1. In Rubik’s cube discourse, why are the solutions called “god” algorithms or “god-numbers”
Within the Rubik’s Cube (and broader puzzle) community, “God’s algorithm” refers to an optimal solving method—one that always produces the shortest possible solution from any given configuration. The idea is that an all-knowing entity (“God”) could see the perfect route to solve the puzzle in the minimum number of moves.
Historical Notes:The phrase gained popularity in discussions around “God’s number,” which is the maximum number of moves needed to solve the cube from any position (20 moves in half-turn metric, 26 in quarter-turn metric). Once that number was proven, the algorithm that always hits that bound if necessary was called “God’s algorithm.”
Informal Usage: It’s not a formal or religious usage. The term is more of a playful nod to an omniscient perspective—an algorithm that “knows” the absolute optimal path.
2. Any relation to how Einstein (and others?) used “god” in connection with the laws of physics?
Einstein’s “God”
When Einstein used phrases like “God does not play dice,” he was typically referring to the underlying determinism or structure in the laws of physics, rather than a personal deity.“God” in this context alluded to the universe’s governing rules, which Einstein believed were elegantly consistent.
Comparing to “God’s Algorithm”
The Rubik’s Cube usage is much more informal. It hints at an ultimate principle (optimality), but it doesn’t really draw from Einstein’s philosophical or theological implications.Both usages share a metaphorical sense of an ultimate or perfect knowledge, but they operate in different domains: puzzle-solving vs. describing physical reality.
3. How is this related to whether the “god-laws” are (a) empirical, as in science, or (b) formal, as in mathematics?
(a) Empirical Laws in Science
Physical laws are discovered through observation, experiment, and inference. For instance, Einstein’s field equations in general relativity are tested against measurements of planetary orbits, gravitational lensing, etc.If they fail in experiments, scientists must refine or replace them.
(b) Formal Laws in Mathematics
Mathematical “laws” (theorems, proofs) are established through logical deduction within an axiomatic system. They don’t depend on experiments; they rely on consistency with axioms.
God’s Algorithm in the Rubik’s Cube falls into the category of formal problem-solving. It’s grounded in group theory and combinatorics—the “laws” behind it aren’t empirical but logical constraints of the cube’s configuration space.So, “God’s algorithm” sits firmly in the “formal” realm of mathematics and theoretical computer science
4. And is there any relation to the various foundational views of mathematics—(i) Platonism, (ii) Intuitionism, (iii) Constructionism, or (iv) other options?
(i) Platonism
Platonists see mathematical entities (like numbers or group structures) as existing in an abstract realm. “God’s algorithm” could be seen as discovered from this realm, a perfect solution that exists objectively
(ii) Intuitionism
Intuitionists argue that math is a creation of the human mind, focusing on constructive proofs. One might say that the “optimal solution” is only meaningful insofar as we can construct it or approximate it with an algorithm.
(iii) Constructionism
Closely related to intuitionism, constructionism emphasizes building mathematical objects step by step. In that vein, the quest for “God’s algorithm” is a constructive process: we want an explicit procedure that yields the optimal path.
(iv) Other Views (e.g., Formalism)
Formalists see math as manipulations of symbols under given rules. The concept of “God’s algorithm” fits well here too: it’s a statement within the formal system describing the Rubik’s Cube group, and we seek a sequence of symbols (moves) that minimize the path.Overall, the concept of a “God’s algorithm” can be interpreted differently based on one’s philosophical stance. Platonists might say it exists out there to be discovered, while intuitionists might say it’s only “real” once we construct it. Either way, the term “God” is more of a metaphor for perfect knowledge than a literal or religious reference.
5. Have there been interpretations of what Einstein meant by “god”?
Einstein’s Own Statements
Spinoza’s God: Einstein often mentioned that he believed in the “God of Spinoza.” Spinoza’s philosophical view is broadly taken as pantheistic, equating “God” with the totality of nature or the universe’s lawful harmony rather than a personal deity.Hence, for Einstein, “God” was a metaphor for the underlying rational structure, elegance, and consistency in the laws of the universe.
Non-Personal Deity: Einstein explicitly rejected the idea of a personal God who intervenes in daily human affairs.He wrote in letters that he did not believe in a God “who concerns himself with fates and actions of human beings.”Famous Quotes and Their Context
“God does not play dice” This phrase was Einstein’s way of expressing skepticism about the randomness and probabilistic nature of quantum mechanics. He believed the universe had a more deterministic or at least deeper, as-yet-unknown, lawful structure.It did not imply a belief in a personal God but rather an insistence on an orderly universe.
Mixed Interpretations
Religious Interpretations: Some theologians and laypeople initially took Einstein’s words about “God” as support for a traditional theistic stance. However, Einstein’s later clarifications made clear he was not endorsing a personal, interventionist God.
Philosophical/Metaphorical Interpretations: Most modern scholars agree that Einstein’s references to “God” were predominantly metaphors for nature’s laws and the deep sense of wonder he felt when studying the cosmos.
