Quick Estimation of Photon Torpedo Max power

Since my last post caused some controversy about how powerful Federation weapons are, and photon torpedoes in particular, I thought I'd take a few minutes while I have a bit of a break to take a rough estimate of the power that photon torpedoes have.

This will be an upper bound estimate. I am going to use "Pegasus" to determine this yield because, really, it's quick and straight-forward, and I'm going to use some loose parameters, but I should be on the proper order of magnitude here, and that's what I'm looking for.

Start with the 5km wide asteroid. Yes, I know it is not solid, but this will overestimate the yield of a photorp. That gives a volume of 6.4*10^10 m^3 of nickel-iron. Assuming iron's density of 7.874 g/cm^3, this yields 5.1*10^14 kg of material.

Now, I'm interested in the gravitational binding energy. This is the minimum energy necessary to blow this mass apart. Now, I do know that in an actual destruction, it won't be scattered to infinity, and I'm also neglecting to include the mass that may be vaporized or melted in the process. Again, I don't think that this will be a terribly large difference, but if you want to go through the time and effort to prove me wrong, go ahead. Please show your work!

This energy is 3GM^2/5r--G being the gravitational constant (6.67*10^-11 m^3/(kg*seconds^2), M being the mass in KG, and r being the radius in meters. So, quick calculation: 4.25*10^15 joules. Sounds like a lot? Well, a kiloton of TNT is 4.184*10^12 Joules. The gravitational potential energy of that asteroid? 1 megaton. And it's supposed to take 250 warheads to take it out? That's pretty weak.

Well, suppose that I melt the thing instead. Melting point is 1811 k, and the heat of fusion is 13.8kJ/mole and the heat capacity is 25.1J/mole. Iron has an atomic weight of 55.845g/mole. So we have 9.22*10^15 mole of iron. Space is pretty close to 0K, so I'm going to use a temperature difference of 1800K for this calculation. This yield 5.44*10^20 joules of energy, or about 100 gigatons of energy.

If it took 250 torpedoes to do this (the payload of the Enterprise), then we have 400 megatons of explosive yield per torpedo. That's much better. However, this is probably a gross overestimate. The asteroid would be blown apart far earlier than this--the gravitational potential energy is much lower, so it is not unreasonable to believe that huge sections would be blown off with each torpedo.

Of course, there is a third possibility: that Riker is just a moron, and it would take far less than 250 photorps to destroy it. It wouldn't take 250 modern nukes to blow that thing to dust.

I'll let you all draw your own conclusions.

(Edited because I erred greatly--I used the heat of vaporization instead of the heat of fusion!  That's a huge energy difference.)

An analysis of the Federation vs the Galactic Empire

I will begin this by saying, simply, that while I do enjoy both Trek and Star Wars, I am by no means a great expert in either. I certainly am more familiar with Star Wars, and I will admit that I am slightly biased towards it. So, if I make errors here, please feel free to correct me.


I'm going to start with describing the Federation. My fist assessment of them is, basically, semi-inept scientists put into a conflict scenario. Why do I say semi-inept. Well, they can treknobabble their way out of some situations, I'll admit, and they do have some truly innovate and exceptionally talented crewmembers. I cannot possibly deny that. However, all that said, they have a very civilian mentality towards, well, everything.


First, let's take a look at their flagship, the Enterprise. It's filled with non-combatants and children. That second part is kind of key. Also, no one has small rooms that you'd see in a combat vessel, or even anything other than a luxury liner. Honestly, those rooms that everyone has are absolutely gigantic. For a place where space must be at a premium, they certainly did not skimp with their quarters. I'm sure they have great food recycling programs (i.e. poop to food via replicator tech), because they simply have to. No room for anything, really. It's a very civilian operation, which is alright if their missions were not frequently "Run here, deal with this crisis where people will be shooting at your ship and may be able to take it out." As you can imagine, this is not exactly responsible behavior. Even if it was just an exploration vessel, that's still very risky--a few hundred families bite it if that ship goes out, and given that they often go into unexplored territory with ancient dangers and hazards, it's all but inevitable that there is a massive loss of civilian life on that ship.


Now, let's look at their security/internal weapon systems. They use phasers. To be honest, this is a bad, bad policy. Why? Well, for one, they don't seem to have consistent effects on various types of materials. Sometimes, on some settings, they do well, other times, they are barely effective. They have a small power plant, which means if they increase power to do more damage against a target, they have fewer shots. It has to be limited power supply, because their overloads are about as effective as a modern hand grenade (give or take). Also, they're not exactly the most well-designed weapon. It's not shaped like a pistol, and it takes that function. Pistols have their grip and design for a reason, and it's not looks. It is function. It fits the hand, it's easy to aim, and it's easy to maintain ease of firing. The phaser has none of that. It fits the hand badly, and has no real way to aim well. If you watch the firefights, and have any actual experience in any armed service, you'd see that any squad with any actual combat tactics would clean them up in no time at all.


While I'm on the phasers, I have another beef: why don't they have shotguns for shipboard security? A good, honest, 10-gauge shotgun with shot or slug. It would do wonders for shipboard defense against the Borg, or any boarding action, really. Any security situation, a shotgun would do well in. Even if they didn't want to kill someone, non-lethal rounds could be used. Even if we hadn't developed them in 1989, I don't see why they couldn't have imagined them for the show. Combine replicator/transport tech into their chambers, and you never have to reload and can switch out rounds on the fly. Seems reasonable enough.


