Whack that sucker hard enough, it'll break
"Oy! Ya fiddling lickspittle doodler, where the fuck have ya got to?"
"Here, My Lord, in the second greenhouse. I was just sketching these fern gametophytes. They're the first I've encountered since we started propagating this cultivar."
"Yeh, right. So.... Which, the dirt?"
"No, Sire, these small green organisms. Their presence indicates that the ferns we brought have--"
"Yer sketchin mold? Jesus. I made a fuckin Michelangelo of mold, I did. The very Leonardo of little tiny flecks of cabbage, are ya?"
"Yes, Sire. As you say."
"You know, if I didn't know better, I'd swear yer weren't my clone at all.... Agh, no mind. Right. So: you know this Martian inter-- embargo thingie? With the War?"
"Interdiction, Lord?"
"Yeh, right, Interdiction. So I'm thinkin -- what a load of crap that is, eh? I mean, how do you even interdite a whole planet, eh? I mean, here it is, not a mere city or nothin mind you, it's a fuckin great gravity well, right in plain sight in the middle of the fuckin Solar System. Big red thing, I seen it dozens a times. I mean, you just lob shite at it, right, an it just lands there, bang, you know? What're they thinkin? I mean, sure, there's re-entry to contend with, but Jesus, they did those probe thingies, dint they?"
"Ports, Sire."
"Wot?"
"'Ports.' Technically you were correct when you mentioned an embargo. The Authorities are maintaining a presence at all the ports of entry, so as to prohibit sanctioned trades and communications entering or leaving the settlements. The word 'Interdiction' is a slight misnomer."
"Well, why they call it that then? Fuckin half-arsed weasel word, innit? You mean embargo, you say 'embargo' is what I say. Might as well call it 'Mommie' an --"
"Ahem. Yes, Sire. I believe it was a reference to the Solar Interdiction."
"Oh, right. Stuck in their minds, I spose, eh? The Icebags pissed em off enough, spoiled their sense of interstellar adventure an Grand Destiny of Man an Made in His Image an all when they found out the lords of this particular corner of Everything's Arse are fuckin great Oorters with invisible rocks fer brains. And so the fussy little monkey bigots spend their dwindlin bluster all runnin around mutterin the damned word all the time. 'Interdiction interdict interdite' this an that and that over there. Gets in yer subconscious, you get a pancultural religiopolitical shock like that, an you mutter mutter mutter to yourself all day long. Start to use words inappropriately. Sign of imminent institutional breakdown, I say."
"Indeed."
"Or ongoing, eh? With the War, eh? That'd count.... You know, I'd flat forgot about the Icebags' Cube. Heh. Funny thing, that, how you can be thinkin about somethin real hard, an miss the big.... Innat interesting? Not that it has any fuckin thing to do with what I been tryin to say all along, oh, no. So. Right. We saw that big darkmass a few days back, right? Headed what? About 40 degrees up out towards Saturn ways, wunnit? Whizzin along about point three or so?"
"Yes, Sire. Would you like to pursue it now? At the time--"
"See, I'm thinkin they're gonna wanna have some, you know, big Bad Motherfucker bang-er-up bombs an shit on Mars, someday soon, yeh?"
"One would imagine both sides would, yes. Those, or food. Possibly both."
"Right, an ships, right? Need darkmass for ships' drives, at least for all those gleamy military needles so they look good in the parade. An, I shall remind you, not to mention this great wobbly filigree of silvery self-fabricated shite we call home, eh? How long to catch it?"
"Hmmm. I believe it would have wrapped by now, or would before we reached it. I can calculate the distance to the Weeuruunie Interdiction Boundary easily; the last surveys of both the boundaries and the darkmasses made before the recent hostilities broke out were very accurate. If the darkmass has wrapped, we will surely be able to catch it without any trouble on the other side."
"Well, that'd be a good part aways back across the Cube, wouldn't it? I'm not fuckin made of money. Or fuel."
"One good-sized harvest of darkmass would more than pay for the effort, Sire."
"Yeh, right! An that is why I said, to you, not five minutes back, 'Oy, where the fuck are ya?' Yer damn lettuce threw me off, that an all your natterin. Here: We're gonna go get all of em."
"..."
"Yeh, heheh, you'd better close your gapin mouth, laddie mine, before you catch a gymnosperm or somethin in it, because see, I got a plan. And didst I not make thee from the flesh of my flesh, or words to that effect? Dost thou not trustest me who made thee in mine image, O my Sunny Jim? Heh. See this? Right here? This in here is original brains, they are. Yours a mere Derivative Work."
