“Software is eating the world”

Quoted here, from which also this:

The connected world we’re building may resemble a computer system, but really it’s just the regular old world from before, with a bunch of microphones and keyboards and flat screens sticking out of it. And it has the same old problems.

Evgeny Morozov would agree.

A mathematician’s view on integration in health and social care

Though the answer may be integration, we don’t always know what the question is.

Similarly, though we often say “integration”, it’s not always clear what type of integration we mean. There are at least four interpretations of what we meant when we talk about “integration”:

  • Integration across any of primary, secondary and tertiary healthcare
  • Integration across health and social care (and education and housing and etc.) boundaries
  • Integration of resources and processes
  • Integration at the level of the individual.

As a mathematician by training, integration has another particular meaning to me. I thought it would be useful to reflect on what integration means from a mathematician’s perspective and so what we might learn from this in the context of health and social care.IntegrationMathematically, integration is the reverse process of differentiation. Differentiation is all about rates of change across different variables in a system. Differentiation is a way of thinking about the world as a result of combining infinitesimally small changes at particular points in time or space.

Integration, on the other hand, gives you a bigger sense of the whole. It tells you not just about rates of change but the overall picture you have: the sum total of what exists in time or space.

Differentiation is easier. It’s exciting (think Mick Jagger swaggering around a stage) and has no room for anything but the most important stuff. If there are any ‘spare’ numbers floating around then the process of differentiation gets rids of them – they disappear.

Integration, as any mathematician will tell you, is far harder. It’s a slower, altogether more considered process that requires more sophistication (think Bjork). There are some tricks you can use to make it slightly easier – such as integration by parts – but the challenge of integration remains.

And because integration is the reverse of differentiation it adds in an unknown factor: the arbitrary constant (from which this blog takes its name). Where differentiation has no space or time for the arbitrary constant, integration very deliberately includes it and recognises it. This unknown factor – an unidentified ingredient – is a vital component of integration.

(Interestingly, the only time the added, unknown ingredient of the arbitrary constant doesn’t play a part in integration is if you explicitly define the boundaries within which integration happens. By specifying these limits so exactly the arbitrary constant is cancelled out.)

If we were therefore to try and summarise what we know about integration from a mathematical point of view we’d say something like this:

  • Integration is harder than differentiation – though there are limited tricks to make it easier
  • It gives a bigger picture across a wider area than a specific view of just one point in time or space
  • It has a secret ingredient – the arbitrary constant – which his fundamental to capturing this bigger picture
  • This secret ingredient disappears only if you define exactly the boundaries of what integration is trying to achieve
  • Integration is a subtle, complex process that takes time and understanding to do.

Thus, though you wouldn’t immediately think it, the mathematical conception of integration tells us everything we need to know about successful integration in public services, especially across health and social care and beyond.

Examples of changing your mind

Understanding the process of how and why someone changes their mind seems vital to me. As I’ve noted before, understanding this is of fundamental importance to the process of public sector change.

Here’s a nice article on whether economics can change people’s minds (via Marginal Revolution), including examples of where it has done exactly that.

Altogether, there are many examples of economists who change their minds, even when doing so involves repudiating their own previous research and policy positions. Maybe these economists are special and possess an inhuman lack of bias. But I doubt that.

Feel free to share examples of where you’ve changed your own mind, particularly when it comes to public service reform.

A brief thought on disability in A Theory of Everything (updated)

Theory of EveythingTo the cinema to watch A Theory of Everything.

The perspective on disability the film brought was, I thought, excellent. It explicitly included reference to the impact Professor Hawking’s impairment had on his life and the people around him. From a practical view it showed the adjustments the Hawkings had to make in their lives, and the importance of good support that came from a range of different people.

Most satisfyingly, the film clearly captures the fact that Professor Hawking realised his ambitions and what he was capable of irrespective of the barriers – physical, attitudinal, practical – that could have prevented this.

This is perhaps best demonstrated in the sequence following his pneumonia in Bordeaux. A doctor proposes a tracheotomy, meaning Professor Hawking will not be able to speak; feeling that Professor Hawking may not survive a journey back home the doctor asks Jane Hawking to consider ending her husband’s life. Jane refuses and instead finds a way that means Professor Hawking can communicate in a different way. Eventually, of course, he speaks using a synthesized voice – something probably as closely associated with him as black holes.

Without necessarily recognising it, A Theory of Everything provides one of the best representations of the Social Model of Disability I can remember seeing.

(From a film point of view, I think Eddie Redmayne as Stephen Hawking and Felicity Jones as Jane Hawking are fantastic. If the Best Actor awards are a straight fight between Redmayne and Benedict Cumberbatch (for his role as Alan Turing in The Imitation Game) then Redmayne should win hands down. Put simply: Redmayne is Hawking, whereas Cumberbatch is Cumberbatch being Turing.)

Update: The Washington Post shares similar thoughts regarding the film’s portrayal of disability (via @angelamatthews4)

Personal Health Budgets and the placebo effect

An idle thought following on from my last post about the evidence base and Personal Health Budgets: what if there’s a placebo effect associated with Personal Health Budgets?

