Limited Supply Problems - Other Problems - The Nonsense of "Threshold"
Limited Supply Problems
Voyager used to be the only Federation ship in the Delta Quadrant. This original premise was maintained through seven years. Alas, the authors were not consequent when they should have taken into account the resulting limitations. New shuttles and new crew members kept popping up as if the next starbase were only a few light years away, not to mention that the ship, despite all the power outages and the frequent skirmishes, was always in perfect shape (the real-world reason being that this allowed to use stock footage any time).
Number of shuttlecraft It may be due to a lack of better ideas that Voyager writers frequently had shuttles get into electromagnetic turbulences and crash on planets. Such a crash is no problem for starships that can simply be resupplied in a nearby starbase, but it is for Voyager. The official Star Trek Voyager Technical Guide V1.0, intended as guidelines for writers (sub-title: "Yes, but which button do I push to fire the phasers?"), ironically says that "Voyager normally carries two[!] standard shuttlecraft, four of the smaller shuttlepods, and four EVA workpods". We have never seen any shuttlepods or workpods. The two lonely shuttlecraft were obviously both supposed to be of Type 6, since this one is depicted in the booklet.
(Star Trek Fact Files)
(Star Trek Fact Files)
Type-9 shuttle (aka Class 2)
(Star Trek Fact Files)
In any case a complement of two shuttlecraft was extremely short-sighted. Lots of standard shuttles of no less than three different types, namely Type 6, Type 8 and Type 9 (for some reason the latter is designated as Type 12 in the Star Trek Fact Files and as Class 2 since the 5th season) were actually seen, and Voyager has probably lost as many as 17 (seventeen) of them in seven years:
|Episode||Type & name||Situation||Definitely lost||Probably lost||Badly damaged|
|Cathexis||6?||Damaged inside nebula, recovered||1|
|Initiations||8?||Destroyed by Kazon vessel||1|
|Non Sequitur||8, Drake||Destroyed in temporal rift||1|
|Parturition||8?||Crashed on planet "Hell", recovery doubtful because of alien threat||1|
|Innocence||6||Crashed on planet, presumed recovered||1|
|Future's End||9||Crashed on Earth, recovered||1|
|Coda||8 and 6, Sacajawea||Crashed on planet, presumed recovered, MSD: Type 8, outside: Type 6||1|
|Unity||9||Cannibalized by ex-Borg||1|
|Rise||6?||Damaged beyond repair in crash, recovery unlikely||1|
|Real Life||9, Cochrane||Damaged in subspace vortex, beamed aboard||1|
|The Gift||9||Destroyed or vanished in the course of Kes' evolution||1|
|Day of Honor||9, Cochrane||Destroyed by Caatati vessel||1|
|Nemesis||?||Shot down and abandoned on Vori planet, salvage very unlikely||1|
|The Raven||8 and 6||Abandoned in B'omar territory, no time to retrieve it, miraculously changed from Type 6 to 8 between two scenes||1|
|Mortal Coil||6||Heavily damaged through protomatter explosion, presumed recovered||1|
|Hunters||9||Captured by Hirogen, possibly recovered||1|
|Drone||9 ("Class 2")||Suffered hull breach, recovery questionable||1|
|Counterpoint||9||Given to telepathic refugees||2|
|Gravity||6||Crashed on planet in high gravity region, salvage impossible||1|
|Dark Frontier||9||Assimilated by the Borg||1|
|Think Tank||?||Pulled into subspace, presumed lost||1|
|Barge of the Dead||9||Damaged in ion storm, salvaged||1|
|Tsunkatse||9||Captured and most likely not returned||1|
|Natural Law||9||Destroyed by energy barrier||1|
Note that apparently minor damages with a few sparks and a bit of a fire inside the cabin are not included. It is evident that such a shuttle consumption is only possible if spare parts for repairing and assembling shuttles are available. We could imagine that most of the components of a shuttle are relatively simple, and can therefore be replicated. Still, very complex parts like the computer system, which employs quantum level computation, and the warp core would have to be stored. If the crew can build the highly advanced Delta Flyer from scratch, building new standard shuttles from existing plans and materials shouldn't be such a great problem anyway.
