As part of my efforts to reclaim the living room from the children, I’m building a new gaming PC for the playroom. She’s called Bee, and – thanks to the absolute insanity that is The Tower 300 case from Thermaltake – she’s one of the most bonkers PC cases I’ve ever worked in.
Back at the Rollright Stones fire New Year’s Day, per family tradition. This year the younger child counted 74, the elder 59. The curse that prevents you counting the same number twice continues!
I asked the younger child to “help” me calculate how much Yorkshire pudding batter to make for this Christmas dinner.
“Well,” he began, “I’m going to want FIVE Yorkshire puddings, soo…”
I’m not sure which of our children was last in this bath, but the configuration in which they’ve left their toys makes me feel as though I’m the subject of some kind of waterfowl-related shunning.
Perhaps they finally got wind or my heretical opinions on the God of Ducks (may he throw us bread) and they’ve collectively decided to disassociate from me?
The younger child and I were talking about maths on the school run this morning, and today’s topic was geometry. I was pleased to discover that he’s already got a reasonable comprehension of the Pythagorean Theorem1: I was telling him that I was about his age when I first came across it, but in my case I first had a practical, rather than theoretical, impetus to learn it.
It was the 1980s, and I was teaching myself Dr. Logo, Digital Research‘s implementation of the Logo programming language (possibly from this book). One day, I was writing a program to draw an indoor scene, including a window through which a mountain would be visible. My aim was to produce something like this:
My window was 300 “steps”2 tall by 200 steps wide and bisected in both directions when I came to make my first attempt at the mountain.
And so, naively, starting from the lower-left, I thought I’d need some code like this:
RIGHT 45 FORWARD 100 RIGHT 90 FORWARD 100
But what I ended up with was this:
I instantly realised my mistake: of course the sides of the mountain would need to be longer so that the peak would reach the mid-point of the window and the far side would hit its far corner. But how much longer ought it to be.
I intuited that the number I’d be looking for must be greater than 100 but less than 250: these were, logically, the bounds I was working within. 100 would be correct if my line were horizontal (a “flat” mountain?), and 250 was long enough to go the “long way” to the centrepoint of the window (100 along, and 150 up). So I took a guess at 150 and… it was pretty close… but still wrong:
So I found my mother and asked her what I was doing wrong. I’m sure it must have delighted her to dust-off some rarely-accessed knowledge from her own school years and teach me about Pythagoras’!
The correct answer, of course, is given by:
The answer, therefore, is… 141.421 (to three decimal places). So I rounded to 141 and my diagram worked!3
What made this maths lesson from my mother so memorable was that it fed a tangible goal. I had something I wanted to achieve, and I learned the maths that I needed to get there. And now it’s impermeably etched onto my brain.
I learned the quadratic equation formula and how to perform algebraic integration by rote, and I guarantee that it’s less well-established in my long-term memory than, say, the sine and cosine rules or how to solve a simultaneous equation because I’ve more-often needed to do those things outside of the classroom!
So I guess the lesson is that I should be trying to keep an eye out for practical applications of maths that I can share with my kids. Real problems that are interesting to solve, to help build the memorable grounding that latter supports the more-challenging and intangible abstract maths that they may wish to pursue later.
Both kids are sharp young mathematicians, and the younger one seems especially to enjoy it, so feeding that passion feels well-worthwhile. Perhaps I should show them TRRTL.COM so they can try their hand at Logo!
1 You know the one: the square of the triangle’s hypotenuse is equal to the sum of the squares of the other two sides. You could conceivably know it by some other mnemonic, but the essence is that if you know the lengths of two sides of any right-angled triangle, you can derive the length of the third with some moderately-simple arithmetic.
2 Just one way that Logo is/was a cute programming language was its use of “steps” – as in, turtle-steps – to measure distances. You might approximate them as pixels, but a “step” has meaning even for lines that don’t map linearly to pixels because they’re at wonky angles, for example.
3 I’d later become unstuck by rounding, while trying to make a more-complex diagram with a zig-zag pattern running along a ribbon: a small rounding error became compounded over a long time and lead to me being a couple of pixels off where I intended. But that’s another story.
This checkin to GCAJJP3 Kohtauspaikat - Virtual Reward 4.0 reflects a geocaching.com log entry. See more of Dan's cache logs.
The younger child and I nipped across for a photo while we waited for our tram to come.
This checkin to GC1JA6P Töölön kirjasto reflects a geocaching.com log entry. See more of Dan's cache logs.
Very easy find for the kids and I after a delightful visit to the Tram Museum. We went to the coordinates and instantly saw the cache! SL, TFTC, and greetings from Oxfordshire, UK.
This checkin to GCAC54Z Aquarium reflects a geocaching.com log entry. See more of Dan's cache logs.
QEF for the elder child and I while on holiday. TFTC, and greetings from Oxfordshire, UK!
[13:16 local time]
Found the younger child not-in-bed but dancing around his room, using his pyjamas as perhaps some kind of streamers or flags.
Me: “Why aren’t you in bed?”
Him: “I’m sorry; I got distracted by how amazing I am.”
Hard to argue with that.
This post is part of 🐶 Bleptember, a month-long celebration of our dog's inability to keep her tongue inside her mouth.
