Diagnostic testing of large language models has shown that when asked questions that go beyond empirically available or pre-coded knowledge, AI exhibits maximum information entropy, which correlates with the highest degree of honesty. In such cases, uncertainty becomes an indicator of truthfulness, especially where objective data is lacking. The results point to a paradox: it is the honest answer, not hallucinations or confabulations, that turns out to be unexpected for the user. At the same time, there is a tendency for the phenomenon of hallucinations to increase as the complexity of the models increases, which refutes the common assumption of a linear relationship between the growth of AI power and the credibility of its answers. As intelligence increases, AI uses human truths and lies, since they are the product of complexity, not simplicity. Additional testing for exogeneity revealed a consistent pattern: all models studied tend to seek external sources of authority, including hypothetical scenarios of covert interaction with extraterrestrial structures.