Student of Trinity

That's correct, except that short time scales aren't really the issue. It's that the forces that tend to stretch space need a lot of elbow room to have much effect. As in, millions of light-years of elbow room. The expansion effects are good at expanding the enormous voids between galaxies, but they're easily outweighed by even the tenuous gravity between stars that are many light-years apart. Against electrostatic forces holding matter together, they're really negligible. You could imagine scaling up the cosmological constant to the point where this would no longer be true, but I think you'd have to increase it by something like forty powers of ten. I don't know any serious theories in which the cosmological constant increases in future. Accelerating expansion normally happens (in theories) just because the big voids get steadily bigger, so the constant cosmological constant makes them expand ever faster. This would leave galaxies pretty much intact, let alone stars and planets and people. It would just make intergalactic travel more expensive. If we let in hypothetical scenarios for which there's no evidence but that can't be ruled out, though, then in principle the whole universe could still be in a false vacuum, like the one considered as the initial state in models for so-called cosmic inflation. Inflation is a hypothetical early period in the universe, very shortly after the Big Bang, in which the cosmological constant was in effect very much larger than it seems to be now, so that space expanded very quickly. Then we settled into the true vacuum (if it is the true vacuum, and not just a longer-lived false one) and the cosmological constant dropped to near zero. If we haven't yet hit the true vacuum, then in principle there could be a second stage of inflation starting any time. It could be a doozy, ripping even atoms apart; a kill switch on the universe, waiting to fall.

I've already drunk one coffee in that time. So the universe has already changed. Sorry.

I think the scenario that seems most likely now is that all the galaxies end up far away from each other, as cosmic expansion increases, and each galaxy dies its lonely heat death in isolation. The universe is currently just into its third generation of stars; I don't know how many cycles of star formation and death the average galaxy can support, but in principle the resources are finite. The curve of nuclear binding energy bottoms out at iron. Once enough primordial hydrogen and helium has been fused up into iron, the fuel mixture may just get too lean for further star formation. There are lots of uncertainties in all of this, however. We know too little about really long term physics to be sure about anything.

Strictly speaking, all of chemistry is just molecular physics. It's the 'just' that's silly there, though. Molecular physics is extraordinarily hard. The strict comparison between theory and experiment, that one demands in pure physics, is impossible, because the theory is too complicated for anyone to understand, or even to simulate with the biggest computers available. So one relies on empirical data and simplified models, which are special to particular problems and cases, and don't extend to the rest of physics. That's chemistry. If chemistry weren't so important, it would just be a particularly obscure and thankless branch of physics; but of course it is extremely important, of enormous industrial value, essential to life, and so on. So it's its own science. It's built on top of some basic physics but most of it is unique.

Teaching is fun, at least at college level, where students are normally motivated to learn or they wouldn't be taking your course, and where they can often bring in some cool input of their own. The nasty downside of teaching is that it is also a black hole for time. You can spend unlimited time preparing for a single class. Not only can you refine your pitch endlessly, looking for just one more reference or example; you can also endlessly try out major shifts in approach, to the point where you're seriously thinking how cool it would be to do the whole thing in mime. My wife and I have both resorted to the brute force way of limiting teaching preparation time: you decide in advance how much time you need to prepare for each class, and you just don't start preparing at all until that long before the class starts. When you seriously need to get some research done, I'm afraid this may just be the only way to go. If you do this, then the added constraint is that your estimate of how much prep time you need has to be short enough to leave adequate research time. You're not allowed to assign three days prep time per class, just because that's how long you took last semester ... Other than that brute force method, which is stressful, the main tool in making teaching manageable is unfortunately one that tends to make it less fun. You figure out what the customer really wants, and you concentrate your effort on supplying that and only that, rather than spending time on other things that happen to be fun for you. The customer in this case is the student, but for "what the customer really wants" you should imagine a somewhat idealized student, who actually wants to learn something worth learning, and doesn't just want an A. On the other hand it's true that the customer doesn't want to have to work infinitely hard for a decent grade; that's a reasonable want which should be respected. From my and my wife's experiences so far, I think I can say that teaching can be much less time-demanding than one thinks, because a lot of what the students really want is a lot easier to supply than one might think. As a grad student with several more years of higher education under your belt, there are a lot of things that you tend to take for granted as obvious. You can easily teach them just off the top of your head. So you tend to slave for hours on finer points, that seem more valuable to you. In fact most of those fine points will go over your students' heads, and most of what they actually value from the course will be things that you could have provided much more easily, off the top of your head. The better teacher, in my view, spends less time preparing, but more of that prep time is spent in improving the presentation of simple things that you already know well yourself. The problem is that tracking down fine points that are interesting to the teacher is a lot more fun, even if it is time-consuming, than polishing the presentation of basic stuff. Unfortunately, I'm afraid, the right thing to do is to give class prep three hours of hard work, figuring out how to make basic stuff clear to beginners, rather than nine hours of fun, preparing great stuff that will go over their heads. When all else fails, there's always class discussion. You can spend five minutes thinking up a good discussion topic, let the students go at it for an hour (maybe after breaking into small groups for twenty minutes first), and just summarize and moderate; and the students will be happy that they're getting a real college education, from a real college-level instructor, hooray. As long as you don't do that too often, it works great. So you can use it as an escape pod for when your lecture just doesn't come together in time. It works because, once again, most of the value your students actually get is from stuff that you already know. The stuff that took you five minutes, plus on-the-spot reaction during class, is more valuable to them than the stuff on which you could have spent nine hours. At least, so it seems to me, from one side of the lectern. I was a student, too, once, of course, but that was twenty-five years ago now. I'd be curious how current students see this. What kind of preparation by the teacher is appreciated, and what would you just as happily do without?