As far as I understand it (as someone who is neither medically trained nor well-versed in the associated literature) there is good evidence that the placebo effect exists: when a patient takes medication or does something they perceive will help their condition to improve, it does (in either their perception or actuality), even if the medication or thing done has no proven effects.

Thus, irrespective of the evidence base of Personal Health Budgets, if people believe having a Personal Health Budget will make them better or contribute to making them better, will the mechanism of a PHB contribute to making them better?

(Note: just to be clear, I find the current evidence base regarding Personal Health Budgets, captured primarily in the PHB Evaluation, persuasive of the benefits of PHBs.)

How many countries are there? On evidence and PHBs

Image via http://damirbecirovic.com/
Image via http://damirbecirovic.com/

How many countries are there?

This seems like a straightforward question to answer, doesn’t it? Most primary school children could give you an answer, and even if they couldn’t they could quickly look it up in an Atlas.

But perhaps it’s not as simple a question to answer as we think. Scotland and Wales are countries, aren’t they(?), and yet they don’t appear on the list of countries recognised by the United Nations: the UN reckons there are 193 countries, including “the United Kingdom”. My Times World Atlas from 1986 says there were 173 countries. And football’s governing body, FIFA, currently has a list of 209 countries with football rankings.

So, in order to know how many countries there are we need to ask ourselves at least two prior questions: (1) What do we mean by a “country”?; and (2) Who are we asking?

Maybe the question is a bit complicated, so let’s ask ourselves an easier question by going up a level: how many continents on the world are there?

Erm, well. National Geographic reports: “By convention there are seven continents… [but] some geographers list only six [and] in some parts of the world students learn there are just five continents.” Which means the answer again depends on asking other questions, including: (1) What do we mean by a “continent”?; and (2) Who are we asking?

This “facts” business is tricky, isn’t it?

I share this by way of thinking about what we mean by “evidence” in the context of “evidence-based policy” and the recent example of Personal Health Budgets.

A significant announcement by Simon Stevens, the Chief Executive of NHS England, about Personal Health Budgets gave rise to some teeth-gnashing earlier this month.

The gnashing focused on the evidence base that underpins the effectiveness of Personal Health Budgets. Some folks, especially the well-known Ben Goldacre of Bad Science fame, are not convinced by the current status of the PHBs evidence. They think there should be at least a Randomised Control Trial (RCT) to test whether Personal Health Budgets work. Others, including advocates of personalisation in public services more generally, noted both the results of the existing evaluation of the Personal Health Budgets pilot and the value of all types of evidence, especially including the views of patients/users themselves.

Both groups therefore lay claim to “evidence-based policy”, which leads me to two reflections:

  1. It’s hardly an original thought (indeed, there are entire disciplines dedicated to such questions) but we must remember there is value associated with all different types of evidence and research methods. The value derived, and of the associated evidence arrived at, depends on what types of answers you’re hoping to uncover, how questions are framed and what pre-questions and/or assumptions underpin the framing of those questions. Different people have different thresholds for evidence and research methods, quite aside from the fact that one type of evidence or research method that’s a gold standard in one discipline could be next to useless in another.

For me, this is the equivalent of the first pre-question we came to in considering countries and continents: What do we mean by “evidence”?

  1. Let’s not even get into the “policy” bit of “evidence-based policy”. For example, when has policy ever been based on evidence anyway? Does policy making happen in a rational, evidence-led vacuum that is protected from the whims of politicians and public opinion which, heaven forfend, may not be evidence based? Notwithstanding questions of what we mean by evidence, it’s safe to say that not all policy is based on what evidence there is. This is therefore the equivalent of the second pre-question we came to in considering countries and continents: Who are we asking what we mean by “evidence”?

The up-shot of this in the context of the evidence base for Personal Health Budgets is that Ben Goldacre and advocates of personalisation are both right, and they’re both wrong. There cannot be a definitive answer to the question of whether Personal Health Budgets are effective until some other, perhaps unanswerable questions, are considered.

Infinite series, remarkable results, and personalisation in social care

There are many astounding things to be found in maths. One of my current favourites (brought to popular attention by Kottke) is:

1 + 2 + 3 + 4 + 5 + … (to infinity) = -1/12

That’s right. Adding all of the positive integers to infinity equals a small, minus fraction (and thus the joke of the tweet at the start of this post).

If you’re interested in how/why, the video below is a good starter [1].

So what?

Without wishing to make too much of a leap, I think this has two contradictory lessons when it comes to personalisation in adult social care.

  1. If you follow rules and/or processes absolutely rigorously then what you might end up with could confound nearly everyone and what they would sensibly or understandably expect. In some cases, it would be reasonable to suggest things like Resource Allocation Systems could also fall into this category.
  2. If you pursue something in an open-minded way, trusting the way in which you go about it and where the process takes you, then you might end up with a surprising, unexpected, but still wonderful and valid result. Again, in some cases, it’s reasonable to say things like co-production fall into this category.

[1] – Note the word starter. For a brief overview of why the video isn’t rigorous read this excellent article at Bad Astronomy. If you want the maths try this from John Baez (pdf) or read up on the Riemann Zeta function. But be warned: it’s a rabbit hole.