How many shuttles did Voyager have at the beginning and how many were built afterwards? The aft section of an Intrepid-class vessel does not seem to be large enough to hold more than eight Starfleet shuttlecraft, and Neelix's ship which seems to be somewhat larger has to be stored as well. Fitting the Delta Flyer into the shuttlebay is still another problem (see also below). In an optimistic estimation, we can assume that there were eight shuttles aboard when Voyager left for the Badlands. Since Voyager's complement consists of as many as three different shuttlecraft types, it is a good guess is that there were two shuttles of Type 6, three of Type 8 and three of Type 9. This means that at least seven new shuttles of different types must have been built from stored spare parts. Given Chakotay's incredibly funny statement of a "full complement of shuttles" in "Alice", all fifteen until then destroyed shuttles should have been replaced, unless he counts the Delta Flyer as equivalent of four or more shuttles.
Number of photon torpedoes The original complement must have been 40, two of which have been used to destroy the Caretaker Array, armed with tricobalt warheads. This leaves the 38 torpedoes that Tuvok counts in "The Cloud". He states that they can't be replaced. Nevertheless, the number of torpedoes used in the following exceeds 38 by far, even if we take into account only those which were seen or explicitly mentioned as being fired. The resulting lower limit is 93 torpedoes. The only explanation is that the crew has found a way to replicate more torpedoes. Considering that a torpedo should be much less complex than a shuttle or even the Delta Flyer, this is only plausible. The only problem is Tuvok's premature pessimism.
Number of crew members The original crew complement of Voyager was 140. VOY: "Nightingale" eventually tells us that "more than a dozen" people died when the ship was pulled to the Delta Quadrant (VOY: "Caretaker"). This includes the first officer, helmsman, chief engineer, chief medical officer and nurse, who were all seen or mentioned dead in the episode. The number of original crew members of the Maquis ship is not mentioned in "Caretaker" or any other early episode, although it ought to have played an decisive role when the two crews had to work together at the very beginning. "Repression" creates the impression that there are about 35 of the Maquis left on Voyager, considering that "almost a quarter of the crew" is from the Maquis, and the current crew count is 150. Taking into account the high death toll among the Maquis, they should have been 50 in the beginning, which seems way too many for the small ship. Anyway, in all later episodes the joined crew consists of about 140 individuals again, as mentioned in VOY: "The 37's", after several have been killed or have left the ship. These are too few, if we simply reckon 140-12+2+50-x. I doubt that so many (the "x") were killed in the conflict with the Kazons, which would also leave not enough crew members for the following seasons. The number of crew members even *increases* during the 3rd, 4th and 5th season, although again some people are killed. "Distant Origin" establishes a crew complement of 148, as indicated by the Voth's sensors. 150 crew members, except for Chakotay and Harry, die in the alternative timeline in "Timeless". In the 6th and 7th season the number is constant at 150.
The actual problem is that many more than 150 different faces of actors and extras could be seen. Actually, only very few of the supporting cast and the extras were seen more than only once. Not even established names of crew members (who might be shown or only mentioned) are re-used, although this would be imperative on a small and isolated ship. This is why the maximum number of 150 names was finally reached in the seventh season, according to the now defunct site "Roll Call: The Minor Crew Members of Voyager". So unless the crew frequently change their names (maybe many of them got divorced and now use their maiden names ;-)) and even their faces (I think the Doctor can do miracles ;-)), the inexhaustible crew supply is impossible.
Number of Vulcan crew members The number of Vulcan crew members on Voyager is subject to vary, and this becomes a problem in a couple of episodes where this number would matter. In "Caretaker" we can see a Vulcan nurse in sickbay, but she is obviously killed when Voyager is pulled into the Delta Quadrant. We have Tuvok, of course, and Ensign Vorik as another series regular, who appears in eight episodes and survives until the end of season 7. In "Flashback" Tuvok refers to "the other Vulcans on the ship", which indicates that there must be at least one more Vulcan in addition to Vorik. But in "Blood Fever", when Vorik enters pon farr, it appears that the two are alone. At least, if a female Vulcan had been among the crew, it may have been considered at one point that she may "help" Vorik. In "Counterpoint" all telepaths have to hide from the Devore, and this concerns only Vorik and Tuvok. However, in "Repression" there is suddenly a female Vulcan crew member in a red uniform that possibly can't have existed in the two previously mentioned episodes. It remains a mystery where she comes from. Perhaps she isn't telepathic, perhaps she is actually Romulan, as unlikely as it seems?