"My Lord, there are seven mapped darkmasses within the confines of the Interdiction Cube! The expeditions have been planned and in one case executed--"
"Ach, dammit, did I forget to grow yer balls when I made ya? O, ye of little balls. Where's yer sense of... well, greed boy? I mean, come on, you know very well what I paid for that wee 14 million tons of darkmass down there -- three hundred thousand souls, it was, I made myself. And there's a fuckin War on, an a biggie at that, an big war is as a matter of well-known fact big money, QED. First interplanetary war in fuckin history, an who knows how grand an blowy-uppy it'll get, an here we are out in the middle of the Upper Armpit of Nowhere, noteworthily I shall remind you not in the blowy-uppy part of the fuckin War, an we have a fast ship, complete with fuel an partially synthetic brains an little fuckin cabbage leaves growin the orangery. An I might add a unique ship what's uniquely ship-shape enough that it does not need to deal with acceleration in any ways whatsoever, nosiree, but merely communes with the quantum informational thingie for permission and changes frames of reference as if by magic. Come on, there's just seven of em."
"Sire. There are... well, I suppose it..."
"Ahh, see, there's the kind of enthusiasm I like to hear from the fruit of my -- well my cheek as I recall. An -- mind you, mind you! -- as I might have mentioned there's a fuckin War on, see, an so nobody else will be lookin for em. They're all busily ready-aim-firing-oh-no-wait-not-yet with their bombs an asteroids an shit, an noisily diplomatin an televisin at each other, an fundin black labs an gold retrieval missions an shit. Hell, boy, nobody else will even have a fuckin clue where these darkmasses have got to, once that last survey's got a bit obsolete an they go whizzin an wrappin around the Cube a few times! Heheh. Seven, you say?"
"Yes. As I recall the survey was accurate to within one meter, and one centimeter per second velocity. That was about three months ago, so the uncertainty clouds will have spread somewhat by now. And they'd all have wrapped one or more times in that period, adding more uncertainty...."
"Well, we're not a passive observer here, you know. We are, do not forget, in a fuckin awesome space ship. In a pinch we can even make it go 'whoosh' an fart hot hydrogen out its arse an there you are, dealing with yer uncertainties proactively by chasin stuff. Or so I am told, when I am not resigned to merely sittin in the middle of fuckin nowhere consumed with a passion for growin intelligent flower gardens. Or if you prefer we might consider, oh I dunno, maybe usin the fuckin lattice drive we grew last month, instead of just ponderin its quantum splendor an all."
"Indeed, point taken. That said, Sire, we do have a limited amount of fuel, as you mentioned. Each use of the lattice drive to shift our frame of reference will consume a substantial portion of the darkmass we carry. We should plan a course that minimizes the amount of velocity we need to reach their vicinities. Or the most we can reach. It may not be feasible to expect to get all seven."
"Ay, ay -- thank you very much young Master Exposition, but I'll have no half-assed clone talk, you. All seven or nothin."
"Well, the Cube is 11,323,344,384 kilometers across, so--"
"That would be natterin again. Do you always think out loud like that? I might could fix that, you know. Hey, hang on, hang on! People were tryin to figure out how Pluto gets in an out, but nothin else can, right? I mean, why ain't Pluto jumpin all over the fuckin sky every time it crosses the Cube boundary, when every other piece of stuff in the fuckin box just wraps over to the other side unchanged an all, just blip an there you are with the shadows all upside-down of a sudden, eleven billion-an-more klicks from where you started?"
"Something about dark matter, I'm told, Sire, though that seems like a hedge. I suspect the Weeuruunie wrote an exception into the matter filter for Pluto when they constructed the Interdiction Cube, so that early astronomers would not become overexcited if they noticed the planetoid jumping."
"Heh. As if. They was keepin the dinosaurs in, an no mistake."
"Indeed. And those were the astronomers that were meant not to be excited. At any rate, the Cube is of known size, and the position and velocities of the seven darkmasses are known to great accuracy, and of course we know our own position very well. It should boil down to a simple dynamic programming problem."
"Yeh, well, we got what? just below fifteen million tons of darkmass an hydrogen fuel on board. So no needless sightseein. We give a wee tap on the gas, we coast, we nab, we prod again, got it? Extended burns will leave us sittin out here twiddlin our thumbs up our asses an eatin gynocarps an shit. No offense, little moldies."
