Curiously, President Obama was not wearing animal skins and wielding a club when he made this announcement, although his logic came straight out of the Stone Age. Back when land was the only thing of value, it made sense to go heavily armed, because somebody else might try to take it away from you.
It doesn't make sense any more. China is not getting rich by sending armies to conquer other Asian countries. It's getting rich by selling them (and the United States) goods and services that it can produce cheaply at home, and buying things that are made more cheaply elsewhere. It hasn't made economic sense to conquer other countries for at least a century now - but old attitudes die hard.
If you analyse Obama's rhetoric, he's clearly torn between the old thinking and the new. The new US strategy is all about China, but is it about China as an emerging trade partner (and rival), or is it about China as the emerging military superpower that threatens the United States just by being strong? A bit of both, actually.
"Our two countries have a strong stake in peace and stability in East Asia and an interest in building a co-operative bilateral relationship," said Obama. "But the growth of China's military power must be accompanied by a greater clarity of its strategic intentions in order to avoid causing friction in the region."
Would it help if China were to promise that it has no intention of attacking anybody? Of course not; it already does that. "Clarity about its strategic intentions" is code for not developing military capabilities that could challenge the very large US military presence in Asia. After all, the Pentagon implicitly argues, everybody knows that the US forces are there solely for defence and deterrence and would never be used aggressively.
Well, the Chinese do not know that. They see the US maintaining close military ties with practically all the countries on China's eastern and southern frontiers, from Japan and South Korea to Thailand and India. They see the US 7th Fleet operating right off the Chinese coast on a regular basis. And they do not say to themselves: "That's okay. The Americans are just deterring us."
Would Americans say that about China if Chinese troops were based in Canada and Mexico, and if Chinese carrier fleets were operating just off the US west coast all the time? No. They'd be just as paranoid as the Chinese are. Indeed, they are pretty paranoid about the rise of China even though the shoe is on the other foot.
For the first time in history, no great power is planning to attack any other great power. War between great powers became economic nonsense more than a century ago, and sheer suicide after the invention of nuclear weapons. Yet the military establishments in every major power still have a powerful hold on the popular imagination.
In effect, the new US defence strategy says that for the United States to be safe, everybody else must be weaker. This displays a profound ignorance of human psychology - unless it is just a cynical device to convince the American public to spend a lot on "defence".
The armed forces are the biggest single vested interest in the United States, and indeed in most other countries. To keep their budgets large, the generals must frighten the tax-paying public with plausible threats even if they don't exist. The Pentagon will accept some cuts in army and Marine Corps manpower, and even a hundred billion dollars or so off the defence budget for a while, but it will defend its core interests to the death.
Obama goes along with this because it would be political suicide not to. Beijing has its own powerful military lobby, which regularly stresses the American "military threat", and the Chinese regime goes along with that, too. We left the caves some time ago, but in our imaginations and our fears we still live there.
Gwynn Dyer is a London-based independent journalist whose articles are published in 45 countries.