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The Science of Hollywood: Hacking All the Internets With Only 10% of Your Brain
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Nukes don't work when you blow them up with lasers. Flying into a laser doesn't make them explode in a nuclear blast. Heck, regular missiles wouldn't work either.
Great triumphant sacrifice scene, but the aliens totally won.
I dunno, Mass Effect 2's quantum entanglement communication array was pretty good.
You've got that scene wrong. The plane didn't have a nuke, the plane just had one regular missile that wouldn't fire but was armed. The plane then flew into the aliens weapon and made that explode prematurely inside the alien ship instead of on the ground. The only nukes in the movie blew up the mothership and houston
If you want, you can integrate an expression for vehicle velocity through time over the course of the ship's transit through the planet. Computing the gravitational acceleration caused by an object you are flying through is rather a headache, though. If I recall it eventually simplifies (for a spherical and radially symmetric w.r.t. density object) to be equivalent to a point mass at the center of the object with a mass equal to the portion of the object's mass that lies within your instantaneous radius from the object's center.
If you just write an expression for velocity, though, you find that: V = (T3 - T1)*thrust/mass + (integral over time from T1 to T2) of gravitational acceleration + (integral over time from T2 to T3) of gravitational acceleration, where T1 is time now, T2 is time at the core of the planet, and T3 is time at the surface on the other side. I've already simplified this by assuming that our engine is magical and therefore our spacecraft's mass is constant; in reality you'd be integrating that term as well.
If we pretend gravity is constant to avoid having to do the integrals over time (i.e. that it only switches direction when we pass the core and doesn't change in magnitude with depth in the planet), we can write V = (T3 - T1)*thrust/mass + Ag * (T2-T1) - Ag * (T2 - T3), where Ag is the acceleration due to gravity.
Obviously our velocity at the end is greater than zero. (And, we can further observe that, since T3-T2 is greater than T2-T1, gravity has made a positive contribution to our velocity compared to the same trip made through flat space--this is the Oberth effect aka a powered gravity assist). Meanwhile, if we'd just pointed our ship straight up from the start, we'd have hung motionless or fallen backwards (the problem stipulates a thrust-to-weight ratio of < 1).
Of course, in reality, even for a thrust-to-weight ratio greater than one (but a fixed quantity of propellant) it may be possible to escape by flying through the planet when you could not escape by just flying away. That's a somewhat less intuitive case, though, so let's stick to the one in the movie.
...although speaking of Armageddon, the default of every detonating device to be a Deadman switch is a little annoying. If you're unaware, a Deadman switch is one where once the device is "Armed" there's an active force preventing the detonation (for example, if a grenade has the pin removed then the lever must be held down to prevent ignition). If the active force is removed (such as the person dying and releasing their grip on the lever in the grenade example), then the device detonates.
The epidemic of Deadman-style switches in movies is because it gives the classic "Red or Blue Wire" bomb disarm sequence - the protagonist must cut the power to the countdown device, while leaving the mechanism preventing detonation still powered. These switches are useful for devices which are intended to explode and where potential damage could prevent the detonation signal, but it's not useful in all circumstances and almost certainly not present on an "overpowered device turning into a bomb". For those devices, simply cutting every wire should be sufficient to prevent detonation.
Probably my favourite subversion of the Deadman switch (or, at least, a variation) is Under Siege 2, where Steven Seagal is told he must guess the correct password to deactivate the laptop controlling the Doomsday Device. Seagal responds by just shooting the laptop and the badguy holding it who says, "Didn't think of that..." before dying.
Consider a ball that bounces perfectly (and no air resistance).
If you hold it still 6m above the ground, and drop it, what happens?
Well, it accelerates towards the center of the Earth at ~9.8m/s^2, and at some point hits the ground, at which point it bounces perfectly, and begins moving upward - still accelerating at ~9.8m/s^2 towards the center of the Earth. Because it bounces perfectly, it comes to rest at exactly 6m above the surface again.
This is because all you've done is created some potential energy (by lifting the ball to 6m to begin with), converted it into kinetic energy (by dropping it), and then had it converted again to the same amount of potential energy (by the ball "lifting itself" up to 6m again).
You agree with all of that so far?
Okay, now throw the ball straight down, instead of just dropping it.
