Probably not the entry you wanted me to write, but, whatever that entry might be, I probably don't have time to write it. (Or even this, really, but...)
So, the other week, I restarted my computer for some reason, and, when it turned on, found that the display was messed up; it didn't stretch all the way to the right side of the screen, leaving a black bar there, and the bottom of the display extended past the bottom of the screen. Like the software thought my screen had a different aspect ratio than it does.
Restarting the computer didn't help. Going into the "Monitors" settings couldn't fix it; the various resolutions listed simply weren't of the right aspect ratio, and all left the same problem as before. I had downloaded some updates that day and had assumed those caused it; I would have tried uninstalling them, but I couldn't remember what they were. Should I try digging into xorg.conf? Well, I considered it, but ultimately decided screw it, I'll just upgrade the whole damn OS! I was still using Linux Mint 13, after all; they're on 16 now.
And so I downloaded Mint 16, booted up a Live CD (really a USB drive) -- and yes, the problem still occurred when running off the Live CD, which I think maybe I should have noticed as suspicious -- and, hey, it solved the problem! (It also did other neat things like, now I can hibernate my computer again. Not that I really need to; suspend is pretty damn good at saving power.) And so it went.
...until today, when I restarted the computer to find the problem occurring again. What?? What the hell am I supposed to do about that? Uh... restart it and hope it goes away? Hey, it worked!
So offhand it looks like what we have here is in fact an intermittent hardware error, where it misreports the screen resolution to the software. Yikes. It is a bit odd that before, it just happened to go right after I upgraded the OS, but, I dunno, what else can I conclude? Guess I should take it to a repair place maybe? Well, for now I'll just resort to "turn it off and on again" as necessary, and hope it doesn't get stuck in that state again like it did that first time...
In fact, the problem happens really early in the boot process, before the machine even gets to the bootloader! That should have struck me, but...
So recently there's been this whole big fuss over Stephen Hawking claimed there are no black holes with event horizons and people are saying "There are no black holes!" and other people are saying "What are you talking about he just said there are no event horizons" and well a hell of a lot of silly things are being said when, as I understand it, nothing complicated is going on, just a bunch of sloppiness with language. As far as I can tell, this is all just a question of what we mean by the phrase "black hole". (Maybe. See bottom.)
Originally, "black hole" meant a body so massive even light could not escape from it, regardless of direction of travel. That is to say, having an event horizon was a defining characteristic of a black hole. These were hypothetical objects and none were known.
Then, candidates for black holes were found, and more evidence confirmed it, and astronomers were like "Yay, we've found black holes!" Of course, such objects weren't necessarily black holes as such; just something close to it. Still, one way or another, these objects have become referred to as black holes.
Now Stephen Hawking is saying there are no event horizons. This does mean there are no black holes in the original sense. It does not mean the various objects that have been called "black holes" do not exist, just that they are not quite black holes in the original sense.
Now here's what's bugging me here -- what in space is new about any of this?
Some time ago I asked relativist Sarah Kavassalis on Formspring (now lost to the internet) just how sure we are that black holes can actually form in finite time. I don't have her exact answer to hand, obviously, but essentially it was: Black holes cannot form in finite time in general relativity. What astronomers call black holes, and what relativists call black holes, are not really the same thing, and one day she should really get around to writing something about this. (Apologies to Dr. Kavassalis if I'm misremembering.)
So if that's really true... what's the big deal? Didn't we already know this? (Of course, if that's really true... why does it seem nobody really talked about this before now?)
Anyway, it seems to me there's really not much going on here, it's just a language issue. I am worried though that I might be missing here. If that's the case, can anyone clarify?
So about a year ago I noted that "Appendicitis: The Movie" had been taken down from YouTube and was, it seemed, lost, and the only person who might have a copy was not someone any of us were really in contact with any more. But there was still the possibility that I might be able to find the guy and recover it from him.
Long story short, I emailed him, asked him if he might be willing to try to dig it up, he said he didn't have time right then but maybe he'd do it later. Then we both forgot about it.
A few days ago I remembered about it and thought to ask him about it again. And the answer is no, it's not really going to be possible; it's just lost.
Oh well. We at least have my attempts to explain it. :)
EDIT: Ugh, LJ mangled this due to some bad syntax on my part. Managed to pretty well recreate it though.
So! Solutions are up for Mystery Hunt, and you know what that means!
This year I joined Donner Party of N for the Mystery Hunt. Despite a number of people expressing interest earlier, I didn't really get much of anyone from Truth House to help out unfortunately (though Sam and Beatrix each joined in briefly). Oh well.
The story is -- I thought Strange New Universe still existed, since I still got mail from Mystery Hunt HQ on their mailing list. But a few days before the Hunt I realized -- I'd never gotten any mail from the actual *team* on the mailing list. So I emailed Tim Black, a friend of Youlian's who'd officially put me on the team last year, and asked him what was up. I also sent an email to Kevin Carde asking if I could join his team. Well, I got a reply from Tim; SNU had dissolved he said, but I'd be welcome on Donner Party of N. And so it was. (It later turned out Kevin was also on Donner Party this year.)