"Gametophytes, Lord, but only the sporophyte stage of this cultivar have organs of hearing.... There is one problem."
"Yeh. The fuckin War, eh?"
"Yes, Sire. We will need to avoid a substantial region around the core of the system, unless we pass through at relatively high speed. More than one millicee, for example. I suspect we will be better served if we use the Interdiction Boundary to wrap across the Solar System instantly. It does increase the complexity of the tour planning somewhat."
"Right. So hop on it, boyo. I'll wake up the ship an the others, an then let's go nab us all the darkmass anybody's ever not seen, before they get wise to us."
"I will be done here momentarily, Sire."
"An did I ever tell you ya sound like Mister fuckin Spock? I didn't build that in, did I? You do it on purpose, don't ya, as an actin out thing. Heh. No, wait, I know, you talk like that Vizier fellow in that old movie, innit? Not sure that's entirely appropriate for a fourteen year old boy, now, is it?"
"No, Sire. Not at all."
"Heh. Smartass. But always remember -- Derived Work."
The Weeuruunie Interdiction Cube is 11 323 344 384 kilometers on each edge, measured to within one centimeter, and is as near as can be determined perfect cube with center coincident with the center of mass of the Sun, and oriented so that one particular corner is aligned permanently with the center of mass of Neptune. Any object more complicated than a formaldehyde molecule (except for some reason the planet Pluto and its moon) attempting to pass across the boundary in any direction from either side is instantaneously transported to the opposite face at the exact equivalent position, without loss of velocity or any noticeable inertial effect. The easiest way to visualize this is to recall the late 20th century game Asteroids, in which objects disappeared off the right side and reappeared on the left instantly; topologically, an Asteroids screen maps the Euclidean space of the screen onto the surface of a torus, while the Weeuruunie Interdiction Cube maps the Solar System onto the "surface" of a higher-dimensional torus. As far as matter is concerned the boundary is equivalent to continuous space; you could in theory stick your arm across it and goose somebody eleven billion kilometers away, with no ill effects beyond a slap, though you would be unable to see where your arm had gone -- the boundary implements an intimidating suite of information-based filters... well, let's just say it's "magic" and make this shorter.
Note: The wrapping property of the Interdiction Cube means the shortest distance to a given point from your location might lie in any of 27 possible directions.
By common convention, spatial coordinates inside the Cube are referred to relative to the Neptune corner, with that described as (0.0, 0.0, 0.0) and the opposite corner as (1.0, 1.0, 1.0). The particular orientation of axes is unimportant for the problems here, but suffice to say they are determined by long negotiations by a series of squabbling multinational bodies, and subject to change on short notice.
The seven known darkmasses are not conventional matter, though they are affected by the Interdiction Cube in both the typical and an unusual manner. Unaffected by gravity, they only move in straight lines at constant velocity with respect to the Cube, though the particulars of their size, vectors of motion and speed differ from darkmass to darkmass. Little is known about their composition, which is one reason it is referred to by physicists as "eccentric matter", even though it forms the basis of the new lattice drive technology and has numerous other engineering and military applications. It is very dense, though practically invisible, and does not create or experience gravitational fields. Which is a big part of why it's called "eccentric."
The most modern ships (such as yours, and some military vessels) which rely on darkmass-fueled lattice drives are also -- as a side effect -- unaffected by external gravitation. If sufficiently advanced (as is yours) they can change velocity within one second by transforming darkmass into conventional matter and expelling it... well, let's just call it "magic" and make this shorter, and will travel in a straight line (also relative to the Cube) until the velocity is actively changed again.
Whenever the lattice drive is activated, determine the amount of darkmass expended using this algorithm: First, calculate the magnitude of the change in velocity vectors. For example, from rest v=(0,0,0), a jump to v=(0.0000001, 0.0000001, 0) is an absolute change of Sqrt[2]*10-7. Multiply this by the mass being moved, in tons, and that is the percentage of darkmass consumed by the maneuver. So for example a ship weighing 40 million tons of which 12 million tons were darkmass that undertook the previous maneuver would lose 5.65% of the darkmass it was carrying, or 678823 tons, instantaneously. This percentage is independent of the absolute amount of darkmatter on hand (except in terms of its mass), so small ships carrying small amounts of darkmass can be very maneuverable.
Remember, it's eccentric matter.