Where does the ball end up?
Well, it ends up higher than 6m, because when it hit the ground it was going a little faster (acceleration from gravity + acceleration from throw)*, and therefore had more kinetic energy, and therefore the final resting spot has to have more potential energy, which means it needs to be higher.
* MATH!
Vi = 0m/s
Vf = ?m/s when it hits the surface
A = g = ~9.8m/s^2 towards the surface
T = time in seconds
S = distance = 6m above the surface
Vf = Vi + A * T
S = Vi * T + (1/2) * A * T^2
Since Vi = 0 ...
Vf = A * T
S = (1/2) * A * T^2
T = ((2 * S) / A)^(1/2)
Vf = A * ((2 * S) / A)^(1/2)
Vf = 9.8m/s^2 * ((2 * 6m) / (9.8m/s^2))^(1/2) = ~10.8m/s (and elapsed time is ~1.10s)
You can check the work by running that time number through the equation for S, above:
S = Vi * T + (1/2) * A * T^2
S = 0 + (1/2) * (9.8m/s^2) * (1.10)^2 = 6m
Okay, so we know the velocity of the dropped ball. What's the velocity of the thrown ball when it hits the surface?
We're going to cheat and use a refactored version of the above equations to save effort:
Vi = 2m/s towards the surface
Vf = ?m/s when it hits the surface
A = g = ~9.8m/s^2 towards the surface
T = time in seconds
S = distance = 6m above the surface
A = (Vf^2 - Vi^2) / (2 * S)
Plugging in our earlier numbers to check ...
A = ((~10.8m/s)^2 - 0) / (2 * 6m) = 9.8m/s^2 (CHECK!)
So ...
A = (Vf^2 - Vi^2) / (2 * S)
(2 * S) * A = (Vf^2 - Vi^2)
(2 * S) * A + Vi^2 = Vf^2
Vf = ((2 * S) * A + Vi^2)^(1/2)
Vf = ((2 * 6m) * 9.8m/s^2 + 2m^2/s^2)^(1/2)
Vf = 11.0m/s
So, since the thown ball has a higher velocity when it hits the surface, it's kinetic energy is higher. Therefore, when it bounces perfectly, it will convert that extra kinetic energy into additional potential energy when it finally comes to rest. The only way to do that is by coming to rest at a higher altitude relative to the surface.
In the spaceship example, we're dealing with essentially the same thing, except instead of bouncing off the surface, you're just flying through the core of the Earth - the effect is the same, just slightly more gradual (gravity switches more slowly from pulling in the direction of travel to the direction opposite travel, and goes from ~9.8m/s^2 to 0ish, but it does so symmetrically, which is important). And, moreover, instead of just a single throw to start things off, you're burning your engine the entire way down into the core and back out again, which only magnifies the difference between your starting potential energy and your ending state on the opposite side. So, with enough thrust and a long enough time in which to do it, you can, in fact, achieve escape velocity on the other side even if you couldn't on the original side.
So, uh, kudos to the original movie for actually doing something kind of cool.
Nope - "flying tangential" is what regular orbits do (remember that orbiting the Earth isn't about going up; it's about going sideways really, really fast; all the up is there for is to get you out of the atmosphere and its velocity-killing drag).
So, if you're already in a stable orbit around the Earth, any amount of thrust at all is enough to get you to escape velocity eventually (so long as, as noted, you don't run out of fuel first).
The trick, though, is that you need to already be in a stable orbit; if you're not in a stable orbit, then eventually you'll fall back to Earth if you don't have enough thrust to overcome the ~9.8m/s^2 pointing back down to the center of the Earth.
Steam: Elvenshae // PSN: Elvenshae // WotC: Elvenshae
Wilds of Aladrion: [https://forums.penny-arcade.com/discussion/comment/43159014/#Comment_43159014]Ellandryn[/url]
NSFW
Skip to 2:36 for the relevant discussion on "non-lethal" takedowns
Hollywood medicine in a nutshell
but they're listening to every word I say
On a completely different topic: in the movie Cloverfield, there's a scene where the head of the Statue of Liberty lands in the street after being blown off by an explosion. Originally, the prop head was life sized; but test audiences thought it looked too small to be real. The version in the final film is 150% of life size, and people still thought it looked too small (including me, I'll admit).
but they're listening to every word I say
It obviously steers into plot-hole territory, but it's more simply just a matter of "if mystery goop does X under condition 1, then it should always do X under condition 1." If it suddenly does Y instead, it's going to start feeling like you just needed it to do Y, and didn't know how else to make that happen.
