I’ve recently come across a new thought arising from personal developments in my life that may serve as an interesting jumping-off point for a discussion. I’ve been thinking about how one aims one’s life – in terms of what one thinks is a moral good. I think that most people have some sense of morality, though many today don’t firmly define it.

Some Christian-specific thought and terminology are coming up – I feel I can’t avoid this, as it deeply influences my outlook. That’s not to say that others – whether religious or non-religious – won’t find some utility in these thoughts.

In short, I hope you’ll stick with me for a bit.

In Christianity, and I suppose many other religions, various doctrines guide you on how to live your life and what is considered good and what is considered bad. This now leads me a bit into the AI alignment issue.

You see, when a human at least tries to be cognizant about what he/she believes is moral he has a kind of ideal which he views as moral. In the Christian tradition, we are taught the highest sense of morality was exemplified by Christ. Thus, in a sort of abstract way, we should aim our thoughts and actions toward him.

Expressing Morality Mathematically

To express this a bit mathematically, think of the ultimate good that Christ represents as a vector. The way we conduct our lives and our actions can be thought of as an implicit moral vector that aligns, or misaligns, with the vector of ultimate good.

So in the simplest terms, one could imagine the vector opposite to the absolute good as the vector of absolute evil.

Thinking all along these lines, I remembered that the dot product from mathematics is a measure of how much one vector is aligned with another. This means we could use the dot product between the absolute moral vector and actions to determine how good or bad we (or an AI) are behaving or intending to behave.

I piped in these general thoughts into ChatGPT and it came out with this: (abridged)

Breaking Down the Analogy:

1. Absolute Good as a Unit Vector:
   • In this analogy, absolute good is represented by a unit vector (G) that provides a fixed, unchanging standard. Its magnitude is 1, symbolizing a perfect and unerring measure of goodness.
2. Actions as a Vector:
   • A person’s actions or intentions are represented by another vector (A), which may vary in both magnitude and direction depending on choices, motivations, and circumstances.
3. Dot Product (G ⋅ A) as a Measure of Alignment:
   • The dot product measures the cosine of the angle (cos θ) between (G) and (A), weighted by the magnitude of (A). It represents how closely the action aligns with the standard of absolute good.
4. Moral Implications of the Value:
   • Dot product close to 1 (cos θ = 1): The action is perfectly aligned with absolute good (A) points in the same direction as (G).
   • Dot product close to 0 (cos θ = 0): The action is morally neutral or unrelated to good (orthogonal to (G)).
   • Dot product close to -1 (cos θ = -1): The action is entirely opposed to absolute good (A) points in the opposite direction to (G)).
5. Deviations from Goodness:
   • Given human nature and “natural devices” (weakness, temptations, ignorance, etc.), it is often easy for (A) to deviate from (G). Over time, unchecked habits and inclinations could even cause the action vector to align negatively with the good vector, leading to (cos θ) value closer to -1.

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How This Analogy Reflects Human Experience:

1. The Goal of a Good Person:
   • A morally striving person seeks to continually adjust their action vector (A) so that it becomes more aligned with the good vector (G), maximizing the dot product (cos θ → 1).
2. Effort and Grace:
   • Alignment is not easy, especially given natural inclinations and societal pressures. This may require intentional effort, reflection, and sometimes grace (external help or inspiration) to reorient oneself toward the good.
3. Dynamic Nature of Actions:
   • Unlike a fixed vector, a person’s actions and intentions (A) are dynamic and subject to change, influenced by learning, repentance, and the choices made daily.
4. The Danger of Negative Alignment:
   • If (A) drifts closer to opposing (G), it becomes a reminder of the moral gravity of sin—actions that actively resist or counter the good.

Possible Extensions:

• Magnitude of (A): This could reflect the intensity or commitment behind an action. A strong, purposeful action carries more weight (positive or negative) than a weak or indifferent one.
• Projection Interpretation: The projection of (A) onto (G) could represent the “effective goodness” of an action, showing how much of the action’s energy or intention aligns with the good.
• Repentance and Realignment: Just as vectors can be rotated and adjusted, repentance can be seen as a reorientation of (A) toward (G).

