Dork Scratchings

Quantum physics slash Silicon Valley drama Devs features an interesting architectural idea, namely a floating laboratory.  In order make a laboratory float you need very lightweight construction materials and it seems that they've solved this problem by using Menger Sponge bricks, which are very lightweight indeed. A Menger Sponge is a 3D version of this To make a Menger Sponge you need to perform an iteration.  Start with any shape, then make 8 copies each scaled down by a factor of 3, and use them to construct the perimeter of a square.  Then take that shape and do the same operation, and keep repeating.  The picture above shows that you end up with the same thing whether you start with a solid square or a hollow square.  But actually it doesn't matter what shape you start off with (as long as it's bounded). So, what's the area $A$ of the 2D version Menger Sponge shown above?  We can see from the first row in the picture that it's made up of 8 copies of...

Fossil Fuels are dragging your pension down!   At the end of last year I finally managed to switch to a fossil fuel free pension.  The journey wasn't completely straightforward, but it was worth it and hopefully this will become a lot easier in the near future. Why do this? There's a bunch of things you can do to reduce your carbon footprint including giving up flying and eating less meat, and I recommend all of them.  But right at the top has to be to stop investing in fossil fuel companies.  A typical pension pot in the UK is around £88,000 of which - typically - 4% is invested in oil, gas, and coal.  That's three and half grand of your money going directly to the likes of ExxonMobil.  If you simply spent this much on tax free petrol it would buy you about 8.8 tons of fuel which would create about 29 tons of CO2, or about 5x the annual emissions of an average Brit.  But investing probably results in an order of magnitude more emissions $^\dagger$ ...