Gödel Machine — Jürgen Schmidhuber / Serious Science

Summary

The transcript introduces girdle machines, self-referential and universal problem solvers that optimize self-improvement. Inspired by Kurt Gödel's foundational work in theoretical computer science and his identification of the limits of mathematics and AI, these machines can rewrite their own code upon proving its utility. The concept addresses the potential of meta-learning and assures that self-modification is globally optimal, without surpassing traditional computational limits.

Takeaways

• 🤖 Girding machines are self-referential, universal problem solvers designed to make provably optimal self-improvements.
• 📈 The concept of girdle machines formalizes the ideas of I.J. Goode from 1965 on intelligence explosions through self-improving super intelligences.
• 💡 Kurt Gödel, the founder of theoretical computer science in 1931, introduced the first universal coding language based on natural numbers, influencing the development of girdle machines.
• 🔢 Gödel's universal coding language enabled formalizing operations of any formal axiomatic system or digital computer, representing storage in the form of integers.
• 📚 Gödel's work included self-referential statements that highlighted the fundamental limits of mathematics, theorem proving, computing, and artificial intelligence.
• 🌐 A girdle machine rewrites any part of its own code upon finding a proof that the rewrite is useful, guided by a problem-dependent utility function.
• 🔍 The proof searcher in girdle machines tests computable proof techniques, generating new theorems and lemmas from axioms.
• ✅ The initial software of a girdle machine, including the proof searcher, can be rewritten if a provably useful self-rewrite is discovered.
• 🚀 The self-rewrite must be globally optimal, as the proof searcher ensures no better alternative self-rewrites exist.
• 🔄 Girdling machines can handle uncertainty and probabilistic settings by incorporating standard axioms for representing uncertainty.
• 🧠 The meta-learning behavior of girdle machines allows them to learn how to learn in an optimal mathematical sense, collapsing multiple meta levels into a single level.

Q & A

What is a girdle machine?

A girdle machine is a self-referential, universal problem solver that can make provably optimal self-improvements. It is inspired by Kurt Gödel's self-referential formulas and is designed to formalize the informal remarks on intelligence explosion by I.J. Good in 1965.

Who founded theoretical computer science and introduced the first universal coding language?

Kurt Gödel founded theoretical computer science in 1931 and introduced the first universal coding language based on natural numbers or integers.

How does a girdle machine represent data and programs?

A girdle machine represents data in the form of integers, which can be axioms and theorems, and programs as sequences of instructions that manipulate the data.

What are the fundamental limits of mathematics, theorem proving, and computing identified by Kurt Gödel?

Kurt Gödel identified the fundamental limits by constructing formal statements that talk about the computation of other formal statements, leading to the discovery of statements that cannot be proven by any computational theorem prover.

What is the role of a proof searcher in a girdle machine?

The proof searcher in a girdle machine systematically and efficiently tests computable proof techniques to generate lemmas and new theorems, aiming to find a provably useful computable self-rewrite.

How does a girdle machine ensure that self-rewrites are globally optimal?

A girdle machine ensures global optimality by proving that the self-rewrite is useful for all future self-changes, and that there are no alternative self-rewrites that are better than the current one.

Can girdle machines handle uncertainty and probabilistic settings?

Yes, by inserting standard axioms for representing uncertainty and dealing with probabilistic settings into the original software of the girdle machine, it can handle uncertain worlds and maximize future expected rewards.

What is the main point of the self-referential setup in a girdle machine?

The main point of the self-referential setup is that it automatically collapses all meta-levels into a single meta level, proving that any self-modification is a useful basis for all future self-modifications affected by the current one.

Are girdle machines more computationally powerful than traditional computers?

No, girdle machines are not more computationally powerful than traditional computers like Turing machines. However, any traditional computer can become a self-referential girdle machine by loading it with particular self-referential software.

What limitations of computability and self-improvement were identified by Kurt Gödel?

Kurt Gödel identified the fundamental limits of computability and self-improvement by demonstrating through his incompleteness theorems that there are inherent boundaries to what can be proven within a formal system, and thus, to the capabilities of computation and artificial intelligence.

How does the girdle machine implement meta-learning behavior?

The girdle machine implements meta-learning behavior by learning how to learn in an optimal mathematical sense, constantly seeking self-improvements that are provably useful for future self-modifications.