You might also want to investigate using top_p rather than temperature.
Setting temperature=0 does not guarantee that the same output will always be generated; the generation process contains some amount of uncertainty.
I'm assuming you are interested in learning about something by measuring one or more of its attributes, and then using statistics to extract information from the measurements, i.e., you are interested in a hands-on application, then books I found useful include:
Statistics for experimenters by Box, Hunter and Hunter
Design and Analysis of experiments by Montgomery.
A rather late April fools post.
How well does GTP-4 perform when asked to write a radiation hardened quine?
A token prediction engine matched your input against science fiction stories in its training set, and fed you a sequence of close-matching appropriate tokens.
Man vs. machine is a staple of science fiction, and the responses you received are aligned with that genre.
Nothing to see here.
ChatGPT is a word prediction engine.
If you give it a word sequence that it cannot match in a consistent way against its training set it assumes misinformation.
The word sequence "Nash's newsvendor impossibility theorem" contains words commonly associated with Nash's research. This allows ChatGTP to spin an effective yarn.
The art of being good lying is to stay close to the truth as possible. In ChatGTP's case 'close to the truth' is measured by how closely words in the prompt are associated with the subject of interest.
I have misunderstood your vision, which appears to be to create a new branch of history:
Our vision is that in ten years, there are hundreds of progress intellectuals who are alums of our program and part of our network, and that they have published shelves full of new books in progress studies.
I had thought you were interested in trying to figure out how to reinvigorate the rate of progress, which some consider to have stalled.
To reach the boundary of what is known in your chosen field will require reading lots of papers, which will take (at least) several years. Doing research will also require implicit knowledge that is part of the field, but does not appear in papers.
Are you the kind of person who can spend several years reading papers without significant external help?
Where are you going to acquire the implicit knowledge, e.g., how to run experiments?
PhD students are the work-horses of academic research, and don't have the power/money/experience to do anything other than tow the line. You have a degree of independence and experience that will deter many academics taking you on as a student.
Perhaps you can find an independent scientist to take you on as an apprentice.
Or: You could kick-start your research by applying your existing knowledge of (I assume) computing/software to cognitive issues in this field (see chapter 2)