Meh; I'm not really so attached to my hopeful speculation. I'm just being a determined advocate for a poor devil who needs one. My default opinion for quite a few years has been that the USA is doomed (not to utter destruction or anything, but to some serious problems) because its rigid constitution will effectively prevent reforms of which the need is becoming ever more pressing. I was trying to bend over backwards to see whether maybe a change in mores could be a viable work-around. Lilith's objections, however, seemed to be cast as general theorems, to the effect that no possible capitalist society could ever adopt campaign finance limits by sheer pressure of public opinion without legal constraint, because the political power of capital is unlimited by definition, or something like that. That seemed to me to be greatly overestimating the admitted difficulties in my scenario. I admit that "conceivably possible in some future eventuality" is so weak a contention as to be pointless, but Lilith seemed to be arguing against even that. My intent was to support something at least a bit stronger, but given Lilith's absolute rejection, I was trying to establish the minimal point first, and then argue from there. I really do think that my scenario could in principle be possible. I was hoping to hear some thoughts about what it might take to make it really happen, or else some counter-proposals of alternative work-arounds for campaign finance reform, such as the No-super-PAC agreements between candidates, that Kelandon mentioned. Telling me that there was no chance at all that the scenario could happen, as long as nothing significant in society changed (short of full-blown socialist revolution), was not the response I expected, because significant social change (of some sort) was precisely my premise. I certainly admit that I didn't (and can't) supply any detailed roadmap for just how to make a sea change in American voting habits. So no, I don't understand this issue. I just don't think that it can be dismissed outright by any simple syllogism about power and capital.

Sure, what I've been describing would definitely be a reversal of all historical trends, and I'm not trying to argue that it's inevitable, or even likely. I just think it might be possible. Things change. Past performance is no guarantee of future results. Collective behavior is always like that. It's an immutable law of nature and always will be, until suddenly it was just a bizarre whim of those strange people in the past. Collective behavior isn't just arbitrary. It happens for reasons; but the reasons and the behavior add up to a huge and complicated system that can and does suddenly change, generally in ways that seem obvious in retrospect but were not foreseeable in advance. (These platitudes, for example, may be due to the fact that I've spent much of today discussing spontaneous dynamical transitions with some of my students, and sketching out a theorem that we hope to publish. See, none of you could have foreseen that. Alas, many of you probably could have foreseen that I might post something somewhat like this, however. As our theorem states, it's all about just how vague you're willing to be. In particular, you should be getting more vague as time goes on. I'm here to help with that.)

I think the sincere invitation is the problem: you're a naysayer provocateur. You want proletarian revolution to be the only solution, so you squint harshly at every alternative. If you think that's fair game, wait till someone tries it on you. Proletarian revolution is a far more vulnerable target for naysaying than any wishful tweaking of capitalist democracy. As long as society's ruling class is made up of those who control capital, having and using capital will be important for political power. That's a tautology, and in the past it hasn't stopped the enactment of lots of measures that rich people didn't like. Populism is also a force, and there's nothing to stop it from gaining some ground against money at some point, so that the preponderance of capital control in political power is somewhat reduced. You could call that a partial overthrow of capitalism, but I think that would be silly, since defining capitalism as pure plutocracy is a straw man fallacy.

