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We don’t have much ice left to melt in comparison, and the levels haven’t changed much in the last 100 years really.
evidence doesn’t seem to support this thesis
Still sometimes the data does indicate sharp, dramatic changes, such as the Younger Dryas, about 12K years ago. After the recent glacial period ended, roughly 14K YA, there was a plunge back to glacial temps over a couple centuries which lasted about 1200 years, then very suddenly the temperature rose almost 20C.
https://en.wikipedia.org/wiki/Younger_Dryas#/media/File:Youn...
The issue with doubting ancient temperatures, is that one has no faith in the predictions of science for the present, as this is the basis/metric in use.