[U]sing 1870-1928 data, a prediction using that (log-)linear trend leads to an error of only 1% for the level of GDP per capita in 2008. Of course, the picture is misleading in the sense that in some cases it took a long time for the economy to come back to this trend, but it is still interesting that it returned to the same trend. It could have returned to the same growth rate but at a different level but that's not what we see, we see that the output loss is always recovered after a number of years. This suggests that the supply side of the economy (innovation, technology) is unaffected by output fluctuations.
In other words, booms and bust variations from the long term trend tend to very evenly balance out. In the post-WWII period, moreover, booms and busts have been considerably more tame than in the earlier era.
At a time when the economy is in a serious funk, this fact offers considerable hope for the future.
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