Since I just mentioned it, their transportation tech is sorely underused from a tactical perspective. We know that it is quite possible to duplicate people with it, each with the same memories and skillsets of the original. Given how it's supposed to work, this is, to be honest, quite feasible. So why is it that there isn't a dedicated squad of assault troops, volunteers all, who transport clone into combat in shipboard actions, wreak all kinds of havoc with targeted sabotage in enemy ships, even to the point of critical overload of reactors? You'd have no net losses of your own, and your enemies would suffer catastrophic losses. The Borg don't do this, the Klingon don't, no one does. But it is quite highly possible to do so. I could understand ethical limitations on this (creating clones to die, but that's pretty much what a two-way transport via transporter is anyhow), but Klingons certainly don't have that kind of limitation.


Even if the idea of using it to replicate assault troops for boarding actions is repugnant, it could be used for highly ethical purposes. Just keep a log of people who transport down on away teams. Hey, look, Tasha Yar isn't dead any more. Data is a unique resource, and they want to make more. There are ethical concerns with taking him apart to do so, but Data seems to have no objections to a replication via transport. That would either enable research into creating more sentient AIs or it could simply negate the need for such research--every ship could have an android to serve as officer. But that aspect is never used. It's kind of baffling, really.


Another baffling thing is their use of the holodeck. It seems that, every so often, it goes horribly wrong, and nearly destroys the ship somehow. So the first question is "If it does this every so often, why do they let people use it at all?" The second question is "Why haven't they weaponized this at all--Picard was willing to to take out some Borg once, so why isn't this standard practice?" The third question is, "Why isn't this extremely powerful training tool used heavily for training of various types of espionage and combat missions?" Think about it--you can have a fully realistic combat experience, minus actual death of personnel, whenever you needed it. One would think that there would be at least a team of agents who used it routinely for such things, given the number of problems that the Enterprise deals with.


All in all, they seem to be, basically, civilians who are only half-heartedly transitioning into a military position. And, to be fair, that fits their supposed character--explorers and scientists, exploring a galaxy that is still new to them. They're still learning from everything, all the time. And their domestic problems are largely settled, I'd imagine--they have replicators and holodecks, so it's hard to imagine anyone would truly lack a basic necessity. And those things can't be that expensive, since they are apparently in every crewmember's luxurious cabin, no matter their rank. If they were, then the Federation would be, well, bordering on corrupt military dictatorship, and I want to give them the benefit of the doubt there.


They are quite successful, however, and there is a great reason for this: their enemies are utterly incompetent morons. The Borg, for instance, have a time machine. They want to beat the humans. So they use it to go back to a few days before the launch of the first warp drive, which would be noticed by the Vulcans and then they'd be integrated into galactic society. That plan is moronic. They have a time machine. There is a much better time to hit earth, hard, and irrecoverably--it's called "before the pyramids were built." Seriously, there would be little to no resistance when they show up literally from nowhere and proclaim themselves now in charge of Earth. Most such peoples would worship them and gladly let themselves be assimilated. Problem completely solved. No pesky humans, and a planet that has had no real mineral or environmental exploitation is now in their grasp. Simple. But they can't do this, at all. They had the imagination to use a time machine, but why give the humans even the slightest chance to succeed? Heck, here's a more salient question: Why did they go to Earth, then use the time machine? They could have used the time machine, then gone to Earth, thus avoiding the huge Federation fleet that damaged and nearly prevented their whole operation. Something just seems off here.


And the Klingon! Strength and honor, but sneak attacks via cloaking tech are okay. Sure, I get that. Ambush is legitimate, and I have no gripes with that. But I do have gripes with them using the bat'leth. That's not exactly a practical weapon for a humanoid (please note the lack of weapons like that in human history, and realize that it's for a good reason). Okay, it's a sacred thing. But why use it at all? They're supposed to be hard-core, but they just seem to be, well, kinda bad at combat. Despite near total militarization, they never really seem to be able to get anywhere.


The Romulans? Sorry, but they have battleships, actual battleships, that can cloak, but they can barely make headway either. They supposedly have this great covert ops program, but they never seem to be able to get even a small raiding fleet anywhere deep into anyone's territory. They get caught in pretty small nets. Look, space is big. Really, really, really big. Our nearest neighbor? 4 light years away. Given warp-drive technology, they could take a non-direct route, and totally avoid almost any picket. Instead of the perimeter of a circle to defend, the Federation and Klingon Empire have a sphere to defend. That area goes up dramatically, and there simply is no way to practically defend it. A raiding fleet could do immense damage, and could force an opponent into guarding certain lanes heavily, and hanging around their outposts exclusively. This is a classic guerrilla campaign. But they can't seem to be able to do this. Yes, their infiltration was caught by an innovative technique, but the point is that they shouldn't have even been at risk of that in the first place.


So the Federation's enemies seem to be, more or less, pretty much worthless, which is why the Federation is still viable--their foes are just less competent than they are.


Now, how about the Empire? The Empire has one truly glaring weakness, and it's called "The Emperor." Really, that man just doesn't understand how a trap works. He uses himself as bait, and actually shows up. Then he has his whole fleet of capital ships not fire at the enemy fleet so he can have some fun. Even if the rebels never took down the shield, that still cost him quite dearly because rather than quickly and utterly annihilating the Rebel fleet, he loses many valuable capital ships--including the Executor. So, that's a big drawback.