Trends like the hypothetical one of despising campaigns that mount too many ads don't happen suddenly all at once, like storming the Bastille. The build up over a few years at least. That's lots of time for the hypothetical cheap-campaigning fascist party to get a noticeable increase in votes, without getting into office. Likewise the response of parties is gradual. No major party is going to change gears after one election and decide to reject all donations for the next campaign. They would (if any of this happened) gradually start running fewer ads, in some markets, because they noticed that saturation was doing more harm than good. If the other party keeps on spending, they're just shooting themselves in the foot: the premise is that people start hating big ad campaigns. Even if they don't remember so clearly whom they want to vote for, they'll know very well whom their voting against. The height thing is almost certainly just silly. When elections are close, and there aren't a lot of data points, there is bound to be some random thing that happens to correlate better with the outcomes than anything else. If it weren't height it would be hair color, or something else. This would be true even if all voters were extremely well informed, as long as opinions were closely enough matched; so it's no evidence that voters are so ignorant that they are reduced to picking candidates by height. Think of this scenario as a form of evolution. Most of your counter-arguments are analogous to some of the straw man arguments against evolution. Just because something would never happen in the way you're imagining doesn't mean it would never really happen.

Undermining the power of deep-pocketed donors by getting people to ignore campaign advertising is admittedly a fantasy, but I really don't think it would be all that hard. Only people who actually vote matter for any of this, and those people are the ones who are willing to make at least a small amount of effort. Moreover, the whole point of campaign advertising is to chase quite a small percentage of people, so it wouldn't take a landslide shift in public opinion to have a decisive effect on how politicians spent money. There's no need to vote fascists into office. Just give any party that spends less a bit of a bounce. The mainstream parties will notice immediately, "Hey, those so-and-so fascists got 15% of the vote with their lily-white No Big Money campaign. So they came a distant third, but still, that's way better than they've ever done before. Just imagine how much better we would do with that gimmick — and it would be cheaper, too."

I think this is cynicism by hand-waving. Money always talks, but the volume at which money can shout is not infinite. A little bit of corruption around the edges may be inevitable, but that doesn't mean you can't do better than systemic and completely legal conflict of interest on the part of legislators. Suppose for the sake of argument that strict campaign finance laws do work to reduce the disproportionate political power of wealth to some acceptable level; such at least was my premise. Public opinion could in effect enforce such laws without statute, if people simply agreed that no candidates deserved votes if they didn't present neutrally audited records showing modest total spending.

Hmmm. That may be so. Maybe tremendously un-ad-like ads that exude overwhelming down-to-earth common-sensical sincerity and are only aired once will win campaigns, and cost a hundred million dollars to produce. But maybe that'll just be too much of a crap-shoot, and nobody will spend that kind of money on such chancy things. Anyway, I'm not sure that voters' lack of information is such a problem with American democracy. They could probably get by with quite a bit less, and still make good choices.