Donner Party didn't have a wiki, only Google Docs, which was a bit of a pain; when Sam was trying to help out I was just like "yeah I can't figure out how to let you access the spreadsheets unfortunately". Still, it worked. It had to; most of the team was off-site, based in Chicago. Apparently we had so few people on-site that they had to make special allowances to allow us to do the runaround. (Did we even make it to the runaround? I don't know what the rules were.) Towards the end, for whatever reason, there just didn't seem to be many people around and so I was largely working solo. (Everyone working on the runaround? But there's no way we could have made it there by then.)
We ended up solving about 40 puzzles, which is apparently considered pretty good for a team our size. We hadn't unlocked the Knights round when the coin was found, and still hadn't unlocked much of the Tea Party and Mock Turtle rounds. Oh well. I tried a little bit of solving, mostly solo, after the coin was found, but not very much.
Anyway! What follows is obviously spoiler-filled, so...
( Cut for spoilersCollapse )
...and I should probably go get some actual work done now.
Today was this semester's organizational meeting of the student combinatorics seminar, when we decide on what topics we want to hear about and try to see who we can get to talk about them. One topic last year that we agreed on was the Artic Circle theorem; however, we ultimately didn't end up getting anyone to talk about it so that never got done. So this semester, the Arctic Circle theorem was first on the list; we didn't even count votes for it, Chris just drew a box around it to indicate that it's in. Later, when circling the other topics we'd agreed on, the ones with lots of votes, he drew circles around them.
Later, someone who'd missed this asked, "Why does the Arctic Circle theorem have a box around it?"
Someone replied: "Because it's a frozen vertex."
Just realized I forgot "coplanar".
EDIT: Also, "covariance", which does not really belong with "covariant".
Also, you know what? I should really put up my Space Alert min/max analyses on the website at some point... I'll put that on my todo list...
Of course I'm writing more about Space Alert.
So yesterday there was a bunch of Space Alert with Mickey and Nick and Oren. Oren has the expansion, so we played with those cards in and with specializations and with variable-range interceptors. (Mickey was captain, I was comms, Nick was security.)
First game was all yellow threats -- except serious internal, those were white. (Oren apparently thinks mixed decks are silly.) It went pretty well, so next game, why not? All yellow threats!
When that went pretty well too, there was only one thing to do... yup. Red threats. External only -- internal was still yellow. This went less well. We drew the Executioner, and despite Nick's warnings, I screwed up and ended up getting knocked out by it; we survived, but largely due to luck. And to avoid getting knocked out, we did have to miss the mouse in 2nd phase and eat a delay. Still, the Executioner isn't as scary as I thought it would be. (The Seeker still scares me though. We didn't draw that.)
Did we want to put in red internal? Should we? That last one was pretty shaky... well, Nick wanted to, so we did. Not red serious internal though. (Those are pretty much all terrifying.)
And, uh, we survived. Of course, it helped that the phasing troopers happened to pass X on a phase-in turn and stay in lower red. Still -- we survived! I'm wondering if I might have to get the expansion sooner than I was intending. (Well, it's out of print right now anyway; and hopefully in a second printing they'll have fixed the misprints.) (Also, we still haven't tried any *campaigns* at Truth House...)
...I suggested we go to *all* red threats, but that was not done.
1. Red threats are not as scary as they seem at first; most just require a bit of counting. Not that the people back at Truth House are at all ready for them. The serious red internals still seem terrifying though (and so does Seeker).
2. Energy management is different with this crew. We had Mickey as captain and designated energy person; he handled all that, though he didn't always update it on the board. You had questions about energy, you talked to him. Different from how we do it at Truth House, with always explicitly marking energy and not having any central person manage it. Both seem to work, but maybe depends who you have. Remember that I played with Space Alert with Mickey, Nick and Oren first, so I learned this way first; when I introduced the game at Truth House, and tried captaining and doing this, I failed pretty badly at it. As did everyone else who tried it.
3. White shield trick is a bit easier when you're playing with specializations and one player is an Energy Technician!
4. Let me say a bit more about specializations, actually. I actually played with specializations before playing with heroic actions, but very little; I didn't really get a feel for how they were different from the base game. So let me say more on that.
To a large extent I'm not really a fan -- Data Analyst and Energy Technician, for instance, remove the spatial aspect of cracking a canister or hitting the mouse, which I feel like is making things a bit too easy. On the other hand, interceptors become much more useful when you have a Squad Leader who can get to them instantly; they're a bit too hard to use in the base game, IMO (I've mentioned this before). Not sure how I feel about Rocketeer. One thing worth noting though is that while the Squad Leader can repair their battlebots anywhere, they can't do a heroic battlebot action! That ability, often so crucial in the base game, is missing if you're playing with specializations. Medic and Special Ops offer some ways to get some of the same effect, but at more of a cost. This might be a good change -- as I've said earlier, heroic battlebot actions often obviate any need to repair the battlebots. (But perhaps not if you're playing double-action missions. Which we weren't.)
(Naturally I think the whole sort-of-experience-system thing is pretty stupid. If I do get the expansion, and play with specializations, I think I'll do it as "one game with just basic to get used to it, then straight to level 3 all the time".)
I'm really unsure what to think of Hypernavigator; we didn't play with one this time. (Mickey was Energy Technician, I was Pulse Gunner, Nick was Squad Leader, Oren was Rocketeer.)