But, tech-wise, it's clear that they are better off, from a military standpoint. They have actual rifle-gripped weapons, and that makes a difference in boarding actions. Or ground combat. They have all sorts of ground combat weapons, and they're really good with them. My previous bit on Stormtroopers should attest to that.


Now, they do lack transporter tech, but that may be for religious/ethical/practical reasons. It's not a great combat maneuver, really, given that large ships tend to have large crews and the transport limit is pretty small. Given that thick armor makes good scans harder, it would be all but impractical in their ships. Plus, you are sort of killing yourself and hoping your clone does well. So there may be an ethical or religious consideration there.


But their ships are larger, pack more firepower, and have larger crews. Their crews are military, and do seem to have combat tactics down. Their engagements occur at longer distances than is typical in Trek (maybe a few dozen km or so in Trek vs a few hundred km as point blank in Star Wars). They use fighters as screens and for various other supporting roles. They clearly are a militaristic group, and are good at it.


Before anyone mentions Ewoks, let me point this out: The Ewoks joining, at all, was literal divine intervention. Imperial scouts certainly noted their xenophobia, and counted on the rebels being unable to effectively join with them, which would serve as a good secondary threat to taking out any incursion force. If Threepio hadn't happened to look just like a God to them, then it would have been game over for the Rebels. They'd not have been able to count on them in any fight.


But, even barring that, it's not fair to say "LOL stormtroopers get taken out by teddy bears! HAHAH DERP!" because, really, that's not exactly what happened. Outside of mechanical traps vs the AT-STs, they were of very limited direct effectiveness against the Stormtroopers. Their primary use was surprise against an already engaged foe. That's pretty huge, even against disciplined elite. It creates a new front to fight against, and it distracts them quite dramatically. Their attacks against the Stormtroopers show this--mostly, they drive them from cover, or ruin its effectiveness, and that really is a huge factor in any legitimate firefight.


Overall, the Empire has an extreme advantage, in sheer combat ability and experience. But, let's consider this thematically. Star Trek is about moral dilemmas that an exploring population faces. That is the core theme here. Star Wars? That's about massive conflict, across the galaxy. And since moral certainty is part of this, then ethical considerations don't appear. In a conflict mode, the Empire would probably win, all things equal.


This is in no way to say that the Trek isn't fun, or worthwhile, but I am saying that, in the end, a war would see the Federation probably losing.

Warfare, Dungeons and Dragons Style

Warfare is one part of the underlying fabric of the Dungeons and Dragons universe. It provides a political backdrop, where more than just the heroes smiting random creatures dwelling in random holes goes on. The world's face is changed by warfare, on occasion. So, fittingly, in 3.5 Wizards of the Coast published Heroes of Battle, which talked about this exclusively. Good book, overall.


However, it mentions two possible methods to examine warfare--either as "medieval" or "modern" inspired", with medieval being more traditional, with formations, set-pieces, and so forth where modern has all the fantastic elements being used much like we'd see on a modern battlefield--sorcerers leading squads and giants stomping and smashing their way in. Wizards teleport into garrisons, open their gates in daring commando raids. Sounds pretty sweet. The question is, however, is this "realistic" for D&D?


What I mean by "realistic" is, given the standard population and distribution, can a nation actually afford to, or build, such an army? Well, let's take a look at the basics and make a few assumptions here. I do not know, as I write this sentence, what will be concluded.


Before I do that, however, I'm going to make a guess: it would require a vastly different population distribution to even begin to pull off. To begin with, the idea of a "modern" inspired battlefield has fireballs exploding commonly, so formations are just a good way to get killed. But does that jibe with history? Not really. Historically, firepots and other catapulted weapons like that could inflict great devastation on men in the field. These weapons did exist, but they were somewhat inaccurate, so their use close in was limited. However, other factors such as the terrain and guarantee of hand-to-hand combat meant that the risk was worth taking--when someone is trying to stab you in the chest, it's nice to have only one direction to worry about that coming from. In fact, standing shoulder to shoulder with the other soldiers didn't really disappear until WWI (sort of) and really left for good in WWII. A big reason for this is that weapons that were capable of long-range, accurate, fire were not commonly available until then--and had not been really adapted to. You were most likely to inflict damage if a number of other men are standing shoulder to shoulder with you shooting in the same direction. Of course, that meant that your were a better target, but there's always tradeoffs. Now, the advent of rifling made standing shoulder to shoulder really deadly, as Pickett's Charge will attest, but until rifled weapons were widespread and commonplace, that's an unlikely scenario. Lee assumed that rifled weapons were not yet mass produced (they were, and that was why the charge failed). That's the key here--in order for these kinds of weapons to make an enormous impact, they must be commonplace enough that they can be used readily. A single man with a rifle can hit a few select targets, but a hundred together can devastate incoming forces with lesser arms. And that is the key--are magical means of sufficient quantity to be so fearsome as to wholly change the face of warfare? That would probably depend on the campaign setting--if wizards are quite common, and magic is within the grasp of the common man, as gunpowder weapons were as armored men disappeared from the field.


At first blush, barring a high-magic setting, this really seems not to be the case. A peasant makes 3 gold a month, and a scroll of even a simple spell is in the hundreds of gold, putting magic well beyond the financial means of 90% of the population. So it doesn't seem that it will be terribly common on the battlefield. But this may be a mistaken notion.


