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Numbers Look Like Leaves in Set Theory

2024-12-28

While learning ZFC set theory, the author discovered that the graphical representation of natural numbers using Von Neumann ordinals, when rendered using a force-directed graph layout, strikingly resembles leaves. The article details the recursive definition of Von Neumann ordinals and their tree-like structure, visually demonstrating how numbers from 0 to 16 take on a leaf-like form. The author concludes by questioning whether this 'leaf' shape is inherent to the structure of Von Neumann ordinals themselves and plans to investigate the set-theoretic representation of rational numbers.

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(www.christo.sh)
AI set theory von neumann ordinals mathematical visualization

AGI Attempt on the Tokio Runtime: A Failed Biologically-Inspired AI Experiment

2024-12-26

A developer attempted to build an AGI system based on a biological neural network on the Tokio runtime. He built an asynchronous neural network and trained it using genetic algorithms, but the experiment ultimately failed, achieving a maximum score of only 3. The author suggests that Tokio's inability to efficiently handle the massive number of neural impulses, and the optimization strategy of the genetic algorithm, might be responsible for the failure.

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(www.christo.sh)
AI biological neural network