Einstein’s Personal “Religiousness”
Awe and Wonder: While he did not follow an organized religion, Einstein described himself as feeling a “cosmic religious feeling”—an awe at the grandeur and mystery of the universe.He used “God” as a shorthand for that awe-inspiring order, rather than a being with personality or will.
Key Takeaway
Einstein’s “God” is best understood in the context of Spinozistic or pantheistic thought, focusing on the harmony and unity of nature. It was a poetic or metaphorical use of the word “God”—far removed from the typical doctrinal or personal interpretations found in many religions.
Last question series: (1) The notion of “god” and “gods” originated (etymologically?) from supernatural and metaphysical beliefs — beliefs which non-religious people believe to be false. Why choose “god” as the metaphor for the discovered and empirically supported truths of physics? (2) Does it fit any better (or worse) to scientific findings than Dawkins’s “Flying Spaghetti Monster”, or, for that matter, “Beelzebub”? (3) Even if it is just a metaphor for the sense of awe at the universe and its laws, why call that “god”? (4) Doesn’t that make awe a metaphor for the notion of god? (5) Last: since the notion of god(s) in its origin anthropomorphic, hence personal, is it not a mark of an inapt trope if one then has to qualify it with “put I don’t mean a personal or supernatural deity”?
The term “god” has a deep cultural and linguistic resonance. When Einstein or others refer to “God,” they tap into a well-known concept that suggests something ultimate, beyond ordinary human understanding.
Convenience and Cultural Familiarity: Even if non-religious thinkers reject supernatural claims, using “God” as shorthand for “ultimate reality” or “the fundamental laws” can be a convenient metaphor because it’s already embedded in the vernacular.
Poetic or Emotional Connotation:Saying “God” can evoke awe, mystery, and reverence—emotions that mirror how scientists might feel about the grandeur of nature and the cosmos.
The “Flying Spaghetti Monster” was coined satirically to highlight perceived absurdities in certain religious arguments. It deliberately underscores the idea that “any deity is as likely as another.”Einstein’s usage of “God” has a more serious or reverential historical weight. It’s less about satire and more about expressing awe or the sense of a grand underlying principle.
Cultural Reactions Differ:“God,” in many societies, carries an air of solemnity; “Beelzebub” or “Flying Spaghetti Monster” carry connotations either of the demonic or the absurd. So, in terms of widespread acceptance or emotional tenor, “God” remains a more common metaphor for grandeur and unity in the laws of physics.
Historically, philosophical and scientific writings have often co-opted religious or theistic language to express wonder. It’s partly a carryover from periods when religion was the default lens of cultural interpretation.
Connotations of ‘Ultimate’ or ‘Absolute’: Calling it “God” connotes something all-encompassing, a concept that stands in for “the ultimate nature of reality.
”Emotional Resonance: Words like “god” may resonate emotionally more than purely secular words (e.g., “the laws of physics”), especially for expressing profound awe.
Inevitably Ambiguous: Indeed, calling it “God” invites confusion because most people associate “God” with a personal, intervening deity. Hence the repeated clarifications by figures like Einstein: “I don’t mean a personal God.”
Metaphor vs. Literal Meaning:
Metaphors often extend words beyond their literal origins. Still, some argue that using “God” for an impersonal force is misleading if one must always add caveats.
Rhetorical Power vs. Precision:
Pro: Using “God” can evoke a stronger emotional or rhetorical impact.
Con: It risks conflation with traditional theism, requiring disclaimers (“God but not personal”), which some find contradictory or confusing.
Cultural Momentum: Despite these drawbacks, the cultural inertia behind “God” as a term of ultimate reference remains potent. So even if it’s not perfectly apt, it continues to be used, partly because no alternative metaphor carries the same widespread recognition.
Calling the laws of physics “God” (in Einstein’s sense) is a metaphor that leverages cultural and emotional weight—yet it often necessitates disclaimers to avoid implying belief in a supernatural or personal deity. Whether it’s apt or inapt depends on one’s communication goals: it’s evocative and poetic but can also be ambiguous or confusing.
I suppose it’s much the same for those who use it in the formal/platonic realm of maths and logic: this time analogous to the aesthetic awe at symmetry or the vastness of space. Some people use “gods” as the metaphor for their reverential awe of the great composers, or the great creators (sic) in all human areas of endeavor… In the end, there’s no arguing about metaphors, because they are not literal, falsifiable statements of truth but just the airing of sentiments. The anthropomorphic metaphors especially…
Thought about metaphors and reverence in science for a couple of seconds Indeed—metaphors, especially those involving “god” or “gods,” tap into cultural and emotional resonance rather than strict, literal statements. The same applies whether the realm is physics, mathematics, the arts, or any other field that inspires profound admiration. Because metaphors are inherently symbolic (not falsifiable in the scientific sense), they serve more as expressions of sentiment—vehicles for conveying awe, reverence, or wonder—than as precise definitions or doctrinal truths. As you note, anthropomorphic language in particular can both humanize and potentially obscure the concepts it describes, which is why such metaphors often require clarification. Ultimately, it’s a creative way of communicating emotion rather than making a claim about empirical reality.