So, let's look at casting spells then. In order to cast fireball, a wizard needs to be 5th level, or a sorcerer needs to be 6th. I'm going to take a look at the number of wizards/sorcerers of that level or greater in a given settlement, and then I'm going to make a few assumptions. They're going to boil down to one conclusion: that this represents the total number of mages available for war at any given time. I do know that, of course, there will be at least 3-4 times as many in the world, but they simply are not available for drafting like this outside of the most dire of circumstances. Unless they owe duty to a lord, getting them to show up would be quite expensive, to say the least, and not necessarily likely. Drafting any skilled tradesman would be hard, as the guilds would not stand for this, and it's hard to imagine that wizards guilds would be much different. However, certain wizards would certainly owe the state their training, and so could be required to show up under certain circumstances. Sorcerers are more independent, so are less likely to be forced into service, but many might show up for whatever other reasons. I'd imagine similar for wizards. Being academic, I doubt that most wizards would have plenty of battle spells handy--most don't spend their time fighting in dungeons and otherwise risking their necks. I'd also imagine a cap to the power of a wizard showing up. I doubt that a level 20 wizard would show up to any battle, period, unless his tower was threatened, and that army would be foolish to even attempt such things. But, overall, I think that the overall numbers of wizards/sorcerers should closely resemble the city population.


So, with that determination, let's take a look at what we get:


From a large town, we have a 75% chance of a wizard being available to cast a 3rd level spell, and a 50% chance of a sorcerer. Small city, we have 2 guaranteed of both, with a 7/16 chance of one additional, which includes a 1/16 chance of two additional for wizards, and no additional for sorcerers. A large city will have 5-6 of both,and a metropolis will have 6 of each. That's not very many. Given the relative scarcity of any settlement classified as a city, even if this is just 10% of the total number of wizards/sorcerers of that tier available, there simple aren't more than a few dozen, at most, that could be called up for a battle. Even if we allow for half of all casters to be called, it's still only five or six dozen across the whole kingdom.


Then we have to consider the limitations of casting. Across all those 60 (again, tops) casters, we have maybe 140 castings of mass-combat worthy spells (I discount low-tier spells with single targets because against 10,000 or more on the field, these aren't much use). And that's all the spells available. These spells represent various choices on the part of the wizard in preparation, and on the sorcerer in initial selection. They have a vested interest in not dying, as does the army, so I doubt that they'd use all of them on offensive load, or even friendly buffing. Of that, I expect maybe half to be considered "ready" for use at any moment. So, again, tops 70 castings. Then consider the other casters on the opposing side. They'll have similar numbers, and probably will be looking to counterspell some of the more dangerous and obvious spells--only a great fool would not order some wizards to ready an action to counter incoming spells. So this further drops the usefulness.


Again, this is across all forces. Not just for battle A or whatever--every group of various size will have mages with it, depending on the size of the force. Maybe, at most, a dozen mages will accompany any contingent, and that is being very generous.--So, of all that, expect 3-12 castings of a level 4 or higher spell, total, available, for any battle. That's just not impressive.


One could counter with "well, they have wands and scrolls", but let's look at the cost of such consumables. A level 1 wand, with 50 charges, costs 750 gold, and a level 5 scroll of fireball (minimum for creation) is 375. That's a lot of money, enough to equip a number of lesser warriors or a knight in full armor. And, don't forget that these are expended. After the battle, there's less of any of those left. That armor? Yeah, that's still there, and can be recovered and refitted for a new recruit with relatively little expense for lighter armors. Heavier armors will certainly be the personal property of the owner, and go on to his heirs--and refitting them will be simpler than others.


Also consider what the loss of these means. Loss of a scroll to the enemy is disastrous--they now have another potent asset that can destroy large numbers of your forces. Loss of the armor? Well, some men are better equipped, but likely not enough to tilt the battle. Remember, the posit here is that wizards and sorcerers would tilt the battle with their power moreso than a handful of warriors (and I will not disagree with this premise, it is quite accurate as far as it goes), so granting that to the enemy is major. These supplies are easy to carry and conceal, which makes them a prime target for theft and vandalism. That means more resources to guard and secure them, which means their combat expense is much higher.


Then we have placement. They'd have to be scattered, otherwise enemy mages will simply engage in ferocious counter-battery fire, and that will be the end of the mage cadre. Wizards and sorcerers are not the hardiest of folk, and a handful of fireballs at them would effectively end them.


All told, while these would be potentially devastating, it's just hard to see them being the decisive factor outside of extraordinary circumstances--such as exceptionally powerful mages show up unexpectedly, or enemy mages are not present, etc.


Heroes of Battle does mention the cost of equipment (like I did above), and said that arming a 1st level sorcerer with a wand of magic missile and a fireball scroll would be no more expensive than a knight, and potentially much more devastating. Well, let's look at that. A knight with full-plate armor will be of at least 3rd or 4th level, and therefore have 20-50 hp. That sorcerer? Maybe 8 or 9, and that's a stretch. His AC? Maybe 14, again, tops. The knight? 20, at least. So who would you trust with expensive and dangerous assets like that? The green sorcerer, or the trusted veteran? I wouldn't give the sorcerers such weapons, at least not at that level. That's just ludicrous.


Now, with all that said and done, what do I think about modern-inspired warfare? Well, if you want it, go ahead. But you'll need large, industrial, populations to support is, just like you need large, industrial, populations to support a modern army with artillery support. It can fit in with your world as much as you want it to. Just make sure that the background fits.

