The Least Interesting Man In The World

Awhile back, xkcd published a comic about the Least Interesting Man In The World. Whether the man in question could ever actually exist is a fascinating thing to think about; briefly, it depends on the terms of the question and on the definition of ‘interesting’.

If we accept that ‘interesting’ means ‘would draw interest from a normal, human observer by some intrinsic or displayed quality’, then there can never be a Least Interesting Man In The World.

Take the individual from the original xkcd. Let’s say that all his character flaws and uninteresting habits—his general dullness, in other words—have led to him being named the LIMIT (omitting the W to make the acronym look better). Immediately upon being named the LIMIT, he would become a curiosity in his own right (based on the conjecture that advertising anything as the extreme end of a spectrum—worst person in the world, best maple syrup in Vermont, etc—causes interest in that thing) and thus no longer be the LIMIT. And as soon as he stops being the LIMIT, he would lose the added interest of his position as the LIMIT, and instantly become the LIMIT again, and lose it, again. He is a walking paradox, and can never remain stable long enough to enjoy his title as the LIMIT.

Unlike, say, this fellow.

 There are several ways to get around the paradox. We might separate intrinsic interestingness from the added interestingness of the position as LIMIT, allowing the LIMIT to exist in both states (as LIMIT and as LIMIT-plus-LIMITinterest) simultaneously. We might hypothesize an individual so massively uninteresting that he retains his title as LIMIT even despite the interest the LIMIT brings; this view involves imagining interestingness as an objective quantity that can be overridden by a greater force, in a manner analogous to gravity.

 Or, and this is my favorite, we could assume that the least interesting man in the world is forced into this paradox involving the title of LIMIT, and that he would be effectively unobservable from there on. In other words, the LIMIT would be trapped in a kind of singularity of interestingness and uninterestingness. Since he would switch roles as many times a second as he could be observed, the case could be made that no one would be able to observe the effects of the paradox. The title of LIMIT--call this one LIMIT-B—would then pass to the second least interesting man in the world, who would ascend to the top spot by virtue of his predecessor’s descent into unobservability. It’s an open question as to whether the paradox would claim him as well, or whether he would simply acknowledged as being as close to the LIMIT as man can get while still remaining visible.

Alternatively, the entire issue might just vanish into a black hole.

Final Black Hole Note: This Is Absurd

A couple of black hole notes ago, I was able to roughly deduce the size of the Vulcan black hole in Star Trek (2009) and take a stab at its mass. I'm decently confident in my conclusions to date, but it occurs to me that there must be some other mechanism at work when there's a great deal of red matter involved. I think the massive amounts of red matter used in the creation of the Final Black Hole somehow gave it more gravitational attraction, and perhaps more mass than it should reasonably have.

I conclude this because, as I noted last time, the Enterprise can travel faster than light, and should therefore have been able to pull away from the black hole without any trouble. In the quest to try and fit all of J.J. Abrams' nonsense into an astronomically coherent system, I'm going to see what it would take for the FBH to have the kind of gravitational attraction that it did.

At the end of the movie, before they blow up the black hole with antimatter, the Enterprise goes to full warp in order to escape from the FBH. I couldn't find an exact value in the Star Trek Wiki for how fast "maximum warp" is, in terms of kilometers per hour; it did say that Warp 1 equals light speed and that Starfleet ships could manage Warp 9 at best during this time period, but I don't know what scale they're using. Warp 9 could be 9x light speed, or it could be nine levels up on an exponential, logarathmic or just arbitrary scale. I don't know. Thus, I'm forced to try Plan B.

