While camping in Zion National Park last week, some friends and I discussed prediction capacities and limitations, considering cases such as weather forecasting and prophecy.
One friend argued that, due to weather forecasting limits, we will never be able to predict weather beyond a couple weeks. As we try to forecast further into the future, the resources (computing and otherwise) required increase faster than the accuracy they enable, eventually rendering the pursuit impractical -- and perhaps even approaching an impassable asymptote. This seems to be true of predictions generally: the value of forecasted details (quantitative or qualitative) increases slower than the cost of their enabling resources.
Another friend observed that important events in Mormon history happened on dates that match those of important events in Jewish history, suggesting that God predicted events thousands of years in the future. For example, Joseph Smith may have received the gold plates on Rosh Hashanah.
Could posthumans, monitoring and administrating our world from an external vantage point, accurately predict our weather in high detail one month in the future? It seems posthumans would have access to vastly more and superior resources, but that doesn't address the practical problem of decreasing marginal returns from prediction investments. Maybe posthumans could predict our future perfectly because our world is running in something like a giant DVR that can be forwarded and reversed, but that doesn't answer the question of whether they could predict the recording before watching it through the first time.
Whatever their other capacities and limitations might be, posthumans would certainly have at least one powerful predictive tool: engineering. Passive prediction of an event thousands of years in the future may be impossible, but active prediction could stage the event. Passive forecasting of the weather one month in the future may be impossible, but perhaps the forecast can be created. Foretellings become forthtellings, and predictions become productions.