Dr Tom Philp

Chief Executive Officer

In a previous blog[1], I made the case that a paradigm shift needs to occur in the field of cat modelling if it is to evolve to effectively tackle existential societal challenges in the coming years and decades. The name of our venture, Maximum Information, derives directly from an analogous paradigm shift that occurred in the early 20th century in the field of physics, often referred to as the Einsteinian revolution[2]. Read on to discover why the Einsteinian revolution represents a valuable lesson for catastrophe (cat) modelling, how it feeds into our venture’s name and logo, and how that impacts our long-term vision and purpose.  

Until the late 19th century, classical (or Newtonian) mechanics pre-dominated all physics-related fields of research. Based on the concept that all matter exists as distinct particles that follow rigid, precise, and continuous laws of motion, the field of related research can be traced as far back as Aristotle and Democritus in the 4th and 5th centuries BC[3],[4]

In the early 20th century, however, practical experiments began to show that certain observations could not be reconciled with the central theoretical principles of classical mechanics (e.g. Planck, 1901[5]; Einstein, 1905[6]). A new theory of mechanics was needed to explain these observations; this has since grown into the field of quantum theory. While highly complex and often extremely unintuitive (at first even Einstein himself was uncomfortable with the ideas, famously stating "God does not play dice with the universe" to vocalise his displeasure), the theory has been colloquialised as the “Schrödinger’s Cat”[7] thought experiment - a simple illustration which highlights quantum theory’s paradoxical absurdity to the layperson.

The thought experiment shows that, under certain conditions, quantum theory would predict that a cat (or any other living being, for that matter) would exist in a state of being both dead and alive at the same time. The cat would only take a single state (either alive or dead) after observation by (or interaction with) an external party. While obviously an absurdity at the scale of living beings (how can anything be both alive and dead at the same time?), at sub-atomic scales our universe seems to follow this quantum reality – particles only take a definite form at the point they are observed or interacted with. Until then, they exist in a “superposition” of multiple states[8].

At heart, then, early quantum theory predictions necessitated a shift away from the belief that we can achieve absolute precision on estimates of the state of the world (as predicted by Newtonian mechanics), at least at sub-atomic scales. During subsequent philosophical debates about the nature of knowledge, Erwin Schrödinger, Niels Bohr and Werner Heisenberg all grappled with the newfound theoretical limits of predictability, with the new revelation that particles could never be predicted deterministically and precisely, but only within some uncertainty space until they were actually observed. 

This represents an apt analogy for cat risk. Historical catastrophic event data – the data that underpin the frequency assumptions in contemporary cat models – are rare, almost by definition. The historical record should therefore be considered under-representative at best. While this raises a difficult challenge for quantifying cat risk, cat modelling has already been set up to attempt to tackle this by using probabilistic (or stochastic) methods to extend the historical record beyond our direct observations. However, there is a key challenge in the use of the probabilistic cat model output operationally at present: the probabilistic space that we create is almost always averaged away to allow us to collapse the uncertainty toward a mean estimate, even though we know the mean estimate is likely misleading. 

To use quantum theory to highlight the issues of simplistic averaging over a probabilistic solution space, our logo is that of the Hydrogen wave function (3,2,0), or a d-orbital of the electron cloud space for the hydrogen atom. Many readers of this blog, likely in school chemistry lessons, will have seen an idealised view of a hydrogen atom with a nucleus & proton in the centre, and an electron spinning around in a circular orbit (as seen in the left plot below). In reality, the orbit of the electron is much more complex and variable (as described by the various iterations of the hydrogen wave function in the right plot below). In a specific energy state (3,2,0), the cloud space that the electron could exist in takes the shape of our logo – at any given moment, the electron could exist in any of the two egg shaped clouds, or in the donut shaped cloud around the centre. Importantly - the electron cannot exist (i.e. has a zero probability of existing) outside of these spaces. It certainly cannot exist in the centre of the image (ie where the nucleus would be, and where an average of the three regions would predict) and, even more paradoxically, the electron cannot ever exist in the spaces between the three regions – instead, it will disappear from one area and re-appear in another. Averaging between them therefore makes little sense.

On the left we see the idealised hydrogen atom with proton in the nucleus and electron orbiting around, while on the right we see the more accurate depiction of solution spaces for the electron location as predicted by the hydrogen wave function.

While this type of argument may seem like a scientific abstraction that is detached from risk worlds, a direct example of this occurring to date in cat modelling would be the presence of the Atlantic Multi-decadal Oscillation (AMO) and its impacts on North Atlantic Hurricane risk. Ignoring for now the complexities & nuances of whether the AMO truly exists, it can be said to either be in a positive or negative state, with the negative state substantially decreasing basin-wide activity, and the positive state substantially increasing it. What is certain, in an AMO-existent world,  is that the average state of the two is a state that can’t possibly exist. Thus, average hurricane activity over these types of periods would be an abstraction akin to averaging the electron location over all three possible clouds in our logo. The “average” prediction of these states would have us believe that the true value lies in the centre of the image (where the nucleus would be). In reality, that is one of the places that the true answer cannot exist. Instead, we should be asking – what are the best and worst outcomes of the places the answer can truly lie?

While this may seem to imply that we need a significant re-tooling effort to operationalise this thinking in our current cat risk management processes, our cat models to date actually already provide this type of information – it is mainly that, in the name of operational efficiency, few attempt to look at it. This is likely the start of unpicking many “unknown-knowns” that exist in cat model development, but have historically been overlooked.

Quantum theory, then, provides a valuable analogy for cat modelling that risk managers should take heed of. While debating what the concept of a complete state of knowledge had become under quantum realities, in his book “Science and Humanism”, Erwin Schrödinger stated: 

The equivalent of this complete knowledge in classical physics is in quantum physics a so-called Maximum Observation, which yields the Maximum Knowledge that can be obtained, nay, that has any meaning.”[9]

Here at Maximum Information, where the Schrödinger's Cat thought experiment has taken on a whole different meaning, we equip you with the tools and data to reach the state of Maximum Knowledge possible in the fundamentally quasi-quantum world of cat risk. 

[1] https://www.maxinfo.io/blog/moving-on-from-the-pre-paradigm-of-catastrophe-modelling
[2] P.66 https://cte.univ-setif2.dz/moodle/pluginfile.php/13602/mod_glossary/attachment/1620/Kuhn_Structure_of_Scientific_Revolutions.pdf
[3] http://classics.mit.edu/Aristotle/physics.html
[4] https://www.iop.org/explore-physics/big-ideas-physics/atom#gref
[5] In German: https://onlinelibrary.wiley.com/doi/10.1002/andp.19013090310
In English: https://web.archive.org/web/20080418002757/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html
[6] In German: https://www.zbp.univie.ac.at/dokumente/einstein1.pdf
In English: https://sites.pitt.edu/~jdnorton/lectures/Rotman_Summer_School_2013/Einstein_1905_docs/Einstein_Light_Quantum_WikiSource.pdf 
[7] https://www.wtamu.edu/~cbaird/sq/2013/07/30/what-did-schrodingers-cat-experiment-prove/
[8] And are represented in quantum theory as a wavefunction, as described here: https://phys.org/news/2012-04-quantum-function-reality.html
[9] https://archive.org/details/erwin-schrodinger-nature-and-the-greeks-and-science-and-humanism/page/n177/mode/2up