At FQXi we're excited to launch our latest essay contest, with generous support from the Fetzer Franklin Fund and the Peter and Patricia Gruber Foundation. The topic for this contest is: Undecidability, Uncomputability, and Unpredictability.The contest is open to anyone, but the judging rules are slanted towards their own members, and and the panel of judges is secret.
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. The contest is open now, and we will be accepting entries until March 16th.
Last time I submitted an essay, it was summarily rejected without explanation.
When was that "brief time in history"? The 19th century, I guess. By the 1930s, we knew about chaos, undecidability, etc.
Did scientists in the 19C really believe that someday a computer could be programmed to determine all mathematical truths and predict all physical phenomena? I doubt it. That would require a belief in a extreme form of determinism, and a depressing view of humanity. We would all be pre-programmed robots. Some man's brilliant mathematical idea would be no better than memorized digits of pi. A computer could do it better.
My hunch is that 19C scientists believed that humans were better than just robots, and that there were limits to knowledge.
If I told them that in 2019 we would have useful 5-day weather forecasts, would they have argued it should be possible to forecast weather months or years in advance? I doubt it.
When quantum mechanics was discovered in the 1920s, it described physics on an atomic level, as previously not possible. Scientists learned that they could make amazingly precise predictions, and that there were fundamental uncertainties blocking other types of predictions. Which discovery was more surprising? My guess is that the ability to make precise predictions was much more surprising.
Does any of this relate to agency and intelligence? I will have to think about it.