The Complexity Slider - Finding Hypotheses at the Limits of Human Knowledge

The Percolation Point: A theory on complexity as it relates information density and human comprehension by Dr. Barend Mons and Dr. Erik Schultes

Hackathon Idea: The Percolation Point Hypothesis Generator - Mapping the Limits of Comprehension

Project Description:

This project challenges participants to develop a hypothesis generation engine that explores the relationship between hypothesis complexity and information density, specifically focusing on identifying the "percolation point"—the theoretical limit of human comprehension where information density sharply declines despite increasing complexity.

Background:

Dr. Erik Schultes and Baron Mons propose that within scientific literature, there exists a correlation between the complexity of a hypothesis and its information density, up to a certain point. This point, the percolation point, represents the limit of human comprehension. Beyond this point, while complex hypotheses can still be generated (especially with the aid of LLMs), their information density plummets, leading to potentially misleading or nonsensical outputs that mimic scientific plausibility but lack grounding in reality. This project aims to visually and computationally demonstrate this concept.

Challenge:

Develop a hypothesis generation engine with a user-friendly interface that includes a "complexity slider." This engine should:

1. Generate Hypotheses:

   • Produce hypotheses based on a provided subset of scientific literature.

   • Allow users to control the complexity of the generated hypotheses via the slider.

2. Information Density Tracking:

   • Implement a method to track and visualize the information density of the generated hypotheses.

   • This method should be able to cite and prove the validity of a hypothesis via the provided literature when possible.

3. Percolation Point Identification:

   • Identify and visually represent the percolation point—the point at which information density drops significantly despite increasing complexity.

   • Demonstrate that hypotheses beyond this point, while generated from the same algorithm and literature subset, lack provable support.

4. Interface:

   • Create a simple website interface with the complexity slider and visualization of the information density.

   • The interface should clearly indicate when hypotheses are provable via literature and when they are not.

Technical Requirements:

• Literature Processing: Ability to process a subset of scientific literature.

• Hypothesis Generation Algorithm: Development of an algorithm capable of generating hypotheses with varying levels of complexity.

• Information Density Measurement: Implementation of a method to quantify information density.

• Data Visualization: Creation of a visualization that shows the relationship between complexity and information density, highlighting the percolation point.

• Web Interface: Development of a user-friendly web interface with the complexity slider.

Evaluation Criteria:

• Accuracy in identifying the percolation point.

• Effectiveness of the information density measurement method.

• Clarity and usability of the web interface.

• Ability to prove and cite information from the provided literature.

• The overall ability to demonstrate the concept of the percolation point.

Potential Impact:

This project has the potential to provide valuable insights into the limitations of current AI-driven hypothesis generation and highlight the importance of contextual understanding in scientific research.

Notes:

• This is a challenging project that requires a strong understanding of the scientific literature.

• Participants are encouraged to work in the open and seek feedback on the Discord channel

• Idea is based on percolation theory https://en.wikipedia.org/wiki/Percolation_theory
• [AI Generated] A Data-Driven Approach to Funding Academic Research: Leveraging Percolation Theory on Knowledge Graphs of Scientific Assertions