That said, a speed of 0.05 of the speed of light is the absolute speed limit for lattice-driven ships inside the Interdiction Cube, for reasons that remain obscure, though it is thought possible that "wild" darkmasses could travel faster.
Ships can harvest fuel from a "wild" darkmass by first intercepting it, then matching velocities (thus requiring a minimum of two uses of the lattice drive). 1000 tons of darkmass can be taken on board per second.
The seven known darkmasses' masses, positions, and velocities as of 2 678 400 seconds ago exactly are
Question #1: Ignoring uncertainty in the above measurements, and relativistic effects, where are each of the seven darkmasses now (2 678 400 seconds later)?
Question #2: The ship is located exactly at Cube coordinates (0.82, 0.86, 0.44), and has at present a relative velocity of (0,0,0), and has 14 000 000 tons of darkmass fuel on board for the lattice drive. Again ignoring relativistic effects and uncertainties, which of the seven darkmasses is the best to visit first, if the point is to maximize the average rate at which fuel is acquired (or lost) over the entire duration of the operation?
Question #3: What is the best route that visits and completely harvests all seven darkmasses, but which completely avoids entering the spherical region centered on the sun, of radius 400 000 000 km (The Warzone)? By "best" we again mean the one that maximizes the average rate at which darkmass is harvested over the duration of the operation, as well as the total amount of darkmass on board at the end?.
Question #You Thought I Completely Forgot About the Title, Didn't You?:
"There has been a complication, Sire."
"Fuckin fuck! What?! I was just puttin more memory into this philodendron here. Don't sneak up on me like that! Dammit. Sorry, sorry, wee plantie. Waddya mean, 'complication'?"
"Well, our earlier visits to the wild darkmasses have been more... tentative than this trip. When we colocated with the first darkmass...well, it broke."
"Broke? No, wait, let me guess. It 'broke' 'eccentrically', I'll wager."
"Yes, Sire. It seems that exactly half of the darkmass was somehow knocked off by our abrupt arrival, and is now proceeding in the same direction we were originally headed when we colocated with its position, traveling at our previous velocity."
"Like a halfa fuckin billiard ball, eh? But we still have half of what we expected to be waitin for us? Fuckin Oorters, eh? Makin weird shit happen just cause they can. Someday I think I wanna meet one of them. An take him apart. Betcha his brains're worth a mint an a half."
"Yes, Sire. So, from the readings we've taken, we would need to colocate with the darkmass at a relative velocity of no more than 10-9 to avoid this phenomenon. Coinciding with a darkmass at any lower velocity, we should be able to retrieve it entirely; higher, and half will fly off just as fast as we arrived."
"Well, hell, that'd take a pantload more fuel, then, wouldn't it, slowin down like that? Fuck! Agh! But if we don't, we need to chase down the pieces as we make em."
"Indeed, Sire."
"Well... just figger it out. You're a smart lad. Make it fuckin so. An gimme that chip."
So: After completing the acquisition of the half-darkmass you first encountered in your original route, describe a new route to the remaining seven (including the half of the one you thought to take out completely) and harvests every one, in the shortest time, and with the largest remaining amount of darkmass fuel on board, completely avoiding the Warzone, under the new rule that if the velocity of the ship relative to the darkmass upon arrival is more than 10-9 (in lattice coordinates), half of the darkmass is lost in the direction you were moving, at the velocity you were moving.
Bonus question #1: That uncertainty thing. It was mentioned. It turns out to be valid. Indeed, the position of the darkmasses was only mapped to within one meter (they are, as we have pointed out several times, very dense), and their velocity only accurate to within one centimeter per second. First, what are these infinitesimal-sounding distances in proportion to the Cube edge? More important, if the center of each darkmass was somewhere within a sphere of radius 1 meter centered on the reported coordinates, and the velocity accurate to within one centimeter per second in magnitude and 0.01 arcsecond in direction [no, we didn't mention that; clones don't recall everything], how large a region might you have to search to find each darkmass?
"Here, My Lord, in the second greenhouse. I was just sketching these fern gametophytes. They're the first I've encountered since we started propagating this cultivar."
"Yeh, right. So.... Which, the dirt?"
"No, Sire, these small green organisms. Their presence indicates that the ferns we brought have--"
"Yer sketchin mold? Jesus. I made a fuckin Michelangelo of mold, I did. The very Leonardo of little tiny flecks of cabbage, are ya?"
