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common flaw with charts is the data behind them. How much trust do we need to have in the data?
Everything is only as good as the data. It's hard to make a blanket statement, but a lot of this is really good, at least on a relatively coarse timescale over the last hundred years and change -- regular recordings from weather stations or the heartbeat of other institutional processes.
Longer timescales you get things like growth rings in trees, oxidation of different metals, and the artifacts of other physical processes. The difficulty there is other sources of variance, I believe, but taken in concert with other things, it's compelling data.