5. Holy crap the expansion is so much more *complicated* than the base game -- both because of specializations and because the threats are way more complicated. Even the non-red ones can be really complex; take a look at Ninja! With the base game, you can learn the rules really well and predict all the weird interactions; with the expansion, that seems less possible. (What happens if your Special Ops is parasitized, and you would defeat the parasite (knocking them out) in the same turn they have a protected action? Is the parasite still defeated? According to the online FAQ, no! But that doesn't seem to follow from the other rules at all.)
EDIT next day: Actually, looking over the base game again, this is less true than I thought; it does have some weird interactions you couldn't really predict and just have to learn. But again, this is much more true of the expansion.
EDIT: You know what I just noticed? Even though defeating the Parasite requires knocking out a player, I'm pretty sure the Parasite is only worth 16 points if killed, not 18. I could be misremembering but I feel like I would have noticed that.
Also, the sometimes-relevant distinction between "moving really really fast" (what heroic movement does and what the Squad Leader does when he rushes to the interceptors), and "teleporting" (every other teleportation-like effect) is confusing. (When explaining heroic movement, I usually explain it as "teleporting", but in the expansion, that's not correct.)
So, the question: How does the expansion affect the lowest and highest possible scores?
Well, I can't answer that, because to seriously answer that would require sitting down and working it out and probably actually owning a copy of the expansion. But I can at least now say what is in there that would affect it.
Ways to get additional points beyond 69:
1. Double-action missions. These raise the total threat value from 7 (8 with 5 players) to 10 (12 with 5 players); I'm assuming we're using the standard ones and not the easier ones. However, in my opinion, it should really be considered a separate problem if you're doing this, so I'll consider this separately.
2. Red threats. This is the other obvious one. Surviving a red common threat is worth 4 points (as opposed to 3 for yellow and 2 for white) and the other numbers are derived in the usual way. (There's a little bit of variation which I'll describe in a moment.) But in fact there are smaller ones...
3. Data Analyst basic action -- use of this action gets you +1 point, so there you go.
4. Data Analyst advanced action -- use of this action allows you to get up to 4 extra points.
5. This one's not really that relevant, but it is technically possible. By using the Medic's or the Special Ops's advanced action against the Seeker, you can avoid being knocked out by it (though your battlebots will still be disabled). The Seeker is worth 15 points if killed instead of the expected 12 to compensate for the knockout effect, meaning you normally only get 12 points out of it despite its listed number being higher; this allows you to get 14 points out of it (with Special Ops) or 13 points out of it (with Medic). Of course, that's still less than you'd get from just killing a serious red threat instead.
So, with the expansion in, and 5 players, a perfect game becomes 8*8+25+1=90 points for a normal mission, and 12*8+25+1=122 for a double-action mission (not 117 as I said earlier). Whether these are actually achievable, who knows.
But what about the question of getting points *below* -28? (Here I'm assuming a normal mission.) Note that in the base game, we had an absolute lower bound of -36 (no positive points and all the penalties), a lower bound of -30 based on analyzing the audio tracks and how few threats you can let through, and an actual minimum of -28 (assuming I'm correct).
Let's address these in reverse order:
1. Plasmatic Fighter -- the Plasmatic Fighter can knock people out, but is a white common threat (!). This probably makes -30 achievable.
2. More slow threats. The expansion adds in more threats that have an initial speed of 1; IIRC, they all speed up later, but these should still be useful for lowering point values, just as the Man-of-War is. (The Juggernaut unfortunately isn't really useful for these purposes.) Many, IIRC, are yellow or red, but in this context that doesn't matter.
3. Calling in threats. Several of the serious red threats call in another threat; these threats are only worth the points of a red common threat (4/8) instead of a red serious threat (8/16). This is still too many points to be helpful for this, but it's worth noting. A called-in threat may not appear until quite late, making it easy for it to be neither killed nor survived. However there is one case that is helpful...
4. Sealed Capsule. The Sealed Capsule is the one red common threat that calls in another threat; it is worth no points at all. (Yellow and white threats never call in other threats.) Now that's helpful for reducing your score! Especially because, once again, the called in threat may not appear until quite late.
5. Hypernavigator basic action. The Hypernavigator's basic action can be used to have threats move one less space that turn. The application is obvious.
6. Hypernavigator advanced action. This allows the ship to jump to hyperspace after turn 10 or 11 instead of 12 (although there is always a "turn 13", no matter what). The application, once again, is obvious. So, point 1 should allow us to achieve -30, and points 2-6 should allow us to achieve -36; indeed, they seem like overkill for achieving -36. Although, of course, I haven't checked this. But it may even be possible to get below -36...
7. Medic advanced action. Using this action costs you a point. So, with it, it's quite possible that -37 might be achievable! And that of course truly is an absolute lower bound.
And that of course is as far as I'm going to go with the matter until such a time as I actually get the expansion.
Looking through the rulebook, I see variable-range interceptors are really only meant to be used with double-action missions. Well, whatever. We can play it how we like...
Barring use of the Medic's advanced action, which could also be applied in the case of the Seeker -- of course, the Medic didn't exist then...
So, a while ago I wrote this entry about what it turns out is called Moser's shadow problem; shortly after I locked it because uh it turns out Jeff didn't want people knowing he was working on the problem. But it turns out that he has since solved that problem, along with Yusheng Luo. (And so in particular, that entry can now be unlocked.)
