A new uncertainty principle

and its application to modelling climate change risk.

Ron S. Dembo

November 18, 2024

Abstract

We introduce a new uncertainty principle, inspired by the original Heisenberg Uncertainty Principal. Our main objective is to set conditions for proper modelling of uncertain futures.

The discussion here takes place in its application to climate change risk modelling. For this case it is particularly relevant because, as of today, almost all solutions for climate financial risk, and almost all discussion papers use a flawed approach to measure such risks. Consequently, their results may misrepresent these risks.

The Uncertainty Principle

We live in a quantum world. Physicists and Cosmologists trying to understand our world, and the very basis of matter today, agree that it behaves in a weird stochastic manner. If you were sitting in the nucleus of an atom, and were pinpointing an electron’s location, trying to measure its momentum, you would find that its momentum would be completely random. And, if you specified its momentum, its position would be highly uncertain.  This is known as Heisenberg’s Uncertainty Principle[1] and is a fact that is so alien to our world view. It is not the world we see around us and is not intuitive. But it is a fact. Even Einstein, when quantum theory emerged, was known to dismiss it saying: “God does not role dice”

He later accepted that the world we live in is governed by the laws of quantum physics and the Heisenberg’s Uncertainty Principle.

There is another similar uncertainty principle that governs any mathematical modelling of the future. And it should govern the way we think about measuring future risk.

In a climate change world, we need to understand how hazards may impact physical infrastructure at some location at some point in the future. For a given point in the future, in some fixed location, the hazards are uncertain.  Alternatively, for a given point in the future, if the hazard is known with certainty, the location could not be known with certainty. That is, we can’t have a situation where both the hazard level and location can be known with certainty.   

The Climate Uncertainty Principle:

When trying to explain the future risks that climate change poses, given a location and future point in time, the hazards that could cause a specific impact at that location, are fundamentally uncertain. Conversely, given a hazard with a specific impact level at some determined point in the future, the specific locations that will be impacted by that hazard are fundamentally uncertain.

This uncertainty principle operates in a macro world where Newtonian physics guides our intuition and our models. But as our macro world becomes more stochastic, when we are looking at a very uncertain future, our uncertainty principle applies.  It might seem like it is an obvious idea but, if it truly were, we would not see much of the modelling that is accepted by regulators, banks, asset managers etc. today.

How do we know this principle is true? Imagine if it were not true. Then we could pick a location, and we could pick a hazard value for any location at any time in the future. That would mean we would have perfect foresight or alternatively said we would be in a deterministic world. This is clearly false.  Therefore, the uncertainty principle holds Q.E.D.

Conclusion 

This principle and our conclusion that the Climate Uncertainty Principle must hold may seem to be obvious. If it were obvious we would be seeing quite different requirements from regulators for reporting on climate change. Whenever we at riskthinking.AI raise the issue of the necessity for a stochastic approach to measuring climate risk we get the question: “Is a stochastic better than a deterministic approach?”

That question is irrelevant. The Climate Uncertainty Principle is clear. This is not a question of which is better – there is no choice. When selecting a building in a specified location, at a specified point in the future, any climate hazard that may affect the building is uncertain. This is a consequence of the Climate Uncertainty Principle and should not be analyzed using a deterministic value – its value may be represented by a probability distribution.

Picking a single pathway to begin an analysis of climate risk for some future period is therefore in conflict with a fundamental principle. Unfortunately, this is the norm today.

It is no different than evaluating the risk of a bond in the future and only allowing a narrow band of future interest rates to be considered and may miss its most important risks.

[1] Neil Turok, The Universe Within, House of Anansi Press 2012