Smart Life (part 2) - Resolving the Godel's paradox on the blockchain as a solution for a decentralized trusted protocol
Smart life refers to the one "contract" that forms the foundation to the intelligence we name life. This contract is a code for a protocol of a blockchain which download itself from the blockchain and is expressed in a language based on a logic that asserts the last block's consensus regarding the mathematical axioms is true.
Now let me break this grandiose statement to its components and then show you how Godle's incomplete theorem and the halting problem presented by Turing are a solution rather than a problem for a complete and trusted decentralized system.
Blockchain consensus mechanism means that if the majority of "people" you know (nodes in the network) say that something is true then it will become true, thus you too should agree that it is truth
Next you want to put the protocol itself on the blockchain so any changed made on it have to be governed by the consensus mechanism.
Now we come to deal with the Godel's incompleteness theorem which define the paradox of what became to be known as the halting problem. A state in which a conflict arise and the program can not decide which is the true statement. Turing theorem asserts that there is no algorithm which can solve the halting problem.
Yes indeed. there is no algorithm to solve the halting problem , but there is an algorithm which governs the consensus mechanism and the consensus mechanism can solve any halting problem.
Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of the natural numbers. For any such formal system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.Employing a diagonal argument, Gödel's incompleteness theorems were the first of several closely related theorems on the limitations of formal systems. They were followed by Tarski's undefinability theorem on the formal undefinability of truth, Church's proof that Hilbert's Entscheidungsproblem is unsolvable, and Turing's theorem that there is no algorithm to solve the halting problem.
Well, you should now ask , is that all? can I now trust the network to keep the terms of the contract I signed?
My answer is NO. It may take a few splits and turns before you are able to form the branch on which you may place your contract safely.
The first and most important one is brunching away from Turing complete logic based language and chose one of many options for a restricted less expressive language in which contradictions are rejected and every term you made on your contract can be proved ahead, based on the mathematical consistent structure.
Now the only question left to ask is can we trust our personal contracts on such platform which let consensus be the highest power of all to assert what is true and what is not?
Amazingly enough the answer is YES! That is since the consensus do not deal with your personal issues, it only need a consensus of the mathematics axioms forming the complete logic. Once that is set all brunches can communicate with one another based on an algorithms which is set to trust the mathematical truth set by the root chain consensus.
Eventually the network will form a fractal structure like that picture below.