Worth noting here that in 1989, Chazelle, Edelsbrunner, and Guibas figured out that the answer is yes... if we modify the problem slightly, by allowing projections from finite light sources instead of just light sources at infinity. (I think technically they wrote it in terms of faces rather than vertices, but this makes no difference.) But allowing finite light sources can make a difference, so the original problem remained unsolved. Now, apparently, that gap is closed.
Unrelatedly, I'm also unlocking these two old entries. (Yeah, unlocking old entries has become more of a "when I feel it's appropriate" thing rather than a strict time-based thing.)
In this entry I want to consider the questions, "What is the lowest possible surviving score in a game of Space Alert?" and "What is the highest possible score in a game of Space Alert?". (I like to say that dying is -∞ points, but that is not very interesting.)
Let's be clear on the parameters of the problem -- this is Space Alert without the expansion. (Because I don't have the expansion, and there doesn't seem to be a list of the cards available online.) 4 or 5 players may be used. The players are actively trying to achieve the lowest/highest score. Any deck of threats may be used, any set of tracks, etc.; we assume we are allowed to rig all the decks (damage tiles etc.) and that the players know in advance everything that will happen. The audio track must be one of the 8 normal missions provided.
Some terminology: Let's define the "total threat value" of a mission to be the number of common threats plus twice the number of serious threats. This is a useful quantity, because serious threats of a given difficulty level are (with a few exceptions) worth twice as much as common threats of that same level. Furthermore, it is constant across mission types -- it's equal to 3 for the test runs, 5 for simulation or advanced simulation (6 with 5 players), 7 for a mission (8 with 5 players), and if we include the expansion, it's equal to 8 for the easier double-action missions (10 with 5 players), and 10 for the standard double-action missions (12 with 5 players). So for our purposes now this quantity will always be equal to 7 or 8.
First, the maximum problem; this is the easier one. There's an obvious upper bound on the maximum possible score, which is 8*6+21=69. (8 total threat value, times 6 points for killing a yellow threat, plus 21 points from the window.) 69 points is a "perfect game"... but is it actually possible?
Well, after several hours of trying to construct such a scenario, I can report that the answer is yes. Solution (and hints towards my solution) is spoilered for those of you who really want to try this yourself. Note of course that there may well be other solutions that look very different; this is just the first one I found.
Use 5 players. OK, that's not really a hint. Use audio track 8.
Trajectories are as follows: T3 blue, T6 white, T4 red, T1 internal.
Threats are as follows: T+3 Overheated Reactor, T+4 Psionic Satellite, T+5 Nebula Crab, T+7 Juggernaut, T+8 Scout.
Players will move in the order Red, Yellow, Green, Blue, Purple.
Turn 1: Red hits C, all other players change decks. (Green, Blue, and Purple are delayed.)
Turn 2: Red changes decks, Yellow hits B, all other players do nothing.
Turn 3: All players press C. (7 points.)
Turn 4: All players press C. (7 points.)
Turn 5: Red uses heroic B (the other side of which shows upper red). Yellow presses B. (Overheated Reactors killed.) Green moves blueward. Blue changes decks. Purple heroically rushes to upper blue. (Psionic Satellite reaches X. All players are delayed.)
Turn 6: All players do nothing.
Turn 7: Yellow moves redward; all other players press A. (Psionic Satellite killed; Nebula Crab takes 3 damage. Nebula crab reaches X.)
Turn 8: Red and Green move redward. Yellow and Purple change decks. Blue presses C. (Nebula crab reaches Y.)
Turn 9: Purple presses C; all other players press A. (Nebula Crab killed; Juggernaut takes 4 damage. Scout reaches X.)
Turn 10: Blue changes decks; Purple presses C; all other players press A. (Juggernaut killed.)
Turn 11: Red moves blueward; Yellow heroically rushes to lower white; Green presses B; Blue presses A; Purple moves redward. (Scout killed.)
Turn 12: All players press C. (7 points.)
...I didn't list what the *other* sides of the cards do, but it's pretty easy to fill these in in a manner consistent with the contents of the deck.
I do have to say, though, that the maximum problem seems kind of silly if you don't include the expansion, which raises this upper bound to 12*8+21=117. Or... is it even higher? I seem to recall reading that threats that call in other threats have their scores a bit weird. And, actually, I guess just the possibility of calling in other threats should raise that bound, shouldn't it? I don't actually have the expansion. Crap. Yeah, this is why I'm ignoring the expansion.
Anyway, so the minimum -- how about lower bounds? Well, there's an obvious lower bound of -36 -- all penalties, nothing else. Now wait, you say, shouldn't that be 7*2-36=-22? Because you get 2 points for surviving a threat? No! It's possible to neither kill nor survive a threat without dying; remember you only count as having survived a threat if it reaches Z. That said, we can certainly make a lower bound based on this idea.
The longest track, T7, is 16 spaces long; a threat needs to advance 15 spaces to reach Z. If it has speed 3 or more (let's assume everything is constant speed for now), it will assuredly reach Z regardless of when it appears. If it has speed 2, however, it will have to appear by turn 6 to reach Z; and if it has speed 1, it will never reach Z. One can come up with similar numbers for the other tracks; I won't go into details here. Note that straight-up "speed 1" threats do not exist -- there are two "speed 1" threats, the Man-Of-War and the Juggernaut, and both speed up. It's straightforward to compute numbers for both of these. (Be careful, the Juggernaut has the odd property that it sometimes arrives *sooner* on longer tracks.) There are no threats that lose speed so these are not a concern.
