A Brief History of Time – Stephen Hawking on good theories

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A Brief History of Time - Stephen Hawking

Learning from Stephen Hawking

Physicist Stephen Hawking wrote a wonderful book on cosmology in 1988, A Brief History of Time: From the Big Bang to Black Holes. Here, he explores interesting inquiries in science, from our place in the Universe to the unification of physics. Like Richard Feynman’s The Character of Physical Law, I thoroughly enjoyed the accessibility, clarity and intrigue in Hawking’s work. Moreover, Hawking’s reflections on what constitutes good science and theory offers important lessons for scientists and non-scientists (including those in finance). In this post, we’ll review a few lessons that we took from Hawking’s ideas, drawing some parallels to investing at the very end.

The character of good theory

In physics, a theory is a model of the universe, or a restricted aspect of it. Models relates quantities in its specifications to the observations we make in reality. They usually comprise a set of rules and initial conditions. On this basis, Hawking suggests that there are two requirements to having a good theory. Firstly, the model must describe many classes of observations without too many arbitrary elements. Secondly, the model should offer specific predictions about the results of future observations.

Popper’s emphasis

Hawking points out that all physical theories are provisional. These theories are hypotheses that we can never prove. Even if prior experiments support our hypothesis, we cannot say with certainty that the next experiment will agree as well. Conversely, we can have a theory disproven if we find just one observation that disagrees with its predictions. Here, Hawking cites philosopher Karl Popper. Popper emphasises that good theories must make predictions that we can disprove in principle or falsify by observation. It’s a simple but central idea to keep in mind.

Possibility’s grip

Hence, good theories must stand the test of analytical and empirical rigour across time. We’ll have to modify or abandon our theory if new observations are found to contradict their predictions. In reality, this is not always so easy for us to do. For example, Hawking describes how the scientists that found that the universe could not be static, according to Newton’s theory of gravity, did not go on to suggest that our universe might be expanding. Even Albert Einstein introduced a cosmological constant in his formulation of the general theory of relativity to conform to the belief that the universe was static. While these examples refer to great minds at the edge of mystery, they show how our historical understanding of the world can have a powerful grip on our sense of imagination and the possible.

Aristotelian tradition

Hawking also points out the limitations of Aristotelian tradition. It was an outmoded philosophical view that believed that one can determine the laws of the universe through thought alone. Hawking points out that humanity had to wait more than a millennium until Galileo actually bothered to verify and falsify the Aristotelian belief that heavier bodies fall at greater speeds. Testing and inverting our hypothesis might help us to uncover the flaws in our beliefs. This can help us to achieve a deeper understanding of our subject.

Fundamental errors and limitations

“When the facts change, I change my mind. What do you do, sir?”

John Maynard Keynes

Since scientific progress often involves the process of falsification via observation, making mistakes in our theories and beliefs is unavoidable. Yet when faced with errors in our beliefs, we sometimes prefer to double down. Sometimes we’ll look for new but mutually inconsistent arguments to defend our positions. Others may even pretend that they never held those beliefs or assessments at all. Hawking suggests it is much simpler and easier to admit that we were wrong on paper. He cites Einstein again, as a great example, who described the cosmological constant as the biggest blunder of his life.

But there are many more challenges to developing good theories, more so than just recognising our mistakes. Some features are embedded in nature itself. Hawking points out several potentially fundamental limitations to making predictions about the universe. This includes the self-referencing paradox, uncertainty principle, incompleteness theorem and three body problem. We touch on these ideas very briefly as follows.

A paradox in self-referencing

Scientific history provides an account of our incremental understanding. That is, we are learning increasingly about the underlying order and constituents of behaviour of the universe. However, Hawking suggests that finding a complete unified theory to describe our entire universe might face a paradox. It assumes that we can observe the universe and arrive at logical deductions freely and rationally. While this is reasonable with incremental progress, a complete unified theory would have to determine our actions and outcomes itself.

Hawking then wonders why such laws and conditions might allow us to arrive at the right conclusions. It is also plausible that such a system dictates we arrive at the wrong conclusion or no conclusion at all. To rationalise this, Hawking posits that maybe some form of natural selection in scientific ideas might take place. This might allow us to arrive on theories that are closer to the universe’s ‘truth’.

