When black holes collide

I thought I'd give the people who show up from time to time to complain about my occasional political posts something new to grumble about, so today we're talking physics. (Not so strange given how I view roleplaying, which is that it's about everything.) And don't panic. I'm going to do all this in terms a child could understand, honest.

I had a question about black holes that used to puzzle me as a teenager:

Say you’ve got a black hole of 4 million solar masses, so roughly 50 AU across. (I’m taking a really big one so that its tidal forces don’t turn everything that falls in into spaghetti.) An astronaut wearing a wristwatch falls towards it. What do we see? My understanding is that we’d see the astronaut slow down as he or she approached the event horizon, finally appearing to come to rest on the event horizon, very red-shifted and the watch display apparently having stopped. (From the astronaut’s point of view he or she accelerates towards the event horizon, the entire universe around them is blue shifted, and their watch continues to tell the time accurately right up to the moment they go through the event horizon – and maybe after as well? But that’s a whole other question.)

OK, now what if instead of an astronaut we drop another supermassive black hole into the first one? As the event horizons touch, do they freeze in place there like two balls glued together?

1. If not, then in watching the rate of merging of the horizons we’d be getting information out about how fast the two singularities are moving together. From our perspective we’d suppose them to move together infinitely slowly, but in any case no such information can escape the black hole.
2. But if they do just stay frozen like two balls touching at a point, then the universe should be festooned with very oddly-shaped black holes, apparently made up of lots of aggregated black spheres stuck one onto another like a 3D Mandelbrot set.

I don’t think that’s what the maths says. All black holes are supposed to be featureless and (nearly) spherical. So do they go from the two-balls-touching state to the one-big-ball state in a quantum leap – to coin a phrase?

For half a century I kept asking that question but never got a satisfactory answer. One astrophysicist did tell me that I was making the mistake of using second-order geometry when I needed to consider fourth-order geometry, but I live in this universe not the maths one. I wanted an explanation I could chew.

And eventually (there might be a life lesson in this) I figured out the answer for myself. I could have done that decades ago, too, if I'd just stopped to think that I'd packed a huge assumption into the original question when I envisaged them as both remaining spherical up to the point of contact. So here's that answer -- and look, Ma, no maths!

Imagine two supermassive black holes of equal size in otherwise locally empty space. At a wide separation they are spherical (if they're not rotating). The size is defined by the Schwarzschild radius, the point at which a particle cannot escape the gravity well of the black hole.

As the holes get closer together, consider two particles, one on a line between the two black holes and just within hole #1’s Schwarzschild radius, the other on the same line but the far side of hole #1 and just outside its original Schwarzschild radius.

As the gravity of hole #2 begins to have a significant effect, the particle between the two gets a gravitational boost that would allow it to escape the original radius. Conversely, the particle on the far side now has to escape not only hole #1’s gravity but the additional pull of hole #2.

So the effect as the holes approach each other is that the event horizons bulge on the far side and flatten on the near side. The extent of the event horizon becomes less on the near side and greater on the far side so that they resemble two distorted lenticular blobs that will (as they get closer and closer) asymptotically adopt the shape of hemispheres that will then merge into one new larger sphere.

If the physics of spacetime curvature allowed that process to be entirely seamless then there would be no release of energy, but of course the two merging holes don’t precisely resemble sections of a greater sphere even at the moment of contact – at that point, there’s an anomalous dimple in the curve around the great circle bisecting the new event horizon. Hence the associated burp of around 5% of the mass, and the new horizon of the combined hole will only extend as far as the inner part of that dimple.

I’m just guessing that you could compute the proportion of energy released purely from the geometry, mind you – I retain more faith in maths than I do mathematical ability, these days. And of course, an observer at infinity would say there was only one black hole there in the first place. But that's a detail.

The mutants

I don't often cross-post to my personal blog, but this month I'm talking about Daleks -- with some side detours into SF writing in general -- so that might be of interest even if you're not a comics fan.

More science here on Friday. Not fiction, this time, but fact. I'll be talking about big balls of wibbly-wobbly, timey-wimey stuff. Set your dematerialization circuit.

IF critique

This made for a lovely start to my year: an in-depth, considered and very flattering review by D F Chang of my four Critical IF gamebooks. "Compelling characters, perfectly plotted, amazingly written..." I didn't bribe him to say that, honest. Mr Chang's comments on Once Upon A Time In Arabia are more than fair, and three out of four A-ratings is nothing to gripe about. I just came across the video by accident, but you can bet modesty won't stop me sharing it every place I can.