[Previously here were two paragraphs giving a probable lower bound based on this idea. However, the numbers were wrong, and it ultimately yielded no improvement, so I don't feel like fixing it. Let's skip ahead a bit.]
I guess we'll have to analyze the actual audio tracks. There's only 8 of them after all. We'll consider both what happens with only 4 players and with only 5 players -- while having fewer threats may seem better, let's remember that with 4 players, one can only get -8 points from knockouts, not -10. After a bit of work, we find the following (not necessarily unique) minima for points let through:
Track 1: 10 points (put T7 on red); 12 points with 5 players.
Track 2: 12 points (put T6 or T7 on blue); 14 points with 5 players.
Track 3: 6 points (put T7 on blue and T6 on white, with T+6 being the Man-of-War); still 6 points with 5 players (put T5 on red).
Track 4: 10 points (put T7 on blue, with T+6 being the Man-of-War); 12 points with 5 players.
Track 5: 12 points (put T7 on red and T6 on white); still 12 points with 5 players.
Track 6: 12 points (put T6 on red); still 12 points with 5 players (put T7 on white).
Track 7: 10 points (put T7 on red and T6 on white); 12 points with 5 players.
Track 8: 6 points (put T7 on red and T6 on white, with T+5 being the Man-of-War); still 6 points with 5 players (put T5 on blue).
OK. And it's pretty clear these are indeed minima, so we get a lower bound of -30 points. Still, it's not clear whether this is achievable. Let's consider -- achieving this requires knocking out all players. But there's not too many ways to do that in the base game. Especially since whatever delivers the knockout must either A. be white or B. do so without reaching Z. The only white threats that knock out are the Battlebot Uprising and the Commandos (both serious internal). The only threats that knock out without reaching Z are the Battlebot Uprising (serious internal), the Executioner (serious internal), and the Power System Overload (common internal); however, the Executioner and the Power System Overload each lack the ability to knock *all* players out, and so if we are relying on one of them to deliver the knockout, we must have both. (Or rather, Executioner can knock all players out, but it can't both knock out all players and disable both battlebot squads.)
From this we can see that -30 is not achievable with track 8, since its only internal threat always reaches Z (meaning it must be white) but is also common, incompatible with the above. Track 3 can be ruled out for similar reasons. Thus -30 is not achievable. And since the only common threat that knocks out is Power System Overload, and it can't knock out all players by itself, one can deduce that -29 is not achievable either.
And -28, it turns out, is achievable. Solution is spoilered if anyone wants to sit down and figure it out themselves.
Audio track 8, 5 players. T7 red, T6 white, T5 blue, T4 internal. T+3 Hacked Shields (blue), T+4 Psionic Satellite, T+5 Man-Of-War, T+7 Frigate, T+8 Gunship.
I'm not going to go into details of how it's executed because, well, it's fairly obvious -- pick up battlebots, fiddle with the shields, get knocked out. You need 2 shield up on red. You also need exactly 2 shield up on white, which means first you'll have to hit B in lower red before filling up the white shield. Don't worry about the blue shield, it'll take care of itself. Point is, you'll survive with all players knocked out, both squads disabled, 6 damage on each zone, and a mere 8 points for threats survived, for a total of -28.
So we have an answer to our question: The maximum possible score is 69, and the minimum is -28.
...yeah, I basically spent all day on this instead of working. But now I'll never have to do this again! Unless I someday try to figure out how the expansion affects it, anyway.
So. I've been playing a bunch of Space Alert lately with the people here at Truth House. (I bought it because I thought I might actually get people to play it, and, holy crap, it actually worked.) Mostly with Andy, Seth, Ryan, and Dan (Ryan in particular got kind of obsessed with the game...).
When we started out we often did disastrously. Things got a lot better once we started taking marking energy usage seriously. Eventually Ryan was (along with me) playing every game and we made him captain because, well, he seemed to be the best at it. Before long we could consistently beat white-threat missions... well, unless we just really screwed something up. Which is always going to happen now and again.
So we started mixing in the ordinary yellow threats. It took a bit, but before too long we could handle those pretty well too. So we mixed in the serious yellow external threats. Those posed more of a problem. I'm not sure we ever really got to the point of really being able to handle those, but we certainly beat them a few times.
Ryan graduated this semester and was leaving Ann Arbor on Wednesday, so Tuesday we played a few games and, even though we weren't really sure we were ready for it, we mixed in the serious yellow internals as well. (Dan is also going back to Australia shortly.) The first few games they didn't come up, so in the last game we reduced the density of white threats in all the decks. Indeed, Contamination came up, and we killed that, but ended up dying anyway.
Then yesterday I played with Justine, Angus, and Nick -- all of whom had played before, but not in a while, and never with any yellow threats in. (Seth was also in for one game.) So we went down to only white threats, and, well, it was tough. I'm not convinced this is yet a crew with whom we want to add in yellow threats.
