Wolfram, Stephen

computer scientist, mathematician, theoretical physicist; founder and CEO of Wolfram Research, creator of Mathematica, Wolfram|Alpha, and the Wolfram Language; his second appearance on the podcast, focused on the newly launched Wolfram Physics Project

Stephen Wolfram: Fundamental Theory of Physics, Life, and the Universe

Lex Fridman Podcast · Sep 15, 2020

• Stephen Wolfram
• Wolfram Physics Project
• computational irreducibility
• hypergraph
• causal invariance
• general relativity
• quantum mechanics
• principle of computational equivalence
• metamathematics
• Ruliad

Core ideas

Wolfram frames the Wolfram Physics Project as an attempt to find a small, simple computational rule that, run enough times, generates everything in the universe — space, time, matter, and physical law — from a lower-level "machine code" beneath both. His starting assumption breaks with a 2,000-year-old tradition (from Euclid through Newton and Einstein) that treats space as continuous: instead, space is made of discrete "atoms" connected only by relationships (a hypergraph, a generalization of a graph where edges can connect any number of nodes), with no inherent coordinates — akin to knowing only a social network's connections, not anyone's address. Time is the repeated application of a simple rewriting rule to this hypergraph ("if you see this small pattern, transform it into this other pattern"), applied wherever it matches, in essentially arbitrary order; matter and particles are simply distinctive knotted structures within the same hypergraph, with roughly only 1 part in 10^120 of all its activity corresponding to anything we'd recognize as physically notable — the rest maintains the "infrastructure" of space itself.

The central technical payoff is deriving, rather than merely modeling, the two pillars of 20th-century physics. Special relativity emerges from "causal invariance" — the property (familiar from simpler cases like sorting a string or multiplying out algebraic terms) that no matter what order you apply the rewriting rule in, you get the same underlying "causal graph" of dependencies between events, which Wolfram argues is why it doesn't matter which reference frame an observer chooses. General relativity emerges by defining an analog of curvature for a hypergraph (based on how the "ball" of points reachable within N steps grows, analogous to circle area on a curved surface deviating from πr²): given causal invariance, computational irreducibility, and finite dimensionality, this curvature is claimed to obey Einstein's equations, with energy and momentum interpretable as the flux of causal edges through space-like slices, from which E=mc² also falls out. Quantum mechanics is handled via a "multiway graph" of all possible branchings and mergings of rule applications; a new "branchial space" (the space of quantum states, with distance corresponding to entanglement) turns out to obey the same underlying deflection mathematics as spacetime curvature — meaning general relativity and quantum mechanics, in Wolfram's account, are "facets of the exact same theory." He extends this to explain the double-slit experiment (destructive interference as two branches ending up unmergeable in branchial space), the quantization of particle spin (an emerging, not-yet-finished derivation involving directed vs. undirected hypergraphs and homotopy groups), and the boson/fermion distinction (merging vs. branching behavior in the multiway graph).

Wolfram repeatedly grounds all of this in "computational irreducibility" — his 1990s-derived Principle of Computational Equivalence, holding that almost any sufficiently complex computational process (a brain, the weather, physics itself) is exactly as computationally sophisticated as any other, so there is generally no shortcut to predicting outcomes short of running the process step by step. Science, in his framing, has always worked only within scattered "pockets of computational reducibility" (the motion of planets was crackable; who wins a battle was not); he applies this directly to COVID-19, arguing the pandemic exposed a mismatch between public expectations that "science" can always deliver a definite predictive answer and the reality that many real-world systems are irreducibly complex, requiring step-by-step simulation rather than clean prediction. He treats this irreducibility as reassuring rather than bleak — a mathematical guarantee that neither individual lives nor the universe are "boring," since nothing (not even a hypothetical superintelligence) can jump ahead and already know the outcome.

Extending the same computational framework beyond physics, Wolfram describes a "Ruliad" — the multiway graph generated by applying not just one rule but every possible rule — arguing that because of causal invariance, an observer's choice of physical laws is really just a choice of "reference frame" within this larger structure, meaning radically different intelligences (aliens, or even a description of "what the weather is doing") could describe the same underlying computational reality in mutually incomprehensible ways. He connects this to "metamathematics" — modeling all of mathematics itself as paths through a multiway graph of theorems derived from axioms (illustrating with an analysis of Euclid's 465 theorems, finding the existence of the five Platonic solids to be the "hardest," at 33 proof-steps from the axioms) — and speculates that deep abstract mathematical structures like higher category theory's "univalence axiom" are mathematically equivalent to his physical causal invariance. He also notes surprising cross-domain resonances: connections between his causal-graph formalism and blockchain-style distributed ledger reconciliation, and between automated theorem-proving's "critical pair lemmas" and branch pairs in his multiway graphs, which he attributes to the extreme minimality of the underlying model (comparing it to how simple cellular automata rules end up modeling everything from traffic flow to epidemiology). Asked to comment on Eric Weinstein's independent unification efforts, Wolfram says Weinstein's gauge-theory-centered approach isn't obviously wrong and might connect to features (like local gauge invariance) that Wolfram's own models are close to explaining, while noting skepticism that Weinstein has advanced much past his decades-old PhD thesis.

On why fundamental physics fell out of fashion as a research priority (his analogy: after early bursts of "we're almost there" optimism — Greek atomism, Newtonian gravity, Maxwell's fields — physicists concluded the problem was simply too hard and moved on to already-productive "higher-level" physics), Wolfram compares his hoped-for impact to Copernicus: not primarily practical, but a shift in what people are willing to trust mathematics/computation to tell them even against common sense. He's cautious but intrigued about downstream engineering implications (speculative ideas like "spacetime tunnels" or a "vacuum cleaner" manipulating the energy density that maintains space's structure to produce repulsive gravity), comparing current skepticism about engineering the fabric of reality to 20th-century skepticism about high-speed data transmission over copper wire. He closes on the question of why the universe exists at all, offering a tentative answer modeled on Gödel's second incompleteness theorem: that no entity embedded within the universe can, from within it, establish or prove why the universe exists — an undecidable question by construction — while still finding this compatible with human meaning and specialness, since in his framework there's no more "impressive" alien or superintelligence lurking beyond us, only different, computationally equivalent instances of the same underlying computation.

Excerpts