October 2024 Archives

Note #24871

Just received an unsolicited marketing email from a company that I asked to remove me from their systems eleven and a half years ago (!).

I haven’t heard from them since then.

The marketing email is sent using a platform that “uses AI to help you seamlessly connect with your customers”. By which I assume the platform means “we’ll crawl your email history to find anybody we can possibly spam”.

Just gonna go grab my GDPR/DPA2018 beating-stick. This is gonna be a fun one.

Hero of Alexandria

A little under two millennia ago¹ there lived in the Egyptian city of Alexandria a Greek mathematician and inventor named Hero², and he was a total badass who invented things that you probably thought came way later, and come up with mathematical tricks that we still use to this day³.

Inventions

Illustration of an aeolipile, showing a heated sphere or cylinder of water spraying steam in two different directions, causing it to rotate. — If you know of Hero’s inventions because of his aeolipile⁴,known as “Hero’s engine”, I’ve got bad news: it was probably actually invented by his predecessor Vitruvius. But Hero *did* come up with a way to use the technique to make a pneumatic temple door that automatically opened when you lit the fires alongside it.

Hero is variably credited with inventing, in some cases way earlier than you’re expecting:

automatic doors (powered either by pressure plates or by lit fires),
vending machines, which used the weight of a dispensed coin to open a valve and dispense holy water,
windmills (by which I mean wind-powered stationary machines capable of performing useful work),
the force pump – this is the kind of mechanism found in traditional freestanding village water pumps – for use in a fire engine,
float-valve and water-pressure based equilibrium pumps, like those found in many toilet cisterns, and
a programmable robot: this one’s a personal favourite of mine because it’s particularly unexpected – Hero’s cart was a three-wheeled contraption whose wheels were turned by a falling weight pulling on a rope, but the rope could be knotted and looped back over itself (here’s a modern reimplementation using Lego) to form a programmed path for the cart

Illustration showing mechanism of action of a fire-powered automatic door: heated air expands to displace water into a vessel whose now-increased weight pulls ropes wrapped around two wheels which pull open a pair of temple doors. — It’s just headcanon, but I choose to believe that the reason Hero *needed* to invent the fire extinguisher might have involved the number of “attempting to make fire do work” inventions that he came up with.

Mathematics

If you know of Hero because of his mathematical work, it’s probably thanks to his pre-trigonometric work on calculating the area of a triangle based only on the lengths of its sides.

But I’ve always been more-impressed by the iterative⁵ mechanism he come up with by which to derive square roots. Here’s how it works:

Let n be the number for which you want to determine the square root.
Let g₁ be a guess as to the square root. You can pick any number; it can be 1.
Derive a better guess g₂ using g₂ = ( g₁ + n / g₁ ) / 2.
Repeat until g_N ≈ g_N-1, for a level of precision acceptable to you. The algorithm will be accurate to within S significant figures if the derivation of each guess is rounded to S + 1 significant figures.

That’s a bit of a dry way to tell you about it, though. Wouldn’t it be better if I showed you?

Put any number from 1 to 999 into the box below and see a series of gradually-improving guesses as to its square root⁶.

Interactive Widget

(There should be an interactive widget here. Maybe you’ve got Javascript disabled, or maybe you’re reading this post in your RSS reader?)

Maths is just one of the reasons Hero is my hero. And now perhaps he can be your hero too.

Footnotes

¹ We’re not certain when he was born or died, but he wrote about witnessing a solar eclipse that we know to have occurred in 62 CE, which narrows it down a lot.

² Or Heron. It’s not entirely certain how his name was pronounced, but I think “Hero” sounds cooler so I’m going with that.

³ Why am I blogging about this? Well: it turns out that every time I speak on some eccentric subject, like my favourite magic trick, I come off stage with like three other ideas for presentations, which leads to an exponential growth about “things I’d like to talk about”. Indeed, my OGN talk on the history of Oxford’s telephone area code was one of three options I offered to the crowd to vote on at the end of my previous OGN talk! In any case, I’ve decided that the only way I can get all of this superfluity of ideas out of my head might be to blog about them, instead; so here’s such a post!

⁴ If the diagram’s not clear, here’s the essence of the aeolipile: it’s a basic steam reaction-engine, in which steam forces its way out of a container in two different directions, causing the container to spin on its axis like a catherine wheel.

⁵ You can also conceive of it as a recursive algorithm if that’s your poison, for example if you’re one of those functional purists who always seem somehow happier about their lives than I am with mine. What’s that about, anyway? I tried to teach myself functional programming in the hope of reaching their Zen-like level of peace and contentment, but while I got reasonably good at the paradigm, I didn’t find enlightenment. Nowadays I’m of the opinion that it’s not that functional programming leads to self-actualisation so much as people capable of finding a level of joy in simplicity are drawn to functional programming. Or something. Anyway: what was I talking about? Oh, yeah: Hero of Alexandria’s derivation of square roots.

