The proof of the pudding is in the eating

The modern version of this phrase is, apparently, “the proof is in the pudding”. Which makes less sense than the original.

But I suppose it is consistent with other phrases that have been shortened. I couldn’t care less was shortened by a whopping 2 letters and an apostrophe to the contextually nonsensical I could care less, which is used to convey the same meaning as the original. I’m not sure that the phrase my bad is a shortening of anything, but whenever I hear it I think “your bad breath?”

The original phrase the proof of the pudding is in the eating is a nice pithy statement of the scientific method, essentially. Perhaps we might even view the phrase “by their fruits you shall know them” as being in a similar vein.

We all use some ‘model’ of what we think might happen, some expectation, in all sorts of ways every day. Science, in a sense, is a just a way of formalizing and checking an expectation.

In modern physics there is a tendency to eschew ‘meaning’ in the modelling - you can often read statements along the lines of “the job of physics is to determine the how and not the why”. In essence this viewpoint is trying to get across the idea that physics is just about supplying the mathematical rules (the how) and not to describe ‘reality’ (the why). I think this view has become more prevalent mostly because of quantum mechanics which is a set of formal rules in which ‘meaning’ is very difficult to perceive - there are many arguments about whether, or to what extent, the mathematics of QM corresponds to “what is actually happening”. In some sense that’s a nonsensical phrase in QM which, formally, is just a way of linking a preparation of a state with the outcomes of a measurement - what actually happens in between these two things is a bit (a lot) of a grey area.

I’m definitely more of an old-fashioned physicist. I want to understand - and that understanding, for me, is underpinned by some (assumed) model of what’s “really” going on. Merely being able to calculate stuff is not, in my view, the same thing as understanding at all.

Of course, we should always, always, remember that however wonderful the pudding tastes, our models, and the understanding we burden them with, are only provisional. We might think we’re tucking into a strawberry pavlova, but what we’re really eating is an Eton mess.

Models, and modelling, have fallen into some disrepute recently. It’s hardly surprising when the various models that have been employed to “understand” and predict the spread of covid have been almost uniformly incorrect. Now I’m OK with that. Being wrong is not a great sin. Scientists get it wrong. Lots and often. And that’s part of the process - it’s how science advances. Or at least it’s how it advances, provided you put things right.

The problem has not been that the models went wrong (very badly wrong in some cases) but that too much weight was given to these models in the first place - and that this weight continued to be given to the modelling when it was blisteringly clear it was producing garbage. In pudding terms we ordered a salted caramel and chocolate mousse, but ended up eating a smoked haddock and fenugreek ice cream.

We even saw the extraordinary sophistry of the head of UK’s SAGE modelling team trying to claim that the models weren’t predictions, but scenarios. If you’re going to attempt to CYA I think opting for granny pants is probably better than reaching for the sheerest of gossamer thongs.

Models are, and continue to be, extremely useful things in science. Just because some covid models were weaponized in terroristic ways by governments, does not mean that all models are weapons of mass delusion.

So, let’s see what a simple model of a viral outbreak might tell us. What insights might we glean? Of course, I’m assuming an a priori particular model that viruses exist and cause disease and that a virus can be transmissible in order to generate this, new, simple model. That this a priori model is essentially correct seems almost incontrovertible to me based on many pieces of scientific evidence - so that’s the position I’ll take, whilst recognizing the (very slim) possibility there is another theory of disease that explains all of the observations with similar success.

One observation that is well-explained by the viral theory is the existence of lineage specific antibodies in response to different viral lineages. It’s hard to see how this kind of thing arises if viruses themselves aren’t responsible. That we can see the variant-specific response in the body is just one piece of evidence amongst very many.

We’re going to model an outbreak of a disease using a simple gas model. We have a bunch of atoms whizzing about at random in a box. They’re all blue except one red one. The red one is ‘infectious’ - if it strikes a blue atom it turns it red and this new red atom can go on to ‘infect’ other blue ones.

You can see that when the outbreak is just beginning almost every single collision is going to result in a new infection - so we get a very sharp rise in infections (very close to exponential) - at least initially.

Now let’s see what happens during a 2nd ‘wave’, according to our model. Here we have a number of atoms that have previously turned red, but over time turn green. These previously ‘infected’ atoms are now ‘immune’ and if they collide with a red atom nothing happens.

It should be clear that the 2nd outbreak is not going to be able to proceed as sharply as before - the rate of infection will be lower than the 1st, at least according to this simplified model. This is because whilst the collision rate might be the same the red atom in the 2nd box is spending some of its time colliding with green atoms.

Note that simplified model also predicts that lessening the ‘collision rate’ (by lockdown, for example) ought to have a meaningful impact - yet we know it didn’t. So approach this simplified model with appropriate caution!

Now I’ll be the first to admit that this is a very simplified model - but the prediction, the expectation, is that any 2nd outbreak will not be as temporally aggressive as the 1st. This is indeed what is observed for outbreaks that have ‘waves’. Acquired immunity has a significant damping effect.

The ‘natural’ progression is towards a much more benign influence of the virus as acquired immunity kicks in with its damping effect. This is what happens in the ‘real’ world and eventually an equilibrium is reached where there is a significant amount of community immunity.

As things progress we expect a lessening impact for subsequent waves - although a 2nd wave might be more deadly in terms of numbers depending on the length and severity of the 1st wave (seasonality, which is not well-understood, might not allow a full progression in the 1st wave, for example). But by the time the 3rd wave, if any, comes along we would expect a noticeable lessening of the overall impact.

Joel Smalley has recently published a very worrying graph showing excess mortality in Chile.

To my, admittedly inexpert, eye this does not look like anything I’d expect from a ‘natural’ progression of a viral outbreak with ‘waves’.

My expectation has largely been driven by the simplified model above (and thinking about modifications to make it more ‘realistic’).

The 2nd peak might fall within my expectation - it’s consistent with what we saw in the UK in terms of excess death.

But things in Chile are not at all what I would expect in the presence of an effective vaccine - and Chile has a very high percentage of people vaccinated.

What I think we’ve done is completely buggered up the expected ‘natural’ progression of covid. Of course, that’s what vaccines are supposed to do - they’re supposed to completely bugger up this natural progression - but in the opposite direction.

I don’t know what Pfudding I’m supposed to be eating - but it sure as heck doesn’t taste like what I ordered.

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