In the movie, the Enterprise travels from Earth to the Vulcan home world. Now, according to a canon reference in a Star Trek novelization book I happen to own, the Vulcan home planet orbits 40 Eridani A. This is a real star, located 16.45 light years from Earth. Now, here's where it gets slightly stupid: we see the Enterprise both entering and exiting warp in the movie. If we assume that the movie is taking place in real time (and there's compelling evidence to do so; Kirk's in a tearing hurry the whole time), we can know the time it takes for the Enterprise to travel that distance. In the film, that's five minutes and 17 seconds. Meanwhile, Wikipedia gives one light year as 9,460,730,472,580.8 km. That times 16.45 is 155629016273954.16 km. That divided by 317 seconds is 490,943,269,003.01 kilometers per second. Light travels at a geriatric 300,000 kilometers per second, so when the Enterprise is at warp, it is traveling at 1,636,477 times the speed of light. Which means that the gravitational pull of the black hole is 1,636,477 times the speed of light, plus more, since the Enterprise was slowly pulled in by the black hole. WHICH MEANS that as soon as the black hole was created, Kirk and Spock and everyone aboard both the Romulan ship and the Enterprise should've been pulled inside immediately (when they weren't at warp) and DIED.


In conclusion, J.J. Abrams has literally violated every single rule* of what we know about black holes. Fuck that noise.

*Multiplication of mass, abuse of the Schwartzchild radius, we can see the unseeable black hole on the screen, no red-shift in the communications from Nero's ship, evidence of an accretion disk where no matter exists to make one, more abuse of the Schwartzchild radius AND SO ON.

Bonus Black Hole Note! The Enterprise Was Never In Any Danger!

At the end of Star Trek, the Enterprise is caught in the gravitational well of the black hole, seemingly inescapably so, and escapes only by ejecting what's basically a huge bomb into the black hole and riding the blast wave out (undamaged). SPOILERS.

"aaaaaaah..."

"CHOOOOOO!!!"

If warp speed is faster than lightspeed (which it is), the Enterprise should be able to escape the black hole without all the histrionics, like firing the warp core (which apparently isn’t strictly needed for the ship to go into warp) into the black hole FOR INSTANCE.

Here’s how. The Schwartzchild radius defines the area within which you would need to exceed the speed of light to escape, and so constitutes the effective boundary of a black hole (since we can’t see anything inside because light cannot escape). The Enterprise isn't within the Schwartzchild radius. We know this because nothing can escape once it's inside the event horizon (same thing, but sounds cooler) of a black hole, yet even when his ship has almost been swallowed, Nero is able to send transmissions to the Enterprise. Thus, the event horizon is the actual black border that we see on screen, and anything forward of that can still escape, and the Enterprise never crosses that line.* Therefore, the escape velocity that the Enterprise needs to attain should be less than the speed of light. Therefore, since warp speed exceeds lightspeed, the Enterprise should be fine,** and no huge goddamn bomb is necessary!****

Hooray! Now Kirk can go contract more alien STDs!

*Supplementary reasons: We (the camera) can see the Enterprise, so it hasn't passed the event horizon because the light reflected off of it can bounce back to us. Also, the accretion disk of the black hole helps define its boundary, which the Enterprise doesn't cross. What was it formed out of? I have no idea, since there was no matter around at the time other than Nero’s dead ship (which went straight in) and the Enterprise itself. Regardless, it’s there, and that provides a crude way of telling at least where the Schwartzchild radius isn’t. The disk will be outside the radius, and the Enterprise is outside the disk.

**Not to mention, since warp speed exceeds lightspeed, the Enterprise could theoretically be within the Schwartzchild radius and still be able to use its normal warp engines to escape. It's a question of how far they would be able to go into the black hole.***

***The movie ignores the "spaghettification" thing--the thing where the pull of gravity on the part of the ship closest to the black hole will be stronger than the pull of gravity on the farthest-away part, so the Enterprise will start to stretch out like a strand of spaghetti as it gets closer to the black hole--so I see no reason why I shouldn't ignore it as well. Phooey on you, spaghettification.

****One more thing: They hurled the huge bomb into the black hole, into the event horizon itself! Nothing can fucking escape the event horizon unless it has a magical warp-drive, and no matter what radiation the explosion generated, its maximum speed would still be the speed of light! Thus, it couldn't escape! Thus, that entire explosion in space is a crock of shit!*****

*****Done now, but there's another one coming. Hold onto your helmets. Also, celebratory penguins again!

Red Matter: Trying to Explain Black Holes in Star Trek

Preface: I KNOW that Star Trek (2009) played merry hell with all sorts of physics. I'm not trying to explain how contrary they run to regular, ordinary physics; that's just too damn easy. What I'm going to try to do is explore their black hole physics, and see what the implications are when you bring them into line with the parts of black hole physics that they didn't explicitly rewrite. It's... oh, forget it. Just read on. Or don't. Whatever makes you happy.