Anyway. All this is prelude to the story I want to tell right now. Tonight, Geoff Scott hosted a game night. First we played a few games of The Resistance -- which, I gotta say, though it's apparently still weighted towards the spies (the "Mafia", the "bad guys"), certainly seems to be easier for the Resistance (the "townspeople") than Mafia is. Resistance won 3 out of the 4 games. Basically, it seemed to me, the game forces the spies to act rather more openly than the Mafia do in Mafia. Of course a lot of that could be us not having the hang of it yet. In particular, in one particularly embarrassing incident, when straight-up asked "Are you a spy?" in the final game (I was), I started kind of giggling; simply saying "No" at that point wouldn't have been believable so instead I went with "What the hell is this?" and only then stating "No I'm not a spy." It didn't work. But, like, it's a little ridiculous, because I'd never do that during Mafia; I'm a decent Mafia during Mafia. Somehow, though I was prepared for "Are you Mafia?", I wasn't prepared for "Are you a spy?". Nor was I generally a good spy most of the time. (First and last games I was outed very quickly; second I managed to convince people I was Resistance, but I tried to be too tricky and cast a "mission success" when I should have cast a "mission failure", and that ended up us getting us in the end.)
(You know, it only now occurs to me that I was on the losing side every game.)
Er right but the point was Space Alert. So after that we played Space Alert. I had intended to play things other than Space Alert, because I'd play so much of that recently, but Geoff was saying we should play something... well, I don't remember what the conditions he said were, but Space Alert fit perfectly, so I suggested it.
Crew was me (captain), Geoff (comms), Julian, Jordan, and KK. (We didn't bother appointing a security officer.) Julian, Jordan, and KK had all played before, but it had been so long that we did a full rules explanation anyway. (I suggested we play one round of simulation first, but Geoff wanted to start on full mission.) The first game or two didn't go very well -- lots of non-marking of energy especially -- but by the third game we'd gotten some of the hang of it (though we still died). The fourth game finally we survived (with 28 points or so). (Side note: Geoff has the first edition, where Stealth Fighter has its speed misprinted as 4 instead of 3. I didn't realize what was going on there until well into the game so we decided to just play it as 4. It wasn't a problem.)
Then Geoff says, OK, one more round; and since this is our last round, let's play with all yellow threats! You must be kidding, I say. The people I play with at home with have played well more than you and they're not ready for such a difficulty level; we're certainly not. We're going to die horribly. Well, let's try it, Geoff says. It's a Vlaada Chvátil game; dying horribly is the point!
And so it was. All yellow threats. And somehow... we won. With 50 points. That's such a large number I don't even know what to make of it. OK, we've had some high-30s wins here at Truth House, but... 50 points. Every threat killed -- Minor Asteroid, Nebula Crab, Phantom Fighter, Major Asteroid, Power System Overload. Only one damage (on red zone, from when we killed the Minor Asteroid). And we even had time to look out the window, for 1 point in phase 2 and 3 points in phase 3. Everything basically went perfectly.
I mean I'm not even sure what to say about this. Obviously we had a bit of luck, but... the people in the math department are just that much better than the people here at Truth House? Well, I guess that's not too unbelievable, but it's still kind of astonishing. We really did have quite a bit of luck though -- the Overload could easily have wrecked us; we needed to coordinate perfectly, all of us hitting B at the same time in 3 separate stations, in order to bring it down. (Plus one additional point from me on the turn before, and one additional from one of those Bs being heroic.) And the one point of damage that got through knocked out the blue gravolift. Fortunately, we didn't need it to get into position -- we already had someone in lower blue to fire on the Minor Asteroid, I was already in lower white manning the main reactor, and Geoff used his heroic action to rush to lower red from the bridge. So in fact knocking out any of the gravolifts wouldn't have caused a problem... OK, I guess that's a bit less luck than I thought. Still!
(I'm pretty sure had the Executioner or the Seeker come up, it would have been a slaughter. Those two really scare me.)
Anyway, 50 point victory, holy crap.
Well, one thing worth noting -- there are basically two ways that threats can be harder; they can be harder to deal with (increased probability of failure), or do worse things to you if you fail to deal with them (increased disutility of failure). (Though sometimes they can be intermingled, e.g. with Psionic Satellite.) I'm of the opinion that the game is harder (and more fun) when things are primarily hard the first way rather than the second (with one or two of the second for splash). Firstly, the latter tend to make things too all-or-nothing; either you die, or you survive with a huge number of points. Except the funny thing was, Power System Overload really is a hard-to-deal-with threat! Which is why it's so surprising we survived; Major Asteroid is not exactly scary, you know? (The Nebula Crab is a little, but they just zapped it before it could reach X.) If it had been more of the second sort of threats, our survival would have been less impressive.
Secondly, the first are just more interesting -- you have to spend more time figuring out what the hell you're doing in the first place; you can't just quickly come up with a simple plan and do it. (For the same reason, I prefer more smaller threats to fewer larger threats.) I think a game where there's more damage, and more chances for damage to screw you up (rather than just killing you outright), is more interesting. Although, I guess, even with a lot of damage, it often just isn't a problem -- guns frequently take damage after you've stopped using them, for instance. And who really cares if the shields are damaged? It is a little disappointing. Actually there's a number of things in the game that just don't seem to come up much. I mean, the interceptors, obviously -- those seem to be mainly used if someone's picked up a squad of battlebots and has nothing else to do -- but the one that really sticks out in my mind is repairing battlebots; due to the fact that you never have more than 2 internal threats per game, the existence of heroic battlebot actions, and the fact that few threats both have 2 hit points and fight back, it's just rarely necessary. Probably more necessary in the expansion when you have double-action missions with threats (and also harder threats).
