greswd said:Both Hawking and Dyson have said that Godel's incompleteness theorems prove that it is impossible for us to formulate an absolutely fundamental Theory of Everything.
Is that true? Do the theorems apply to the physical world as they apply to the realm of mathematics?
DarkoDornel said:M-theory is close, but to many million miles away from the theory. I believe we would be able to know our universe. But others no chance. String theory is other failure for ToE. There is a beautiful equation there, but something does not complete the reality. There is ways to marry GR with Quantum Theory.
DarkoDornel said:Hawking is pulling on strings ( pardon the pun!). There is no theory of everything, it does not fit in too the realities of universe. We think of the theories of today and the past has a house, we dig the foundations, and we layed the floor...and that is it. I do not believe in the big bang at all!
Godel's Incompleteness Theorem is a mathematical proof by Kurt Godel that states any formal system of mathematics is either incomplete or inconsistent. In simpler terms, there will always be true statements within a system that cannot be proven within that system.
Godel's IT has implications for the physical world because it suggests that there may be fundamental limitations to our ability to fully understand and describe the universe using mathematical models. This means that a Theory of Everything (ToE) may be impossible, as there will always be aspects of the universe that cannot be fully explained or predicted.
Yes, Godel's IT has been applied to fields such as computer science, philosophy, and linguistics. It has also been suggested that the theorem may have implications for the study of consciousness and human cognition.
Yes, Godel's IT is widely accepted as a significant and groundbreaking discovery in mathematics and logic. However, its implications for the physical world are still a topic of debate and further research is needed to fully understand its implications.
Yes, there have been attempts to reconcile Godel's IT with a Theory of Everything, such as the concept of "self-referential universes" where the limitations of Godel's IT are accounted for in the structure of the universe itself. However, these attempts are still theoretical and have not been fully proven or accepted by the scientific community.