Mary Gardiner (puzzlement)
I don’t own a car, so while I’m a bit late in life for this tradition, I’ve nevertheless been driving my father’s car while my parents are overseas. They’re back today, so last night I decided to fill the tank for them before they got back.
I wasn’t coming into this in the best of states. I had a three year old child in the car. It was evening peak hour in Sydney, and although I was yet to realise that events in Moore Park were slowing traffic even more than usual back as far as the Lane Cove tunnel (for reference, Moore Park and the Lane Cove tunnel are 15km apart on entirely different sides of Sydney Harbour), I had already had to turn from Lane Cove Road onto Epping Road, which has to be one of the worst designed intersections of all time, except for all other intersections of major arterial roads in Sydney, which are also awful in peak hour. (For example, it was often considerably faster to get off my bus on the Pacific Highway, walk 1km around onto Epping Road, and catch an entirely new bus further ahead in the queue than it used to be to wait for the bus to turn that same corner.) But Lane Cove and Epping is my especial enemy after most of a decade at Macquarie University, I can’t even go into it now. And finally, I was late to meet my sister, who was sitting on the front step of my house in the dark.
Then I pull up to a pump, which is also (I knew) on the wrong side of the vehicle, run back and forth between the drivers seat and the fuel hatch (on opposite sides of the vehicle) until I find the latch for it, unhook the hose from the bowser, drape it over the top of the car, and get a good look at the fuel cap for the first time. “DIESEL”.
Before everyone reaches for smelling salts, all that happened here is I said “oh for real?”, put the ULP hose away, got back in the car, moved it, hunted around on foot for the diesel pump, found it, moved the car there, filled the car, spilled big splotches of diesel all over my dress (that made for a fun drive home, ugh, sorry your car interior smells of diesel Dad, but I also note it smelled strongly of cattle before that), paid for the fuel, got back in the car, apologised profusely to my 3 year old — who is very well behaved in cars, those of you who’ve heard my story about him in planes will be surprised to hear, and who hadn’t peeped the whole time other than to say “oh no Mama diesel” sympathetically — and drove home in infuriating traffic, about 45 minutes late to hand over the car to my sister.
So far so good right? But my point is this. That label “DIESEL” was in a nice elegant thin font in white letters on the fuel cap. It was big but it didn’t look so terribly important, I can imagine “TOYOTA”, say, being lettered much the same (or “NO SMOKING” which is important in general, but less so to me in particular). I probably only would have needed to have been in about a 10% worse mood to have just missed it entirely and filled the tank with ULP, which I just now confirmed is as expensive a mistake as I thought it was, and this morning my parents would be flying into the country in order to find that I’d wrecked the engine. Good grief.
My point is this: it would be nice if that cap was, say, all in red, and burned to the touch in the close proximity of ULP or something (yeah yeah, not really). In order to avoid a mistake that would cost weeks and ten thousand dollars to rectify, and moreover would be at the expense of my father’s very car reliant job too, there’s elegant white lettering on black? There aren’t even differently sized or shaped interfaces? At least I can take a UI design lesson from it: I will always in future imagine evening peak hour, a toddler, running late, and how to help that person not spend ten thousand dollars on a momentary oversight.
And if you have a diesel vehicle and want to loan it to your frazzled adult daughter (or frazzled adults of your acquaintance in general) I see that there are after market mis-fuelling prevention devices. Good to know someone stepped in. Although at this particular service station, I would have had to pull it off again because it was a high flow bowser. So, you know, not exactly ideal still.
Week 5 of the Alphabet Sufficiency: F.
A few years ago, a friend’s children were in the target age range for the Toy Story franchise, and he told me with some shock that his eldest had “missed the entire point” of Toy Story in being Team Buzz Lightyear rather than Team Woody. And I nodded sagely, having only ever seen Toy Story 2 and that on its cinematic release. I knew only that Woody is the old faithful toy and Buzz Lightyear the new advertising pushed successor toy.
Well, now I’ve seen Toy Story, and frankly, I’m not Team Woody, and that’s putting it mildly. In fact, Woody horrifies me so much it’s part of the reason I’m Team Sid.