Actually, tonight's crew was pretty keen on shields. I tried to convince them that shooting more was really just better most of the time, but they were not so convinced. Personally, this experience playing with a little more shielding and a little less shooting seems a data point in favor of "No, it really doesn't work as well." Although -- Ryan came up with this neat trick with the shields I'm teaching to people now. It is: On the first turn, someone refills the white shields; on the second turn, someone cracks a canister. Isn't that a bit early to be cracking a canister?, you say. Or at least, I said at first. Well, maybe, but this seems to work pretty well -- running out of energy by the end of the game due to insufficient canisters has generally not been a problem for us. (Certainly not compared to running out of energy due to people failing to mark, or people getting delayed, or not having people in position... you get the idea.) As I recall, when I learned to play, and played with Mickey and Nick, we typically had an unused canister at the end of the game. And often there just isn't much else to do in the first few turns, so, why not? Shields on white!
ADDENDUM next day: Well, OK, one reason not to is that it will seriously hurt you if you draw Crossed Wires...
Maybe shields are also something we could use a bit more in cases where we're deliberately not killing a threat, as often happens with the asteroids. But that needs proper timing -- it should be after the shooting is done. Of course, often, after the shooting is done, there's no more energy left, and in that case having someone draw energy just to put it in the shields seems wasteful. If there's energy sitting around in a side reactor to shield with, it would make sense, but drawing from the main reactor to do it -- especially having two people to coordinate to do it -- doesn't seem worth it.
Anyway. I think I've rambled a bit. I think that's all I had to say on the matter. I'll stop here.
This is Dan the first-year who lives here now, not Dan Zemke.
(From the math department.)
Naturally, before the game started I kept making jokes about "Why do you asume the Resistance is the good guys? This game is just Resistance propaganda!" Later after a few votes on forming a team failed, I commented, "What an inefficient system they want to replace our government with!"
In fact, I was a spy in 3 out of the 4 games we played.
But on the good side, with the first edition, the canisters aren't rolling away all the damn time.
Although, the Seeker kind of maximizes the first of these, and I'm not sure I'd consider the Seeker fun. I guess it goes a little too far. But, well, I've yet to actually encounter the Seeker, so we'll see.
[...] In my view this is exactly the sort of thing that demonstrates why its wrong to dismiss string theory as "non-predictive". This attitude simply fails to grasp that string theory is not analogous to the standard model, but to quantum field theory. People still have to write down a model in order to make a prediction, just like always. Now that process just has taken on a totally different set of constraints, that in many ways are far more restrictive than before. Scientifically the only difference is that now we call it "choosing a vacuum", but its scientifically the exact same thing as "postulating a Lagrangian" in quantum field theory, like the one that earned Higgs and Énglert the Nobel Prize.(Yes, this is a followup to this old entry.)
I used to think I understood mass-energy equivalence. Well, to the extent that you can understand it without seriously learning modern physics, anyway.
It seemed to be pretty simple: Mass simply is energy. That is to say -- well, there are two things we mean by mass, right? Gravitational mass and inertial mass, though of course relativity demands that the two are equal. Well, both of them are simply equal to energy -- this is only meaningful of course if energy has an "absolute zero", but, well, apparently it does. Energy warps spacetime around it, attracting things to itself; and the more energetic a body, the more its inertia. When something speeds up it gains mass and when it slows down it loses mass. An object on earth has slightly less mass than that same object 1000 miles above the earth. Rest mass of a particle I guess is just how much energy it takes to create that particle ex nihilo -- OK, I imagine there's a better explanation than that if you actually understand QFT, but I don't.
Except I keep reading that the notion of "relativistic mass" (i.e. γm0) is not really right, and it shouldn't be used, because it acts like mass in some ways but not others, and it shouldn't be thought of as mass, and objects shouldn't thought of as gaining mass when they accelerate.
(...on the other hand, there do seem to be number of contexts where I see "mass" being used to mean "relativistic mass". So I dunno.)
This doesn't make sense to me. So you're telling me that if I have, say, 2 protons and 2 neutrons, and I put them together to form an alpha particle, they do lose mass because of the energy difference, but if they're moving really fast and I declerate them, they don't? Huh?
"Energy is mass" I can kind of wrap my head around. "Energy is sometimes mass" is just weird.
So I decided today to try to get some work done other than writing. But what? I could work on this hard problem that I've gotten nowhere on... or that hard problem I've gotten nowhere on... oh! I'm currently writing the paper where I explain the computational side of what I've done, so this would be a good time to go back over the code and improve it -- there's a few optimizations I've intended to implement for a long time. Well, one big one, anyway.
Surprisingly, playing around with the program, I found a bug I never noticed before: When run in "all information" mode, and input a number which is divisible by 3 a fair number of times, it sometimes just crashes rather than output anything.
I have no idea why this is -- well, OK, I haven't sat down and looked into it, but knowing how my code is structured, I already have a guess. Still. Guess I'd better fix that before worrying about how to speed things up...
