Vladimir_M comments on Irrationality Game II - Less Wrong Discussion
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In the context of this discussion the important thing is what could be reliably predicted in 1941, so we should ignore the possible effects of the atomic bomb.
Assume that the entire U.S. navy is destroyed in January 1942. A reasonable realistic scenario, if everything went really well for Japan, may be this:
Now in this situation, being a U.S. general, what would be your advice given to Truman? Would it be "let's continue in a low intensity war against both Germany and Japan until we have a strong enough navy, which may be in 1947 or 1948, and then start taking one island after another, which may take two more years, and then, from the island bases supplied through the U-boat infested Pacific start bombarding Japan, until the damned fanatics realise they have no other chance than to surrender"? Or would it rather be "let's accept peace if it's offered on honourable terms"?
Even in that scenario, Japanese victory is conditional on the political decision of the U.S. government to accept the peace. My comments considered only the strategic situation under the assumption that all sides were willing to fight on with determination. And I don't think this assumption is so unrealistic: the American people were extremely unwilling to enter the war, but once they did, they would have been even less willing to accept a humiliating peace. Especially since the Pacific great naval offensive could be (and historically was) fought with very low casualties, and not to mention the U.S. government's wartime control of the media that was in many ways even more effective than the crude and heavy-handed control in totalitarian states.
Now, in your scenario, the U.S. would presumably see immediately that its first priority was navy rebuilding. (An army is useless if you can't get it off the mainland.) This means that by 1944, Americans would be cranking out even more ships than they did historically. I don't think the Axis could match that output even if they were in control of the entire Eurasia.
(The U-boats would have been a complicating factor. Their effectiveness changed dramatically with unpredictable innovations in technology and tactics. In actual history, they became useless by mid-1943, although Germans were arguably on the verge of introducing dramatically superior ones at the time of their capitulation. But in any case, the U-boat factor cuts both ways: Americans could swamp the Pacific with even greater numbers of U-boats and wreck the entire Japanese logistics, as they actually did.)