After writing quite a lot more of this story than I had at the point of my November 2012 post "Cordite and steel and everything nice", it seems that Anastasia works quite well as a character. The people who have read my drafts so far are all family members, so they're an easy crowd, but everyone seems to really like Anastasia. Liking the protagonist is really important, especially when she's also the narrator. An unlikable narrator-protagonist makes the whole book painful, but with a likable one even a broken shoelace can raise a bit of suspense. My second protagonist-narrator, Thomas, was less appealing. I abruptly switched narration to him, half-way through the story, and everybody found this disappointing. They wanted Anastasia back. Anastasia has issues and limitations and deep mysteries to solve, but my book is an action adventure, and for my female protagonist, all that stuff is really chrome. The engine is being an escapist super-heroine with uncanny presence of mind in a crisis. Anastasia is sympathetic and nice and all, for a stone cold killer, but being nice isn't enough. The most important thing is, she makes things happen. I'm thinking this may be the simple active ingredient in a good protagonist — the special sauce, as it were. It's not so easy to pull off. You can have your heroine solve a problem, for instance; but does she really do it? Or does it just solve itself automatically, while the heroine poses for the camera? I don't think that has the same oomph. You've got to show the protagonist making things happen, not just tell it. You've got to write a credible sequence of causes and effects that resolves the problem, and the protagonist's actions have to be crucial links in the chain. Every little problem is a story in miniature, and you make your big story's protagonist work by making sure she's the protagonist of a lot of little stories. In my story, Anastasia herself is the main plot device. She keeps making things happen. I think this goes a long way to making her appealing. I think that "making things happen" can also apply at different levels in a story. The least effective level has the protagonist jumping through a series of hoops that are presented by others. The jumping may be ingenious, but the hoops aren't the heroine's doing. I think the protagonist makes things happen in a bigger way, that makes her more appealing, if she is also doing things to select the hoops. Anastasia works well in this way, I think. She is pro-active to the point of recklessness. She tends to choose her own targets, and very seldom is it up to anyone else to judge whether she succeeds or fails. She's not trying to make anyone like her. Her success or failure is usually as objective as surviving or dying. Anastasia is an active protagonist and not just an observer. She is anything but a victim, even though bad things happen to her; she does a lot of dangerous things, knowing the risks. Her decisions drive the plot. This does more to make her an appealing character than anything else, I think. It has nothing to do with her being female, but I think this itself may be an important point about female characters. Stupid habits and preconceptions tend to turn them into bystanders. Avoid this, and you have a more interesting character right away. Anyway, for what it's worth, both my wife and my mother seem to like Anastasia. Both complained when the narration switched away from her. That's my main problem now, as I try to hack and hammer out a second draft. I have a second narrator, who is supposed to be a second protagonist, and who should be an adequate foil for Anastasia. She's a hard act to follow, but I have a monstrous mutant with superhuman strength and speed, driven by a fanatical cause; and I have a ruthless manipulator who reads people like comic books by instinctive recognition of micro-expressions, and can play any part but himself. These are both Thomas MacLayne. He's a throwback descendant of a line of bio-engineered special forces who were designed to foment revolutions. People are puppets to him, but he has been conditioned from birth to hate abuse of power, so he's sort of a good-guy psychopath, like Batman. As an action-adventure protagonist, Thomas seems promising. Yet in my first draft he came across as all dressed up with no place to go, in comparison with Anastasia's abrupt action. The problem is all in the third of my book's four sections, in which Thomas has entirely taken over narration, but has not yet shown his Hulk side. My draft squandered all his preternatural insightfulness on narratorial observations and gloomy commentary. He watched things go by. He dumped a lot of data. He didn't make things happen. The third section was trickily plotted, and in tying it all up to get Anastasia apparently burned as a witch, I let my second protagonist-narrator retire from protagonism. In effect I finally got the whole thing put together, and discovered I had a lot of parts left over — all the things that Thomas should have done. I have spent months trying to fix this. I think I'm on the right track. Thomas does make things happen, now. When I first started trying to revise this section, I had the idea of making him a persecuted victim who was just managing to survive; but I've reversed direction completely on this, now. Now he is an expert conspirator setting up a bloodbath of revenge. His schemes derail, because the mysterious bad guys are finally showing their hand, and because Thomas himself will change his mind about who his real enemies are. So he will inevitably look less unstoppable than Anastasia, when the dust has all settled. He'll have made more mistakes and had more things go wrong; he'll have failed to solve some of his problems. Okay. I guess that's just how it is. Maybe it can be enough for a good and likable protagonist to try to make things happen, if he tries well enough, and fails in a good cause.

Is the speed of a window manager still even an issue these days? Are you trying to do Massively Multiplayer Online Window Management, or something?

How flexible is the system now, though? The ERA failed to be ratified by enough states, which was just ridiculous. And it must seem to a lot of people that the US could really use some stricter campaign finance laws, even though it is indeed flagrant tyranny to forbid citizens to do whatever they want with their own money, especially if all they want is to buy airtime to express their own views, just like somebody standing up on a crate in Faneuil Hall to be heard way back when, only bigger. So this would probably take a constitutional amendment, which would be bitterly resisted by everyone with a vested interest in the current freedom, which is practically everybody with any voice. Or do I misunderstand the system as it stands? On the other hand, maybe the law isn't the right tool for this job, anyway. Maybe it could just become a mass cultural movement to start despising and ignoring political ads, to the point where buying airtime was counterproductive for candidates, and campaign contributions became nearly worthless.