Heisenberg’s uncertainty

The potential for such scientific determinism is complicated when we consider the implications of quantum mechanics. Unlike classical mechanics, quantum mechanics does not predict single results for an observation. Instead, it predicts a probability distribution of potential outcomes. This is because, according to Werner Heisenberg’s Uncertainty Principle, there is a fundamental limit to the precision of certain value pairs (e.g. position and momentum) for quantum objects that we can predict from initial conditions. And this is due to the wave-particle properties of nature at very tiny scales. Thomas Young’s double slit experiment, was an early and important demonstration of such behaviours in effect. Quantum is such an unusual and unintuitive feature of our physical world; and yet of central importance to our understanding of nature.

Gödel’s incompleteness

Similarly, Hawking provided an outline of Kurt Gödel’s incompleteness theorem. Gödel showed that there are some mathematical questions that we cannot answer (e.g. prove true or false) within a set of axioms; and that we cannot prove a set of axioms as consistent unless we adopt a different / additional set of axioms. This discovery had profound implications for the philosophy of mathematics, physics and science. And given we exist inside the universe, Hawking suggests that the incompleteness theorem and uncertainty principle may impose some fundamental limitations on our capacity to understand and predict the universe.

Three body problem

Furthermore, even if we had a completely unified theory of the universe, the computational challenge and energy requirements of making long-term predictions might make it impractical. For example, Hawking points out that there is no general closed-form solution to describe the motion of just three bodies governed by Newton’s theory of gravity. Numerical approaches are required instead. And the difficulty in finding solutions to such problems tend to grow with the number of agents and interactions, and complexity of the theory. For complex real-world situations, we might have to make do with approximate methods to describe a variety of probable outcomes. The universe itself might be its own best calculator.

Appeals to Occam’s razor

One implication of all this, according to Hawking, is that we face great difficulties with predicting future events in the physical universe because we are unable to measure our present states with complete precision. While there might be a law to describe the universe for an outside observer, we ourselves are governed by the laws inside the universe.

Hence, Hawking describes the value and temptation of Occam’s razor for developing models. We might opt to remove the features in a theory that we cannot yet observe. And while these limitations in a predictive sense are not yet as relevant to progress in the natural and social sciences today, given how much more there is to learn and discover, it’s helpful (and fun) to stretch our understanding of what is possible and what is not.

Subdivide and specialise

“Extreme specialization is the way to succeed. Most people are way better off specializing than trying to understand the world.”

Charlie Munger

When it is too difficult to describe an entire system with a single model or theory, we tend to subdivide and manage it with partial theories. In many cases, this allows us to understand the behaviour of a subsystem without the need for a theory of other constituents we do not yet understand. Similarly, the speed in which science has progressed has made it impossible for any one individual to understand an entire subject or subset of knowledge. Hawking believes that one has to be a specialist to have the opportunity at understanding even a small percentage of scientific theories. One will have to devote their entire lifetime to such a specialisation if they hope to advance the frontier.

A microcosm in finance

“There are two kinds of forecasters: those who don’t know, and those who don’t know they don’t know.”

John Kenneth Galbraith

The topics that Stephen Hawking reflected on, in our opinion, extend to challenges in business and investing. This includes constructing good theories, recognising our mistakes, subdividing and specialising, and overcoming the conceptual and computational challenges in prediction. We might interpret our endeavours in macroeconomics and finance as a microcosm of the grander challenge we face with understanding our environment. For example, it is difficult to develop financial theories and innovations that generate reliable predictions and results. This is attributed in part to the complexity of macroeconomic systems, dependence on small and uncontrolled sample sizes for evidence, and the reflexive behaviours of people (akin to the observer effect).

Tendencies and unknowables

“I’ve never been able to predict accurately. I don’t make money predicting accurately. We just tend to get into good businesses and stay there.”

Charlie Munger

It is perhaps due to these challenges that many investors prefer to focus their time instead on understanding the fundamentals of business. Investors like Charlie Munger have talked about the difficulties in predicting the macroeconomy accurately. Likewise, Howard Marks prefers to think about market cycles in tendencies and probability distributions, acknowledging its inherent uncertainty and unknowables. Warren Buffett too has recommended we focus on what is important and knowable within our circle of competence. Perhaps by recognising what we do not or cannot know, we can begin to construct wiser theories and mental models to inform our decision making. Charlie Munger has said that “acknowledging what we don’t know is the dawning of wisdom”.

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Further reading