Sanity Checking

A typical kinematics question that might get asked during a university PhysicsI course might look something like this :

At t = 0 a blue car and a red car accelerate from rest. The blue car is 200 m behind the red car at this time and accelerates with a constant acceleration of 0.3 m/s^2. The red car’s acceleration is a constant 0.1m/s^2. How long does it take the blue car to catch up with the red car?

I’ll be the first to admit that this sort of question is about as interesting as growing one’s toenails but it’s the kind of thing that students would be expected to solve. Typically, after some reminders about things like units and dimensions and significant figures, kinematics is the first thing that gets addressed in the course. It ought to be revision for most students.

If you want to make the question a bit more spicy you could perhaps cast it as a falcon chasing after his prey - but it’s the same tedious calculation you have to do.

You’ll be pleased to know I’m not going to go through the solution of this question, but one thing I tried to do, and mostly failed to achieve, was to get my students to approach the solution algebraically. I’d try to get them to work out what the solution had to be in general terms - and then substitute the specific numbers in the question to generate their answers.

This has two principal benefits. Firstly, it enables a general formula to be written down so that if different numbers occur in the question you don’t need to do the calculation all over again. An example here might be if the question went on to say “if the blue car’s acceleration is halved to 0.15 m/s^2 how much longer does it take for the blue car to catch up?”

If you have worked out the formula, you don’t need to do the calculation all over again to answer the follow-on question.

A second big benefit of doing it all algebraically is that you can check your answer (to some extent). With a formula it’s possible to check the units/dimensions. If you end up with something that has different units/dimensions on both sides of the equals sign you know you’ve done something wrong.

You can also see if your formula predicts the right sort of things. In the car problem we can see that the higher we make the blue car’s acceleration, for example, the shorter time it will take for it to catch up. It’s an expectation on the formula - and if the formula you derive does not have this feature in it, you know you’ve done something wrong.

The weird thing is that generating the formula usually requires exactly the same steps, mathematically, as it does to do it with the numbers inserted and yet most students really struggled with the abstraction to algebra.

Knowing when you’ve gone wrong is a really, really useful thing to master.

What, then, are we to make of the recent chart posted by Joel Smalley in his recent substack posting?

COVID Pressure on the National Health Service of Scotland.

The chart shows hospitalizations with covid for Scotland pre and post vaccination.

Now, I understand that virus outbreaks are significantly more difficult to model from first principles than one-dimensional kinematics problems involving two cars. I also understand there’s an issue with exactly what is meant by a “covid admission” but it’s unlikely that Public Health Scotland radically changed their definitions pre and post vaccination in order to make the vaccine look bad.

And this looks bad for the vaccine. Very bad.

This graph looks nothing like I would expect to see from a widespread vaccination campaign with an effective vaccine. It doesn’t pass the sanity check. Admittedly, I can’t check it in an algebraic sense like I can with the kinematics formula I would derive for the cars, but this doesn’t look like the progression of a respiratory virus I would expect to see after 18 months of vaccination with an effective vaccine.

More to the point;

it doesn’t look like the progression of a respiratory virus I would expect to see in the ABSENSE of vaccines

In car terms it would be like if the blue car had an acceleration of 0.1 m/s^2 and the red car an acceleration of 0.3 m/s^2 and we’d worked out that the blue car caught up with the red car in 200 seconds. The red car is accelerating more than the blue car and so the blue car would never catch up. Our expectation here would tell us we’d done something horribly wrong.

Whilst there does seem to be a few things we don’t understand properly about how viruses are transmitted, what triggers them, and seasonality, and so on, the general picture, and past experience, shows us that we don’t expect ‘waves’ to just keep going on and on (and getting more frequent) and getting worse over time.