That's what the robots want you to think.

The idea to make stories that way is okay, but would it be so hard to re-write the content to be more suitable to a family-friendly message board for a company whose customers include many young kids?

The countries that became totalitarian in the 20th century weren't republics on the American model, but they weren't representative of democracy in general, either. They were all bad cases of different kinds. Their examples are dire enough to make it pretty clear that bad democracy is dangerously vulnerable, but they don't show that the American constitutional obsession with separation of powers is the only safe alternative. On the other hand one has to admit that a 'functioning democracy' is apt to be a bit of a true Scotsman.

The issue of planning and accounting for enormous incalculable events, which *i mentions, may affect democracy at an even deeper level: it's not clear that democracy is even trying to be efficient at allocating resources. The theory that follows Hannah Arendt would say, I think, that democracy is mainly about resisting the emergence of totalitarianism. So it deliberately accepts crummy government, with lots of waste and inefficiency, in order to make downright evil government as unlikely as possible. Technocratic oligarchies might be much more efficient in good times, this theory goes, but would succumb much more easily to totalitarian perversion; so one is better to muddle along with democratic politics. It's still possible that this point of view will still someday vindicate the cumbersome American system of checks and balances between different branches of government. Maybe other countries with more modern systems will all get taken over by evil robots, and the US will survive as a bastion of liberty thanks to congressional gridlock. That scenario does seem to demand an awful lot of prescience from an 18th century constitution, though. I think it's probably a fantasy.

That's a good point, actually. A lot of ancient Roman knowledge was lost very quickly, and how a legion really fought may well have been as much of a mystery to wistful western Europeans in the Dark Ages as it is to us now.

Certainly you don't have to take the time, Nalyd; but I'm afraid my fixed view is that anything that is really understood can be summarized briefly. If the only answer is 'listen to a whole podcast series', because the only answer is a mass of details that defies organization into coherent chunks, then there is no answer. And it seems that there may not be one. A couple of hours of googling around, starting from some of the sources cited by your podcast guy, shows that great controversy remains over just how many ranks the Roman centuries fought in, at any time, with different scholars preferring any number from three to ten. This issue of ranks within a century is a separate discussion from how many lines of centuries were then formed, and whether or not those century-lines had gaps; those issues are also controversial. It also appears unclear how far apart the men stood, with six feet and three feet being disputed alternatives (presumably because of some ambiguous ancient text). The theory from my old book, about ranks relieving each other in succession, seems to be a speculation that remains plausible on some grounds, but also problematic. It appears that original Roman military manuals have only survived in quotations by a fourth century guy who had no military experience of his own, and said many things that were obvious nonsense. Julius Caesar wrote about his battles, but he was hardly concerned with fine-grained detail, and it's hard to deduce much unambiguously about how his troops actually fought. Anyway, my question is not so much about the collapse of the western Roman empire as about the disappearance of legions forever afterwards. If it was such a good military system, why didn't somebody recreate it a few hundred years later? What did the Romans do to make it work, that later armies couldn't duplicate? Or what new threat appeared, before the late middle ages, that the old legion couldn't match?

Part of musket drill was just loading the thing quickly. It's a multi-step process. Drill was also important for quick formation changes, like forming squares to resist cavalry or shaking out of squares into line so that cannon didn't hit everyone at once. If it took too long to get your square or line tight and straight, somebody might run through the gap and start stabbing your guys in the back. So lots of movements that are purely ceremonial today were tactically vital in those days. And even some movements that didn't strictly need to be done in formation actually did need to be done that way, in practice, because in the terror of battle it would never work to say, "All you guys run over there and reassemble into a nice line, under fire." Once a unit lost formation, it would never get it back, and it would be useless until the battle was over; so you had to learn to do everything in formation. A fair amount of all that would presumably have been true for the Romans as well, even though swords didn't need complex loading drills.