Holodeck vs. replicator energy During the first two seasons Voyager suffers from a permanent shortage of energy, which requires to ration replicator meals and obviously serves to justify the necessity of Neelix' kitchen. However, the holodeck seems to be in use the whole time, although this amusement arguably consumes much more energy than a small replicated meal, irrespective of the fact that most of the holomatter is usually recycled to energy. Moreover, the outside views show that almost all windows of Voyager are lighted, whereas most of the windows of the Enterprise-D were dark. Furthermore, all 15 decks have full life support. If I were a crew member, I would rather forgo additional luxury than my favorite food. The replicator rations are not mentioned any more in the third and forth seasons, while the crew are still enduring (or meanwhile enjoying) Neelix' cooking.
The usual explanation for the permanent operation of the holodecks is that they have an independent power source, as it was established in a few episodes and explicitly shown in "Night" were the hologrid was "frozen" when the computer failed. Seven says: "Independent subsystems are operational: environmental controls, holodecks." Anyway, what else should the allegedly independent holodeck power source be than a fusion or even a matter/antimatter reactor? What could be so special about them that they wouldn't be able to supply other systems too? Is there nothing like a simple "transformer" that could convert the plasma energy levels (i.e. the voltages) if they are different on the holodeck? Even if they are incompatible, the basic fuel (anti-) deuterium would be the same for all systems on the ship. So here is no reason to believe that if all other energy is gone, the holodeck can't serve as a spare power source. Much less is there a reason that fuel would be available for the holodecks, but not for the replicators.
The Delta Flyer The construction of the Delta Flyer within a few days, as seen in "Extreme Risk", is a similar miracle as the transwarp shuttle in "Threshold" (see below). Moreover, I wonder why it has taken four years until Janeway realizes that a larger auxiliary craft could serve Voyager much better than the small, slow and fragile standard shuttles that are frequently shot down or lost in magnetic storms. So if they could build the Delta Flyer in no time, why didn't they do it much earlier? Another problem is how the Delta Flyer is supposed to fit into the shuttlebay. Read here.
The aeroshuttle "The bottom of the Primary Hull or saucer holds a single aerodynamic shuttle capable of atmospheric travel as well as interplanetary flight at speeds up to Warp 3. The AeroWing can carry various combinations of crew and cargo; the usual flight complement numbers four crewmembers." This is what the Star Trek Voyager Technical Guide V1.0 says about Voyager's version of the captain's yacht. The AeroWing, now called "aeroshuttle" was never mentioned, let alone shown on screen, though. Star Trek: The Magazine depicts details of Voyager's saucer bottom, showing the aeroshuttle which is quite obviously intended to be a runabout-sized shuttle with its own maneuvering thrusters. So why was the aeroshuttle never used in six years, although it would have been an option so many times, considering situations in which a standard shuttle would have been too small or too weak? There are four theories:
1. The aeroshuttle was badly damaged at the very beginning of the show. I think this statement is hard to maintain, since everything was always repairable on Voyager, and building the completely new Delta Flyer seems more difficult. Even if the aeroshuttle were actually damaged beyond repair, it should have been mentioned at least at the time when it happened and several more times, something like "too bad we don't have the aeroshuttle".
2. They actually didn't need the aeroshuttle, or they wanted to preserve it. I don't think there is any reason to believe that, since Janeway didn't do anything to avoid dangerous situations in six years, so why should she be concerned about this auxiliary vessel? It is especially valuable? If so, why didn't they use this supershuttle at least for safe missions, or is it merely for decorational purposes? I think we may safely discard this idea.
3. The aeroshuttle actually doesn't exist. The shape on the bottom of the saucer is something else that accidentally resembles something like an independent shuttle or captain's yacht. This is actually the best excuse for not using or only mentioning the aeroshuttle. On the other hand, the Enterprise-D captain's yacht was not mentioned in seven years of TNG either although it definitely exists. Yet, the latter was only an unarmed oversized sublight shuttle supposed to ferry important diplomats.
4. The aeroshuttle does exist, but it wasn't aboard when Voyager left for the Badlands. The structure on the saucer underside is a hatch or some sort of cover that will be removed once the aeroshuttle will be installed. But why would this cover have something that definitely looks like maneuvering thrusters?
