The Math of Pandemics is Hard
28/09/21 16:00 Filed in: Mathematics
All the arguments about the right thing to do in a pandemic made me take a step back and wonder why is this so hard for a community to agree on what is to be done. Intelligent people come to wildly different conclusions about the right thing to do. In many cases different sides of an argument cannot even agree on the facts they are arguing over.
This is not going to be an article on a moral philosophy and the ascendance of rights over responsibilities. Instead I ponder a more basic problem:
Perhaps this can explain some of the difficulties we have in seeing our way through as a community
This is not going to be an article on a moral philosophy and the ascendance of rights over responsibilities. Instead I ponder a more basic problem:
Is the maths of a pandemic just hard
The dominant mathematics of contagion is that of exponentials. While this is the mathematics that underlies much of finance and physics, it is not the mathematics of the every day.
Exponential processes are both:
- Poorly handled by our intuition
- Inherently difficult to calculate
Perhaps this can explain some of the difficulties we have in seeing our way through as a community
The mathematics of the every day seems to be rooted in addition, subtraction and multiplication. But even multiplication is a process of repeated addition. This is good enough for basic commerce and most of our daily activities.
While some people and professions deal with more complex mathematics, every day; the general public always seem surprised by the story of the wise man who offered to paid in a grain of rice on the first square of a chess board, two on the second, four on the third, 16 on the fourth … and eventually owning the kingdom's food supply by the 64th square.
This suggests that the mathematics of powers and exponentials are not easily handled by our intuition (system 1 if you happen to be interested in psychology) and need calculation for us to comprehend (system 2).
Contagion is fundamentally exponential.
A friend of mine insightfully described second year electrical engineering as learning to approximate various parts of exponential curves with linear equations so we could do the math in the exam. (The big trick was knowing when to use which bit and how much of the curve)
Worse still the mathematics of exponentials is highly sensitive to initial conditions when estimating an unknown power. It is very easy to end up with widely varying estimates of the unknown power and given that sampling is definitionally incomplete knowledge, early estimates can be wildly off.
Best practice in the area seems to have settled on averaging (actually I suspect there is a more sophisticated clustering approach throwing out outliers) a large number of models in an effort to create a more stable and reliable result.
We seem to have a perfect combination of issues to drive a conversation to conflict:
While some people and professions deal with more complex mathematics, every day; the general public always seem surprised by the story of the wise man who offered to paid in a grain of rice on the first square of a chess board, two on the second, four on the third, 16 on the fourth … and eventually owning the kingdom's food supply by the 64th square.
This suggests that the mathematics of powers and exponentials are not easily handled by our intuition (system 1 if you happen to be interested in psychology) and need calculation for us to comprehend (system 2).
Contagion is fundamentally exponential.
A friend of mine insightfully described second year electrical engineering as learning to approximate various parts of exponential curves with linear equations so we could do the math in the exam. (The big trick was knowing when to use which bit and how much of the curve)
Worse still the mathematics of exponentials is highly sensitive to initial conditions when estimating an unknown power. It is very easy to end up with widely varying estimates of the unknown power and given that sampling is definitionally incomplete knowledge, early estimates can be wildly off.
Best practice in the area seems to have settled on averaging (actually I suspect there is a more sophisticated clustering approach throwing out outliers) a large number of models in an effort to create a more stable and reliable result.
We seem to have a perfect combination of issues to drive a conversation to conflict:
- Highly variable estimates
- Difficult to do mental mathematics (system 2)
- Terrible to 'guesstimate' (system 1)