I'm really quite fascinated by the "R number" or (sorry) "R rate" terminology tweets. It's something worth studying post pandemic as a math bio communication case study with a huuuuuuge amount of published examples. Fertile grounds! (1/n)

But it also touches on something much more profound, that I hope some wordy mathsy person is going to write a great thing about.

...but until then....

The biggest, most important, and almost mystical idea in maths, as far as I'm concerned, is the "isomorphism". The idea that you can take one thing, for example a person running, and then "map" that onto a set of numbers

So an amount of ground covered becomes a distance, as a number, a time elapsed becomes a static numerical thing, and speed (carefully distinguished from momentum by ignoring the size and weight of the moving thing) becomes another number.

Now for the magical part: we then mess around with the numbers, using "rules" derived from triangles or "algebra" tricks - and then claim straight faced that the results can be "mapped" back to the world of running people without losing truth or significance!

So we take a new problem, "map" it onto some other problem that we've had plenty of practice with, mess about until we've found a solution, and then "map" this solution back to the original context.

(A particularly good trick is to turn a concept - any concept at all - into lines and points in 2 or 3 dimensions. Because our brains are amazing at that stuff, and we often find visual, graphed, problems much easier to solve than the same problems presented some other way.)

The big trick of maths, then, is to recognise that almost any given problem (eg in economics, physics, healthcare) has mirrors in several other fields, and to try out all these analogies because our intuition might be better in one of them - or a solution may even be known!

If you get a mathematician drunk, ask them _why_ lexicographical symbol manipulation, geometry, Laplace transforms or whatever preserve truth about the physical world. It will be fascinating. (Assuming you're also drunk)

But most of the time they (we?) forget about this miracle. Which brings me back to R.

The idea of an isomorphism is that there's something about the shape or the structure of two problems that makes them - more or less - the same.
And this sameness, in many minds, becomes the bigger thing, the underlying fundamental truth shared by both situations.

The best way of representing this shared truth is often an equation - precisely because it's so dry and abstract and boring and devoid of context - that's the whole point - that it strips away so much - that's the beauty of it! It's the commonality in its purest form!

And that, as far as I understand, is the world that R lives in, and the world within which hard statements about R can be made. Where it gets messy is in the mapping, in and out, from real people to numbers in equations and then back again

So there's some concept, called R (not R something, just "R") that can be approximated from tables and is very important in equations and simulations. But journalists very rightly ask what does it mean?

To some mathematicians, describing it in words is a step back - we already distilled the equation! Why now dilute it back to the messy world? We had clarity, why bring back the clouds?

But it's important to remember that this is the hard part. Mapping between different types of maths is easy (*cough*). Mapping to and from the real world is hard. So we hesitate. We go silent. And we let the journalists and their deadlines fill in the gaps.

I think twitter's been a great remedy for that, letting experts talk directly, and forcing them to put their thoughts in words!

But we probably need to work a bit harder still, to not be seduced by the shiny clean "pure" side, to not base our self-worth on "concreteness" of abstract results but to stay on the messy side, recognising that if we're needed anywhere it's here.

(it's very late, forgive me if I'm very wrong)

TLDR "What does it mean" sounds like an invitation to abstraction for many of us in applied mathematical sciences, but the opposite is usually true and we should be brave and spend more time trying that.