Why Indiana Jones was a Terrible Hero, Part One

I might catch a ton of flak for this one, but oh well.


First of all, I don't mean that the first three movies weren't fun and entertaining, or that Indy isn't a bad-ass.  That's not the point at all.  What I mean, however, is that Indiana Jones only made things worse in Raiders of the Lost Ark and Last Crusade.  That's right, Indiana Jones nearly handed over the free world to the Nazis on a silver platter, and really the only thing that kept them from using divine artifacts was direct divine intervention.  God effectively covered Indy's ass, and let's be honest, if He is going to smite the living hell out of those who would abuse Jewish and Christian relics, I don't think that Indy needed to get involved.


Let's take a look at the Raiders of the Lost Ark.   First, the opening reveals that Indiana Jones is, basically, a thief who steals priceless artifacts from under the noses of people who actively protect them for money.  So we're pretty shaky on his moral grounding here, and movies, like all stories told to children or young adults (the groups that this movie was horrifyingly aimed at, considering later actions) do serve to send moral lessons.  They convey the idea of what is good and right.  We know who to root for, and how to feel about them.  Indy is the hero, and he's a big damn hero.  Who steals from natives. 




Then, he gets a commission from the US government to retrieve the Ark of the Covenant because the Nazis, who in 1936 aren't really on the threat radar of anyone to this level, were trying to get it.  So first, he goes to an old flame in the ass-end of the world.  This "old flame" is a much younger woman who he hasn't seen in some time.  As in "she was certainly under-age when he boinked her" some time ago.  And, given the looks of the female students in his classes (which he apparently can just randomly abandon at whim, with no negative consequence whatsoever, another great example of morality), he may have, um, plundered their tombs as well.  You know, young, impressionable, girls smitten with a rugged adventurer.  And he's their teacher.  Or father's friend/colleague.  This dude's MO is pretty shady, let's be honest.  And, the first thing that his old flame reminds him of?  That he just walked out on her after he got what he wanted and decided to move on to something else.  Just like his classes!  Thus far, we have thief, ephobophile, and highly unreliable character.


That's a weird point in the internal consistency--this guy bails pretty quickly on commitments.  Why did the US government hire him?  He's supposed to be good, but his record is pretty much losing to Belloq.  Why didn't they hire Belloq?  Oh, the Nazis did already.  So they hired the guy that gets everything he finds stolen by Belloq.  Swell move there, OSS.


So, he goes to her, gets her to give him the only thing he really wanted (the amulet, not her post-pubescent womanhood) on the condition that she tags along.  In the process, Belloq basically follows him to this artifact to take it from him.  Then he goes and finds out that Belloq somehow has a copy of the amulet, and is digging in the wrong spot.  In other words, if he left right then it would be years and years before Belloq even figured out that he was digging in the wrong spot, if the Nazis even bothered to fund it that long.  Already the officers in charge were complaining about how long it was taking and the lack of results.  Do you think that they'd keep funding that dig after a few months more of bupkiss from the supposedly accurate amulet?  Of course not, they'd have assumed they had a bad lead, or whatever.  So if he did nothing at this point, the Nazis never would have had the Ark.


But he goes and digs up the Ark.  Like 100 meters from a Nazi encampment.  If the goal is to keep them from getting this thing, maybe that's not a great idea.  But I suppose his paycheck is pretty important too.  Then, in the twist no one could possibly have foreseen except everyone but Indy and Sallah, Belloq steals the Ark from him right after he gets it.  Does this guy not learn from his mistakes, or what?


So now, he has to get it back.  And he does, by killing a bunch of German soldiers.  And, since 9 years later, everyone finds out that these guys were going to start killing Jews in a bit, he is sort of vindicated by history.  But, basically, he kills a bunch of security guards for doing their jobs. 


Then, he puts the Ark on a ship.  And, rather than deep-sixing the Ark so that way the Nazis can never, never, never get it, ever, he just keeps it on board.  And then, the Nazis take it from him.  Again.  So, he stows away on a submarine, somehow, for a few days or weeks.  How he manages this, I will never know, since those things have no unused space whatsoever, but I guess he's just good at the first part of stealing part of being a thief.


Then, he's about to blow up the Ark.  And he refrains.  Not because the Nazis will kill Marion, not because his shot will certainly do it anyhow, not because destroying God's Covenant might piss him off, but because he can't destroy history.  Even though he doesn't want the Nazis to use it to smite the whole world. 


But, in the end, it doesn't matter.  The Nazis open it, and all die horribly.  And, given that this movie is sort of targeted at kids and young adults, this is pretty disturbing.  But this does render his every action moot.  If he had stayed at the University, banging his students, nothing would have changed.  The Nazis either never would have found the Ark, thus not being a threat, or would have brought it to Hitler and his senior staff, and opened it in front of him in 1936.  This would have been awesome for the Jews, because basically, the Nazi party would have imploded, since everyone who was capable and in a leadership position would have been destroyed.  That's a good thing.  Indiana Jones succeeded at preventing God from smiting Hitler in 1936. 

On the Economy of Dragons, Fermi Problem style.

This is a post regarding Dungeons and Dragons, particularly 3.0/3.5/3.75, as I am most familiar with the magic involved, but it applies to previous editions somewhat.