A brief recap of Toy Story for those of you who don’t have children or aren’t playing along with Pixar at home. First, concept: toys are alive and sentient, but only when no one is looking. Andy, child, loves cowboy toy Woody the best of all, but for his birthday he receives space ranger Buzz Lightyear who becomes at least co-equal in his affections. Meanwhile, when Andy is absent Buzz also usurps Woody in the affection of the actual toys. His main weakness is that he is utterly unaware he is a toy, giving Woody an opening to trick him into travelling to a “space port” (a space-themed pizza place). Both toys become separated from Andy’s family and end up in one of those arcade claw machines, and are acquired by Sid, an older boy who is Andy’s next-door neighbour and who mistreats toys. After various mishaps, Sid is about to launch a small rocket with Buzz attached into the sky, when Woody raises all Sid’s other toys in rebellion. Woody and Buzz then pursue the moving van containing Andy’s family’s possessions and eventually rocket into Andy’s car where he finds them as if they’d been left there all along. Aww.
And what I’ve tried and failed to hide in that summary is that Woody is an utter jerk for most of the movie. Before Buzz’s arrival he’s portrayed as the patronising father-figure of the toy room, running it like a corporate office, surrounded by bemused toys and a small number of uncertain sycophants. Really appealing. He displays some real fear and loneliness after Buzz arrives and he’s swept from his prime position on Andy’s bed, but only in complete privacy. Once he discovers Buzz’s weakness he is triumphant and merciless, mocking him to his face. “You think you’re a real spaceman? Oh all along I thought it was an act.” He then proceeds to manipulate every one of Buzz’s resulting traits — singlemindedness, a belief that his mission requires him to return to space — at first trying and failing to get other toys to join the mockery and then realising that he can get Buzz to act based on his beliefs. Sure there’s a sort of redemption arc in which Woody saves Buzz from Sid and turns down a few opportunities to leave him, but by then his fate was sealed. Even Mr Potato Head isn’t as anti-Woody as me.
Meanwhile, Buzz is pretty appealing, as long as all-American (all-Galatican?) hero works for you. He manages the other toys in a loose military model rather than a corporate model, where at least there’s room for improvement rather than the system being set up to manage their (presumed) static inadequacies. He treats Woody as more-or-less an equal (admittedly based on rank; he believes Woody to be the local sheriff) and trusts without question that Woody is transparent and honest; at least it doesn’t make me want to spit in his face. He’s easily manipulated, but his view of the world is very far from consensus reality: if I am actually a sentient child’s toy, I’ve probably been easily manipulated too in my time.
I am not unsympathetic to my friend’s child here. Given a choice between a Woody doll and a Buzz doll, I know which I’d choose. But the narrative point of view, which positions Woody’s behaviour as understandable and forgivable, bugs me so much that I ended up naturally sympathetic to the antagonist.
Let’s re-evaluate Sid. First, to be fair, even from my point of view, he has some serious failings. The most serious is that he’s not at all kind to his younger sister. Which is grave indeed, but I do notice that his sister doesn’t seem to be frightened of him, and when Sid displays weakness (extreme fear of toys, not unreasonable given he’s just discovered they’re sentient and dislike him) she immediately and thoroughly takes advantage. He doesn’t seem to have decisively established dominance in the family and it’s implied that his mother has the final say outside of his bedroom. His other failing (to me) is the scene where he’s shown being pretty brutal with the arcade equipment. He does also do a couple of villain-marked things, like cackling while thunder rolls, but that’s not actually an immoral act. The Doylist explanation for this is pretty obvious — he’s being positioned as the villain — but my Watsonian explanation is that he is playing at being the villain, the bad-boy toy torturer. A lot of his other “failings” from the narrative point-of-view are the atmospherics surrounding him, which look like Pixar straight-out buying into dubious cultural tropes about people who listen to metal. Skull on your t-shirt, evil, not the same thing.
And see the thing is, except when they’re his sister’s toys, what Sid does to toys isn’t actually wrong. He has no reason to begin to suspect they’re sentient. (And the movie does something really annoying here: it’s OK to reveal this to Sid to save Buzz in particular… why? It wasn’t OK to reveal it to save Hannah’s doll, for example.) And what he does with them is frankly rather cool and inventive. A baby doll’s head with mechanical spider-legs? If my kid does that I’ll take photos and puff about it in my parenting blog. He’s also a pretty good actor, what with the thunderclap cackle, and the different voices he used to enact his surgical scenes, in which he appears to be a mash-up of Dr Frankenstein and standard medical dramas.