I don't think the ball example actually helps any. It does not matter whether you throw the ball straight down or straight up. It's potential energy is going to end up the same and it will bounce at the same height.
I think of it as more about the difference between wireless network and wired network. Also their systems were presented as being on multiple separate networks. The Cylons could hack wireless networks at a range. A wired network not physically connected to another would require physical access to each network.
how does the balls potential energy not change when you add energy to it by throwing it down or up? The ball will come to rest at a higher point than it started before you added energy.
EDIT: Yes, as @Veevee pointed out, throwing the ball up works just as well as throwing it down, because throwing it up just causes it to come to rest at some point higher than the 6m it started out at, which is a higher PE state than where it was a 6m, so of course it'll be moving faster when it bounces perfectly off the ground, and therefore come to rest higher than 6m (in fact, it'll come to rest exactly where it stopped when you tossed it up). I don't think that's actually the question you're asking, though, so see my post below.
That's only true if, when you throw the ball up, you can actually throw it up harder than gravity is pulling it down.
For a normal ball, that's easy - you can very easily generate a thrust-to-weight ratio greater than 1 with your arm, and so the ball move up (to a higher potential energy state) before falling back down, at which point it will bounce perfectly and return to the height it hit at the top of your throw.
However, the original problem posits a ship that can't actually escape, which means it cannot generate a TWR greater than 1 (e.g., it must fall towards the surface faster than it can run away from the surface*), so the best it can achieve is to fall more slowly.
Assuming that the ship starts at rest, then, the math stays the same, it's just that their net acceleration is, say, ~7.8m/s^2 (e.g., gravity is pulling it towards the center of the Earth at 9.8m/s^2, and the ship is burning away from the center of the Earth and generating -2.0m/s^2).
Running that through the same equations (Vi = 0m/s):
A = (Vf^2 - Vi^2) / (2 * S)
(2 * S) * A = (Vf^2 - Vi^2)
(2 * S) * A + Vi^2 = Vf^2
Vf = ((2 * S) * A + Vi^2)^(1/2)
Vf = ((2 * 6m) * 7.8m/s^2 + 0m^2/s^2)^(1/2)
Vf = 9.7m/s
As you can see here, the velocity it has when it bounces is smaller than the velocity it had when you just dropped it (10.8m/s). Therefore, the kinetic energy is less, and so the potential energy when it comes to a stop again after bouncing will be less. Thus, the ship burning away from the breaking-apart-planet will not escape.
We can run the same experiment with the ship burning towards the planet's (empty) core, as well (Vi = 0m/s, still). Except, this time, you burn in the direction that gravity is pointing to start at 2m/s^2, and then, after you hit the middle, you burn away from gravity at 2m/s^2. (We'll also assume a really small planet.
A = (Vf^2 - Vi^2) / (2 * S)
(2 * S) * A = (Vf^2 - Vi^2)
(2 * S) * A + Vi^2 = Vf^2
Vf = ((2 * S) * A + Vi^2)^(1/2)
Vf = ((2 * 6m) * 11.8m/s^2 + 0m^2/s^2)^(1/2)
Vf = 11.9m/s
So, when you burn your 2m/s^2 engine in the direction of gravity, you reach 11.9m/s when you reach the center point (which is your new Vi). Once you reach the center point, you're going to keep burning at 2m/s^2 in the direction of travel, but now gravity switches direction on you. So, your new acceleration is -7.8m/s^2 (e.g, gravity is now pulling the other way). So what's your speed when you hit 6m above gravity center on the other side?
A = (Vf^2 - Vi^2) / (2 * S)
(2 * S) * A = (Vf^2 - Vi^2)
(2 * S) * A + Vi^2 = Vf^2
Vf = ((2 * S) * A + Vi^2)^(1/2)
Vf = ((2 * 6m) * -7.8m/s^2 + 11.9m^2/s^2)^(1/2)
Vf = 6.9m/s
So, by burning with gravity on the way in, and against it on the way out, you've gained 6.9m/s of delta-V just by "falling" 12m.