"Yes, Sire. As you say."
"You know, if I didn't know better, I'd swear yer weren't my clone at all.... Agh, no mind. Right. So: you know this Martian inter-- embargo thingie? With the War?"
"Interdiction, Lord?"
"Yeh, right, Interdiction. So I'm thinkin -- what a load of crap that is, eh? I mean, how do you even interdite a whole planet, eh? I mean, here it is, not a mere city or nothin mind you, it's a fuckin great gravity well, right in plain sight in the middle of the fuckin Solar System. Big red thing, I seen it dozens a times. I mean, you just lob shite at it, right, an it just lands there, bang, you know? What're they thinkin? I mean, sure, there's re-entry to contend with, but Jesus, they did those probe thingies, dint they?"
"Ports, Sire."
"Wot?"
"'Ports.' Technically you were correct when you mentioned an embargo. The Authorities are maintaining a presence at all the ports of entry, so as to prohibit sanctioned trades and communications entering or leaving the settlements. The word 'Interdiction' is a slight misnomer."
"Well, why they call it that then? Fuckin half-arsed weasel word, innit? You mean embargo, you say 'embargo' is what I say. Might as well call it 'Mommie' an --"
"Ahem. Yes, Sire. I believe it was a reference to the Solar Interdiction."
"Oh, right. Stuck in their minds, I spose, eh? The Icebags pissed em off enough, spoiled their sense of interstellar adventure an Grand Destiny of Man an Made in His Image an all when they found out the lords of this particular corner of Everything's Arse are fuckin great Oorters with invisible rocks fer brains. And so the fussy little monkey bigots spend their dwindlin bluster all runnin around mutterin the damned word all the time. 'Interdiction interdict interdite' this an that and that over there. Gets in yer subconscious, you get a pancultural religiopolitical shock like that, an you mutter mutter mutter to yourself all day long. Start to use words inappropriately. Sign of imminent institutional breakdown, I say."
"Indeed."
"Or ongoing, eh? With the War, eh? That'd count.... You know, I'd flat forgot about the Icebags' Cube. Heh. Funny thing, that, how you can be thinkin about somethin real hard, an miss the big.... Innat interesting? Not that it has any fuckin thing to do with what I been tryin to say all along, oh, no. So. Right. We saw that big darkmass a few days back, right? Headed what? About 40 degrees up out towards Saturn ways, wunnit? Whizzin along about point three or so?"
"Yes, Sire. Would you like to pursue it now? At the time--"
"See, I'm thinkin they're gonna wanna have some, you know, big Bad Motherfucker bang-er-up bombs an shit on Mars, someday soon, yeh?"
"One would imagine both sides would, yes. Those, or food. Possibly both."
"Right, an ships, right? Need darkmass for ships' drives, at least for all those gleamy military needles so they look good in the parade. An, I shall remind you, not to mention this great wobbly filigree of silvery self-fabricated shite we call home, eh? How long to catch it?"
"Hmmm. I believe it would have wrapped by now, or would before we reached it. I can calculate the distance to the Weeuruunie Interdiction Boundary easily; the last surveys of both the boundaries and the darkmasses made before the recent hostilities broke out were very accurate. If the darkmass has wrapped, we will surely be able to catch it without any trouble on the other side."
"Well, that'd be a good part aways back across the Cube, wouldn't it? I'm not fuckin made of money. Or fuel."
"One good-sized harvest of darkmass would more than pay for the effort, Sire."
"Yeh, right! An that is why I said, to you, not five minutes back, 'Oy, where the fuck are ya?' Yer damn lettuce threw me off, that an all your natterin. Here: We're gonna go get all of em."
"..."
"Yeh, heheh, you'd better close your gapin mouth, laddie mine, before you catch a gymnosperm or somethin in it, because see, I got a plan. And didst I not make thee from the flesh of my flesh, or words to that effect? Dost thou not trustest me who made thee in mine image, O my Sunny Jim? Heh. See this? Right here? This in here is original brains, they are. Yours a mere Derivative Work."
