Mining the Computational Universe: Stephen Wolfram on What AI Can and Can't Be Told to Do

Wolfram opens with a 2009 story about showing Wolfram Alpha to Marvin Minsky, a friend who had seen question-answering systems for years. Minsky was unimpressed at first, but Wolfram told him this time it actually works on real questions. It took about five minutes for Minsky to realize it was useful, and Wolfram demonstrates with queries such as the ratio of MIT students to Cambridge's population.

Making that work needs natural-language understanding, data sources and the ability to compute from data. His surprise was that the critical piece of language understanding turned out to be knowing a lot about the world, with the parsing itself secondary. A query about the International Space Station needs radar-derived orbital elements and celestial mechanics to say when it will next rise over Boston.

He describes this as deliberately "cheating" relative to earlier AI. Instead of reasoning like people did in natural philosophy, the system uses the last 300 years of exact science: solve the differential equations of motion and get the answer. As a kid he was interested in AI, and around 1980 he concluded you would have to build something like a brain, but later realized mere computation was sufficient.

To build Wolfram Alpha he visited a reference library and set out to automate answering questions from all that knowledge, working through a few thousand domains. He did not start from a grand ontology but worked up from hundreds, then thousands, of working domains, building shared frameworks as themes emerged. The core system is about 15 million lines of Wolfram Language code plus terabytes of data.

Wolfram live-demos the Wolfram Language, which began with Mathematica in 1988. It is symbolic, so a graph, an image or a variable is just a piece of data to compute on, and so is something like Boston. Natural-language input is interpreted into precise symbolic code, and he plots a path between Bostons, including one in the Philippines, and builds a shortest tour of South American capitals.

He calls the approach knowledge-based programming. Most languages have a few primitives tied to what a machine can do, plus libraries; his crazy idea has been an integrated system with knowledge and algorithms for many domains built in coherently. He shows it spanning geography, 3D bone meshes and anatomy data, saying keeping the design coherent has been the story of his last thirty years.

On machine learning, he identifies a picture of a giant panda in a few hundred milliseconds, lists runners-up, and drills into the net, which is represented symbolically on top of MXNet. He truncates the net after ten layers to inspect the intermediate representations, and then trains a LeNet on a sample of MNIST digits starting from random weights. He is showing a version due out the following week.

Zooming out, Wolfram asks what is possible in principle with computation. To model something you need definite rules, and the most general way to write rules is a program, so he asks what the space of all possible programs looks like. He chose cellular automata, a very simple kind of program in which a row of black and white cells updates by looking at each cell and its neighbors.

Of the 256 possible rules of this type, many are trivial; one rule just spreads black cells, and a few make nested patterns. Then comes his "all-time favorite science discovery", rule 30. Starting from a single black cell, it makes a big complicated pattern, regular on one side, and the center column is for all practical purposes random.

The center column was used as the random number generator in Mathematica and the Wolfram Language for many years before being retired for a somewhat more efficient one. Wolfram draws two lessons. Even simple programs can have complicated behavior, which matters for modelling nature, and for technology you can just search the computational universe for a program with the property you need, finding a good random generator after searching only a few dozen programs.

Wolfram compares this to mining the natural world: people used magnets before they had a theory of ferromagnetism. Deep learning is a little like this, relying on differentiability to home in on incrementally better solutions, while he has done a lot of exhaustive search across trillions of programs. He applies the same idea to mathematics, enumerating axiom systems to find the simplest one for Boolean algebra.

Human engineering has mostly built things where we can foresee each step, he says, but programs mined from the computational universe can do much more, more efficiently. Optimal sorting networks, for example, look complicated rather than like something built by step-by-step reasoning. The catch is that such results are hard to understand.

The reason is what he calls computational irreducibility, a consequence of the principle of computational equivalence. Once a system's behavior isn't easy to analyze, its computation is probably as sophisticated as it can be, so our brains can't outrun it and jump ahead to the answer. Making the most efficient use of computation will thus inevitably mean running into irreducibility everywhere.

He demonstrates an automated proof, in 102 steps, that the NAND operation is commutative, from the tiny axiom he found for Boolean algebra. The proof graph shows many complicated machine-generated lemmas. He first produced a version of this twenty years ago and completely failed to understand it.

The point of a proof, Wolfram says, is to let humans understand why something is true. Wolfram Alpha can compute an integral in milliseconds, and its step-by-step solution, which he admits is "completely fake", has nothing to do with the internal computation but is a story created for humans. A machine-generated proof is a lousy story; it would be better if one lemma were something Gauss had proved and every textbook contained.

Neural networks are similar. When asked how a net knows a picture is a panda, we might guess eyes and roundness and fur, but it learned its own criteria, optimal for its training, to separate a panda from thousands of other categories. Human languages have maybe 30,000 to 50,000 words that evolved for our world, whereas the network has effectively invented words for distinctions that have nothing to do with ours.

So there is an "ocean of computation" on one side and the things humans know how to think about, expressed in language, on the other. Wolfram sees the Wolfram Language as his best attempt at a bridge: a language a machine can execute directly and one humans can use to think in computational terms. Part of the AI problem, he says, is how to tell AIs what to do, and a precise language is how to access that computation and civilization's accumulated knowledge.

Wolfram describes a recent blog post about a friend's project to send discs representing human achievement on spacecraft, and how hard it is to tell whether something is an artifact at all. He finds it interesting that AI is our first example of an alien intelligence. Questions such as what it is thinking and what its purpose is resemble those we would ask about extraterrestrial intelligence.