Consider it this way: Andy’s play is pretty conventional. There’s a stick-up. The woman gasps in fear. The brave sheriff saves the day. Hooray! Sid’s play is more transformative, both physically transforming the toys and mashing together whatever tropes suit him: medical drama, medical horror, ground control, meteorological reports, generic Evil Overlord cackling. Sid is the fan and the hacker. Really Sid’s main mistake in my book was not sending Woody on a one-way rocket ship. It’s OK Sid, you weren’t to know. I’m still Team Sid.
Week 4 of the Alphabet Sufficiency: V.
I’ve circled on ‘value’ for a long time; this is the prompt of this essay series for which I’ve started writing four times. My relationship with value is ongoing, and I’ve got hidden writings now on how I try and tell if other people value me, on my relationship with the sunk cost fallacy, on the epistemological problems with measurement (that is, a measurement and reality are not the same thing), and even on irritating probability mind tricks that depend on weird phrasings.
But the sunk cost fallacy suggests I should pick something bite-sized and be done with it, so here it is: I am coming to value my PhD work. (Status of that: I’ve finished writing and been examined and done my required corrections. I’m waiting for university sign-off and eventual graduation. So, I’m not a PhD holder, but I will be. I’m a PhD finisher already.)
This has been a while coming. There are lots of things wrong with the PhD process, maybe less so in Australia than in some other countries and maybe less so in computer science than in some other disciplines, if only because for some computing employers outside the academy it’s seen as a positive signal rather than a negative one, as is the stereotype of how a PhD is seen in some other fields. (Note, stereotype; I know nothing of the reality.)
And it’s much easier to feel warm and fuzzy about something when the hard bit is nearly a year in the past, too. Somewhere in my photo collection there’s a self-portrait of me late last May, at 11pm, eating the spag bol my sister dropped off in a care package, alone in darkness. You know you’re at a peak life-stress when Steph drops off food: the other time last year was when I was unexpectedly hospitalised for a week last year. It was a cold evening, I remember taking the photo to email my family and I don’t know that I felt that was I was doing was valuable at the time so much as simply wanting it to be in the past. And also wanting to warm up. I did two things last May: write stuff, and learned a whole lot about climbing Everest (mostly from Alan Arnette’s blog). Not metaphorically, literally, because May is the end of the Everest climbing season. The Everest climbers and I were both cold, and both working hard. I felt we had a lot in common. Even if they got better photos than I did.
So, we need to allow for rose-coloured glasses, very much so. And I’ll also note that I don’t think a PhD is the only, or the best, or a better, way to obtain a lot of what I value from it. But it comes down to this: I wrote about 100 pages in 2 months. In that time, I did a small amount of experimental work (obviously most of it was done by then), I evaluated a lot of sources, and I did a lot of work in explaining things. I can tell you (but won’t, here) how I could re-do the whole thing, much better. And I did so much work independently — not always well in hindsight, but work — that every other project in my life pales in terms of sheer clinging onto the side of the mountain trying not to fall down it.
It will be a long time before I can decide if I did any of this well even in the (frankly unlikely) event that I read it end-to-end ever again. But the value I’m deriving from simply having done it is not negligible. It takes a lot of written material to intimidate me now, for one thing. I can read scientific literature outside my field and have some idea of how to scale the mountain. I feel much happier about having done it than I did at any time in 2012, including the day after handing it in. Its value probably still doesn’t come to seven years of opportunity cost, but it has some.
Bonus value: this blog entry has caused me to go back over my journals of last May, which include a few hilarious (entirely to me) moments:
[The thesis] also probably going to be longer than I expected: probably 150 pages or so in terms of sheets of paper, around 100 to 110 pages of non-appendix content.
Amusing or horrifying, your call: I sent it to the printers ten days after writing that, with 140 pages of non-appendix content and 201 total, so I blew my own projected page estimate by over 30 pages of prose in a week and a half. (I added a lot this year in response to my examiners too: the final version hasn’t been printed but is around 155 pages of non-appendix content and 230 total.)
Full disclosure: like many theses, it is double-spaced. It’s difficult to word-count accurately when you write in LaTeX, but it’s about 65000–70000 words, give or take, including appendices, which is a bit long for a science thesis, but that’s not unusual in computational linguistics.