Dragons in D&D have the overwhelming need to gather up large amounts of coinage over their lengthy lifespans, to the tun of hundreds of thousands of gold pieces.  These vast sums sit, inert, in the floors of their lairs (or somewhere similar), waiting for adventurers to slay the dragons and steal the gold for themselves.  Often this is justified via institutionalized racism (i.e. you know whether or not a dragon is good or bad solely on the color of its skin), but it needn't be.  However, the real importance of this is to be explained shortly.


Dragons, as they enter their twilight, decide that they aren't going to leave their horde behind for some schmuck to just take.  Dragons, in their nigh-infinite greed, seek to literally take it with them.  They consume their entire hoard, leaving behind nothing at all, before they head off to a graveyard to die, or transform themselves into a portion of the landscape, or something similar.  The point is that an aging wyrm simply destroys his hoard before dying.




Also of import is that the dragons value their hoards, and those of others, by the physical size of the pile of coins.  Larger piles equates to larger prestige, to the point where some dragons use vast amounts of copper coins under their more valuable gold and silver coins to enhance the size and therefore prestige of their hoard.  A wyrm's hoard can easily exceed 300,000 gold pieces in value, which is no trivial sum.  Further consider that magical items count for half of their nominal value for assigning comparative wealth to a hoard.  This means, primarily, that a dragon will certainly do his utmost to have his stash mostly in coins--or nearly so as is practical, not just because they love piles of cash (literally) but because of the prestige it brings.


So let's make some assumptions here.  Let's say that a dragon, in general, prefers to keep his hoard as 15% coins, period.  For a great wyrm, let's average their net value to 300,000 GP (though this may be off, I am just making some sort of educated guess here).  This means, that on average, a dragon holds approximately 50,000 in coins at any time (I rounded somewhat there, but none of these values are hard and exact, so please excuse some minor discrepancies).  We'll say that 80% of that is in gold, the rest in silver, copper, and platinum in some mix or another.  Given that a coin weighs canonically 1/50th of a pound, we can say that there is 40,000/50 pounds of gold in coinage, or 800 pounds of gold coins.  That is a rather hefty sum, but we're not finished here.  We can also guess that, in order to maintain sufficient breeding populations and the like, and that the population will generally reach equilibrium barring humans deciding to exterminate dragons (which is unlikely, since dragons would certainly take exception to his pastime, and their wrath is terrible indeed).  So, for the sake of argument, this means that every decade or two, a great wyrm enters twilight and decides to end it.  We're considering across all types, but the chromatic ones die younger than the metallic (and they said only the good die young).  So, over a century, say 5-7 die like this, and are replaced by others aging.  It's lonely at the top, but it rather has to be.


This means that every century, 4 tons of gold are excised, outright, from the world.  Maybe more (a lot more) maybe less (but not terribly much.)  Over the course of a dragon's typical lifespan (1200 years or so), this means that 50 tons of the stuff is vanished from the world.


Now, if we take Faerûn as an example, we have 20,000+ years or so of recorded history.  It is not hard to assume, then, that dragons were around for most of this, and were mostly in a relatively stable population such as described above, or were averaged out to such.


This means then, over Faerûn's history, 1,000 tons of gold has been removed, permanently, from the economies of the world.


That seems like a lot, right?  I mean, this is a crude estimate, but is probably a lowish estimate.  There could easily be more dragons for this time frame, or they could hold more gold, etc


The US currently holds more than four times that amount in it's treasuries, as bullion.  That, in turn, is 2.5% of Earth's supply, that has ever been mined from the Earth.


Let's examine another angle.  There are twelve age categories of dragon, from Great Wyrm down to hatchling.  Now, let's assume that each category has one fifth of the previous category of members, to compensate for them dying to each others' and adventurer's hands.  And, going with the above assumption of death rates, we have ~20 worldwide dragons of great wyrm age or so at any given time, two of each type.


That means there are 100 wyrm, 500 ancient, 2,500 very old, 12,500 old, 62,500 mature adult, 312,500 adult, 1,662,500 young adult, 8 million juvenile, 40 million  young...this puts a population of dragons in the billions, minimum.


So I must revise downward my previous estimate of 5 per category beneath.  3?  That puts the total at 3^12 wyrmlings, and that is 1.5 million so we aren't much better off. 2?  That puts the total number of dragons at 2^13-1, or just over 8,000, per variety.  That seems much more reasonable.  That still is a fairly tiny population, but that does mean ~ 80,000 dragons overall.  So, we're in a good ballpark.  That revises downward the estimate of gold removed by dragons through death down somewhat, by a factor of 5 or so.  Hey, we're getting somewhere, right?


Now, let's look at how much gold they're hoarding.  300,000 on average for the top.  And, I'm going to guess 2/3 of that for each lower category.  That's 300,000 * (2/3)^11, or ~3500 for the wyrmling hoard.  Looking at the table in the Draconomicon, I get that a CR 3 hoard is 2700 GP and a CR 4 is 3600 GP.  So, I'm pretty close, I think to this estimation.  Close enough for the math at hand.


We can write an algorithm for each successive generation's wealth hoarded in terms of the previous, and this is actually fairly simple.  Twice as many, each holding 2/3 of the previous generation's wealth, so we have 4/3 of the total, average, wealth, held by each successive generation.  The wyrms hold 400,000 per dragon race, ancient ~530,000 and so on.  The jth term equals 4/3 of j-1, and we say that j(1)=300,000.  We can factor out the 300,000, so we get a nice steady sum:


4/3+(4/3)^2+(4/3)^3+...(4/3)^11=122.27.  A nice little sum that Wolfram Alpha did for me.  Multiply by 300,000, and then by 10 (for each major species of dragon), and we have...366,831,501 held by dragonkind collectively.


