Happy Polyamory Day y’all. (Plus max props to Petra without whom I’d have forgotten about it, like most years.)
Closest thing I did to celebrating it was going out to the pub last night for beer and food with my metamour, while our partner-in-common took our kids to see a film. Polyfam life isn’t always glamorous; but it is full of love.
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.
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.
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”.
Happy Stone Circle Sunday! The youngest and I went out to Avebury Henge, the world’s largest neolithic standing stone circle and henge.
I don’t want to withdraw any of our children from sec [sic] education lessons.
However they’re spelled, they’re a great idea, and I’m grateful to live in a part of the world where their existence isn’t the target of religious politics.
But if I can withdraw consent to receiving emails about sex education in Comic Sans then that’d be great, thanks. 😅
Today’s Hide And Seek With The Kids is brought to you by the Bishop’s Palace, St. David’s, Wales.
What’s that, girl? Two children are lost somewhere in this bookshop?
Yeah, I should probably find them and take them home for lunch.
Y’all seemed to enjoy the “overworld” map I shared the other day, so here’s another “feelie” from my kids’ ongoing D&D campaign.
The party has just arranged for passage aboard a pioneering (and experimental) Elvish airship. Here’s a deck plan (only needs a “you are here” dot!) to help them get their bearings.
In preparation for Family D&D Night (and with thanks to my earlier guide to splicing maps together!), I’ve finally completed an expanded “overworld” map for our game world. So far, the kids have mostly hung around on the North coast of the Central Sea, but they’re picked up a hook that may take them all the way across to the other side… and beyond?
Banana for scale.
(If your GMing for kids, you probably already know this, but “feelies” go a long way. All the maps. All the scrolls. Maybe even some props. Go all in. They love it.)
8-year-old, looking like a haystack: “Why do I have to brush my hair? I did it yesterday!”
White’s move. Mate in three. A giant chessboard is the perfect environment to teach a child some basic chess strategy, right?
Brought the kids up Knipe Scar with limited and challenging art materials (huge sheets of paper and thick marker pens) for a lesson in drawing what a landscape makes you feel, rather than focusing on what you can actually see.
“I know that losing your job was hard,” my 8-year-old said to me this evening, “So you can borrow this.” He handed me his newest soft toy.
“It’ll help you feel better when you’re sad. Keep him for the week.”
😭
8-year-old, angry: Give me that fucking thing right now!
Me: [Child’s name]! That’s not an acceptable way to ask for something!
8-year-old, calmer: Sorry. PLEASE can you give me that fucking thing?