May 29th (the day I ordered the printing of my examination copies):
I said to [my supervisor] that some people do all the training for a black belt and then don’t take the test (actually I don’t even know if this is true, but I said it) because they know within themselves that they are worthy and so…
He said “No. No no no no no. No way.”
The ‘f’ word for next week is ‘favourite’.
I flew home from the US yesterday and when I arrived in Sydney I got a message from my husband saying that Malcolm Tredinnick had died. According to this piece by Simon Dulhunty, he was found on Monday to died at home in Sydney, possibly after a seizure, while I was at PyCon 2013.
I’ve known Malcolm slightly since my first linux.conf.au in Sydney 2001. In late 2004 I interviewed for a job at CommSecure (since closed) where he was then working, having been a lead developer of and continuing to maintain and develop a real-time data delivery system for the Hong Kong stock exchange. (The eventual end of that contract was the reason CommSecure later closed.) He was also my boss for about half of 2005 until I left to begin my PhD in early 2006.
I still caught up with him at technical events, the last long conversation I remember with him was at PyCon AU 2011 where my husband Andrew and I had a very Malcolm conversation with Malcolm, which roved over the paperwork hassles of having no fixed address (Malcolm travelled a lot and went through periods where he housesat or lived in serviced apartments for a while), the Australasian chess community, and some gentle mutual trolling between him and Andrew over narrative testing.
What I will remember most about Malcolm is that he was a teacher at heart. I never personally had this relationship with him, but I knew several people at CommSecure and elsewhere who Malcolm had tutored or mentored in programming, often over a very long period of time. Elsewhere I know he had taught mathematics (long before I knew him, he very nearly completed a PhD in mathematics when his area suddenly became fashionable and about 50 years of work was done in 6 months by incoming mathematicians) and chess. I will also remember his dry and sadonic approach to nearly everything (for a very recent example, Malcolm gives useful parenting advice), combined with “really, how hard could it be?” used both straightforwardly and distinctly otherwise. Goodbye Malcolm.
Update, funeral plans: Ray Loyzaga who was Malcolm’s close friend, and long-time founder-CEO of CommSecure, has announced that Malcolm’s funeral will be at 2:30pm Thursday April 4, at Camellia Chapel, Macquarie Park Cemetary, North Ryde, Sydney.
- Goodbye Malcolm by Jacob Kaplan-Moss on the Django blog
- Goodbye Malcolm (Tredinnick) on LWN, with comments
- Malcolm Tredinnick memorial on Storify
- Twitter, Google+, Flickr
- video and audio of him speaking are everywhere, see for example:
- linux.conf.au 2003: Using autoconf, automake and friends (audio only)
- linux.conf.au 2004: The GNOME Platform Libraries (audio only)
- PyCon AU 2011: Behaviour Driven Development
- linux.conf.au 2012: What is in a tiny Linux installation?
- PyCon Asia/Pacific 2012: Fun with Iterators and Generators, Maps of Imaginary Lands
- PyCon Philippines 2012: Maps of Imaginary Lands, Functional Programming in Python
- DjangoCon 2012: The Dungeon Master’s guide to Django’s ORM (“I’m Malcolm, you may have heard of me from projects such as… Django!”)
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Australia.
Week 3 of the Alphabet Sufficiency: A. I’m just late this week. I’ll probably have some commentary on that at some point.
I saw the solar eclipse in November, or at least the right half of it, and thus began a six month dabbling in general relativity. It all started innocently enough, looking at astronomy websites to learn about, eg, why there isn’t a solar eclipse every month, which isn’t a relativity question at all..
Since New Moon occurs every 29 1/2 days, you might think that we should have a solar eclipse about once a month. Unfortunately, this doesn’t happen because the Moon’s orbit around Earth is tilted 5 degrees to Earth’s orbit around the Sun. As a result, the Moon’s shadow usually misses Earth as it passes above or below our planet at New Moon. At least twice a year, the geometry lines up just right so that some part of the Moon’s shadow falls on Earth’s surface and an eclipse of the Sun is seen from that region.
Well that’s that answered, but I’d made the mistake of visiting Wikipedia, and we all know how Wikipedia works:
Or actually, we don’t quite, because Randall Munroe apparently uses Wikipedia differently from me. If I end up on Wikipedia, I won’t be spread out among William Howard Taft and wet t-shirt contests, I will be in one of two places: poisons, or black holes. I can’t explain the poisons thing either, but black holes are pretty self-explanatory: relativity! spacetime! breaks down! infinite density! spagettification! gamma ray jets!
