cp's mathem-o-blog

This visualisation shows for each council or unitary authority how many hours a week you’d need to work, earning minimum wage, in order to pay the median rent for a one-bed flat. The minimum wage is a national constant.

No justification is given for using the median rent. In a fair world, the median rent should be paid by someone on the median income. Assuming that people earning the minimum wage are the lowest earners¹ and make up X% of the population, then an upper bound for rent paid by people earning minimum wage should be the Xth percentile, if housing is provided fairly². If you’re not paying attention to this kind of thing, you might as well just say “average” instead of “median”.

Finally, there’s this:

Note that these figures are dramatic simplifications, used for illustrative purposes only: in reality tax payments, tax credits, housing benefit, council tax, utility bills and more substantially alter these figures.

So the figures are meaningless anyway – benefits might be so generous that very little of the lowest earners’ pay goes towards housing, or taxes might be so high that people really need to work many more hours than this statistic claims in order to keep a house.

Supposing that all of these problems are sorted out and we calculate a reasonable-sounding number of hours to work to earn rent each week, what should that number be? What if house prices plummeted but food became very expensive? I can’t think what these numbers are telling us that raw rent data aren’t already.

A question has occurred to me: would I be making life worse for those worse off me by living in a flat cheaper than I should be or, on the other hand, would spending a higher than average proportion of my income on rent drive prices up, having an effect on the bottom end of the market? I suppose taking a cheaper flat reduces the prices of nicer ones. This is why I don’t like economics.

1. this isn’t true: people earning cash in hand, for example, might earn less than the minimum wage but they still have an effect on house prices [↩]
2. another large assumption. [↩]

A long time ago, I realised that IKEA’s shopfitters must be experts in fractal dimension – they manage to lay out their shop so that you have to walk past every single thing they’re selling. You can’t just nip into IKEA – you have to go through the whole hour-long “It’s A Small World” of affordably wobbly furniture even if all you want is some kitchen utensils from the bit at the end.

I’d been meaning to add something about this to the Maths in the City site but it required going in to IKEA and taking a picture of their floor plan for illustration. I just remembered this morning that I’ve already taken one of those pictures, so I spent half an hour writing up this article – Fractal Dimension in IKEA.

Maths in the City posted this on twitter:

In order to make a number we can call, we need both of \[n=(10x)(13i^2)\] and \[m=\frac{\sin(xy)}{2.362x}\] to be integers. MATH PROBLEMS? continued »

Following this pair of tweets about water:

A bucket full of water contains more atoms than there are bucketfuls of water in the Atlantic Ocean

— The QI Elves (@qikipedia) February 5, 2012

.@qikipedia There are 10,000× more molecules per pint of water than pints of water on earth. (3×10^21 pints/earth vs 2×10^25 molecules/pint)

— Matt Parker (@standupmaths) February 5, 2012

The obvious question is, at what point are the two numbers the same? Or,

If you put all the Earth’s water into containers of the same size so that each container carries as many atoms of water as there are containers, how big is each container?

Putting all the world’s water in buckets continued »