World Solve

Enclosing shape problems, like finding the smallest circle or polygon containing a set of points, are solved for many specific shape types, but a fully general theory covering every possible enclosing shape remains incomplete. This connects computational geometry with practical applications like facility location.

Some philosophical traditions argue meaningful experiences hold deeper value than accumulated possessions, while others see this distinction as less clear-cut than it first appears. This unresolved question shapes broader debates about consumerism and what truly constitutes a fulfilling life.

Genuine altruism seems to require giving without expectation, yet human relationships often naturally involve some sense of reciprocal obligation. This unresolved tension complicates our understanding of charity, friendship, and generosity.

Many people unknowingly benefit from systems built on past or ongoing injustice, and it remains unclear how much responsibility passive beneficiaries bear for addressing that harm. This unresolved question underlies major debates about privilege and structural inequality.

Unconditional love suggests acceptance regardless of behavior, yet moral responsibility seems to require holding loved ones accountable for genuine wrongdoing. This unresolved tension appears constantly in personal relationships and family dynamics.

Free expression is broadly valued as essential to a healthy society, but some speech can contribute to tangible harm, creating an unresolved tension between liberty and protection. This debate remains central to discussions on censorship and hate speech.

If an artificial system behaves as though it's suffering or happy without any confirmed inner experience, it remains unclear whether this simulated behavior deserves any genuine moral weight. This unresolved question is becoming increasingly relevant as AI systems grow more sophisticated.

Many social systems implicitly reward productivity with greater respect or resources, yet most ethical traditions insist human worth shouldn't depend on usefulness alone. This unresolved tension underlies debates about disability, aging, and social value.

Promises are generally treated as morally binding regardless of changing circumstances, but this can sometimes conflict with what seems like the genuinely better or more compassionate choice. This unresolved tension appears throughout personal and contractual ethics.

Competition can drive genuine excellence and innovation, but it also guarantees that some participants will predictably fail through no unique fault of their own. This unresolved tension underlies debates about fairness in education, employment, and markets.

Habits often develop gradually without deliberate intention, raising questions about how much genuine responsibility a person bears for behavior they didn't consciously choose to cultivate. This unresolved question complicates debates over addiction and personal accountability.

Democratic systems generally depend on active citizen participation, yet forcing engagement as a moral duty seems to conflict with respecting individual autonomy and personal priorities. This unresolved tension shapes ongoing debates about civic responsibility.

Languages carry unique cultural knowledge and identity, but preservation efforts sometimes conflict with the practical choices speakers themselves make about which language serves them best. This unresolved tension complicates cultural preservation debates.

Many significant social advances were achieved only after considerable struggle and suffering, raising the unresolved question of whether that cost taints or is separate from the value of the progress itself. This tension shapes how societies remember pivotal historical movements.

Public figures often face harsher scrutiny for behavior that would be judged more leniently in private citizens, and it remains unresolved whether this distinction is genuinely fair or simply a social double standard. This unresolved tension shapes debates over accountability and public trust.

Actively seeking out disagreement can strengthen understanding and reduce bias, but there's no clear consensus on whether this is a genuine moral obligation or simply a personal virtue. This unresolved question touches on intellectual humility and the ethics of belief.

Even societies that claim to reward merit often still allow inherited advantages like family wealth or connections to shape real opportunity. This unresolved tension complicates efforts to build a genuinely fair and merit-based system.

Rare catastrophic events can cause immense damage despite low probability, while everyday risks accumulate steadily but attract far less attention or resources. This unresolved tension complicates how societies and individuals should rationally allocate concern and resources.

Emotional openness is often seen as essential to genuine connection, yet it also exposes people to real potential harm, and no clear consensus exists on how much vulnerability morality actually requires. This unresolved tension shapes both personal relationships and broader social trust.

Symbolic acknowledgment can carry real emotional and social significance, but it's unclear whether it can ever substitute for more substantive forms of repair or restitution. This unresolved tension remains central to ongoing debates about historical accountability.