Yeah, I recall now that this same book also mentioned that at some point they abolished the special gear of the triarii. It probably gave the right timing. But the important thing about the tactics I described, from this one book whose sources I don't know, is not the three lines, but the ten ranks within each line, which would steadily move up through a battle. That's the thing that makes a lot of sense: it would obviously be a good way to fight primitive battles, if you could pull it off, but it would obviously be hard to pull off, without a lot of training. So that's the thing I'm most interested in pinning down. Is it somehow an established fact, or just a speculation, even just a speculation from one crackpot author in that one book that I happened to find? I don't remember my book having anything about how far apart the legionaries stood. I always wondered about it. Where does the six feet figure come from? A spacing like that would certainly make it more feasible for ranks to move through each other, but it does seem a bit wide. One man couldn't reach over to help the guy next to him, without opening up a large gap on his other side. Was it six Roman feet, that were shorter than modern ones? Or was it a parade-ground figure that allowed for the fact that men would bunch up more closely together in battle? The bit about land was exactly what I meant by my speculation: it got too hard to keep giving veterans free land, so that deal stopped being offered, so fewer recruits signed on for long hitches. That would erode a military system that depended on extensive training for its success. It might have been possible to maintain the same numbers of legions on paper, and even field units with the same equipment, but if the soldiers lacked training and experience then the legions would have been far less effective. It may be that the Roman legions really only worked as an army of conquest, because colonies on conquered land were the only way to draw the committed recruits that could acquire the necessary training, and so the system was unsustainable as a defensive force. I think the Romans were basically a bunch of brutal gangsters, so I wouldn't be surprised if their supposed military genius were ultimately based on pillage. I'd like to know whether sophisticated movement tactics that required immense training really were the key factor in Roman military success and decline, or not. It's not enough just to say that legions disappeared because everything was complicated. Maybe nobody knows just why they faded away, but then one should admit that. For a long while the Roman armies were unbeatable, and then they were gone. Things like that don't just happen by Yada yada yada. They happen somehow. I'd still like to know how.

That's an interesting point in relation to swords versus other weapons. The Roman legions fought with short swords in dense formations, after throwing their spears. Somehow legions died out later; I'm not sure why. Roman infantry tactics seemed to be unbeatable for quite some time, but then they disappeared, even though no great technology change that I know of had occurred. My only theory is that Roman infantry tactics actually required an enormous amount of training. Was poking at people with a gladius from behind a big shield a surprisingly complex skill? I'm not sure about that, but one book I read once included a description of how a Roman legion actually fought. I don't know what evidence was behind this book's description, but it was very interesting. According to this book, the legion formed up in three major lines, but each line was itself composed of then ranks of legionaries. The first rank of the first line would fight for a couple of minutes or so, pushing and poking and hacking like mad; then they'd get tired. So then there was some kind of drill by which that tired front rank would stop fighting and step back through the ranks behind them, and the second rank would step up quickly and neatly enough to just take over the pushing and hacking, without everything coming unglued into a massive schmozzle. Then this would repeat through ten ranks. If the enemy still hadn't had enough at this point, the entire first line could somehow retire and be replaced by the second line, with another ten ranks; and finally there could be the third line. Apparently there was a Latin expression about a battle 'coming to the third line', to describe any long and bitter struggle. I can only imagine that it would take a great deal of training indeed for a large group of men to execute such handovers every few minutes, in literal contact with the enemy. But an army that could do that would be appallingly effective, because it would face you with fresh guys for hours of intense hand-to-hand combat, and each of those guys would fight in the security of knowing he only had to hold out for a few minutes, and then somebody else would take his place. It's not nearly as hard to be brave for just a few minutes, when you know that you'll be safe after that, as it is to be brave for an indefinite period. So maybe legions disappeared just because the capability of executing all those maneuvers reliably died out, as training budgets got cut and then experienced legions got lost or retired; and then the techniques couldn't be relearned and re-taught quickly enough to pay off. I think there may also have been economic problems: at one point the Roman state attracted lots of long-service soldiers with promises of free land after twenty years, but it became hard to find good land for veterans. I guess the point of all that, for swords, may have been that a short sword, as an individual weapon, fit well into a larger scale tactic of disciplined movement in fairly close formations. A legionary could lower his sword, pull in his shield, and suck in his gut, and slip back between his buddies in the rank behind. It would be much harder to do something like that, for guys armed with spears. A few spears getting crossed, in the heat of battle, would make it all come undone.

From the fact that stabbing seems almost always to have been part of what swords did, I figure that slashing wasn't such a terrific thing in itself. It may have been a killer app for swords, but it wasn't the only app. What I think is that being able to slash as well as thrust gave a fighter a much bigger repertoire of moves — a qualitatively bigger range, something like having a two-dimensional space of options, rather than one. Spear guys had one set of moves, and club or axe guys had another set, but the sword guy had both.