⁶ Why yes, of course I open-sourced this code.

PortAventura

Made it through a day and a half of theme park fun with the kids. Time for a much-needed beer, then as long a sleep as circumstance will allow.

Sex With Monsters

This is a repost promoting content originally published elsewhere. See more things Dan's reposted.

Simon Shadows (via Oh Joy Sex Toy)

Just in time for Halloween, this comic (published via the ever-excellent Oh Joy Sex Toy) is fundamentally pretty silly… and yet still manages to touch upon important concepts of safer sex, consent, aftercare etc. And apparently, based on Simon’s portfolio, his “thing” might well be that niche but now fun-sounding genre of “queer/monster horror”.

Dan Q did not find GC448J6 EL TRESOR DEL POU DEL MON

This checkin to GC448J6 EL TRESOR DEL POU DEL MON reflects a geocaching.com log entry. See more of Dan's cache logs.

The geokids and I had to give up after an extended search. We solved the riddle (we think) and counted steps, but, being unsure, hunted for a nearby map and attempted to un-do he farmer’s mistake. Still no luck. 😔 Sadly it’s our last morning in the city so this one might have to remain a blue spot on our map for a while, though I’m sure I’ll think of something I missed when I get back to my computer.

Dos Huevos

For some reason, the breakfast chef assumed that when I asked for two eggs benedict that I might want them on two separate plates. As if I WEREN’T totally planning to scoff them both myself! 😂

Dan Q found GCA8R9X Xemeneies a Barcelona #2 Foneria Giralt

This checkin to GCA8R9X Xemeneies a Barcelona #2 Foneria Giralt reflects a geocaching.com log entry. See more of Dan's cache logs.

An early morning walk from my hotel while I waited for the rest of my family to wake up brought me to this, another old chimney. I’ve really been enjoying discovering these relics of the industrial history of this part of the city.

Unusual and well-disguised cache container! 😁 First name in a clean new log sheet too; thanks to the CO for maintaining their caches! ❤️ SL, TFTC/GPC. Greetings from Oxfordshire, UK!

Dan Q found GC1788D Torre Agbar

This checkin to GC1788D Torre Agbar reflects a geocaching.com log entry. See more of Dan's cache logs.

My 7-year-old, who’s really interested in skyscrapers, was excited to point this one out to me upon our arrival in Barcelona on Saturday, observing that it looks very similar to “The Gherkin”/30 St Mary Axe, a highly-recognisable London landmark. He’s right, it does, and it’s a shame he couldn’t join me on this geocaching expedition but he was still around asleep when I set off.

I stood pretending to wait for a bus for a little while, then quickly found, signed, and replaced the cache. TFTC/GPC!

Dan Q found GC6TKBN MALIP – Monument a les il·lusions perdudes

This checkin to GC6TKBN MALIP - Monument a les il·lusions perdudes reflects a geocaching.com log entry. See more of Dan's cache logs.

After failing to find this yesterday, I came back earlier this morning for another go. Thanks to the hint, I was pretty confident I’d been looking in the right place, and a message from the CO helped confirm this (gracias!).

There are, in my mind, two significant challenges to this cache:

1. It’s a challenging and unusual hiding place and you will need to use the hint. I see from previous logs that some people used the hint… and still got stuck! Got to look around and see what it could mean. This bit… I got right. In fact, I touched the cache yesterday but just didn’t know it for sure!

2. It’s a busy area in which searching for a geocache… looks a bit suspicious! I came at almost 08:00 yesterday and, probably because it was a weekday, the area had lots of muggles. I felt self-conscious hunting for the cache and that made it harder. Coming back today an hour earlier made all the difference.

A really sneaky cache good enough to hunt for twice. TFTC/GPC. FP awarded. Greetings from Oxfordshire, UK.

Dan Q found GC1BA7C Parc central del Poblenou

This checkin to GC1BA7C Parc central del Poblenou reflects a geocaching.com log entry. See more of Dan's cache logs.

QEF while on my way back to my hotel after a morning of exploring the area. GPC.

Dan Q did not find GC6TKBN MALIP – Monument a les il·lusions perdudes

This checkin to GC6TKBN MALIP - Monument a les il·lusions perdudes reflects a geocaching.com log entry. See more of Dan's cache logs.

An extended search bore no fruit this morning. Worth help of the hint and an initial survey I was pretty confident in what kind of thing I was looking for, but though i inspected many candidate hiding places I couldn’t quite find it. Perhaps I’d do better at a less-busy time.

Dan Q found GCARWF7 Antigua Fábrica de Tallada i Lora

This checkin to GCARWF7 Antigua Fábrica de Tallada i Lora reflects a geocaching.com log entry. See more of Dan's cache logs.

Visiting from Oxford, UK, I woke up early this morning and decided to come out for an explore before my partner and the children got up. A walk through the park brought me to this delightful piece of industrial history! With the hint, the cache was soon in hand and the log signed. GPC!