Mr Chang raises a few interesting points, some of which have been addressed in earlier blog posts but this is a good opportunity for a recap. There were six Virtual Reality gamebooks but I only wrote the four that were republished as Critical IF; Mark Smith wrote Green Blood and The Coils of Hate. I wrote Down Among The Dead Men first, then Necklace of Skulls, then Heart of Ice, and finally Twist of Fate -- which was retitled Once Upon A Time In Arabia for the new edition.

Mr Chang has some valid criticisms. He doesn't like 'Necklace of Skulls' as the wizard's name. My only defence is that the nobles and kings of the Maya tended to be called things like that, if we interpret their names literally: Bird Jaguar, Sky Witness, Centipede Claw, Shield of the Sun, Curl Snout. It was anyway fashionable to translate them like that in the '90s, rather than attempt to recreate the sound of the names (K'inich Kan B'alam, for instance) which are even more deeply lost in the mists of time.

I agree that my inspiration was flagging when it came to the Arabian book. Or maybe I was trying too hard to recreate the picaresque feel of the Tales of the Arabian Nights boardgame, where the goal is likewise to scoot all over the world in order to achieve riches and honour. Probably I lavished too much energy on Heart of Ice and had nothing left to spare for the final book, and the deadline didn't permit me to take a break and recharge. That's why, when editing the new edition of Twist of Fate, I took the opportunity to change the lame title and rewrite the introduction to the story.

But how marvellous it is to hear of readers still getting pleasure from books I wrote twenty-five years ago and more. I'm nearer the end than the start of my writing career, but that reward never gets old.

Pointing the finger

British literary critics of the 19th century had the notion of the "Young Lady Standard", which was a kind of family-friendly U-rating for novels that would not offend the sensibilities of a Victorian girl. Because of this, British literature often shied away from the sort of forthright depiction of life you find in French or Russian novels of the time. There was a feeling on the Continent that literature was an art form and had a right, indeed a responsibility, to mirror life warts and all. In Britain literature was the forerunner of early-evening television.

Even so, authors like Jane Austen were not the twee and cosy yarn-spinners that many suppose. Lady Susan Vernon is an amoral, manipulative adventuress who deserves a place in the ranks of dark antiheroes alongside Vic Mackey and Walter White; Catherine Morland runs afoul of predatory sexual vindictiveness; Lizzie Bennet takes on a real-life dragon for very high stakes; Becky Sharp is willing to betray even those who love her just to squirrel away some cash. Nonetheless, though depths of human depravity are certainly there to be inferred in 19th century British literature, those are all pre-watershed conflicts. None of them is described with the uncompromising raw honesty and occasional breathtaking brutality of authors like Balzac or Chekhov.

Dickens wrote stories to stir your emotions, but he and his readers knew they were parlour entertainment, to be read by the whole family -- a "safe space" in entertainment. A Victorian paterfamilias who opened a novel to be confronted with the likes of Madame Bovary might well have stormed back to the bookshop and thrown it through the window.

I think something similar is behind the uproar we sometimes see nowadays over "unsuitable" content in roleplaying games. There are some people who play games the way those Victorian families read novels; there are others who expect games with no holds barred. This has led to the concept of the "x-card" -- sadly nothing to do with homo superior, but a mechanism to interrupt games whose scenes or subject matter a player is unhappy with. To quote from the blog I linked to there:

"The x-card is used to signal that a boundary has been crossed or that a player is not OK with the content. The game stops immediately, and discussion shifts to the reason why the card was used."

For me that's as absurd as calling a halt to a disturbing play or movie. If you don't like what you're seeing, don't tell me about it; there's the exit. But there's a category disconnect here. I regard roleplaying games as art, no different from literature, theatre, cinema, poetry, and painting. The people who advocate x-cards want their games to be morally uplifting and to avoid upsetting anybody, just like those family novels for the Victorian fireside. We have different expectations.

