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.


Maths at the British Museum


The Bank Holiday was a great chance to get out and remember why it’s so good to live in London. The two highlights for me were a visit to Foyles Bookshop on the Charing Cross Road and a trip to the British Museum.

Every time I visit the British Museum I am reminded that the roof of the Great Court is one of the best visualisations of maths I’ve ever seen. Imagine, if you will, a huge box that stretches up from the ground to many hundreds of feet into space, well beyond the roof of the Great Court. Then what that magnificent roof does is pick out a wonderful, wonderful surface in that vast 3-dimensional space.

There’s no better physical manifestation of a manifold, of topology, or of what is simply a solution to an elegant equation than that roof.