Let's put that number in comparison.  90% of the world is peasants, of the 1st level variety.  And, sticking with Faerû, the global population is approximately 45 million, at least by summing the populations of the nations.  Now, 90% of these people live on 2GP a month, and even the next 9% don't live substantially more lavishly (say, up to maybe 100 GP/month for the highest end of them, and twice that for the top tier).  Let's just look at the poor end.


.9*45000000*2*12=972,000,000 coins passing through their filthy hands annually.


That's nearly three times the money held static by the dragons.  Now, in the US, the bottom 80% hold or consume ~7% of the financial wealth of the nation.  Let's keep that number, even though really, it should be much lower.  That means that the rest of the mortal races have ~ 12 billion gold coins, or so, in their collective hands.


That is 40 times what the dragons own.


So, how does this compare with earth?  Well, Wikipedia's page on the US Bullion Depository states that there is ~168000 tons of gold on Earth or so.  And, let's guess that of that coinage listed up there, a third actually exists in coin (the rest passing from person to person, constantly, which gives a velocity of money of 3, so this is pretty high, actually considering that the US had a velocity of 1.6 or so in the 50s), and half of that is gold.  So 2 billion gold coins, at 50 to the pound gives us 20,000 tons of gold in circulation, total.  If we revise it to 1 or so, then we still have only 60,000 tons of gold coins.  Given their limited population and extraction capabilities, 60k tons sounds about right.  Dragons, again, have 2.5% of that.


So what does this mean?  Realistically, killing off the entire race of dragons and spending their gold won't destabilize the global economy at all.  So if your DM tells you that you are going to destabilize a national, or even largish city's, economy by spending all that cash, you can tell him that he's dead damn wrong, and you have the math to back it up.

Regarding the Accuracy of Stormtroopers

Preface:  I originally posted this on Reddit, and I thought this would make a suitable first post for this blog.


Stormtrooper accuracy is something of a joke on the internet. They never seem to hit any important person when they shoot at them, missing constantly. There's a Cracked article on it, for god's sake. Everyone has heard the joke.


It's a complete and total lie, and it ignores the relevant details of the events.


To prove that they are, in fact, crack shots, watch the opening sequence in A New Hope. Here we have a number of stormtroopers charging into a narrow breach into heavy fire, yet they are able to gun down more rebel soldiers in cover than they take in casualties! This is not amateur night here--these are stone cold killers, destroying their foes mercilessly. They are so effective that the defenders fall back almost immediately.


Then, the next time their accuracy is mentioned, it is in the examination of the corpses of a bunch of child-sized aliens. That's right, they were able to kill a number of small targets with expert precision. Now, it was off-screen, but you cannot get that kind of consistency and precision randomly. It beggars the imagination to think that their aim is terrible.


So why can they never hit Luke and Leia in the Death Star? They were ordered not to. The escape was allowed--recall that Tarkin and Vader discussed exactly that the minute the Falcon left. They needed the princess to go to the hidden fortress so they could track them there. She already had refused to give them accurate coordinates, even as her homeworld was destroyed before her eyes. She would never break, never talk. So she had to escape.


Now, killing the one guy escorting her to the ship, or any of the vital crew to the small craft, would be counter-productive to that enterprise. But, they have to make it look good. The escape triggered an alarm. Even if it hadn't (highly unlikely--they command was far too competent at their jobs to let anything slip through), Vader knew that an escape was on--he felt the presence of Obi-wan. Vader is quite competent, and so would have certainly alerted command to this. After all, he did have a discussion about it with Tarkin before seeking out Obi-wan.


The only reasonable conclusion then is that the stormtroopers, fanatically loyal and dedicated to the cause, were ordered to attack but miss when doggedly pursuing these escaping prisoners. And, miss by a small enough margin that it looks good. Recall the bridge scene--blaster fire was erupting around the edges of the doorframe that they were standing on--inches from serious harm. Yet, despite that large volume of fire, in single-shot mode, no hits were scored. And well it was that none did! Had a single shot hit the princess, it could have killed her. It could have wounded her severely enough that escaping with her would have been implausible, and they would have instantly been alerted to the fact that it was a set-up.  Even if it had been non-lethal in nature, it easily could have crippled her, making escaping with her impossible.


It nearly was--Leia thought it too easy. However, any hit would have made it obvious if they did escape, since even if it wasn't lethal, it would have dramatically slowed the party down, destroying any illusion.


As such, from A New Hope, all evidence is that they are, in fact, excellent shots and quite loyal, willing to die for the cause without a moment's hesitation on the order of Lord Vader.


One could argue, terribly, that it is simply the quality of the weapon that is a problem. That is patently absurd. The Empire has the resources to build a space station the size of a small moon without being noticed. It wasn't public knowledge that the Death Star was built--it came from nowhere and blew up a planet. No one believed that possible until it happened, which was the point.


This means that they have a logistical train that routinely delivers massive amounts of material across the galaxy, such that it draws little real attention. This cannot be cheap--the cost of transport alone would be immense. But they are somehow buying weapons on the cheap? That makes no sense. They'd make sure that these things were very accurate, and consistent, before the purchase of every lot. Their quartermaster corps would see to that, and they must be sufficiently competent to do so because they were able to build a moon in secret. That's no mean task. So their weapons must be accurate.


