Sunday, May 27, 2007

Determination

A subject that regularly arises to bedevil space warfare discussion at sfconsim-l is the Lanchester equations. These are a set of differential equations, worked out appropriately enough in the middle of World War One, that quantify a basic military truth: Fortune favors the big battalions.

In fact she favors the big battalions even more than we think. In the movie the bad guys always attack the hero one at a time; even samurai heroes get to finish off six enemy ninja at once before the next six step up to fill a hole. In a real fight, when one battleship has sunk its opponent it simply shifts its fire to the next enemy ship; if the battle is uneven to start with it quickly gets more and more uneven.

The rallying cry at the Battle of Maldon in 991,

Our hearts must grow resolute, our courage more valiant,
our spirits must be greater, though our strength grows less


Is all bleakly to the point in the face of the Lanchester equations: You can fight bravely, but you are going down anyway.

All of which leads, via comments by Doug on my last post, to determinism in history and fiction. Do individuals and their actions count for much, or do the big battalions of historical forces carry the day? In fiction the plucky heroes may not always win but they always matter.

Even in Romance, however, Lanchester has his say, by setting the limits of the plausible. Our hero swordsman may be able to vanquish half a dozen foes because his blade is swift and his heart pure, but we don't push his luck and have two dozen guardsmen descend on him all at once. Or if we do, we let discretion be the better part of valor, and the hero decamps quickly across the rooftops.

Otherwise, the reader begins to suspect that the author is tipping the balance. Of course the reader knows that the author is tipping the balance ... but if the story can't make them ignore it, then the story is in trouble.

9 comments:

Bernita said...

I always like incidents of battlefield tactics where a small flank attack at the right time turns the tide.
Largely a case of exceptions proving the rule, of course.
G.G.Kay is good at this - particularly in A Song for Arbonne.

Anita said...

Good morning.

There are real world situations the Gentle Author may use to get his/her hero out of the superior numbers crack.

Motivation or the fight/flee choice: Nice bit in the HBO Rome series. Scene: Battle of Pharsalus. Caesar and Pompey are about to decide the course of history. Jules is in deep do-do. As his slave/confidant points out, "You're out numbered, infantry 3 to 1, cavalry 5 to 1."
Jules answers, "Yes. We must win or die. Pompey's soldiers have other options." The battle was decided by one cohort of reserves standing its ground against Pompey's cavalry. The Gentle Author can give the bad guys the flee option.

The morale factor, subset, home court advantage: In real world and Romance people will put up a hellva battle against impossible odds (and sometimes win) when they're fighting for something/someone they believe in.
Beloved home is always a good one. Saving your One True Love always works. An ideal is another, re Dune.

"You can do everything right and still lose," Jean-Luc Picard. Subset, Stupidity equation. Battles and wars aren't chess games; they're crap shoots -- in a mine field. It doesn't take much to tip the balance - the horseshoe nail comes to mind. Ney's cavalry troops forgetting to spike the Allies' cannon. On the other hand, the bold tactical at exactly the right time, thank you Colonel Chamberlain. Or the right decision at the wrong time, too bad Admiral Nagumo. The Stupid equation was best summed by a WWII general, "You win wars by making one less mistake than the enemy." Re Hornblower vs. el Supremo aka Don Julian Alvorado.

In short, while superior numbers are important and often critical, Gentle Author can realistically save the hero's hindquarters without Gentle Reader thinking, "Oh, gimme a break."

Carla said...

Well, the laws of physics and physiology had better be respected - a cannonball will only do so much damage, a man can only fight for so long before exhausted, chop somebody's head off and they will die, and so on. An author who diverges too far from those is likely to give me problems suspending disbelief. Sci-fi can set some of its own rules by inventing new technology, but they have to be consistent.

Within those, though, there's scope for the individual to matter. Size matters, but so does what you do with it, and sheer blind luck plays a (considerable) part. It's like statistics, I think. On the average, you get the average outcome (the bigger army wins), but there's a hell of a wide range out on the tails of the distribution.

Anonymous said...

One unfortunate thing about space warfare is that it's virtually a perfect information environment. Winchell Chung's Atomic Rocket page discusses this in depth -- basically in space everyone can see you, see where you're going, and knows when you'll get there. They also know how much mass you're bringing along, which gives them a very good idea of your capabilities.

In other words, it's _much_ more like a chess game or a wargame than any warfare in human history.

Which suggests that in space, the big battalions will often win without firing a shot.

Cambias

Rick said...

There are sort of two issues here, space warfare and the broader question of Against All Odds.

Cambias sums up the generally accepted view at sfconsim-l, where people have thought about this a lot. Space is big, but it is dark, so bright things - meaning anything much above absolute zero - show up all too easily. No way to conceal your cavalry behind a ridge or back up in the woods.

That does still leave the other factors Anita mentions - such as who is willing to take the grim chance, or sees no choice, versus an enemy who may not be quite so committed. And even in chess (or especially in chess), bad strategy loses.

The odds do set the framework, though - if the heroes win against impossible odds to often, we sense the authorial hand tipping the scales, instead of the story justifying the outcome on its own terms.

Doug said...