His answer to what AI will automate is everything we can describe, but it isn't clear what we can describe. Judgment jobs can be automated; what cannot is deciding what we are trying to do. Looking at a cellular automaton, we can ask what it is trying to do or what its purpose is, and quickly get into a mess.

The principle of computational equivalence says there is no bright line between the computation in our brains and in simple cellular automata, which is what convinced him he could build Wolfram Alpha without a magic bullet of intelligence. He notes that this makes "the weather has a mind of its own" less silly, yet purpose is something that traces back to human history. In his view it makes no sense to talk about automatically generating purpose.

That raises how to tell an AI "please be nice to us humans". He has been interested in a symbolic discourse language, in the spirit of smart contracts, where agreements are written precisely in code rather than legalese, and imagines using the Wolfram Language to write an AI constitution. Natural language can say some things, but complicated ones require more precise symbolic programs.

Answering a question on how Wolfram Alpha unifies knowledge across domains, Wolfram says they have done a couple of thousand domains and each is a gnarly business with its own quirks. He shows a hierarchy of levels of making a domain computable, such as whether meteorite landing sites are strings or canonical geo positions, and the goal is a single canonical representation for everything.

He says it would be lovely to cut humans out of the loop, but that doesn't work, and expert humans who understand the domain are critical. Once enough domains exist, cross-checking becomes possible, and he says Wolfram is the number one reporter of errors in standardized data sources. Basic ingestion can take hours, but a complicated domain made fully computable is probably a year of work.

Asked about influences, he cites Lisp and APL for language design but says he was largely uninfluenced by traditional AI and computational linguistics, which he found he used almost not at all. He explains he came to cellular automata when looking for minimal models of how complexity arises, and his first language, SMP, worked in the opposite direction from reductionist physics. After studying many people, he concludes that moments of inspiration are rare and that discoveries usually come from long, multi-decade paths of small steps.

Asked whether the language could reach philosophy and purpose, Wolfram traces the effort to formalize everyday discourse back to Leibniz, trained as a lawyer, who hoped to reduce legal questions to logic. He says for 300 years almost no one has tried, so the landscape is barren, though he thinks it is not as hard as one might think. A sentence like "I want a piece of chocolate" is mostly describable already, except the "I want" part.

If we hand control to an omnipotent AI with the instruction to "do the right thing", he says, we have no idea what that means, and philosophers have argued about it for two thousand years. Utilitarianism poses the question rather than answering it. He thinks a single golden rule or Asimov-style law for AIs is impossible, perhaps even provably so.

The reasoning is that any system with computational irreducibility will have unintended consequences, so you always need another patch. He compares it to Gödel's theorem, where Peano's axioms need an infinite hierarchy of patches to describe the integers and only the integers. His guess is that AI constitutions will resemble human law, a complicated body that is progressively patched.

Asked what it means for molecules to compute, Wolfram says many kinds of raw material can be programmed to do any computation, and small computers needn't just be shrunken big ones. He imagines algorithmic drugs, molecules that look at a binding site and reconfigure themselves, or decide whether a cell is likely a tumor. Leibniz built a brass calculator that took 30 years, whereas today there may be 10 or 20 billion computers, and he expects eventually everything to be made of programmable stuff.

On searching the space of programs, he says the science is early. Exhaustive search won't miss things you weren't looking for, and Wolfram Language function evaluation, hashing and image processing have partly been made this way. He expects a unification with deep learning's differentiable, incremental approach, perhaps nets that are harder to train but closer to the full computational universe.

Asked how to teach kids about AI, Wolfram says every field now has or soon will have a computational version, so the number one thing is to teach computational thinking. This isn't necessarily writing code, and waves of enthusiasm for teaching coding don't work for most people, much as math education leaves many saying they don't like math. He believes the Wolfram Language is high-level enough that 11- to 13-year-olds can formulate computations, and shows work from his Sunday sessions with middle schoolers, such as the South American tour problem.

A good exercise is choosing the scale of a map from a latitude and longitude. His book for kids doesn't discuss assigning variables until chapter 38. Because computational irreducibility guarantees we'll use things whose insides we can't know, he says we should stop requiring understanding as a criterion; he gained intuition for integrals by using computers to try countless examples.

He finds it a bit disquieting that AIs are creating languages outside our historical one, and that learning one AI's language wouldn't help with the next. He expects machine-learned models of human learners to teach us how to present material, and mentions that a symbolic approach can trace a student's wrong multi-digit sum back to the likely error. A debugging assistant that converses about what the human intended is another goal, and he thinks an AI trained on his three decades of personal data, including every keystroke, could plausibly mimic him.

Prompted by Newton's seashell-on-the-beach quote, Wolfram says calculus is one elegant corner of the computational universe where we can figure out what's going on. Humans have explored a small corner, and everything we care about sits in it. He plays WolframTones, a site that searches programs to generate music, and says composers told him it is a good place to get ideas, the reverse of what he expected.

He describes a feedback loop between what we can describe and what we build: Paleolithic people had no word for table until tables existed. A 1210 AD pattern is the earliest nested fractal he knows of, and art historians wrote about those pieces for years without mentioning the nesting until fractals became a concept about 25 years ago. This is one reason he thinks teaching computational thinking matters, because it adds a new layer of things people can talk about.

He closes on the evolution of purposes. Treadmills and virtual-world goods would be hard to explain to someone from a thousand years ago, and he once found the vision of trillions of uploaded souls playing video games depressing. He then concluded that at any time in history people's activities seem meaningful to them, so purposes can feel meaningful even if they look odd from a different era.