Ignoring that, it still remains the fact that recently looted weapons, from the very racks that these stormtroopers drew from, were quite accurate in the hands of other people who just picked them up and had not drilled extensively on them. These must be accurate weapons indeed, or the Hand of God Himself intervenes upon every shot ensuring the safety of the heroes and the death of the villains.  And, if these weapons were wildly inaccurate, fired by morons barely capable of shooting, the sheer volume of fire directed at the escapees should have felled one of them. 


An alternate explanation proffered by a Redditor was that the Force was strong in Luke and Leia (and Han and Chewie as well), and that twisted fate to protect them so their destinies could be lived out.  That is also an acceptable response, and certainly would feed into this as well.  But, for the purposes of this article, I am not putting this as a primary factor.  Again, the plan of Tarkin and Vader was to see the princess escape, so the war could be won.


Now, consider Empire Strikes Back. We see very little of the battle of Hoth, but we do see them rapidly assembling a heavy weapon even as they take automatic weapon fire, without a moment's hesitation. That requires immense discipline and skill. This goes, again, to demonstrating their intense competency. You do not acquire such coolness under fire without intense and rigorous training. Are we then to believe that they train to just set weapons up, but not fire them accurately? Please.


So, on Cloud City, we again see a large contingent of stormtroopers not hitting the escaping princess and retinue. Again, this is clearly by design. Darth Vader had the hyperdrive disabled--he asked his subordinates this on his command ship. They weren't going anywhere.


However, he needed a back-up plan. They weren't going to leave without Luke, and he wanted his son captured. So he again ordered them to be allowed to escape, but to make it look good. They weren't going anywhere anyhow--they'd just be going straight into the shuttle bay of a Star Destroyer, unable to jump to hyperspace. He knew that Luke had been developing his skills, so it is not unreasonable to assume that he could send a message via the force to effect an extraction. Luke could flee, and Luke is certainly clever and skilled enough to find a way past guards--or at least, past enough that he could get out. Then, the Falcon would "rescue" him, leave atmosphere, and promptly be captured, leaving Luke firmly in the hands of Vader.


And why the Falcon?  What other ship would Luke trust, implicitly?  This is a back-up plan, a contingency.  


Lobot being able to lead a security detail anywhere? There were enough storm troopers to garrison the city, so why allow local cops to do anything?  Their loyalty hasn't been established, or really built up at all.  They can't be trusted. That's either a gross oversight, one that is unbelievable given that Vader himself ordered the Falcon to be disabled, or deliberate. He knew Calrissian would attempt to break the Princess and Chewie out--why do you think he kept altering the deal, pushing it well beyond the boundaries that Lando would accept? Did he think that Lando would simply go along with this, without resisting? Surely not.  Remember, the goal was them to get on the Falcon, because it wasn't going anywhere no matter what. 


It has been pointed out to me, on Reddit, that Vader could have sent a cloudcar to pick Luke up.  However, as a contingency, this leaves much desired.  First of all, the pilot would be susceptible  to Jedi mind tricks, which Vader suspected Luke was capable of--hence the capture mission.  Even if he did get picked up, Vader assumed that Luke was capable of sending messages via Force-telepathy.  A cloudcar, piloted by mooks, was not reliable enough.


This leaves the final movie, Return of the Jedi. Again, we see nothing but extreme competency and accuracy on the part of the stormtroopers in battle.


During the battle, we never see the results of their pot-shots against rebels or Ewoks, but we do see them laying down a consistent volley of fire, with disciplined shots, and constant ducking back to cover. One could argue this would mean inaccurate shots, but given the first movie's opening sequence, that is hard to believe. They were using the sights to aim, instead of firing from the hip, during this fight and on the ship combat, they did not bother aiming carefully. It's hard to believe they lose any accuracy at all when using a more carefully aimed approach.


So what direct evidence do we have of their shooting? When Han and Leia are attempting to break into the bunker, two successive pot-shots hit a child-sized object behind partial cover, instant disabling the droid, and inflicting a potentially serious wound on Leia. Again, these were shots taken under hasty aim against targets behind cover, while shots were going towards them. This is not an easy thing--ask an infantryman if you disbelieve me.


There are lingering questions about the effectiveness of their armor.  It does seem that a shot from a blaster takes them down, no problem.  However, this doesn't necessarily mean killed--after all, the armor certainly absorbs impact and energy is transferred to it in any shot, which necessarily lessens the severity of any penetrating shot.  In order to be effective versus armored foes, weapons would have to have an increased energy output if they are supposed to be lethal.  That means fewer shots per weapon, which is vital in a firefight. 


Also, the attacks by Ewoks call into question the strength of the armor.  However, it should be noted that we see no kills inflicted by Ewoks, except in special circumstances.  When they directly attacked stormtroopers, with the element of surprise, they were able to drive the Imperials back, or interrupt their firing, or otherwise impede their fighting capabilities.  In a battle, these hindrances can weigh heavily against a force.  The Ewoks didn't have to defeat the Stormtroopers, they only had to occupy them while the Rebel soldiers mopped them up.






The evidence is clear--Stormtroopers are quite accurate and effective soldiers, with top of the line equipment. Claiming otherwise is slander.