sequestering carbon, one Christmas at a time X

His ’n’ hers Christmas presents:

another year, another tree

Due to a variety of circumastances, we got our tree a bit later than usual this year.  The first place we went had only four tiddlers left.  Fortunately, the next place had a decent one.

thick ice

It has been below, or around, freezing for a while now, and there’s a lot of ice around.  Today I noticed that the ice in one of our garden water tubs has expanded about 1cm above the rim of the tub.

Looking at it, I wondered how thick the ice was in total, to give that amount of expansion.  And then, could I calculate the thickness from just this observation?  And could I calculate it without knowing the height of the tub?

So I drew a sketch:

On the right is the liquid situation: water to the brim of the tub (which it was before the freeze).  On the left is the current situation, the top x units of water frozen to make x+d units of ice.  That does indeed look independent of the depth of the tub (unless maybe it is all frozen, which I doubt).

Let’s assume both the ice and water are at 0°C.  Wikipedia tell us that ice has a 9% increase in volume over water, which means that d = 0.09 x.

Since the observed d = 1cm, this implies that x = 11cm (much less than the depth of the tub, so no need to worry about it being frozen through), and so the whole ice layer is about 12cm (nearly 5 inches) thick.

That’s a thick layer of ice!

that's no cat!

Caught on our webcam around lunchtime today.  

Reviewing the images, we initially thought it was the neighbour’s ginger tom Trevor, as he likes prowling round our garden.  But it looked a bit weird.

Then, a few shots further on, we could see its thin legs, and it turned its head.

It’s a deer!  In our garden!  We are not in the countryside: we are surrounded by houses.  Where did it come from?  Where did it go, after it trotted past the car?

sequestering carbon, several books at a time CXXVI

 It's been a while since the last update, so there are rather more in the pile than usual:

Theoretical Computer Science for the Working Category Theorist

Noson S. Yanofsky.
Theoretical Computer Science for the Working Category Theorist.
Cambridge University Press. 2022

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I have been wanting to dip my toe in the sea of category theory for a while now, but have not found a suitable entry point. The books written for mathematicians are impenetrable. Those written for computer scientists lose me in the detail. When I came across this one, a book about computer science, written for category theorists, I was intrigued. I was reminded of a colleague of mine who collected foreign languages: he would learn them by reading a text he knew well in the language he wished to learn (memory offers up the thought it was Macbeth, but it may have been a different Shakespeare play). Maybe I could similarly learn the foreign language of category theory by reading about a topic I know, when written in that language? Especially since the book is a brisk 130 pages.

So, I am definitely not the target audience (being a computer scientist rather than a category theorist). And yet I feel I have learned more about category theory from this book than from any of the others I have tried. Not enough to be fluent, but enough that I can see what the concepts are, how they are put together, and how they can help illuminate a subject.

This was initially available as a PDF from the publishers site. I downloaded, and started active reading, which involved annotating the PDF with questions, thoughts, and ideas. (I come from a generation where annotating an actual physical book is Not Done.) I did skim a few of the more technical parts, but did read the whole thing. I then bought a hard copy.

As well as having a better understanding of Category Theory, I have a new perspective on theoretical computer science: the subset of functions that comprise computable functions is somewhat ugly to formalise.

This is the first in a series of Cambridge Elements: shortish works on Applied Category Theory. This one is highly recommended: I will be looking out for the others.

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For all my book reviews, see my main website.

Covid-19 diary: booster 2!

I got my (now annual?) booster jab today, along with a flu jab.  It was the now familiar efficient conveyor belt approach, with stations providing stickers and checking names, socially distanced queueing, and medical history questioning.  This included: “have you had Covid?”, “Yes, over four weeks ago”, which is long enough to be okay.  In fact, I booked this slot for my jab while I had Covid, as this was when I was contacted to come in.  If only I had been contacted a little earlier!  (Still, at least I now know Covid affects well-vaccinated me like a cold, and not worse.  Well, the current variant does, at least.)

I had the Pfizer jab in my left arm, and the flu jab in my right arm.  I again got a “young person’s flu jab” – because I'm still under 65.  Apparently the over-65 flu jab is higher dose, which may be why my other half had a reaction last year and I didn't.