The Lowdown
Let's get one thing straight right off the bat: I HATED "Threshold." Not (just) because of the lousy writing, not (just) because of the lousy science that explained Paris and Janeway turning into a two-legged giant salamanders, not even the fact that they just abandoned their poor kids on that planet (tsk tsk), but because of how it thoroughly disrespected and mistreated the Trek pseudoscience behind faster than light travel. It confused the term "transwarp" and "Warp 10," and it allowed Paris to travel at that impossible velocity.
What the modern Star Trek era calls "Warp 10" is also fondly called "Eugene's Limit" by the Next Generation Technical Manual, after Mr. Roddenberry himself. But one thing to keep in mind is that it's not a finite number; it's a conceptual limit. It's as if saying "infinity is the highest number"--not quite an accurate statement, because infinity is not a number--it's something that can't be exceeded. Much as your 8-year-old little sibling may protest, there is no such thing as "infinity plus one." Eugene's limit, simply put, is infinite velocity.
We learn in elementary school (or at the latest, junior high) the simple formula--speed (velocity, that is, we know there are differences but you get what I'm saying) is distance traveled over time; v=d/t. If you get in your car and you travel 120 miles in two hours, you're traveling at an average of sixty miles an hour. If you're traveling just over 186,000 miles in one second, you're doing something that's impossible in Einsteinian physics, but you're still traveling at a finite velocity; it'll still take you a positive amount of time to get from one place to another.
What, then, is infinite velocity? Applying some basic algebra knowledge, we know that v will only equal infinity when...anyone?...when t...Bueller? Bueller?...when t equals zero. That is, you get from point A to point B (that is, the distance d), in zero amount of time. You're here AND there at the same instant. Not one second after, not one millimicronanosecond after, I'm talking at the same time. And if we're talking infinite velocity here, because t is zero, that means that not only can d be anything, d IS anything. Points A and B are anywhere and everywhere. This is what the Encyclopedia and the Tech Manual are talking about when they say that traveling at Warp 10/Eugene's Limit/Infinite Velocity means you are occupying every point in the universe. Let's re-read, underline, highlight, and bookmark it. TRAVELING AT INFINITE VELOCITY MEANS OCCUPYING EVERY POINT IN THE UNIVERSE AT THE SAME TIME. Not every point on the planet, not every point in the galaxy, it's every point in the universe. And if you're doing that, it's gonna be a little bit cramped for everyone else.
Which brings us to Thomas Eugene Paris, who allegedly accomplished this feat. In a Federation Shuttlecraft. And he managed to map a chunk of the galaxy. And he plopped himself and Janeway a convenient distance away on a second trip. Riiight. "I've got this jar, and I've managed to collect an infinite number of grains of sand in it! Really!"
And then, to add insult to injury, they say he broke the "Transwarp Barrier." Now, semantically, that could actually work--perhaps Eugene's Limit is the upper threshold of transwarp capability, and traveling at Eugene's Limit means exceeding the capabilities of transwarp (just like "breaking the sound barrier" means exceeding the speed of sound). But the episode gave me the distinct impression that they were equating the two terms--traveling at Warp 10 means traveling at Transwarp.
The problem is, we see others travel at transwarp. The Borg. The Voth. And they sure look like they're not occupying all points in space at the same instant, and they sure do take a bit of time to get from one place to another.
My point is, "Threshold" needs to be
forgotten. All the tapes, scripts, and documenting materials related
to it burned, all entries from the reference materials whited out.
And, as punishment for writing the episode, give the task to Brannon Braga.
So, what's Transwarp if not traveling at Warp 10?
As we see with the Voth and the Borg, it is a means of travel that is different from and faster than known warp technology, but it is far from traveling at infinite velocity. It's got something to do with opening conduits in subspace or something or other, but the pseudoscience doesn't matter. It's pretty darn fast, it's faster than what warp engines seem to be capable of doing, but it's not infinitely fast.
If Warp 10 is Infinite Velocity, how come the Enterprise in TOS and the Alternate Future Enterprise-D in "All Good Things..." traveled at speeds greater than Warp 10?
One word: Recalibration. Warp isn't exactly a measure of velocity...it seems to have something more to do with the generation of warp fields and the energy expenditure involved. As warp technology has improved over the ages, Warp 6 then may be different from Warp 6 now, and Warp 6 in the future; it just so happens that with Federation science in the 24th Century, Eugene's Limit and Warp 10 happened to coincide. The Warp scale may have been recalibrated in the future of "All Good Things..." so that some other number corresponds to Eugene's Limit. (The Lowdown is, the writers wanted there to be noticeable, impressive improvements in Federation technology in the future timeline, so they had Riker call out for "Warp 14").
It could even be a matter of convenience.
Since the current warp scale is asymptotic, speeds faster than Warp 9 have
decimal fractions attached...Voyager's maximum sustainable cruising speed
is Warp 9.975. So something faster would be Warp 9.99, faster than
that would be Warp 9.999, faster than that would be Warp 9.9999, and so
on... You can see how it may be a little awkward when faster velocities
are typical in a technologically improved Federation: "I said Warp
9.99998, Ensign, not Warp 9.9998!" Someone had to eventually
have given up and decided to renumber the darn system.
RELATED TOPICS:
Warp Propulsion
for Dummies
Warp 10, Transwarp,
and "Threshold"
Zefram Cochrane
of Alpha Centauri