Now that the aeroshuttle hasn't been resurrected even in season 7 (although there were plans), we can either say that it never existed, or it was just not installed when Voyager went on the short trip to the Badlands. Since we can't simply deny the shuttle-like structure on the saucer bottom, I like the suggestion that there was just a placeholder for the aeroshuttle or that the aeroshuttle was not yet finished at the time of "Caretaker".
(Star Trek: The Magazine)
The Maquis ship The most important specifications of Chakotay's Maquis ship are uncertain, including its class, size and even its name. When Chakotay, Torres or other Maquis crew members talk about their time on this ship, they should at least call it by its name. The name "Zola" stated in the Fact Files was never mentioned on screen. The latest information on the class name comes from Star Trek: The Magazine. An article tells us of a desktop model of Chakotay's Maquis ship, as well as several displays of the ship where it is a Ju'day-class ship named "Valjean". On websites the Maquis ship is sometimes classified as Peregrine courier. However, the Peregrine courier or fighter is more likely a considerably smaller vessel shown e.g. in DS9: "The Maquis" and also employed to distract the Cardassian fleet in DS9: "Sacrifice of Angels". Chakotay's ship (here named "Liberty") is classified as Antares class in the novel Pathways. There is a lot of confusion about this class name, which the authors are obviously too fond of. In any case this is only one of several theories.
Maquis raider - top
(Star Trek Fact Files)
Maquis raider - side
(Star Trek Fact Files)
Maquis raider publicity photo
(Star Trek Mechanics)
A diagram of the ship is depicted in the Star Trek Fact Files. The windows in the bridge section cannot be used as a reference, since they were not visible in "The Caretaker". The size of the bridge set which seems to be only 5m wide points to a very small ship of only 30m length. This complies with the size of the preliminary raider built for TNG: "Preemptive Strike" where there was a cockpit window instead of the bridge, but it's absolutely impossible to have a crew of 40 to 50 on such a small ship. Three decks may be distinguished, but there are no windows or other details to confirm this. For a crew of up to 50 (see above), an overall length of 60m (for 3 decks with a height of 3m each) appears to be the minimum possible value, but only if there are no real quarters.
The only half-way reasonable explanation for the crew, considering that the small size of the ship is well established, is that the normal crew complement is significantly lower, at most around a dozen. The raider may have been manned with some 50 Maquis because they were going to hijack a Cardassian ship, possibly a freighter, when the Galor-class cruiser foiled their plan and the Maquis had to seek refuge in the Badlands.
The warp nacelles Voyager is the first ship to have foldable nacelles and pylons, at least the first ship we know of. "Because Voyager employs a new folding wing-and-nacelle configuration, warp fields may no longer have a negative impact on habitable worlds, as established in TNG." This sentence from the Star Trek Voyager Technical Guide V1.0 is actually the only hint that the folding pylons may prevent the subspace damage of TNG: "Force of Nature". It was never mentioned on screen.
Another theory is that the efficiency of the warp field can be increased if it is continually tilted as the speed rises, in a similar fashion as on the F-111 and other aircraft with variable wing positions. However, the existing shots of Voyager in space don't make any sense, since only two angles of the nacelle pylons can be observed: 0° (horizontal) for impulse flight, and about 35° as soon as the ship goes to warp, remaining constant irrespective of the speed. While it makes sense for an aircraft to have just two wing positions for slow and for fast hypersonic flight, Voyager's warp drive is offline at impulse anyway, hence not requiring any specific nacelle position. It is not evident why the nacelles are folded up at all every time the ship goes to warp, and why they are not just fixed in the warp position.
Two warp cores? Voyager's MSD clearly shows two warp cores (more precisely, two complete matter/antimatter reaction assemblies), one just behind the deflector dish, and one close to the kink of the hull undercut. Obviously one of them, the one we see in main engineering, is active all the time, while the other one must be a backup. Actually, the aft core is the main core, as we could clearly see in VOY: "Day of Honor" where it had to be ejected. The problem is that it was made a big deal in this episode (and again in "Renaissance Man") that this seemingly only warp core was essential and that the ship could not go to warp without it. But why didn't they just use the second warp core? After all, that is exactly what it was intended for. It is obvious that the second core may not be activated where it is stored but needs to be transferred to main engineering and connected again. But why would this be so much harder to accomplish with the backup core than with the main core that, in both episodes, Janeway doesn't even try it but rather sends shuttles against heavily armed ships to retrieve it?
