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## If you don’t know the present, you can’t think about the future

Hans Rosling on population growth and other, related things.

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There’s a lovely piece in Pieria about a data visualisation exhibition at the British Library, positing John Graunt’s analysis of London deaths as an early spreadsheet.

And yes, there were some errors in it.

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## Second hand water

Randall Munroe, over at xkcd, does some really funny cartoons, and is a physicist by training. Every week he answers a hypothetical question: this week it’s

How much of the Earth’s currently-existing water has ever been turned into a soft drink at some point in its history?

His answer, by the way, is “not much”. On the other hand, almost all of it has been drunk by a dinosaur.

One of the things I really like about these “what-if” answers is the way they demonstrate one of the important aspects of modelling: working out what’s significant and what’s not. And significance depends very much on what the purpose of the model is. Often, Munroe can make some really sweeping assumptions that are clearly not borne out in practice, but are equally clearly the right approximations to make for his purposes. And sometimes he says that he doesn’t know what assumption to make.

An example of a sweeping assumption comes in the answer to

How close would you have to be to a supernova to get a lethal dose of neutrino radiation?

where he assumes that you’re not going to get killed by being incinerated or vaporised.

When, if ever, will Facebook contain more profiles of dead people than of living ones?

the difficult assumption is whether Facebook is a flash in the pan, and stops adding new users, or whether it will become part of the infrastructure, and continue adding new users for ever (or at least for 50 or 60 years). There are also some sweeping demographic assumptions, of course.

(and while you’re at it, read the one on stirring tea)

I’m reminded of two things here. The first is doing mechanics problems in A-level maths: there was nothing difficult about the maths involved, the trick was all in recognising the type of problem. Was it a weightless, inelastic string, or a frictionless surface? It was all about building a really simple model.

The second is those Google interview questions we used to hear so much about, like how many golf balls fit in a school bus, or how many piano tuners there are in the world. The trick with these is to come up with a really simple model and then make reasonable guesses for the assumptions. And, of course, be aware of your model’s limitations.

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## The aging silver lining

A few days ago I noted the difficulty of thinking in terms of dependency ratios: being economically active is a continuum, rather than black or white. There’s another side to the story, too. An aging population can provide opportunity, not only by producing products that appeal directly to a growing segment of the population, but also by providing services to help care for them.

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## Dependency: it’s not black or white

Frances Coppola makes some interesting points about dependency ratios, sparked by this article from The Economist. We often see charts showing the proportion of the population aged over 65 compared to those between 16 and 64, based on the assumption that the former aren’t working and the latter are.

The trouble is, as Frances points out, that the assumption is a massive over simplification. At the younger end, there are a lot of young people in education. In the middle, you’ve got the unemployed and disabled, those not working through choice, and those that are working but who also receive benefits. And at the older end there are increasing numbers of people who are both working and drawing pensions. Being economically active is not an all or nothing state.

Frances argues that, on the whole, there are few people over 65 who are not partially or fully dependent. But the main reason that the raw ratio is misleading is the large number of younger people who are also partially or fully dependent.

The dependency ratio is a crude measure that takes no account of the actual economic contributions made by people in different circumstances and at different stages in their lives. A few over-65s working mainly part-time to top up their state pensions doesn’t invalidate the ONS’s dependency ratio calculation. But a large number of people dependent on state benefits to top up their wages does. We don’t just have a demographic problem. We have a low wage problem.

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## Modelling isn’t just about money

Last autumn I was at an actuarial event, listening to a presentation on the risks involved in a major civil engineering project and how to price possible insurance covers. It must have been a GI (general insurance), event, obviously. That’s exactly the sort of thing GI actuaries do.

The next presentation discussed how to model how much buffer is needed to to bring the probability of going into deficit at any point in a set period below a specified limit. It sounded exactly like modelling capital requirements for an insurer.

But then the third presentation was on how to model the funding requirements for an entity independent of its sponsor, funded over forty to sixty years, paying out over the following twenty to thirty, with huge uncertainty about exactly when the payments will occur and how much they will actually be. It must be pensions, surely! A slightly odd actuarial event, to combine pensions and GI…

The final presentation made it seem even odder, if not positively unconventional: the role of sociology, ecology and systems thinking in modelling is not a mainstream actuarial topic by any means.

And it wasn’t a mainstream actuarial event. It had been put on by the professions Resource and Environment member interest group, and the topics of the presentations were actually carbon capture, modelling electricity supply and demand, funding the decommissioning of nuclear power stations, and insights from the Enterprise Risk Management member interest group’s work – all fascinating examples of how actuarial insight is being applied in new areas. And to me, fascinating examples of how the essence of modelling doesn’t depend nearly as much as you might think on what is actually being modelled.

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## Models and modellers

On 1 March I gave the Worshipful Company of Actuaries lecture at Heriot-Watt University. Here’s the abstract:

Being an actuary nowadays is all about modelling, and in this lecture I’ll discuss how we should go about it. We all know that all models are wrong but some are useful – what does this mean in practice? And what have sheep and elephants got to do with it? Along the way I’ll also consider some of the ways in which the actuarial profession is changing now and is likely to change in the future, and what you should do about it.

And here’s what I said.

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## Are boom periods bad for us?

Apparently, in the USA at least, death rates rise during periods of economic expansion and fall during economic downturns. I don’t know whether this holds in the UK as well. One possible reason for this is that when people feel well off they eat and drink more (and more unhealthily). Another is that people drive more, so there are more car accidents.

Yet another, according to a recent study, is that in good times nursing homes find it more difficult to hire care assistants because of the low wages.

Modelling future mortality rates is seriously difficult.

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## Cause of death

Cause of death statistics are notoriously unreliable, for several reasons. Most notably, most of the information comes from death certificates, which only have space for a single cause. Often, there are a number of factors which together resulted in the death, and it’s rather random which cause is chosen, and which manifestation of it: proximate, ultimate, or something in between.

You might think that an autopsies would help, but comparatively few of them are performed, and in any case they might not produce accurate results: around one in four are of miserable quality, apparently. Autopsies are done the old fashioned way, with scalpels, but it appears that using scanning technology might be quicker, cheaper, and possibly as accurate.

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