On Not Knowing God's Thoughts

After I had spoken my peace with comment about induction in science, the thoughts pouring through my head meant that I was only half-listening to the comments that followed. Yet I was trying to pay attention as they were on the same topic.

Out of the noise that followed, one comment leapt out at me and stuck deep into me. It was made by an Israeli woman named Norma, who was the only woman in attendance this time. She was from a generation older than me, and there was something beautiful about how we almost never saw her full face, as her laptop screen camera was aimed at the wrong angle. Mostly I just saw her hair.

There is an almost built-in Luddite nature of physics. We are among the last to adopt any kind of communication technology. The last time I had given a talk, for example, physicists were using overhead slide transparencies, which are ideal for science, as one can write directly on them during the lecture using a Dry-Erase marker. Two years ago when I came back to the field I was saddened to see that physics had succumbed to the digital revolution, with Powerpoint and PDFs. Something had been lost, but there was no fighting it.

Norma was agreeing with some of the points I had made. What truly got to me was something almost out of the blue. I wish I remembered the exact wording. It was something like: "the universe does not have to follow mathematical laws."

It was not the first time I had heard this remark, but for the first time in my life I think I understood it deeply. But at last I was ready to hear it. It almost staggered me, the realization of what it implied.

In the minutes and hours that followed, the realization came to me. Like all  physicists, I had been predisposed to the notion that of course the universe follows mathematical laws. The essence of physics is the discovery and testing of these laws. Furthermore we know what the fundamental laws of the universe are---the laws of Quantum Mechanics. These laws are expressed in a formal mathematical way.

Then it hit me that I had been thinking about it all in a very limited way. Of course she was right. The universe does not have to follow mathematical laws. It appears to follow mathematical laws. But we do not know if this is true in general. We know it is apparently true for the limited sub-systems of the universe that we can examine with experiment and observation.

For four hundred years we have lived with the civilization mindset that our ability to induce mathematical laws about the universe in our limited fashion means necessarily that the universe as a whole, at large, is a giant mathematical machine, playing out via the ballet of understandable numbers from one state to the next.

But there is absolutely no reason this has to be true. Our success so far is not in the slightest way a proof of this statement. To state that the universe is a giant mathematical machine, even a quantum one, is a giant leap of faith regarding the application of our knowledge about nature that we have induced through experiment. Moreover, our current ability to successfully apply mathematical laws to nature is so limited, and will always be so limited, that will never be able to prove this.

But how could it be otherwise, one might ask? The universe has to be a giant mathematical machine, like a giant computer program, because what else could it possibly be?

To which the answer is a simple: the universe is in no way obligated to follow mathematical laws simply because we as human beings cannot conceive of it being any other way. The Sherlock Holmes type of proof doesn't work here (i.e. once you eliminate every other possible explanation, whatever remains has to be true). Nor does Occam's Razor. There is no guarantee our "simplest explanation," no matter how successful so far, can be generalized to the entire universe.

To think it can be generalized is perhaps the height of human folly, and the greatest leap of logic I can imagine. We can insist all we want that the universe must be understandable by us, but in the end it is a belief that cannot be supported by evidence except in the most peripheral way. There are plenty of folks who would claim that this leap of logic is the most grounded proposition they can imagine, and that anyone who believes otherwise is foolish.

Physicists by and large are more humble than that, thankfully. Most of them know too well the limitations of physics, much more than non-physicists. In some sense, maybe I became a real physicist when I realized this.

There is great freedom in this realization for it allows one to bring the tools of mathematical analysis to the parts of the universe for which we can indeed make valid statements without the burden of believing that we are "knowing God's thoughts," as Einstein supposedly put it. Even atheists probably understand what he meant with that remark.

I often wonder if this last notion---the idea that fundamental theory in physics is somehow the discovery of the "thoughts of God" is one of the principal reasons that theoretical physics largely ground to a halt for the last half century, after such rapid progress up to the mid 1960s.

Personally I am happy just thinking that I am toiling away in a small way, revealing a tiny bit more about the "material plan" of the universe with equations. I am happy seeking God's thoughts elsewhere.