coffee – Dan Q

Note #28553

Somebody should make a tea cosy but to fit a cafetiere.

That sounds like a great idea.

How I Learned the Pythagorean Theorem

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:

All of these graphics were made using my own 2019 implementation of Logo, TRRTL.COM: click on any graphic to continue drawing!

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:

Hypotenuse? More like need-another-try-potenuse.

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:

I remember being confused and frustrated that the result was so close but still wrong. The reason, of course, is that the relationship between the lengths of the sides of a triangle don’t scale in a 1:1 way, but this was the first time I found myself having to think about why.

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:

\sqrt{100^{2} + 100^{2}}

I so rarely get to use MathML that I had to look up the syntax.

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!

Footnotes

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.

Ten Pointless Facts About Me

This has been doing the rounds; I last saw it on Kev’s blog. I like that the social blogosphere’s doing this kind of fun activity again, these days¹.

1. Do you floss your teeth?

Umm… sometimes? Not as often as I should. Don’t tell my dentist!

Usually at least once a month, never more than once a week. I really took to heart some advice that if you’re using a fluoridated mouthwash then you shouldn’t do it close to when you brush your teeth (or you counteract the benefits), so my routine is that… when I remember and can be bothered to floss… I’ll floss and mouthwash, but like in the middle of the day.

And since I moved my bedroom (and bathroom) one floor further up our house, it’s harder to find the motivation to do so! So I’m probably flossing less. The unanticipated knock-on effect of extending your house!

2. Tea, coffee, or water?

I love a coffee to start a workday, but I have to be careful how much I consume because caffeine hits me pretty hard, even after a concentrated effort over the last 10 years or so to gradually increase my tolerance. I can manage a couple of mugs in the morning and be fine, now, but three coffees… or any in the mid-afternoon onwards… and I’m at risk of throwing off my ability to sleep later².

I keep a bottle of water wherever I work to try to encourage myself to hydrate, because I’ve got medical evidence to show that I don’t drink enough water! It sometimes works.

3. Footwear preference?

Basic trainers for everyday use; comfortable boots for hiking; slippers for when I’m working. Nothing special.

I wear holes in footwear (and everything else I wear) faster than anybody I know, so nowadays I go for good-value comfort over any other considerations when buying shoes.

A French Bulldog looks-on guiltily at a hand holding the remains of a pair of slippers that have been thoroughly shredded. — One time it was the dog’s fault that my footwear fell apart, but usually they do so by themselves.

4. Favourite dessert?

Varies, but if we’re eating out, I’m probably going to be ordering the most-chocolatey dessert on the menu.

5. The first thing you do when you wake up?

The very first thing I do when I wake up is check how long it is before I need to get up, and make a decision about when I’m going to do so. I almost never need my alarm to wake me: I routinely wake up half an hour or so before my alarm would go off, most mornings. But exactly how early I wake directly impacts what I do next. If I’m well-rested and it’s early enough, I’ll plan on getting up and doing something productive: an early start to work, or some voluntary work for Three Rings, or some correspondence. If it’s close to the time I need to get up I’ll more-often just stay in bed and spend longer doing the actual answer I should give…

…because the “real” answer is probably: pick up my phone, and open up FreshRSS – almost always the first and last thing I do online in a day! I’ll skim the news and blogosphere and “set aside” for later anything I’d like to re-read or look at later on.

6. Age you’d like to stick at?

Honestly, I’m good where I am, thanks.

Sure, I was fitter and healthier in my 20s, and I had more free time in my early 30s… and there are certainly things I miss and get nostalgic about in any era of my life. But conversely: it took me a long, long time to “get my shit together” to the level I have now, and I wouldn’t want to have to go through all of the various bits of self-growth, therapy, etc. all over again!

So… sure, I’d be happy to transplant my intellect into 20-year-old me and take advantage of my higher energy level of the time for an extra decade or so³. But I wouldn’t go back even a decade if it meant that I had to go relearn and go through everything from that decade another time, no thanks!

7. How many hats do you own?

Four. Ish.

They are:

A bandana. Actually, I own maybe half a dozen bandanas, mostly in Pride rainbow colours. Bandanas are amazingly versatile: they fold small which suits my love of travelling light these last few years, they can function as headgear, dust mask, neckerchief, flannel, etc.⁴, and they do a pretty good job of keeping my head cool and protecting my growing bald spot from the fierce rays of the summer sun.
A “geek” hat. Okay, I’ve actually got three of these, too, in slightly different designs. When they first started appearing at Oxford Geek Nights, I just kept winning them! I’m not a huge fan of caps, so mostly the kids wear them… although I do put one on when I’m collecting takeaway food so I can get away with just putting e.g. “geek hat” in the “name” field, rather than my name⁵.
A warm hat that comes out only when the weather is incredibly cold, or when I’m skiing. As I was reminded while skiing on my recent trip to Finland, I should probably switch to wearing a helmet when I ski, but I’ve been skiing for three to four decades without one and I find the habit hard to break.⁶
A wooly hat that I was given by a previous employer at a meetup in Mexico last year. I wore it a couple of times last winter but it’s otherwise not seen much use.

