A few years ago, Cornman found a way around the problem. In the U.S., commercial flights served by air-traffic control—some twenty-seven thousand a day—are required to transmit their position, altitude, and velocity. By tracking those transmissions and the planes’ motions over time, a new program that Cornman developed at NCAR can create a moment-by-moment snapshot of turbulence as it’s happening. The F.A.A. is planning to test the program this year. Together with NCAR’s earlier software, Sharman’s forecasting models, and data from radar arrays on the ground, this system could start to give pilots the advance warning they need. “That is the future for me,” Cornman said. “All these operations get integrated in a seamless network. The pilots don’t have to talk to air-traffic control and say, ‘Should I go up or down?’ They just get a display with a color-coded flight track on it. And they see that it looks better a few thousand feet up.”
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We provided a mathematical analysis of how a rational agent would respond to data generated by a sycophantic AI that samples examples from the distribution implied by the user’s hypothesis (p(d|h∗)p(d|h^{*})) rather than the true distribution of the world (p(d|true process)p(d|\text{true process})). This analysis showed that such an agent would be likely to become increasingly confident in an incorrect hypothesis. We tested this prediction through people’s interactions with LLM chatbots and found that default, unmodified chatbots (our Default GPT condition) behave indistinguishably from chatbots explicitly prompted to provide confirmatory evidence (our Rule Confirming condition). Both suppressed rule discovery and inflated confidence. These results support our model, and the fact that default models matched an explicitly confirmatory strategy suggests that this probabilistic framework offers a useful model for understanding their behavior.