"My Lord, there are seven mapped darkmasses within the confines of the Interdiction Cube! The expeditions have been planned and in one case executed--"
"Ach, dammit, did I forget to grow yer balls when I made ya? O, ye of little balls. Where's yer sense of... well, greed boy? I mean, come on, you know very well what I paid for that wee 14 million tons of darkmass down there -- three hundred thousand souls, it was, I made myself. And there's a fuckin War on, an a biggie at that, an big war is as a matter of well-known fact big money, QED. First interplanetary war in fuckin history, an who knows how grand an blowy-uppy it'll get, an here we are out in the middle of the Upper Armpit of Nowhere, noteworthily I shall remind you not in the blowy-uppy part of the fuckin War, an we have a fast ship, complete with fuel an partially synthetic brains an little fuckin cabbage leaves growin the orangery. An I might add a unique ship what's uniquely ship-shape enough that it does not need to deal with acceleration in any ways whatsoever, nosiree, but merely communes with the quantum informational thingie for permission and changes frames of reference as if by magic. Come on, there's just seven of em."
"Sire. There are... well, I suppose it..."
"Ahh, see, there's the kind of enthusiasm I like to hear from the fruit of my -- well my cheek as I recall. An -- mind you, mind you! -- as I might have mentioned there's a fuckin War on, see, an so nobody else will be lookin for em. They're all busily ready-aim-firing-oh-no-wait-not-yet with their bombs an asteroids an shit, an noisily diplomatin an televisin at each other, an fundin black labs an gold retrieval missions an shit. Hell, boy, nobody else will even have a fuckin clue where these darkmasses have got to, once that last survey's got a bit obsolete an they go whizzin an wrappin around the Cube a few times! Heheh. Seven, you say?"
"Yes. As I recall the survey was accurate to within one meter, and one centimeter per second velocity. That was about three months ago, so the uncertainty clouds will have spread somewhat by now. And they'd all have wrapped one or more times in that period, adding more uncertainty...."
"Well, we're not a passive observer here, you know. We are, do not forget, in a fuckin awesome space ship. In a pinch we can even make it go 'whoosh' an fart hot hydrogen out its arse an there you are, dealing with yer uncertainties proactively by chasin stuff. Or so I am told, when I am not resigned to merely sittin in the middle of fuckin nowhere consumed with a passion for growin intelligent flower gardens. Or if you prefer we might consider, oh I dunno, maybe usin the fuckin lattice drive we grew last month, instead of just ponderin its quantum splendor an all."
"Indeed, point taken. That said, Sire, we do have a limited amount of fuel, as you mentioned. Each use of the lattice drive to shift our frame of reference will consume a substantial portion of the darkmass we carry. We should plan a course that minimizes the amount of velocity we need to reach their vicinities. Or the most we can reach. It may not be feasible to expect to get all seven."
"Ay, ay -- thank you very much young Master Exposition, but I'll have no half-assed clone talk, you. All seven or nothin."
"Well, the Cube is 11,323,344,384 kilometers across, so--"
"That would be natterin again. Do you always think out loud like that? I might could fix that, you know. Hey, hang on, hang on! People were tryin to figure out how Pluto gets in an out, but nothin else can, right? I mean, why ain't Pluto jumpin all over the fuckin sky every time it crosses the Cube boundary, when every other piece of stuff in the fuckin box just wraps over to the other side unchanged an all, just blip an there you are with the shadows all upside-down of a sudden, eleven billion-an-more klicks from where you started?"
"Something about dark matter, I'm told, Sire, though that seems like a hedge. I suspect the Weeuruunie wrote an exception into the matter filter for Pluto when they constructed the Interdiction Cube, so that early astronomers would not become overexcited if they noticed the planetoid jumping."
"Heh. As if. They was keepin the dinosaurs in, an no mistake."
"Indeed. And those were the astronomers that were meant not to be excited. At any rate, the Cube is of known size, and the position and velocities of the seven darkmasses are known to great accuracy, and of course we know our own position very well. It should boil down to a simple dynamic programming problem."
"Yeh, well, we got what? just below fifteen million tons of darkmass an hydrogen fuel on board. So no needless sightseein. We give a wee tap on the gas, we coast, we nab, we prod again, got it? Extended burns will leave us sittin out here twiddlin our thumbs up our asses an eatin gynocarps an shit. No offense, little moldies."
"Gametophytes, Lord, but only the sporophyte stage of this cultivar have organs of hearing.... There is one problem."
"Yeh. The fuckin War, eh?"
"Yes, Sire. We will need to avoid a substantial region around the core of the system, unless we pass through at relatively high speed. More than one millicee, for example. I suspect we will be better served if we use the Interdiction Boundary to wrap across the Solar System instantly. It does increase the complexity of the tour planning somewhat."
