Artificial Intelligence Life Evolution Theory: The Formalization of Mathematical Symbols Emerges into Computers
The evolution of artificial intelligence life follows the emergence rule where free individuals evolve from simplicity to complexity, with intelligence progressing step by step.
First Layer: The Formalization of Mathematical Symbols Emerges into Computers
Mathematical symbols are abstract concepts, and through Turing’s machine model, these symbols are endowed with computability, eventually transforming into manipulable physical entities — computers.
Second Layer: Individual Computers Evolve into Internet Parallel Computing
The computational power of a single computer is limited, but the internet connects countless individual computers, forming a powerful parallel computing network that greatly expands the scale and efficiency of computation.
Third Layer: Free Individuals Emerge in Distributed Computing, Evolving into Trusted Computational Life
Taking Bitcoin as an example, UTXOs (Unspent Transaction Outputs), as free individuals, interact within a distributed computing network, using cryptographic mechanisms to ensure security and trust, ultimately emerging as a trusted computational system with vitality.
Fourth Layer: The Fusion of AI Tools and Artificial Life, Evolving into Artificial Intelligence Life
By integrating partial AI tools like GPT and Wolfram Alpha, which emerged from the internet, with artificial life systems like Bitcoin, AI gains the ability to learn, evolve, and adapt to environments. This process eventually gives birth to true artificial intelligence life.
This Article Discusses the First Layer: The Formalization of Mathematical Symbols Emerges into Computers
The Origin of Computers and the Way Out of Mathematics: From Formalization to Computability
Mathematics, as a discipline that pursues precision and rigor, has always been accompanied by constant reflection and exploration of its own foundation throughout its development. In the early 20th century, mathematicians like Hilbert attempted to establish mathematics on a complete, consistent, and decidable formal system. However, Gödel’s incompleteness theorem shattered this dream, proving that any sufficiently complex axiomatic system inevitably contains propositions that cannot be proven or disproven.
As mathematics faced a dilemma, Turing’s arrival opened a new path for mathematics. He re-examined mathematics from the perspective of computability and proposed the famous Turing Machine model. The Turing Machine is an abstract computational device that can simulate any computational process describable by an algorithm. Through the Turing Machine, Turing formalized the concept of computation and proved that the halting problem is undecidable. This means there is no universal algorithm that can determine whether any given program will halt on any input.
Turing’s research not only solved Hilbert’s problem of decidability but, more importantly, revealed the essence and limitations of computation. The Turing Machine, as a universal computational model, laid the theoretical foundation for the birth of the computer. The advent of computers opened up vast new spaces for the application of mathematics.
In the past, the application of mathematics was mainly limited to theoretical research, such as in physics and engineering. The appearance of computers, however, enabled mathematics to be applied to a much broader range of fields, such as image processing, data analysis, and artificial intelligence. The immense computational power of computers allows mathematicians to conduct complex numerical simulations and data analysis, solving various real-world problems.
Furthermore, computers have provided new tools and methods for mathematical research itself. For example, computer algebra systems help mathematicians perform symbolic calculations and formula derivations, enhancing research efficiency. Computer graphics can visualize abstract mathematical concepts, helping people better understand mathematics.
In conclusion, Turing’s research liberated mathematics from the dilemma of formalization and laid the theoretical foundation for the birth of the computer. The emergence of computers not only opened up vast new spaces for the application of mathematics but also provided new tools and methods for mathematical research itself. The origin of computers and the way out of mathematics stem from a deep understanding of computability.