Rick Sternbach, the ship's designer, once suggested that the second core was not supposed to act as a backup on stand-by, but that it would merely serve as a set of spare parts. Anyway, why would the ship carry only partial builds where it could have a complete core, and where the MSD shows something that looks like a complete core? It even makes less sense if we consider that usually Voyager would have been under way in the Alpha Quadrant. If the installation of the backup core were really that difficult and time-consuming, a repair ship or tug may have arrived to assist much sooner, so why have a spare core at all? Maybe the second core was irreparably damaged and even abandoned some time before "Day of Honor". Another possible explanation is that parts from the spare core that could not be replicated were already in use in the main core. Or, although this would be a stretch, perhaps the second warp core is designed to supply just the holodecks (see Holodeck vs. replicator energy above)?
The Beta Quadrant taboo Following the flight path of Voyager, it is easy to notice that the Delta Quadrant is not directly adjacent to the beloved Alpha Quadrant, but that there is still the Beta Quadrant in between. After a journey of more than six years and some fast leaps (like 10,000ly with slipstream in "Timeless" and 20,000ly with the transwarp coil in "Dark Frontier"), Voyager should have crossed the border to the Beta Quadrant at latest by the sixth season - which is easy to reckon if we just subtract all the long and short leaps from the initial distance of 75,000ly. Nevertheless, the authors still kept the ship in the Delta Quadrant. The real-world reason was as obvious as it is silly: TPTB thought they would confuse occasional viewers with too much galactic geography. Anyway, for a certain time it was still credible that Voyager was still in the Delta Quadrant, considering that some detours were necessary to avoid the Borg or large anomalies.
Still, it is absolutely unacceptable that the Beta Quadrant was mentioned only three times(!) in seven years, and only once as being on the route to the Alpha Quadrant. This is even worse considering that the Beta Quadrant as the home of Klingons and Romulans and a part of the Federation ought to play an important role. Even in VOY: "Message in a Bottle", where the Prometheus was hijacked by Romulans and was about to enter their territory, the dialogues all said "Alpha Quadrant" instead of "Beta Quadrant". The quadrant wasn't treated much better in DS9 either, for the galactic powers only struggled for the control of the "Alpha Quadrant" - have the Klingons and Romulans forgotten where they come from? I wonder why the wonderful concept of four quadrants was first systematically introduced, only to be effectively discarded later.
The Nonsense of "Threshold"
I think hardly anyone would contradict my perception that no other episode has ever featured so much scientific rubbish as VOY: "Threshold", encompassing a broad range from mathematics over physics and biology to engineering. You know, it's the episode where the crew develops a transwarp drive, Tom goes to Warp 10, evolves to a new lifeform, kidnaps Janeway and has children with her. Bizarre enough. I don't know if it's rather fun or masochism to list the errors of this episode, just decide for yourself.
Transwarp hobbyists Millions of engineers in the Federation have been working at least a century in vain developing transwarp technology. However, the small crew of a starship with limited resources that has gone astray in the Delta Quadrant succeeds in doing exactly this in their spare time and completes the prototype in a matter of a few weeks. Yes, and I am sure in the 21st century the first nuclear fusion reactor will be built on a submarine. Well, Tom mentions something that may justify why the transwarp drive is being built right here and now: "We discovered a new form of dilithium in the asteroid field we surveyed last month. It remains stable at a much higher warp frequency." However, it is nothing more than a myth that it only needs enough power to achieve previously impossible speeds with the same basic hardware.
Infinite speed - awfully fast All official publications and even the episode itself unmistakably state that Warp 10 equals infinite speed. Any infinite figure is merely hypothetical and may exist in a mathematical equation, but never as a measurable physical quantity. Infinite speed is definitely impossible to achieve - even for Q. Even the dialogues in "Threshold" state it's impossible. One could object that it was actually not infinite speed, but just beyond the measuring limit, but it was explicitly stated that Tom has reached Warp 10, which we can expect to be backed by a measurement. Starfleet must be very accurate here, because there is a considerable (infinite!) difference between Warp 9.99999999 and Warp 10.
Fasten your seatbelts If we nevertheless examine what would be necessary to reach Warp 10 in finite time, the acceleration would have to be infinite as well (with warp drive just as with any real technology). Infinite acceleration requires an infinite engine power output and, moreover, an infinite IDF to keep the shuttle and passengers in one piece.