"Right. So hop on it, boyo. I'll wake up the ship an the others, an then let's go nab us all the darkmass anybody's ever not seen, before they get wise to us."
"I will be done here momentarily, Sire."
"An did I ever tell you ya sound like Mister fuckin Spock? I didn't build that in, did I? You do it on purpose, don't ya, as an actin out thing. Heh. No, wait, I know, you talk like that Vizier fellow in that old movie, innit? Not sure that's entirely appropriate for a fourteen year old boy, now, is it?"
"No, Sire. Not at all."
"Heh. Smartass. But always remember -- Derived Work."
The Weeuruunie Interdiction Cube is 11 323 344 384 kilometers on each edge, measured to within one centimeter, and is as near as can be determined perfect cube with center coincident with the center of mass of the Sun, and oriented so that one particular corner is aligned permanently with the center of mass of Neptune. Any object more complicated than a formaldehyde molecule (except for some reason the planet Pluto and its moon) attempting to pass across the boundary in any direction from either side is instantaneously transported to the opposite face at the exact equivalent position, without loss of velocity or any noticeable inertial effect. The easiest way to visualize this is to recall the late 20th century game Asteroids, in which objects disappeared off the right side and reappeared on the left instantly; topologically, an Asteroids screen maps the Euclidean space of the screen onto the surface of a torus, while the Weeuruunie Interdiction Cube maps the Solar System onto the "surface" of a higher-dimensional torus. As far as matter is concerned the boundary is equivalent to continuous space; you could in theory stick your arm across it and goose somebody eleven billion kilometers away, with no ill effects beyond a slap, though you would be unable to see where your arm had gone -- the boundary implements an intimidating suite of information-based filters... well, let's just say it's "magic" and make this shorter.
Note: The wrapping property of the Interdiction Cube means the shortest distance to a given point from your location might lie in any of 27 possible directions.
By common convention, spatial coordinates inside the Cube are referred to relative to the Neptune corner, with that described as (0.0, 0.0, 0.0) and the opposite corner as (1.0, 1.0, 1.0). The particular orientation of axes is unimportant for the problems here, but suffice to say they are determined by long negotiations by a series of squabbling multinational bodies, and subject to change on short notice.
The seven known darkmasses are not conventional matter, though they are affected by the Interdiction Cube in both the typical and an unusual manner. Unaffected by gravity, they only move in straight lines at constant velocity with respect to the Cube, though the particulars of their size, vectors of motion and speed differ from darkmass to darkmass. Little is known about their composition, which is one reason it is referred to by physicists as "eccentric matter", even though it forms the basis of the new lattice drive technology and has numerous other engineering and military applications. It is very dense, though practically invisible, and does not create or experience gravitational fields. Which is a big part of why it's called "eccentric."
The most modern ships (such as yours, and some military vessels) which rely on darkmass-fueled lattice drives are also -- as a side effect -- unaffected by external gravitation. If sufficiently advanced (as is yours) they can change velocity within one second by transforming darkmass into conventional matter and expelling it... well, let's just call it "magic" and make this shorter, and will travel in a straight line (also relative to the Cube) until the velocity is actively changed again.
Whenever the lattice drive is activated, determine the amount of darkmass expended using this algorithm: First, calculate the magnitude of the change in velocity vectors. For example, from rest v=(0,0,0), a jump to v=(0.0000001, 0.0000001, 0) is an absolute change of Sqrt[2]*10-7. Multiply this by the mass being moved, in tons, and that is the percentage of darkmass consumed by the maneuver. So for example a ship weighing 40 million tons of which 12 million tons were darkmass that undertook the previous maneuver would lose 5.65% of the darkmass it was carrying, or 678823 tons, instantaneously. This percentage is independent of the absolute amount of darkmatter on hand (except in terms of its mass), so small ships carrying small amounts of darkmass can be very maneuverable.
Remember, it's eccentric matter.
That said, a speed of 0.05 of the speed of light is the absolute speed limit for lattice-driven ships inside the Interdiction Cube, for reasons that remain obscure, though it is thought possible that "wild" darkmasses could travel faster.
Ships can harvest fuel from a "wild" darkmass by first intercepting it, then matching velocities (thus requiring a minimum of two uses of the lattice drive). 1000 tons of darkmass can be taken on board per second.