I have a player who doesn't like horror scenarios. If we're going to be playing a horror campaign, that's OK; she sits it out. Sometimes there's a grey area. A scenario may not be overtly intended as horror, in the sense of belonging to the horror genre, but horrific things happen. There have been a few times when my players have shocked me to the core with some of the things they're willing to do. And that's fine. It's why I play, in fact, to see those things that emerge unexpectedly from characterization -- sometimes beautiful, sometimes very nasty. It's the same when writing characters. You ask yourself how far they will go, what lines won't they cross, and the answer is often revelatory.

What do you do if you come up with something you know will be shocking, whether as a player or a referee? If I thought my players couldn't handle it then I'd keep it to use in a story, perhaps. But really, if my players were like that then we'd soon part company. They and I know we're not setting any limits.

Taking the blog post I cited again, one of that player's boundaries is "I don't want any romance involving my character." But it's really hard to plan that kind of thing in advance, especially in the improv style of play that gives the best games. When refereeing, I wouldn't have an NPC profess love for a PC if I didn't think the player was capable of running with it. (I'm talking about their acting ability and imagination, of course.) What if one player-character falls in love with another? I'd much rather they both played it. Unrequited love is one option there, and it could develop in interesting directions as we know from countless TV shows and novels. It would be pretty disappointing if a player just said, "I don't want to roleplay that." In that case play your blocking. Reject them, spurn their advances in-character. Don't tell everyone about it.

But what about games in a public forum? Twenty years ago I went along to a convention to sign Fabled Lands books but soon got roped into a series of fascinating mini-RPG scenarios run by the guys behind West Point Extra Planetary Academy. Each game had a different setting and was built as a moral quandary to be played out in twenty minutes. They could hardly have started by saying, "This scenario deals with issues X, Y and Z." It's the trigger warning problem. If you're trying to capture a genuine sense of surprise in the game, you can't give too much away upfront. (Not to mention that the evidence indicates that trigger warnings are of no use in any case to the genuinely traumatized.)

Why have these debates crept into games of late? I think partly because roleplaying is becoming -- well, not mass market entertainment, not by any stretch, but certainly it has opened up beyond the hardcore gaming demographic of the early days. Aficionados take a sophisticated approach to their hobby. The casual fan tends to have a less mature outlook.

Also, American culture has always had a much more censorious streak than European. The idea of shutting down a discussion because it offends somebody's moral code is perhaps natural if your country was founded by Puritans. And because of social media, the Overton window has shifted away from liberalism towards moralism. Hence gripes like this, that maybe do make sense over in the US (American friends, feel free to chip in) but strike most Europeans as potty.

And because most roleplaying derives from genre fiction, and genre sensibilities tend to be a little less grown-up than proper literature, there's a tendency to expect roleplaying games to stick to the soft-soap forms of conflict you get in traditional SF and fantasy. Witness the outcries over Game of Thrones when the writers stepped outside genre norms -- even though that was pretty much the entire thesis of the show from day one.

Anyway, enough theorizing. What do we do about it? Well, surely few gamers want to sit around listening while one player explains their reasons for halting the game. The next stop on that line is struggle sessions, which nobody will enjoy. But those people's sense of offence seems genuinely to overwhelm them, and there's no point in subjecting anybody to an experience they disapprove of. So we're going to need better ways to signal which kind of roleplayer you are. High literary with anything goes, or pulp with puritan boundaries? As long as everyone around the table knows what they're letting themselves in for, I'm sure we can all keep on gaming without needing to call the thought police.

Adventuring on a shoestring

I have a friend who keeps telling me I should do podcasts. It’s flattering because he does a fair few himself and he’s very good at it, but the field is so crowded already. Mike and Roger on Improvised Radio Theatre With Dice, Ralph on Fictoplasm, Jeff and Hoi on Appendix N Book Club – and not forgetting Dirk the Dice on the Grognard Files.

I’m on the latest of those, mostly chatting about Dragon Warriors and Jewelspider but with a bit about the early days of roleplaying. After the discussion, an interesting point was raised about whether DW would have worked better as a single rulebook, the way games like Runequest and Champions were released at the time, rather than as six standard-format paperbacks. (We’d hoped for twelve, but that’s a detail.)

What happened in the early ‘80s was Ian Livingstone and Steve Jackson had a epiphany. They could see that fantasy games potentially had a huge market but had so far failed to escape the niche of sweaty hobby shops. How to get them out of the shadows and into the mass market bookstores? The lightbulb moment must have come while playing a Fantasy Trip solo adventure. ‘Know what, lad?’ I can imagine Steve saying – or maybe it was Ian. ‘Do something like this for kids and we could have a breakout hit.’