*
EDIT2: You can also reverse the above equation, and start with a Vi of 11.9m/s and an acceleration of -7.8m/s^2, and determine at which distance, S, you come to a complete stop (Vf = 0m/s), and compare that against your initial starting height of 6m.
This is left as an exercise for the reader.
Steam: Elvenshae // PSN: Elvenshae // WotC: Elvenshae
Wilds of Aladrion: [https://forums.penny-arcade.com/discussion/comment/43159014/#Comment_43159014]Ellandryn[/url]
First image is dropping the ball. It falls down X, comes back up X' (a little bit lost due to friction/inefficiency of rubber). Second you throw the ball. It falls down X, comes back up X' plus Y - it bounces higher because of the additional energy from you throwing it.
Third, instead of bouncing it goes straight through the gravity well. It falls down X, comes "back up" X'. Then, you add a burst from your engine to your ball/ship. It falls down X, comes back up X' plus Y - and hopefully the total is enough to exceed escape velocity.
I know, but I'm not using it to demonstrate the effect of the bird on the plane windshield, but the effect of a pliable object to a hard object when launched at velocity. It works great for that.
That's one of the few times where the word was used plausibly.
the "no true scotch man" fallacy.
Yeah, in this example, it works the same either way, if you're assuming a single input of energy at the beginning. The ball will have a total energy PE+KE, and either it goes down, bounces back up, and then goes to height X as determined by that initial input, or it goes to that same height X straight away. (And in a real-world setting, it'll always fall short of X if you do a bounce due to losses from air friction, deformity of the ball on impact, and so on. You're always better off just hucking it upward.)
My read is that the benefit of accelerating downward through the planet is if your craft is incapable of generating enough thrust at elevation X0 to overcome the force of gravity at X0. That is, it has insufficient thrust to move upward at all. If this is the case, then accelerating downward through the center of the planet and back up will give the ship an additional amount of energy that will get it to a new elevation X1 that is higher than X0, in hopes that - and this is the key point - the gravity at X1 is sufficiently lower that now your thrust can allow you to move upward. If it can, then you're golden. If not, then you can drop back down through the center again and achieve X2 on your next yoyo-ing, then X3, and so on until the gravity is weak enough at that elevation for your thrust to overcome it.
All of this, of course, assuming that you have enough fuel to maintain thrust for that long. (Though you could only fire the engines part of the time and still achieve a net influx of energy, assuming away friction and other energy losses.) Things get easier if you take into account loss of fuel weight, since decreasing weight would make it easier for the thrust to counter gravitational forces.
Now, if you have enough thrust to move upward, but not enough fuel to maintain that thrust long enough to escape from the gravity well, I'm not sure if yoyo-ing through the planet would help or not. My instinct is yes. I believe that, for a given object at a given elevation, you need a set amount of energy in order to escape from the planet's gravity. It's possible that you could have enough energy contained within the fuel on your ship, but not be able to convert that energy to force fast enough to accelerate upward. (For example, I have enough energy in my body that I could jump really fucking high if I could convert all that energy into thrust at once. But I can't, so all I can do is jump a couple feet in the air over and over again.) By yoyoing through the planet's center, you can convert your energy into motion more gradually and reach a slightly higher elevation, then do it again, and again, until you escape.
Or I might be full of shit, since I'm just kinda making this up as I go along. It makes sense to me, though.
It's even better when a writing team can make a compelling story without using those crutches (I really liked the episodes of Star Trek: TNG when the writers decided that subspace communication should be noninstantaneous) but their presence doesn't irk me.
the "no true scotch man" fallacy.
Source Code did this in a fun way if I remember correctly.
Or vibranium. There's an "explanation" for vibranium that doesn't make sense (it absorbs vibrations). I prefer ELM's explanation which actually makes perfect sense. Either way, part of the conceit is that the scientists made one vibranium shield, they don't really know how they did it, and they never did it again.
Not everything needs to be explained.
the "no true scotch man" fallacy.
The aliens totally won, but not in that sense.