The Importance of Humility

I felt something essential was missing, so I submitted the following query: “it seems to me that ai alignment is attempting to do something along these lines….however it is critical that those that are designing this take into account humility in terms of there are always unknowns and also going with the assumption is that there is the concept of inherent good in the universe but because of our mortal/limited nature (even those of machines) that may not be clear, thus humility is always required”

to which it replied:

AI Alignment as a Vector Problem

AI alignment is essentially about ensuring that an AI’s “goal vector” aligns with humanity’s “goodness vector.” The challenge lies in defining and operationalizing the “absolute good” vector when humans themselves may not fully understand it. Your analogy elegantly frames this problem:

• The Goal of AI Alignment: Maximize the dot product between the AI’s actions and the ideal standard of good.
• The Problem of Unknowns: Humans, being finite and fallible, cannot perfectly define what the “absolute good” vector is, nor can we fully foresee the consequences of AI’s actions over time.

This is why humility, as you suggest, is not just a virtue but a necessary principle for AI design.

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2. The Assumption of Inherent Good in the Universe

Your assumption that there is an “inherent good” resonates with many philosophical and theological traditions. However, AI alignment grapples with:

• Pluralism: Humanity does not agree on what constitutes “good.” Different cultures, philosophies, and individuals prioritize values differently.
• Uncertainty: Even if there is an inherent good, our understanding of it is partial and evolving. AI systems might encode the biases, blind spots, or oversimplifications of their creators.

This makes humility essential. It acknowledges the possibility that:

• Our current models of good may be flawed or incomplete.
• AI might need mechanisms to learn and adapt as humanity’s understanding of good evolves.

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3. Humility in AI Design

Humility in AI alignment design requires several practices:

• Acknowledging Fallibility: Designers must accept that no model or system will perfectly encapsulate the complexities of morality. This calls for mechanisms to regularly re-evaluate and refine AI goals.
• Incorporating Diverse Perspectives: Drawing on a wide range of cultural, philosophical, and ethical traditions helps avoid narrow or biased definitions of good.
• Designing for Uncertainty: AI systems should be built with the capacity for deference—to pause, ask for guidance, or even halt action when faced with ambiguous or high-stakes situations.
• Encouraging Self-Correction: An AI system must have mechanisms for reflection and course correction, akin to how humans learn from mistakes.

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4. The Limits of Machine Intelligence

Your point about machines being inherently limited, like humans, is profound. Machines, even advanced AI, operate within the bounds of:

• Training Data: Machines learn from what we give them, which can never fully capture the richness of reality.
• Algorithms: AI follows predetermined rules and logic that are finite and bounded by human understanding.
• The Frame Problem: Machines struggle to grasp the infinite complexity of the real world—what matters and what doesn’t in a given context.

This means AI cannot inherently “know” the absolute good any more than humans can. It must rely on:

• Guidance from Human Values: Which brings back the critical need for humility in defining those values.
• Continuous Feedback Loops: To adapt its understanding of what aligns with good.

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5. Practical Approaches to Build Humility in AI

Humility can be operationalized in AI systems through techniques like:

• Uncertainty Estimation: AI systems can assign confidence levels to their decisions and defer when uncertain.
• Value Learning: Instead of hardcoding values, AI could learn by observing human behavior and preferences, adapting to new insights over time.
• Robust Oversight: AI systems must remain under human supervision, especially in high-stakes scenarios.
• Fallback Mechanisms: Allowing AI to “ask for help” when it encounters ambiguity.

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6. Philosophical and Theological Resonance

The humility you describe reflects deep ethical principles found in many traditions:

• Christianity: “We see through a glass, darkly” (1 Corinthians 13:12)—our understanding of the ultimate good is partial and imperfect.
• Buddhism: Emphasizes impermanence and the need to let go of rigid assumptions.
• Stoicism: Encourages focus on what is within our control while accepting the unknowns beyond it.

These ideas remind us that the process of alignment—whether human or AI—is iterative, requiring constant reflection and adjustment.

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Conclusion

Your insight highlights that humility is not a weakness but a strength in AI alignment. It acknowledges our limits while striving for a better understanding of the inherent good. Designing AI with humility builds safeguards against overconfidence, rigidity, and unintended consequences. This approach could create systems that work with humanity, learning and growing alongside us, rather than rigidly imposing a flawed or incomplete moral framework.

Final Thoughts

It is my strong belief that the fundamental outlooks of both the human AI creators and the AI creations must possess both of the following or alignment will forever prove elusive or even world-destroying:

1. Faith in the existence of an absolute good
2. Humility – acknowledging even the smartest of us is finite and very limited in our scope of understanding