Meaning, give information about ||3kn|| for all k≥0, instead of just outputting the stabilization length and stable complexity.
At least, I think I remember...
Yeah, yeah, picking on easy targets. Still, I wanted to point this out.
In GGXXAC+ story mode, when you select your character, it gives you a short bio of them -- in-universe, it's supposed to be the PWAB's file on them. The first screen involves information like name, height, weight, birthday, blood type (because after all the game was made in Japan), and... "type".
What is "type", you ask? Well, here are the types for all the characters:
( Boring listCollapse )
So it's some weird combination of species/ethnicity/nationality that is applied quite inconsistently. Bridget is "English" while Axl is "Human/English", despite the fact that they're both human. Justice is type "Gear" despite not being the only Gear on the list -- but Dizzy is just listed as "non-Human" while Testament is listed as "Swiss"! Not exactly the most relevant information! (Sol is just listed as "Human(?)", but it's entirely possible the PWAB isn't aware he's a Gear; I get the idea that few people are, in-universe.) Similarly Eddie is listed as Spanish; seems like they've forgotten this is Eddie and not Zato. Meanwhile, A.B.A is listed specifically as "Homunculus", while Dizzy and Slayer are just "non-Human", and Robo-Ky gets the unhelpful designation of "Humanoid".
You could try to justify this in-story by saying the PWAB's files are quite disorganized, but somehow I don't think that's the reason for this.
Have you heard of the fusible numbers?
They're a recursively defined set of nonnegative dyadic rational numbers. The definition is simple:
1. 0 is fusible.
2. If a and b are fusible, and |a-b|<1, then (a+b+1)/2 is fusible.
(If you allow |a-b|≤1 instead, the result is the same.)
The fusible numbers are well-ordered, and it is conjectured that their order type is... no, not ωω, but ε0. (No, I have no intention of seriously thinking about fusible numbers now or anytime soon. I've got plenty of work to do already.)
Anyway. My point is, if you read the proof of well-ordering, it says nothing about the order type. The paper actually proves that the order type is at least ε0, but doesn't put any upper bounds on it. I mean, I suppose the Church-Kleene ordinal is a trivial upper bound, but that really isn't saying anything.
I note this because in my work, when I prove a set is well-ordered, the proof invariably also supplies immediately an upper bound on the order type. The hard part, strangely enough, tends to be finding a lower bound on the order type! Which is really odd, since that doesn't even require proving well-ordering, and seems like it should be easy, but that's what's occurred in the contexts I've dealt with.
But my point was about upper bounds. Proving well-ordering without an upper bound now feels weird to me, like nonconstructive or something. I don't know that it's actually nonconstructive in any real sense, but there's at least a superficial analogy there -- proving something exists without proving an upper bound on it. (Of course, quite a bit of my work is nonconstructive, at least at the moment. I'd like to have constructive versions of what I can prove, but it's not a priority. Of course right now my real priority is writing...)
I have to wonder if it's possible to extract an upper bound from the proof anyway? (Probably not.) Or if there's some other proof that yields an upper bound? One that isn't so difficult, that is -- I suppose if you could prove it's actually ε0, that would count, but I mean something easier.
Well, like I said, not going to think about it.
A few nights ago I had a dream wherein some people started singing the theme song to a silly science-fiction show that existed in the universe of the dream; the song made reference to some hazards our heroes wanted to avoid in their spaceship. In particular, it would be bad to fall into "the Aptenon, the poisonous gap in space".
...I just don't think I need to comment on that.
(What? I went to Berkeley for two weeks? Yeah, maybe I'll write about that sometime...)
Here's a link.
For those of you that are just tuning in: Let's define ||n|| to be the complexity of n, by which in this context we mean the smallest number of 1s needed to write n using any combination of addition and multiplication. (Note that this is the number 1, not the decimal digit 1. Allowing you to write "11" and say you've only used two 1s would just be silly.)
Then we can define the defect of n, denoted δ(n), to be the quantity ||n||-3log3n; and we can then consider the set of all defects δ(n), as n ranges over all natural numbers. Surprisingly, this set is well-ordered, and its order type is ωω.
...OK, this won't be surprising to you if you've spoken to me anytime in, say, the past several years. But it should be a surprise to almost everyone else. And it's pretty damned neat regardless.
Thanks are of course due to Joshua Zelinsky -- who, after all, defined the object of study of this paper in the first place (defect, that is, not complexity) -- and to Juan Arias de Reyna who not only helped a lot with the editing but also helped organize several of the ideas in the paper in the first place. And other people, but, well, you can check the acknowledgements if you really care about that.
We'll see where I can get this published. In the meantime, this should be quite a bit more readable than the old draft sitting around on my website.
Now I guess it's on to the next paper (for now)... or rather, it already has been for a while...
(It is possible I am misremembering who said what here.)
I was talking to Justine and Seth and Noelle yesterday and I don't remember the context but someone suggested making ants on a log. Only problem was, we don't have raisins at the moment. I have some prunes in my room, I pointed out. Those would be pretty large ants, says Noelle; beetles on a log, maybe?
Today I look at the Wikipedia entry and there it is mentioned, that exact variation with that exact name. I had to check to make sure the edit wasn't made today or last night.
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