Or you can get your poisons and your black holes in the one place:
A supernova or hypernova produced by Eta Carinae would probably eject a gamma ray burst (GRB) out from both polar areas of its rotational axis. Calculations show that the deposited energy of such a GRB striking the Earth’s atmosphere would be equivalent to one kiloton of TNT per square kilometer over the entire hemisphere facing the star, with ionizing radiation depositing ten times the lethal whole body dose to the surface.
Eta Carinae, one of the most massive star systems in the Milky Way, is 7500 light years away. So, imagine that: a radiation jet so powerful that it would deliver lethal radiation doses to us across thousands of light years, if we happened to lie in the path of the axis of rotation at the time of a supernova. Which, luckily, we probably don’t.
I thought, in high school, that I’d be a physicist one day. I read the popular works of Stephen Hawking and Richard Feynman and Paul Davies. In Year 11 and 12, when NSW high school students only take English as a compulsory subject and all else is elective, I loaded up with maths, physics and chemistry. When I went to National Youth Science Forum, I asked to be placed in one of the groups for students most interested in physics. I went to the International Science School for high school students (not especially international, I might add) and poured over the pictures of physics PhDs and postdocs imagining myself among them.
And then various things happened and I’m not a physicist. I didn’t even take university physics in my first year. One of those things was a poor assignment of teacher in Year 11 physics: it was hard to dent my academic performance in high school but possible to dent my academic enthusiasms. Another of those things were that I had a lot of trouble with the intuitions of classical mechanics, especially of tension, and found myself regurgitating definitions by rote to get the right answer, and I had a lot of choices of subjects where I didn’t have to do that. (I hit similar walls with chemistry in first year university and mathematics in second and third year. Probably, like with physics, a break of a decade or two would have helped a lot: I revisited classical mechanics over a few hours with Andrew’s help about four years ago and now I know that in the idealised situations we were dealing with, the ropes and strings are rigid. Such simple things. I might be a scientist now if I’d had more age-peers.)
I don’t even especially regret this, I think my passion for physics was more a passion for strange phenomena than a passion for making novel discoveries of strange phenomena. I’m still not especially good at telling the difference between things I want to research and things I want to read about.
I imagine this isn’t an uncommon way to view one’s personal history, but I feel like I straddled two major technological transitions just as I reached adulthood. The first is the ubiquity of mobile phones: when I started university in 1999, rich kids had them. When I returned for my second year, everyone had them. The second is the Web. I remember writing reports in primary school—if allowed to choose my topic, they’d either be on astronomy or on the human brain—relying on the local library. Which to be fair, was information dense enough for me at the time.
But that’s not how I answer my questions now. Seeing the solar eclipse, meant lots of wiki walks and Google queries that ended in black holes, or at least quite near them. And frankly, for the first time ever, I started to feel like the Internet might be too close to being my mind, externalised, only with more answers. I don’t need to exert effort, I can just mainline facts. I am generally suspicious of “information diet” kind of sentiments: I usually analyse them as in part an aesthetic or moral preference for having to do labour, which I don’t think is justifiable in and of itself. Neither simplicity nor labour are in my opinion a good thing, they’re just means to ends. But… obviously I partake of the culture that creates these ideas and frankly, it’s a little spooky that there’s entire sections of the Internet set up to teach people who are apparently just like me in terms of background knowledge (some) and willingness to do work (little) about black holes and general relativity.
I had better justify the use of the ‘acceleration’ topic first:
In the physics of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein’s observation that the gravitational “force” as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.
And so I will spend my acceleration efforts on general relativity and gravity. You see why you need to be comfortable in your own intellectual laziness on the Internet these days, don’t you?
It’s probably fairly obvious how one gets from solar eclipses to black holes, but for the record, I believe it was via a bunch of reading about solar astronomy, with a detour through Wikipedia: Health threat from cosmic rays. You don’t spend long on cosmic rays before you end up considering this baby:
The Oh-My-God particle was an ultra-high-energy cosmic ray (most likely a proton) detected on the evening of 15 October 1991… Its observation was a shock to astrophysicists, who estimated its energy to be approximately 300 exa-electron volts (3×1020 eV or 50 J)—in other words, a subatomic particle with kinetic energy equal to that of a 5-ounce (142 g) baseball traveling at about 100 kilometers per hour (60 mph).
