Heh, and in the hour and a half I took to write this post, I got ninja'd no less than five times. Oh well, I wrote this and darnit I'll post it!
HB of CJ wrote:...The Sollies will overwhelm the Grant Alliance. Might take 5 years. Yikes!
So ... the war is over and now what? The Grand Alliance will look like Japan after World War Two. Not one brick on top of another. The Grand Alliance is going to lose this one so bad. More Yikes!
While it would take longer than 5 years just due to the requirements of weapons research time, shipyard construction time, and warship construction time, in the long run you are, as has been noted several times by characters in the story, correct. In a stand-up fight the GA is doomed, no matter how many solly fleets or shipyards they destroy or solly planets they occupy. Eventually the sollies will acquire weapons tech close enough to the GA's for their quantity advantage to make up the remaining quality gap, and at that point the GA is screwed.
However, I think you're forgetting that the characters in-universe *know that*, and they're not stupid. They aren't going to blindly continue down this path that they *know* is doomed. That's the *entire point* of the Harrington plan - if the League would inevitably run over the GA in a decade's time, then the way to win is to ensure that the league *no longer exists* by the time that rolls around. And they have the ability to do that.
And that's the critical difference between your WWII analogy and the situation in the story. In WWII the Japanese *were* indeed ultimately screwed, because they had no realistic way to prevent the US from bringing its massive industrial and resource advantage to bear. As you quite reasonably point out, there's jack all you can do when your enemy is outproducing you several dozen times over and has a quality even within shouting distance of yours (and the US quality was arguably *better* than the Japanese in most areas after the war's early stages, to boot). However, the sollies
are not the US. They have the same sort of huge potential resource and industrial superiority, but the situations are massively different in all other areas.
For starters, the US and Japan started the war with broadly similar warfighting capabilities. The Japanese had advantages in several important areas, for sure, and they leveraged those advantages to very good effect during the war's early stages, but the US was still within shouting distance even in those areas and was *ahead* in others. The same is most emphatically *not* the case with the sollies and the GA! The Japanese started the war with 12 fleet/light carriers, and produced another 7 during the war. The US, meanwhile, started with 8 fleet/light carriers and produced 26 more during the war. So, if you count total numbers it was 19 for the Japanese and 32 for the US (1.7 to 1), or if you count wartime production it was 7 and 26 (3.7 to 1). Either way, the US quality was close enough to the Japanese that their numbers advantage was decisive (even ignoring that the American carriers were arguably better by the end of the war). Meanwhile, the GA commanders would *laugh* at 4:1 odds - heck, in terms of weight of metal the battle of Spindle saw 5.8 megatons of Sag-Cs blow *156* megatons of Scientists (27:1!) to smithereens in a single salvo! The Americans could at least stay within shouting distance of the Japanese until their production advantage could equalize the odds, but the solly fleets are literally nothing but targets and will remain so for at least 5 years.
Second, the Japanese could do essentially nothing to attack the US industrial base, and so couldn't hinder the US buildup. Meanwhile, while the GA certainly can't hope to *prevent* the sollies from eventually closing the tech gap and bringing their resource advantage to bear, they sure as hell can slow it down since they (unlike the Japanese) can easily project power wherever they feel like within their enemy's territory. Having your shipyards and research infrastructure completely unmolested makes it a heck of a lot easier to close the gap on your enemy.
And third, and most importantly, the sollies are a hell of a lot less cohesive than the US. The previous two make it harder for the sollies to catch up, but alone they couldn't stop it from happening eventually. This, though, building on the previous two, is what allows for the possibility of the GA's victory. The Japanese could not break the US, and so ultimately the Japanese could not defeat the US. The sollies, though, are a collection of over-civilized, over-soft core worlds with little resolve or overriding loyalty and a whole ton of mostly-subjugated peons with *no* loyalty whatsoever, whose fleets cannot meet *any* quantity of GA ships in battle, and whose defenseless territory is wide open to attack. The idea of the US disintegrating during WWII without ever even being physically attacked is laughable. The idea of the sollies *not* disintegrating under such intense, sustained pressure is equally laughable.
It would require a sustained, concentrated effort on the part of the league for its resource and industrial advantage to actually beat the GA. However, the entire point of the Harrington plan is that the Sollies *will not remain intact* long enough to muster that sustained effort. By the time that they could do the research to close the enormous quality gap enough to allow quantity to tip the balance *and* build ships with the benefits of that research, there won't *be* a solarian league, at least in the sense of a single cohesive entity that actually retains the resource and industrial advantage required to beat the GA.
To make a long story short, right now the sollies are so insanely outclassed in quality that no amount of quantity can make up for it, and by the time they can close the quality gap, they won't have the quantity anymore.