When the ship comes down in the desert at the end, and Ian Malcolm and the Fresh Prince are walking away with their cigars, it's still pretty much intact. I mean, it's on fire and all of that, but it's still mostly in one huge piece. Which means that it's still filled with a whole lot of aliens that didn't die in the crash. So basically now a planet that has had it's entire modern infrastructure wiped out, that has very little command structure or emergency services, has to fend off an invasion from giant, super strong aliens that are super pissed because you just blew up their entire way of life.
The main invasion force may have been on the mothership, but still, the attack ships were enormous, there have to be a significant number of aliens still inside that are combat capable and anxious to head out into the world and cause a ruckus.
Communication is almost always instantaneous in TNG, the only information that will always, without fail, take a long time to reach anyone is a distress signal.
So, assuming we fell through the Earth and the fall was perfectly efficient - what would be the acceleration necessary to achieve Escape Velocity, and would it be insufficient to do it the "usual" way?
So, first let's find Escape Velocity (Ve) from the surface:
Ve = (2GM/r)^0.5
G = Gravitational Constant = 6.67x10^-11 N m^2 kg^-2
M = Mass of the Earth = 5.97x10^24 kg
r = Radius of the Earth = 6.38x10^6 m
So when we hit the "far side" we need to be doing 11174.36 m/s to escape the gravity well.
Now, how long do we have? Fortunately Newton did the hard work, so the period of a single oscillation is:
T = 2π(r/g)^0.5
g = Acceleration of Gravity = 9.8 m/s^2
That's a full oscillation (down and back) so we want to halve that, giving us 2534.4s to hit that Escape Velocity
From that it's just Ve/T = 4.41 m/s^2
Since Ve/T < g, this acceleration would be insufficient to get the ship off the ground but would be sufficient to achieve Escape Velocity via the "through the center of the Earth" method.
Spacecraft don't generally work the same way as a kid hucking a rock.
It also gave us the guy who has no idea what quantum means in Pratchett's novel Pyramids. "Kids, it's going to be quantum!"
I'll agree, with the caveat that sometimes it feels like a cop-out.
I'm thinking of Timeline specifically, where the time machine is described as "a teleporter that breaks down your body, squeezes it through a hole in the quantum foam or some shit, and reassembles it on the other side... only we don't actually know how your body gets reassembled. But it's cool, they know how to to do it on the other side."
Maybe I expect just a little more handwavium from a Chricton script.
Because it represents the point at which they can turn off the engines, if they want to, and would still get away from the planet. If they aren't going escape velocity yet, then they need to keep trying to achieve it (by either burning away from or towards the planet, depending on which direction they're going at the moment).
Other than that, not much - if they haven't yet achieved escape velocity, and their engines are still working, and they won't get far enough out of the gravity well that their engines will be greater than gravity, they can just pick up a little more speed on the next pass through the core.
Steam: Elvenshae // PSN: Elvenshae // WotC: Elvenshae
Wilds of Aladrion: [https://forums.penny-arcade.com/discussion/comment/43159014/#Comment_43159014]Ellandryn[/url]
Ahh, but this was explained in the book.
In the "prime" universe, they've figured out how to break down and transport the bodies to the time-shifted alternate universe. Then, since there's an infinite number of parallel universes, there's one where they've figured out how to reassemble the bodies, but not transport them.
So the characters are transported by one universe and reassembled by another.
Like the ship in my backyard, just waiting for the Earth to split in two. Aaaaany day now...
I mean, Will Smith, after ejecting from his craft (which I'm lead to believe is incredibly hard on one's body) was able to knock an alien out with one punch, and keep it unconscious through routine beatings well enough to wrap it up and drag it halfway across the desert. Sure, Smith is a fighter pilot, and thus likely to be in good shape and trained in fighting, but as a fighter pilot he's also likely to be a fairly small man. All that would seem to imply that the alien bio-suits aren't exactly well suited to combat and are fairly lightweight, let alone the actual aliens inside of them.
Later, that alien was put down with small arms fire, so one could conclude they're not actually physically superior in any substantial way outside of their tech advantage. Bigger, maybe a little stronger, maybe a little armored, but not so much so that an armed human wouldn't be able to take them down.
