Background: The Foundational Questions Institute invites papers to address various topics that are foundational to the physics industry. Thus, their name is perfect.
2019 was the very first time that I tried submitting a paper. It got hung up in an email failure so I was too late. It was a “No go.”
March 2020. This year, I vowed to myself to get an article in early enough to validate that it got through. And, I did. And, it got through, but the PDF that went up on the FQXi website was rather ugly. Images had shifted on the pages and links were not properly interpreted so many were broken. Plus, there were content issues that required much more reflection.
Deadlines are good, but I was too anxious and had not checked my work twice. So, yes, that conversion to a PDF for FQXi didn’t go well… Just too many mistakes. But, the corona virus opened the deadline back up and gave us all another six weeks.
For me, life is always successive approximations. This time, on April 23, 2020, a better version made it through! With this rather boring-looking title (below), it’s the best I can do today: Determinant becomes undecidable, uncomputable and unpredictable. Yet, even this version will now be reworked and further developed.
Undecidability, Uncomputability, and Unpredictability
“For a brief time in history, it was possible to imagine that a sufficiently advanced intellect could, given sufficient time and resources, in principle understand how to mathematically prove everything that was true. They could discern what math corresponds to physical laws, and use those laws to predict anything that happens before it happens.”
“That time has passed. Gödel’s undecidability results (the incompleteness theorems), Turing’s proof of non-computable values, the formulation of quantum theory, chaos, and other developments over the past century have shown that there are rigorous arguments limiting what we can prove, compute, and predict. While some connections between these results have come to light, many remain obscure, and the implications are unclear. Are there, for example, real consequences for physics — including quantum mechanics — of undecidability and non-computability? Are there implications for our understanding of the relations between agency, intelligence, mind, and the physical world?
“In this essay contest, we open the floor for investigations of such connections, implications, and speculations. We invite rigorous but bold and open-minded investigation of the meaning of these impossibilities for reality, and for us, its residents.”
Notes regarding future edits: On page 5 of 10, in the paragraph about Gödel’s constructions, it says, “It didn’t exit until 2011.” That should have been “It didn’t exist until 2011.”