The seven known darkmasses' masses, positions, and velocities as of 2 678 400 seconds ago exactly are
| mass | position (relative to cube axes) | velocity (relative to cube axes) |
| 10 000 000 tons | (0.1, 0.1, 0.1) | (0.00000011, -0.00000022, 0.00000006) |
| 5 000 000 tons | (0.5, 0.2, 0.9) | (-0.00000015, -0.00000017, 0.00000037) |
| 20 000 000 tons | (0.7, 0.9, 0.3) | (0.00000100, -0.00000039, -0.00000012) |
| 10 000 000 tons | (0.2, 0.8, 0.7) | (-0.00000034, 0.00000028, -0.00000021) |
| 60 000 000 tons | (0.5, 0.6, 0.5) | (-0.00000021, -0.00000030, 0.00000035) |
| 5 000 000 tons | (0.7, 0.1, 0.6) | (0.00000018, 0.00000013, 0.00000021) |
| 40 000 000 tons | (0.8, 0.8, 0.1) | (0.00000011, -0.00000020, 0.00000020) |
Question #1: Ignoring uncertainty in the above measurements, and relativistic effects, where are each of the seven darkmasses now (2 678 400 seconds later)?
Question #2: The ship is located exactly at Cube coordinates (0.82, 0.86, 0.44), and has at present a relative velocity of (0,0,0), and has 14 000 000 tons of darkmass fuel on board for the lattice drive. Again ignoring relativistic effects and uncertainties, which of the seven darkmasses is the best to visit first, if the point is to maximize the average rate at which fuel is acquired (or lost) over the entire duration of the operation?
Question #3: What is the best route that visits and completely harvests all seven darkmasses, but which completely avoids entering the spherical region centered on the sun, of radius 400 000 000 km (The Warzone)? By "best" we again mean the one that maximizes the average rate at which darkmass is harvested over the duration of the operation, as well as the total amount of darkmass on board at the end?.
Question #You Thought I Completely Forgot About the Title, Didn't You?:
"There has been a complication, Sire."
"Fuckin fuck! What?! I was just puttin more memory into this philodendron here. Don't sneak up on me like that! Dammit. Sorry, sorry, wee plantie. Waddya mean, 'complication'?"
"Well, our earlier visits to the wild darkmasses have been more... tentative than this trip. When we colocated with the first darkmass...well, it broke."
"Broke? No, wait, let me guess. It 'broke' 'eccentrically', I'll wager."
"Yes, Sire. It seems that exactly half of the darkmass was somehow knocked off by our abrupt arrival, and is now proceeding in the same direction we were originally headed when we colocated with its position, traveling at our previous velocity."
"Like a halfa fuckin billiard ball, eh? But we still have half of what we expected to be waitin for us? Fuckin Oorters, eh? Makin weird shit happen just cause they can. Someday I think I wanna meet one of them. An take him apart. Betcha his brains're worth a mint an a half."
"Yes, Sire. So, from the readings we've taken, we would need to colocate with the darkmass at a relative velocity of no more than 10-9 to avoid this phenomenon. Coinciding with a darkmass at any lower velocity, we should be able to retrieve it entirely; higher, and half will fly off just as fast as we arrived."
"Well, hell, that'd take a pantload more fuel, then, wouldn't it, slowin down like that? Fuck! Agh! But if we don't, we need to chase down the pieces as we make em."
"Indeed, Sire."
"Well... just figger it out. You're a smart lad. Make it fuckin so. An gimme that chip."
So: After completing the acquisition of the half-darkmass you first encountered in your original route, describe a new route to the remaining seven (including the half of the one you thought to take out completely) and harvests every one, in the shortest time, and with the largest remaining amount of darkmass fuel on board, completely avoiding the Warzone, under the new rule that if the velocity of the ship relative to the darkmass upon arrival is more than 10-9 (in lattice coordinates), half of the darkmass is lost in the direction you were moving, at the velocity you were moving.
Bonus question #1: That uncertainty thing. It was mentioned. It turns out to be valid. Indeed, the position of the darkmasses was only mapped to within one meter (they are, as we have pointed out several times, very dense), and their velocity only accurate to within one centimeter per second. First, what are these infinitesimal-sounding distances in proportion to the Cube edge? More important, if the center of each darkmass was somewhere within a sphere of radius 1 meter centered on the reported coordinates, and the velocity accurate to within one centimeter per second in magnitude and 0.01 arcsecond in direction [no, we didn't mention that; clones don't recall everything], how large a region might you have to search to find each darkmass?
posted by Vaguery | 8:37:00 PM
<< Home