Murray Gell-Mann has quite a resumé. He discovered/predicted the quark, won the Nobel Prize, founded the Santa Fe institute, and has made amazing advances in explaining the fundamental laws of the universe. The title of his talk is “Nature Conformable to Herself”. And the main theme seems to be beauty.
Gell-Mann tells us that in 1957, he and colleagues put forth a theory of the weak nuclear force that contradicted seven experiments. But it was very beautiful. And it turned out to be right - all seven experiments were proved wrong. What’s striking, he tells us, is that in fundamental physics, a beautiful or elegant theory is more likely to be right than an inelegant theory.
Gell-Mann points out that Einstein was famously indifferent to experiments that contracted his theories. “It’ll go away,” he’d dismiss an experiment that appeared to contradict his work.
What do we mean by beauty and elegance? It’s not a human role - these laws aren’t just the construct of the human mind, they’re really big. Newton believed that natural philosophy was about discovering these laws. A clue that you’re onto a law is that it “can be expressed concisely in terms of mathematics that we already have.” That’s Gell-Mann’s mathematical definition of beauty.
In trying to build laws of the universe, it’s a mistake to think of a “theory of everything”. Any theory that works will be a quantum theory, which means that it will be probabilistic, even if some of those probabilities are near certainty.
In discovering these laws, we’re “peeling the skin of the onion”, using higher levels of energy, getting deeper into particle structures and closer to the fundamental law. As we peel the onion, we see that each layer is similar to its neighbors - they require similar mathematics. “The manifestation of the law at different scales exhibit approximate self-similarity” - Newton called this “Nature Conformable to Herself”
A simple example of this is the self similarity of the inverse square law of gravity and of electricity, as discovered by Coulomb. This self similarity is a form of symmetry, which turns out to be a crucial clue in discovering universal laws. Maxwell’s equations are symmetrical under any rotation of space. Vector analysis made this math much more concise, simplifying these laws through rotational symmetry - you no longer need laws for x,y,z, but just for systems in any dimension or direction. Einstein used another form of symmetry to simplify a complex set of equations down to two equations.
Trying to simplify and generalize these equations further Frank Yang and Bob Mills offered a generalization of Maxwell’s equations. At first they were purely an abstract concept with no specific application. But these equations turn out to give a very beautiful description of the strong and weak force.
Gell-Mann’s point is a very simple one - “the unreasonable effectiveness of certain parts of mathematics in describing physical reality are consequences of the underlying law of elementary particles and their interactions.” He concludes with the statement, “You don’t need something more to explain something more.”
It’s a beautiful sense of certainty about the knowability and harmony of the universe.
Chris Anderson asks Gell-Mann what question, “he’d die to know the answer to.” He explains that he isn’t just concerned with physics - he’s fascinated by the distant relationships between languages. Gell-Mann believes that language is older than the cave paintings found in Europe, “because I can’t believe they did those paintings without language.” Will we ever be able to understand and prove the relationships between these languages?