation of why quantum morality is computable while classical morality is not:

Key Differences:

1. Superposition and Handling Complex Scenarios:

   • Classical computers can only process one state at a time (sequentially). In moral reasoning, they would need to evaluate every possible moral scenario (or consequence) individually. When moral principles conflict or there are multiple possible outcomes (e.g., justice vs. mercy), a classical computer has to check each path separately, which leads to combinatorial explosion and uncomputability for complex moral decisions.

   • Quantum computers, through superposition, can represent and process many possible moral states at once. They can evaluate a large number of moral scenarios simultaneously, effectively exploring the entire moral decision space in parallel. This feature makes it feasible to compute complex moral decisions in situations where classical computers would be overwhelmed.

2. Entanglement and Resolving Moral Conflicts:

   • In classical systems, resolving conflicts between moral principles (e.g., freedom vs. security) requires evaluating them individually, often leading to paradoxes or moral dilemmas that are hard to resolve computationally.

   • Quantum entanglement allows moral principles or rules to be interconnected in a way that classical systems cannot replicate. In quantum morality, conflicting principles can be quantum-entangled, meaning their evaluation is done in a correlated way. This can resolve conflicts more efficiently by allowing multiple, interdependent moral rules to be evaluated simultaneously and consistently.

3. Quantum Parallelism and Optimization:

   • A classical system, in trying to compute moral decisions, would need to simulate all possible consequences of an action over time, leading to intractable computational costs (in terms of time and resources).

   • Quantum parallelism allows quantum computers to process many possibilities at once, significantly reducing the computational complexity. This ability to evaluate many possible moral outcomes in parallel enables quantum computers to efficiently handle moral decision-making, where classical computers would hit a computational wall.

4. Quantum Measurement and Approximation:

   • Classical computation relies on deterministic results, which is limiting when dealing with subjective or probabilistic elements of moral reasoning.

   • Quantum measurement introduces probabilistic outcomes, which can approximate complex moral judgments without the need for absolute precision. Quantum morality can be computed using quantum systems where approximate answers (such as quantum probabilities) are acceptable for making moral judgments. This flexibility makes it more feasible to compute moral decisions.

5. Reversible Computation and Moral Judgment Loops:

   • Classical computation struggles with self-referential moral dilemmas (similar to Gödel’s incompleteness or Turing’s halting problem), where a moral system must evaluate itself or make judgments about its own rules. This creates infinite loops or paradoxes, rendering classical morality non-computable.

   • Quantum computers use reversible computation, where information is not destroyed and can be "undone." This reversibility allows quantum systems to escape paradoxical loops more easily than classical systems. In quantum morality, reversible quantum computation ensures that moral judgment loops can be computed efficiently without leading to contradictions or non-computability.

Summary:

The magic of quantum computing lies in its ability to handle superposition, entanglement, and parallelism, which allow it to process complex, conflicting, or probabilistic moral decisions efficiently. Quantum morality can be computed because quantum computers can explore multiple moral scenarios in parallel, resolve moral conflicts through entanglement, and approximate moral outcomes using quantum probabilities. In contrast, classical morality is non-computable because classical computers must process moral scenarios sequentially, cannot handle conflicting principles as efficiently, and struggle with paradoxes inherent in moral reasoning.

Quantum computing offers a fundamentally different computational paradigm that makes the complex nature of morality, which stumps classical systems, tractable.