Human AI Collaboration Depiction by Bing

The Berard-Gemini Conjectures

A New Conjecture in Mathematics from a Human-AI Collaboration

This is the full text of the collaboration between me (Berard) and Gemini (Advanced Google Gemini).

I have a math problem for you. Are you ready?

Absolutely! I’m ready to tackle your math problem. Fire away whenever you’re ready.

Ok. We pick any number with an endless stream of digits in the decimal expansion. Start a cursor for a car at the origin facing north. For each digit, follow this protocol: Even means turn right; odd means turn left; then move number of units denoted by value.

Are these instructions ambiguous in any way?

Let’s analyze the instructions for any potential ambiguity:

Potential Ambiguities:

• Endless stream of digits: While mathematically clear, in a practical implementation, one would need to decide how many digits to consider or have a stopping criterion.
• Cursor/car at the origin: Assuming a standard Cartesian coordinate system, this is unambiguous.
• Facing north: Again, assuming a standard Cartesian system, this is clear.
• Even/odd turn and move: These instructions are clear.