JohnVideogames

The Pi Pico W 2 can run micropython, which is a reasonably limited and fun version of python that is accessible for beginners. If the types of projects you have in mind will involve reading simple sensors, turning on lights / speakers / beepers, or responding to buttons then you'll have a good time!

British homes are almost exclusively heated by natural gas boilers; home heating is only a small part of the grid electrical load.

I had to tackle a problem much like this one when analysing the polygons in planar graphs (analysis of planar chemical networks). A fun approach I found was to use a Delaunay triangulation (the dual of a Voronoi diagram; draw the Voronoi polygons and join their centres if they share an edge). Then join the triangles into larger polygons by removing edges that are in the Delaunay triangulation but not in your original planar graph. Once you've got no more edges to remove you've got all the polygons in the graph and convenient triangles for rendering / analysis.

For planar graphs on the surface of a torus, like they faced here, I just ended up adding extra images of the central unit cell, and then removing the excess. Not elegant (lots of weird corner cases) but convenient for visualisation.

It's obvious that you can't solve hallucinations by curating the dataset when you think about arithmetic.

It's trivial to create a corpus of True Maths Facts and verify that they're correct. But an LLM (as they're currently structured) will never generalise to new mathematical problems with 100% success rate because they do not fundamentally work like that.

"Accident & Emergency" - you may know it as the Emergency Room, but it's commonly called A&E in the UK

I love persistent homology; it's such a weirdo bit of maths that topologists keep trying to make useful. Similarly its bigger cousin, Topological Data Analysis, which as far as I can tell is used by people who love weirdo maths but also want to be paid.

I don't see how much good the persistent topology adds here, though. Why bother to do the abstract birth-death diagram and measure the variance in lifetime of these simplices, when the variance and median of the areas in the Voronoi diagram will give you a much easier and more interpretable result?

A black body will emit radiation (and receive radiation) until it's in equilibrium with its surroundings. In theory, the black bit of box radiates heat into space, and receives some of the CMB until both are at ~3K. It's how we cool satellites and spacecraft.

But the effect is quite small, and I'm suspicious of it (as the nearest surroundings are the hot planet, which transfer heat more effectively!)

Matplotlib for python solves this with a SymLogScale, which is allows you to chart (-10 ^3, - 10^2,..., 10^2, 10^3) in the way that you'd expect. It does this by being linear between two small limits (to avoid doing log(0) and upsetting the mathmos) and showing sign(x) * log(abs(x)) elsewhere.

You can probably do the transformation yourself directly on your data, and then do the inverse transformation relatively easily for your tool tips.

https://matplotlib.org/stable/api/scale_api.html#matplotlib....

One percentage point is a four relative percent increase here: (25/24) = 1.041

This is mad (especially from a UK perspective!) and it doesn't cover the key point of insurance: you insure risks that you couldn't afford if they went wrong. I insure my house, my life and my car because it'd be financial ruin for me and my partner if the worst case scenario happened to any of those. Sure, I could avoid going through insurance for small things and negotiate with 3rd parties to get bills down, but that wouldn't make a difference to a £500k house rebuilding cost, car crash settlement, or medical bill.

Similarly, if something went wrong then I couldn't go back and insure that risk afterwards! You can't insure unpredictable events as and when you need them, and there's no point in my organising insurance from the wreckage of my car, house or health.

Some factors you haven't considered:

1) heat pumps make much more sense when you don't burn things to power them. Solar PV, wind, hydro etc powering heat pumps mean you turn energy that is not heat into heat 2) there's no physical reason that you can't run a heat pump in reverse to provide cooling when necessary 3) I need to heat my house along with myself! In the UK there has been a "heat the person, not the home" movement in response to high heating gas prices. Result: a plague of damp and mouldy homes