And that tech advantage? A lot of that is gone. They lose the shields from their mother ship, and the city destroyers are all crashed and presumably pretty fucked up from being taken down, meaning they don't have assured aerial superiority or the ability to move or regroup their bases. They likely have some fighters that survived the explosions, subsequent crash, and further explosions and burning, but it's possible they don't work either (or won't work for long) without the mothership available to provide power (remember the researcher who said the Area 51 ship wouldn't even power up until the big ships arrived). Possibly they've lost their communications as well without the big ships flying (how good was their communication network if they had to hijack our satellites for their countdown signal?).
Humanity on the other hand still has established communications through morse code transmitters, knows where all the enemy ships are, and still has airstrike capability against the now vulnerable alien craft (though greatly reduced from what it was). We've lost some satellites, but not all of them because the aliens wanted to keep them intact for their use. Since the aliens focused on high density population centers and military bases, rural areas still have their airfields and airports still full of planes that could be used as troop transports, or long range bombs for any ground combat. If someone still has the ability to launch ICBMs or some other nuke delivery system against these stationary targets...
What I'm saying is I'd really like to see an Independence Day 2 to clear some of this up.
That's not so much an explanation as a restatement of the exact thing I have a problem with. Chricton stories tend to be more grounded in actual science, and "We built a machine, and it works, but we don't know how or why" feels like a dodge to avoid explaining the back-end of the time machine.
From growing up in a family of biologists, a couple things tend to always stand out in movies:
1) Bird calls almost never match the actual bird being shown.
2) Bats. I can't recall any movie ever portraying the behaviour of these animals correctly. My dad's primary field of study was bats, we rehabilitated injured bats, I spent many trips crawling around in caves, so I got quite familiar with these animals. Hollywood relies pretty much entirely on myths.
That said, I never have much trouble ignoring these aspects and just enjoying the movie as a whole. The only thing that really reduces my enjoyment is when bats get portrayed as a vicious / villainous animal.
But they do know why it works.
The point is that it emphasizes how much differently interacting with parallel universes is from our normal perspective. It's similar to quantum computing, where you can have an effectively infinite amount of processing power. It doesn't matter that you don't know which universe solved the problem, just that one of them did.
And it's not like an explanation in this case would be anything more than "And then we reassemble them on the other side". By avoiding that simplistic explanation, Crichton is able to push more world-building into his novel.
I'm a mechanic. It is blindingly obvious to me that the writers of the Fast and Furious films have absolutely no idea how any of the parts of a car work.
I am with you on all of this, with the exception of the alien going down from a single face fisting from Big Willy Style - remember, he had just crash landed. As for Will Smith, he was likely hopped up on Air Force "go pills", which are basically just amphetamines, and was also peaking on a combat high, so odds are his steam-train like fist had considerably more (if you'll excuse the pun) punch than the average person would have.
So basically we have a chemically enhanced human being vs a seriously injured alien, so we can't be sure what sort of physical prowess they have. The alien did completely trash the lab and everyone in it a short while later though, even though he was injured and his "suit" was opened and damaged during the autopsy.
It also showed some sort of psionic ability that in its weakened state was still able to cause injury to the President before it was riddled with bullets. Who knows how powerful that attack would be if the alien was not injured, or not alone.
Yes. Someone call Roland Emmerich and tell him to make it happen.
The bio suits were not bullet proof(one gets shot mid movie on, will smith punches one in the face knocking it out for hours), they were flightsuits literally so the tiny forms inside could survive whatever environment. They are not going to survive a crash landing, the small fighters remaining were the biggest threat at that point. Also, large pancake objects(Did they say 4000m across?) the size of small cities hanging over head are a thread because they have to come down somewhere. And then you have to scrap that material and disassemble it.
The pro side: Earth literally gained trillions of dollars in scrap and reusable materials, and a boost in technology stolen from working modules.
That's a good rule for fiction in general. Magic in fantasies should be internally consistent too.
Honestly I would have preferred the simplistic explanation, because at least it's an explanation. Observing that something happens, but not being able to understand or explain how it happens because of the way our universe is fundamentally constructed is pretty neat in a scientific/research context, but ultimately leaves me unsatisfied when dealing with fiction. Doubly so when it comes at the tail end of a relatively technical explanation of how your time machine works.