And from there, you’re pretty much considering what happens if Eta Carinae goes supernova. And secretly worrying that whatever the quantum gravity prediction is is less cool than general relativity. Which it probably will be. I own my aesthetic preferences, and they are on Einstein’s side.
After that the true recognition that there are thousands and thousands of people on the Internet really established itself. Every time I thought of a question about black holes, there was some ancient FAQ (1995? dawww) that answered them.
First, ones that had puzzled me for a while. There’s extreme time dilation around black holes from the point of view of a sufficiently distant observer: do they therefore see me hovering around the black hole forever? Do I see the entire universe flash before my eyes before my time is up?
I had assumed the answers were yes and yes, but they’re actually no and no, at least if you stick to Schwarzschild black holes as more ore less everyone does. Matt McIrvin sorts this out pretty much back-to-back in his FAQ:
Won’t it take forever for you to fall in? Won’t it take forever for the black hole to even form?
Not in any useful sense. The time I experience before I hit the event horizon, and even until I hit the singularity—the “proper time” calculated by using Schwarzschild’s metric on my worldline—is finite. The same goes for the collapsing star; if I somehow stood on the surface of the star as it became a black hole, I would experience the star’s demise in a finite time…
Now, this led early on to an image of a black hole as a strange sort of suspended-animation object, a “frozen star” with immobilized falling debris and gedankenexperiment astronauts hanging above it in eternally slowing precipitation. This is, however, not what you’d see. The reason is that as things get closer to the event horizon, they also get dimmer. Light from them is redshifted and dimmed, and if one considers that light is actually made up of discrete photons, the time of escape of the last photon is actually finite, and not very large. So things would wink out as they got close, including the dying star, and the name “black hole” is justified.
As an example, take [an] eight-solar-mass black hole… If you start timing from the moment the you see the object half a Schwarzschild radius away from the event horizon, the light will dim exponentially from that point on with a characteristic time of about 0.2 milliseconds, and the time of the last photon is about a hundredth of a second later. The times scale proportionally to the mass of the black hole. If I jump into a black hole, I don’t remain visible for long…
Will you see the universe end?
If an external observer sees me slow down asymptotically as I fall, it might seem reasonable that I’d see the universe speed up asymptotically—that I’d see the universe end in a spectacular flash as I went through the horizon. This isn’t the case, though. What an external observer sees depends on what light does after I emit it. What I see, however, depends on what light does before it gets to me. And there’s no way that light from future events far away can get to me. Faraway events in the arbitrarily distant future never end up on my “past light-cone,” the surface made of light rays that get to me at a given time.
Fine then, answer all my questions. After reading that I huffed over to Google and typed in “does gravity move at the speed of light?” just to see whether the Internet is all it is cracked up to be. And a different section of the same damned FAQ actually answers this more or less in that form. Actually the answer is kind of cool: general relativity predicts that the distortions that gravity creates in spacetime propagate at the speed of light, yes, but in such a way that in most cases the source appears to be the instantaneous location of the massive object. Which is in turn super-lucky because otherwise you don’t get remotely stable orbits. Which as I recall resulted in a breather at Wikipedia: Anthropic principle but I was willing to fight on for a bit.
I wasn’t done, because I had encountered brief mentions of an interesting property of black hole event horizons, which is that inside the event horizon, one dimension of space becomes timelike, which can be informally considered as “the singularity is in your future”. I kept talking excitedly to Andrew about this late at night, I think when I was supposed to be working on something else (often cooking dinner) and the more I talked, the more I realised that I had absolutely no idea what this really meant. This required actual work on my part in terms of poking at Google queries, but luckily for this project, not very much, and it wasn’t long before I ended up at Jim Haldenwang’s Spacetime Geometry Inside a Black Hole which breaks out mathematics, and is worth a read in full. In addition to some of the mathematics, including that property of event horizons, it talks a bit about the historical development of the understanding of black holes, including the fact that the event horizon was also a singularity in the original coordinate system and it took more than thirty years to show that in some coordinate systems, it isn’t.
Frankly, I remain a little horrified at how little work I had to do to find any of this out. No overdue library books? No interacting with knowledgeable humans in real time? Some time in my 20s the future appears to have arrived with a vengeance, as it so often does. Outside of black holes, anyway.