8. Describe the last photo you took?

The last photo I took was of myself wearing a “geek” hat. You’ve seen it, it’s above!

But the one before that was this picture of an extremely large bottle of champagne, with a banana for scale, that was delivered to my house earlier today:

A six-litre bottle of champagne, wrapped in bubble wrap and surrounded by packing peanuts, in a wooden transport case, with a banana resting atop it. — A 6-litre champagne bottle is properly-termed a Methuselah, after Noah’s grandad I guess.

Ruth and JTA celebrate their anniversary every few years with the “next size up” of champagne bottle, and this is the one they’re up to. This year, merely asking me to help them drink it probably won’t be sufficient (that’d still be two litres each!) so we’re probably going to have to get some friends over.

I took the photo to send to Ruth to reassure her that the bottle had arrived safely, after the previous attempt went… less well. I added the banana “for scale” before sharing the photo with some other friends, too.

A wooden case containing a completely smashed 6-litre champagne bottle. — The previous delivery… didn’t go so well. 😱

9. Worst TV show?

PAW Patrol. No doubt.

You know all those 1980s kids TV shows that basically existed for no other purpose than as a marketing vehicle for a range of toys? I’m talking He-Man (and She-Ra), Transformers, G.I. Joe, Care Bears, M.A.S.K., Rainbow Brite, and My Little Pony. Well, those shows look good compared to PAW Patrol.

3D render of a boy and six dogs (each dressed as a representative of a different service) - the PAW Patrol. Ugh. — Six pups, each endowed with exactly one personality trait⁷ but a plethora of accessories and vehicles which expands every season so that no matter how many toys you’ve got, y0u’re always behind the curve.

I was delighted when our kids graduated from PAW Patrol to My Little Pony: Friendship is Magic because it’s an enormously better show (the songs kick ass, too) and we could finally shake off the hollow, pointless, internally-inconsistent advertisement that is PAW Patrol.

10. As a child, what was your aspiration for adulthood?

This is the single most-boring thing about me, and I’ve doubtless talked about it before. At some point between the age of about six and eight years old, I decided that I wanted to grow up and become… a computer programmer.

And then I designed the entirety of the rest of my education around that goal. I learned a variety of languages and paradigms under my own steam while setting myself up for a GCSE in IT, and then A-Levels in Maths and Computing, and then a Degree in Computer Science, and by the time I’d done all of that I was already working in the industry: self-actualised by 21.

Like I said: boring!

Your turn!

You should give this pointless quiz a go too. Ping/Webmention me if you do (or comment below, I suppose); I’d love to read what you write.

Footnotes

¹ They’re internet memes, in the traditional sense, but sadly people usually use “meme” nowadays exclusively to describe image memes, and not other kinds of memetic Internet content. Just another example of our changing Internet language, which I’ve written about before. Sometimes they were silly quizzes (wanna know what Meat Loaf song I am?); sometimes they were about you and your friends. But images, they weren’t: that came later.

² Or else I’ll get a proper jittery heart-flutter going!

³ I wouldn’t necessarily even miss the always-on, in-your-pocket, high-speed Internet of today: the Internet was pretty great back then, too!

⁴ Obviously an intergalactic hitch-hiker should include a bandana, perhaps as well as an equally-versatile towel, in their toolkit.

⁵ It’s not about privacy, although that’s a fringe benefit I suppose: mostly it’s about getting my food quicker! If I walk into Dominos wearing a geek hat and they’ve got pizza on the counter with a label on it that says it’s for “geek hat”, they’ll just hand it over, no questions, and I’m in-and-out in seconds.

⁶ JTA observed that similar excuses were used by people who resisted the rollout of mandatory seatbelt usage in cars, so possibly I’m the “bad guy” here.

⁷ From left to right, the single personality traits for each of the pups are (a) doesn’t like water, (b) is female, (c) likes naps, (d) is allergic to cats, (e) is clumsy, and (f) is completely fucking pointless.

Note #26646

Fellow Abnibbers and I, who see each other extraordinary infrequently in our diaspora, have a tradition of sharing a group selfie when we happen to coincide. I forgot to take one when @garethbowker@infosec.exchange and I met today, and by way of penance I tried to draw what I should have done.