We possess, at least we used to pre-covid, some mythical things known as natural immunity and infection-acquired immunity. A novel(ish) virus can rip through a more immunologically naïve population in its first wave. There might be a second wave that’s worse if the first wave is prematurely limited by something like seasonality, for example. But after the first and second waves of a reasonably infectious virus the population is no longer as immunologically naïve as it was and subsequent virus ‘waves’ will not get the same degree of traction. This effect is the whole basis of community immunity.

It’s also one of the major planks of the idea of vaccination.

You get vaccinated against a virus so that you don’t get infected (in a clinical sense) if you’re subsequently exposed to the virus. The virus gets in, so to speak, but your immune system has been primed by the vaccine and is able to prevent the virus from replicating - at least that’s the broad brush idea.

Well, that’s the idea we used to have before the powers that be started playing silly buggers with the definition of what a vaccine is.

The second great benefit of vaccination (at least in theory) is that not only does it provide personal immunity, it also affords a high degree of community protection when sufficient numbers are vaccinated. The virus is doing its best, but it keeps on meeting vaccinated brick wall after vaccinated brick wall and can’t infect as well as it used to, and nor can it then subsequently be transmitted to infect someone else. We might describe the virus as being “all revved up with no place to go”.

The only conclusion I can draw from the chart above is that not only is the vaccine not working, it is making things substantially worse. If the vaccine was just saline solution this is not the kind of chart we’d expect to see at this stage of the ‘pandemic’.

A recent substack post by that well-known felicitous feline essentially alludes to this two-pronged aspect of vaccine efficacy

can covid vaccines cause more covid deaths while looking like they prevent them?

EGM points out that even if it looks like the vaccine is doing something in terms of reducing case/infection fatality rates, if it is making it more easy to catch the disease this apparent benefit can be entirely reversed overall.

I got out my pencil and paper and started liberally sprinkling algebra all over everything. I worked out a formula that was unknown to me, but surely well known to experts in the field. It’s a really trivial calculation to do, but what I found was the following.

Suppose you have a vaccine that has an effect on infection fatality rates so that

f(v) = a f(u)

so that the fatality rate in the vaccinated is expressed in terms of the fatality rate in the unvaccinated. A vaccine that made things better, in this regard, would have a value for a that is less than 1.

Now also suppose that the vaccine has an effect on infection rates so that

i(v) = b i(u)

so that the infection rate in the vaccinated is expressed in terms of the infection rate in the unvaccinated. A vaccine that made things better, in this regard, would have a value for b that is less than 1.

It turns out (well, it does if I set things up right and did the algebra right - always a shaky proposition) that the formula for vaccine efficacy can be re-written in terms of these a and b factors and it looks like

vaccine efficacy = 1 - ab

So the formula for vaccine efficacy includes 2 components - one relating to a potential reduction in fatality rate and the other relating to a potential reduction in infection rate.

Prior to covid, at least in terms of understanding in the general population (which was also my understanding), the benefits of vaccination were described in terms of the parameter b. Vaccination, ideally, greatly reduced infection rates and so this parameter b is small (for an effective vaccine) which leads to an efficacy close to 1 - at least ideally.

With covid vaccines we can directly see what the problem is. Vaccination is making people more susceptible to infection, and more frequently (the incidence of re-infections in the vaccinated appears to be much higher). In other words, this parameter b is greater than 1 for the covid vaccines.

If the vaccine reduces fatality rates by 50%, but doubles the infection rate, you’ve just stood still. Vaccination, in terms of overall efficacy, has achieved bugger all. If you now factor in side effects you’re actually in a worse position than before even with no overall effect on efficacy.

The only reason, in my view, that we’re not seeing an alarming rise in covid deaths is because Omicron is milder. We should be thankful for small mercies. But if Omicron turns into a Decepticon, like some are warning it could, we could be in for a whole world of trouble - especially if the vaccines have made us partake of the fruit of the poisoned tree and engendered Original Antigenic Sin, or immune imprinting.

I think the chart posted by Joel is compelling evidence we’ve made things worse by vaccination. The vaccination program fails the sanity check.

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