The thing about these equations is that they are so abstract as to be meaningless. More troops better than fewer troops, well in general any Neolithic chieftain could tell you that. It helps to have more guys backing you up, usually. Of course if you're in a logistics crunch or your transport capacity is limited than sometimes that isn't the case. Their have been historical cases where large armies were beaten by smaller ones that were better supplied or more mobile.

There are of course questions of troop quality and equipment, though generally richer states are the ones who can afford this. The success of modern NATO militaries, or of the RMN in David Weber's Honor Harrington series are both examples of this. In some ways this is just another form of "big battalions" with numbers replaced by cash.

At the core though the study of tactics and strategy revolves around how to beat these numbers. Terrain, maneuver, morale...there are so many variables that make up a battlefield setting. Exploitation of these variables can make a lot of difference in both battles and campaigns.

Of course the way terrain for example affects the battlefield is very dependant on technology. Hastings hill was a good position but nowadays being on a hilltop makes you visible and easy to pick off. Sun Tzu advised against dividing your forces in the face of the enemy, but both the Mongols and the third Reich built offensive strategies based on doing just that.

In space we have no clue what
the affect of fighting in certain ways in certain places will be. How could we do anything more than guess about where or how we ill fight

My problem is this assumption that there will be essentially no tactics, that it will all be up to the computers or that the ability to spot a heat signature means there is no deception. A heat signature tells you where a ship is, where it is going, and it's mass. That's all you get, no information on: Weaponry, intent or allegiance, shielding, propellant supply, crew morale, crew complement, cargo, or larger strategic plan. That's a lot of room for deception, when false transponders and hull camouflage get factored in. Tactics and strategy will definitely change, but I think they will endure; which makes the Lachester equations on one hand a statement of the obvious, and on the other a challenge for the heroic commander of those brave Belter rebels. Or the embattled Imperial garrison commander trying to maintain some semblance of order and sanity in the midst of a hostile rebellion. You know, one or the other.

In short: As a general rule more troops are better than fewer, but those who expect that to be enough tend to get spanked. It's usually better to have more men backing you, and always better to have more money backing you; but commanders who ignore other variables because of their superiority in these regards....wel I hear Saint Helena was lovely.

Doug said...

Sorry if this is a bit Off Topic.

Actually, the thing that really burns me about that whole no-stealth-in-space thing is that it pretty much ruins things for outlaws. Everybody in Space based SF tends to have some band of Pirates out there raiding shipping and giving the military an excuse to keep all their cool ships active in peacetime. But in a universe with no FTL, and where a ship can be spotted across the system, remotely spotting suspected pirates is just too easy. It's just too unlikely for aship to just come close to another by chance, and sensor technology makes it easy to track the pirates back to their hidden base.

Of course this doesn't limit the possibility of crime internal to ships and habitats. The bowels of a space station may make an excellent place for rebels or brigands to hide from the authorities. And the possibility of smuggling men aboard a merchant ship to overcome the crew while they are in flight has some potential. But daring rogues or villainous corsairs in armed spacecraft raiding the trade lanes seem to have lost out.

If the Alliance warship in the original pilot of Firefly had been able to just watch them and track them to Persephone that would have been the end of it.

FTL opens up the possibilities again, since some FTL systems do not include FTL sensors. In a setting like this a group of outlaws could place their base in an uninhabited system where they could not be observed going to and from their base unless a warship was in the system. The base itself might be hidden if it had enough rock mass to radiate heat into and no exhaust.

Rick said...

Doug - I'm going to make a front page post on most of your comments, but one smaller specific note:

In an FTL setting, a pirate/rebel/whatever base off somewhere in an uninhabited system off might hardly need to stealth itself. When you move from the interplanetary scale to the interstellar scale, everything changes - now you're examining grains of sand, looking for one with signs of suspicious activity.

Canageek said...

The big thing you miss here is force-multipliers. Suppose I only have 50 men vs. your 100, but you have muzzle-loading rifles while I have breech-loading. All of a sudden my troops are firing two shots to each of your one, and things look a lot less unbalanced.

Or the side that can use the landscape to its advantage: ambushing a larger force by attacking it from the top of a canyon, or forcing the attacking force to doso in a canyon, where they can only bring a small fraction of their troops to bear at a time.

Really, the math may favour the larger force, but history has shown relying on it is a really bad idea. Just look at pretty much any battle on the eastern front of WWII during 1941 or early 1942.

Also, I've heard a historical rule that an attacking force needs 3 times the number of defenders, if the defenders are fortified and have had time to dig in.

Going to space battle having no features you can take advantage of; it depends on the technology. If your ships run on solar sails or Bussard Ramjets for advantage, the side approaching from the sun has a huge advantage, as current calculations show it would be very difficult to manuver towards the sun using these technologies.

Therefore, even if you have a second engine, you have to burn reaction mass to compensate for what your foe can do with their main engine, leaving them with an advantage during the battle.

Also, I'm curious about how long it would take to scan the sky for a heat signature. When I've done IR spectroscopy in my lab, it is fast, but not still takes about 30 seconds to gather enough scans for a good spectrum, and that is pointed at a fixed sample that is sitting in a black box, not pointed out at the night sky. Now, I'm gathering a full vibrational spectrum, whereas you just want intensity, but I wouldn't overestimate how long it takes to gather data.