The plot device J.J. Abrams came up with in the film is called "red matter", which is apparently different than any other matter that reflects red light.

This isn't a wayward red blood cell, it's black hole fuel!

The basic idea seems to be that when the red matter is released into something, it creates a black hole. But there are conditions under which it won't; you can keep it suspended in a tank, even poke it with a needle and take some of it out, and it's stable. It only turns into a black hole if you provoke it, much like your adorable cat, who will only turn into a hissing, spitting ball of painful death if you step on his tail. Otherwise, he will be calm, serene, and float peacefully in midair (as many cats do).

The trigger for red matter seems to be making it interact with a massive body, such as a ship or a planet. You can't just set a trigger on it and tell it to become a black hole, it has to actually hit the massive object. Moreover, I think it is best used at the spot in the object where matter is most compressed by its own gravity. Namely, the center. This is why Nero used his giant drill to bore down to the center of Vulcan, as opposed to just hurling the red matter at the planet's surface.

Here's where it gets interesting, though. The black hole that's produced has no correlation to the amount of red matter that's used. For example, observe this photo of the planet Vulcan collapsing into the black hole at its core.

Here it is again, a second later. You can see the last remnants of the planet at the center, and then the patch of darkness in the center of the frame that defines the Schwartzchild radius (effectively, the boundary of a black hole).

So the black hole that's produced, by a tiny drop of red matter, is approximately planet-sized. Compare that to the black hole produced when the entire huge case of red matter impacts Nero's ship:

The black hole formed in the middle of Nero's ship; that's why it's on both sides.

Sure, it looks big, but that ship is at best comparable to a big asteroid. Certainly not moon-sized, or planet-sized. The black hole produced from all that red matter was only about the size of the ship!

This leads me to believe that the amount of red matter is irrelevant. What matters is the thing the red matter is used on, and how much mass it has.

Now, this presents a bit of a problem. The black hole produced is not directly correlated to the amount of mass the object has.

Let's assume Vulcan, shown collapsing above, is about the size of Earth (for convenience's sake). If Earth collapsed into a black hole, the black hole produced would be smaller than a grape. A stellar-mass black hole--a black hole with the approximate mass of our sun--comes from the collapse of a star with 25+ solar masses. Yet the red matter made Vulcan collapse into a planet-mass black hole! Thus, red matter must work, not by collapsing the mass already present to its natural Schwartzchild radius (all masses have it; it's theoretical in nature, kinda), but by acting as a multiplier for the mass that's already there. It multiplies the mass of the object it's used on until the radius of the black hole that'll be produced is equal to the radius of the original object.

We can even work out what the multiplier is, within reason. Here's how I did it:

The Schwartzchild radius of an object (what it would be, with its mass, if it were to become a black hole) is about three kilometers multiplied by its mass. Now, the radius of the Vulcan black hole (if Vulcan is Earth-sized) is about 6384 kilometers, since that's the radius of Earth. Divided by 3, that means that you would have to have 2128 solar masses to create a black hole that size!

Earth's mass, obviously, isn't anything even close to a stellar mass. According to Wikipedia, it's about 332,950 times less than the sun. So if we multiply 332950 by 2128, we get 708,517,600. That's the multiplier of the "red matter", if my theory is correct. When the red matter hits a massive object (planet, ship, whatever), it multiplies the mass by 708,517,600 times, causing it to collapse into a  black hole that has a Schwartzchild radius precisely equal to the original object's actual radius.

This is how red matter works. Thank you and good night.

Here's some celebratory penguins!

(Obviously I've had to make some assumptions; Vulcan is supposed to have a stronger surface gravity than Earth, for example, so it's reasonable to assume that it's heavier. However, fuck it, I didn't exactly have precise numbers to work with. And whether the red matter number is the exact multiplier or not, the important thing is I've got a good idea of how the mechanism works and what the multiplier is within experimental error. That's a decent starting point.)