It’s the Third of Bleptember, and this routine-loving pupper is still confused by the fact that the elder child doesn’t come on the school-run morning walk any more, instead leaving early to catch the bus to her new school. Look at those big anxious eyes, poor thing!
This post is part of 🐶 Bleptember, a month-long celebration of our dog's inability to keep her tongue inside her mouth.
The Second of Bleptember brought back the morning school run into this doggo’s routine. And while she was glad of the extra walk, she also seemed glad of the opportunity to lie down in a quiet, child-free hallway upon our return home.
The dog came out for a walk with the eldest kid and I, but we couldn’t stop her sticking her head down rabbitholes!
(Oh, and the dog kept doing it, too.)
Looking forward to the school run starting again next week… so I get a bonus excuses for walks around our beautiful village!
The elder of our two cars is starting to exhibit a few minor, but annoying, technical faults. Like: sometimes the Bluetooth connection to your phone will break and instead of music, you just get a non-stop high-pitched screaming sound which you can suppress by turning off the entertainment system… but can’t fix without completely rebooting the entire car.
The “wouldn’t you rather listen to screaming” problem occurred this morning. At the time, I was driving the kids to an activity camp, and because they’d been quite enjoying singing along to a bangin’ playlist I’d set up, they pivoted into their next-most-favourite car journey activity of trying to snipe at one another1. So I needed a distraction. I asked:
We’ve talked about homonyms and homophones before, haven’t we? I wonder: can anybody think of a pair of words that are homonyms that are not homophones? So: two words that are spelled the same, but mean different things and sound different when you say them?
This was sufficiently distracting that it not only kept the kids from fighting for the entire remainder of the journey, but it also distracted me enough that I missed the penultimate turning of our journey and had to double-back2
With a little prompting and hints, each of the kids came up with one pair each, both of which exploit the pronunciation ambiguity of English’s “ea” phoneme:
These are heterophonic homonyms: words that sound different and mean different things, but are spelled the same way. The kids and I only came up with the two on our car journey, but I found many more later in the day. Especially, as you might see from the phonetic patterns in this list, once I started thinking about which other sounds are ambiguous when written:
(If you’ve got more of these, I’d love to hear read them!)
I’m interested in whether heterophonic homonyms are common in any other languages than English? English has a profound advantage for this kind of wordplay3, because it has weakly phonetics (its orthography is irregular: things aren’t often spelled like they’re said) and because it has diverse linguistic roots (bits of Latin, bits of Greek, some Romance languages, some Germanic languages, and a smattering of Celtic and Nordic languages).
With a little exploration I was able to find only two examples in other languages, but I’d love to find more if you know of any. Here are the two I know of already:
If you speak more or different languages than me and can find others for me to add to my collection of words that are spelled the same but that are pronounced differently, I’d love to hear them.
Special Bonus Internet Points for anybody who can find such a word that can reasonably be translated into another language as a word which also exhibits the same phenomenon. A pun that can only be fully understood and enjoyed by bilingual speakers would be an especially exciting thing to behold!
1 I guess close siblings are just gonna go through phases where they fight a lot, right? But if you’d like to reassure me that for most it’s just a phase and it’ll pass, that’d be nice.
2 In my defence, I was navigating from memory because my satnav was on my phone and it was still trying to talk over Bluetooth to the car… which was turning all of its directions into a high-pitched scream.
3 If by “advantage” you mean “is incredibly difficult for non-native speakers to ever learn fluently”.
Back in 2021, as part of a course I was doing at work, I made a video talking about The Devil’s Quoits, a henge and stone circle near where I live.
Two years later, our eldest was at school and her class was studying the stone age. Each of three groups were tasked with researching a particular neolithic monument, and our eldest was surprised when she heard my voice coming from a laptop elsewhere in the class. One of her classmates had, in their research into the Quoits, come across my video.
And so when their teacher arranged for a school trip to the Devil’s Quoits, she asked if I could go along as a “local expert”. And so I did.
And so this year, when another class – this time featuring our youngest – went on a similar school trip, the school asked me to go along again.
I’d tweaked my intro a bit – to pivot from talking about the archaeology to talking about the human stories in the history of the place – and it went down well: the children raised excellent observations and intelligent questions1, and clearly took a lot away from their visit. As a bonus, our visit falling shortly after the summer solstice meant that local neopagans had left a variety of curious offerings – mostly pebbles painted with runes – that the kids enjoyed finding (though of course I asked them to put each back where they were found afterwards).
But the most heartwarming moment came when I later received an amazing handmade card, to which several members of the class had contributed:
I don’t know if I’ll be free to help out again in another two years, if they do it again2: perhaps I should record a longer video, with a classroom focus, that shares everything I know about The Devil’s Quoits.
But I’ll certainly keep a fond memory of this (and the previous) time I got to go on such a fun school trip, and to be an (alleged) expert about a place whose history I find so interesting!
1 Not every question the children asked was the smartest, but every one was gold. One asked “is it possible aliens did it?” Another asked, “how old are you?”, which I can only assume was an effort to check if I remembered when this 5,000-year-old hengiform monument was being constructed…
2 By lucky coincidence, this year’s trip fell during a period that I was between jobs, and so I was very available, but that might not be the case in future!