The barrier - even more than infinite The "barrier" or "threshold" is mentioned in the episode title as well as in several dialogues. If Warp 10 means infinite speed, there is no such thing as a barrier or threshold to be broken. What could be more than infinite? A possible explanation: Since infinite speed is achieved in finite time, there could be some kind of barrier indeed - namely the barrier where transwarp instead of normal warp becomes active. Beyond this barrier the acceleration could be much higher, yet not infinite. Anyway, from the dialogue we get the impression that the barrier is supposed to be exactly at Warp 10.
Where do you want to go today? It is an absurd assumption put forth in reference works that a vessel moving at infinite speed would occupy all points in the universe simultaneously. Actually, it would just occupy all points along its trajectory at the time of reaching infinite speed, which has to be a straight line, for an infinitely short time. The trouble is that a straight line may get the shuttle back from where it started but probably not across the universe in all directions. The author, Michael DeLuca, or the script writer, Brannon Braga, obviously thought that the pilot of the Warp 10 shuttle would be able to travel to any desired point or return exactly to his starting point. But if the speed is actually infinite or at least high enough to overload the navigational sensors (dramatic blue shift), Tom can reach a certain region of space only by chance - a chance that is virtually zero. And aside from that, if he's everywhere at once, isn't that absolutely equivalent to being nowhere at all?
Don't forget your camera Tom, however, did not only return to Voyager, but also brought lots of sensor data with him. The faster he goes, however, the more will the incoming light and any other form of waves be shifted to smaller wavelengths and also its intensity will increase, until harsh x-rays will finally burn the sensors as well as the rest of the shuttle along with Tom. We have to forgive Trek in general because, using real physics, this would already happen when approaching the speed of light. But warp physics are different, and somehow all inbound light is transformed to something visible and harmless during a warp flight. Unless this flight is infinitely fast. At infinite speed, the radiation intensity would be infinite and require an infinitely strong shielding. Here we go again. Even if he and his equipment survived at a still finite speed, the shuttle sensors wouldn't have been able to record anything but extremely intense x-rays. Or actually an absolutely homogenous omnidirectional finite radiation, owing to his being everywhere at once? It is mind-boggling but what is safe to say is that there is no chance that he could take any pictures of his flight.
We're evolving to newts Tom and later Janeway are said to have "evolved" to newt-like creatures crawling on the floor. Apart from the fact that such a creature can hardly be a species more advanced than a human being, evolution is a process that takes place over at least thousands, if not millions of generations, through mutation and selection. There can be no evolution within the same generation. It is much rather a random process under certain constraints than a program in our genes. Moreover, the result is always an adaptation to current environmental conditions. So even if Tom somehow evolved all alone, that would tell us that a newt is the optimum lifeform for a Warp 10 traveler. ;-)
Breathe or die Why is Tom temporarily not able to breathe normal air during his metamorphosis, but only the strange poisonous gas? This can hardly be a phase of his alleged evolution, since in nature there wouldn't be a well-equipped sickbay to support this.
Genetic magic Agreed, we know similar procedures from TNG: "Identity Crisis", TNG: "Rascals", TNG: "Genesis" and VOY: "Faces". However, while the Doctor already had a hard time to restore Tom when he was only slightly mutated just after his Warp 10 flight, it is even more incredible that he succeeded to restore Tom and Janeway after virtually nothing of their DNA is left.
Anti-matter-dote In order to restore Paris, the Doctor has a fabulous idea - how about feeding antiprotons from the warp nacelles into his damaged cells? Antimatter has been used for all sorts of barely credible purposes in Star Trek before. But dear Doctor, please keep it off your patients, unless you want them to act as a spare warp core or photon torpedo!
Thanks to Christian for the facts about the "Beta Curse", to Andrew Jackson for the quote from "Night", to Timwi for suggesting that the second warp core feeds the holodecks, to Ter Loki for suggestions about variable warp geometry, to Stefan for annotations about the aeroshuttle, to Tim for a suggestion about the Maquis crew, to nixonshead for a remark about Doppler shift, to Dominic for a correction about evolution, to Ambassador for a quote from "Threshold" and to Claudio Puviani for a note about "infinite speed".
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|Last modified: 28.02.13|