The red-braced MBAs among you will have noticed that Ian and Steve didn’t publish Fighting Fantasy themselves, despite owning White Dwarf magazine and a chain of game stores. They pitched it to Penguin Books and lions were shook into civil streets.

Me, I just rode their coat-tails. I figured that all those tweens and teens who’d now discovered gamebooks might also be waiting for roleplaying. So Oliver Johnson and I took ourselves out to Ealing, where Transworld had their offices, and the game that was to be known as Dragon Warriors was born.

What if we had done DW as a single rulebook? I’d been working on an RPG for Games Workshop that they planned to call Adventure (yeah, not my idea) and that would have sold about 2000-5000 copies. The value to GW was mostly that they could sell figurines on the back of it. Adventure never happened because GW picked up the UK Runequest licence, but it had penetrated even my business-blind consciousness that we could sell ten times as many copies if we got a paperback RPG into high street bookshops.

And where would a chain like W H Smith have put a single-volume rulebook anyway? Not alongside the FF books that all the 10-13 year-olds were snapping up. There might have been a corner of the shop where Jane’s Fighting Ships and Formula One books were stocked. You’d never have seen it. We wouldn’t be talking about it today.

And how much would it have cost? The DW books were £1.75 each – in the mid-80s, a little less than $5. If we’d lumped the content of the six paperbacks into one durable hobby-style RPG hardback, call it £15. About fifty quid in modern money. Not a pocket money purchase, for sure.

And would Transworld have been interested? Probably not. The adult division wouldn’t believe there was a market for fantasy role-playing, the kids’ editors wouldn’t commission a £15 hardback. And if they had, Oliver and I would have got an advance of about £2000 each (that's maybe £7000 in today’s money) to keep us going for a year or more while we wrote the whole game and all the scenarios. Passion project though DW was, just to pay the bills we'd have been tempted away by gamebook contracts instead.

Would I rather have released DW as one book? Well, that’s what I was working on in Adventure. It wouldn’t have been entry-level like DW. It would have been set in the world of Medra rather than Legend. The skill system would have been more complete because it was designed as an entire system rather than piecemeal and episodic the way DW came out. There'd have been no elves or goblins.

Would that game have been as good? Apples and oranges. Single-volume RPGs back then were for the hobby market. Paperbacks like DW and FF and Maelstrom were for the mass market. I'm heartily glad that James Wallis eventually reorganized DW into a single book, and it's far easier to find the rule you want that way, but we had to follow the winding road to get to that point twenty years on.

If I'd really understood the business side of gaming at the time, though, I’d have made the rules d6-based. How many schoolkids even knew where to buy icosahedral dice, still less have the pocket money to spare? It was Britain in the ‘80s, a tatty and corruption-riddled backwater off the coast of Europe. The streets were paved with stale chewing gum and flattened fag butts. Off licences had metal grilles to stop people pinching Watneys Party Sevens. The height of dining out was a gristly steak and chips at the Berni Inn. Kids didn’t have the cash to fling at mobile phones and X-Boxes like they do today. Or did, that is, pre-Brexit.

That dice bit I’ll be fixing with Jewelspider. All you’ll need are a couple of six-siders. It’ll be a small-format book, too, though maybe I should do a hardback as well as a paperback edition if only because that will be more resistant to spilled wine and red-hot fragments of dope. Tell you what, though. It’ll be a bit more than £1.75.

The better angels of our nature

I was recently reading an article that dismissed the idea that human beings might be perfectible and that history is generally moving in the direction of civilization away from barbarism, so I thought I'd share this short talk by the delightful Hans Rosling.

It's no proof that we'll end up with the Federation, or even the Culture, but it would be pretty stupid if, for the sake of cynicism, we didn't even bother to try. So my resolution is to do more in 2021 to combat injustice, superstition, prejudice, intolerance and ignorance. I hope you'll join me on the march to humanity's bright future. If we can't get there, don't let anyone say it was for want of effort.

In the meantime I want to wish all the blog's readers a very happy New Year. May your own personal trajectory be ever upward and onward. Let's leave the world a better place in January 2022 than we find it today: more civilized, more rational, more generous, and more compassionate. And if you're looking for a resolution for 2021, how about: get the jab?