How to pack the most data into a single signal
In short: When you send a WhatsApp message, your phone solves a centuries-old geometry problem to ensure the data arrives intact. By understanding how to pack spheres into high-dimensional spaces, engineers create error-correcting codes that shield your information from the noise of the physical world.
The problem of sphere packing asks for the densest way to arrange non-overlapping spheres within a volume. While it sounds simple, it becomes exponentially complex as dimensions increase. In our three-dimensional world, the densest packing was famously conjectured by Johannes Kepler in 1611. He suggested that 'face-centric cubic packing'—similar to how oranges are stacked in a supermarket—was the most efficient, accounting for approximately 74.05% of the total volume. This was only rigorously proven by Thomas Hales in 2017.
Mathematics has solved the optimal packing for dimensions 1, 2, 3, 8, and 24. Beyond these, very little is known, forcing mathematicians to establish 'bounds'—upper and lower limits on potential density. A recent breakthrough by Dr. Matthew Jenssen and his team at King’s College London improved the lower bound for high-dimensional sphere packing for the first time since 1947. Unlike previous studies that focused on neat, highly structured 'lattices,' this team used random methods to find unstructured packings.
The discovery is significant because it aligns with predictions by Nobel Prize winner Giorgio Parisi and Francesco Zamponi regarding the density of unstructured packings. This isn't just abstract theory; these high-dimensional geometries are essential for error-correcting codes. These codes encode information so that it remains resilient against interference or 'noise' during transmission over phone lines or digital networks. Additionally, physicists use these models, such as the hard-sphere model, to conceptualize the structures of matter.
Opens the Intellect+ feed with this card first. Swipe up for the next one.
Sources
- Summary by Intellect · source: King's Mathematician helps solve sphere packing problem centuries in the making | King's College London
- Also: Sphere packing
To cite this card, link to https://intellectplus.co.uk/app/science-sphere-packing.
How we source, check and correct cards: Editorial standards.
General information, not professional advice. Spotted an error? Flag the card or see corrections and complaints.
Intellect Plus is a visual educational discovery platform for exploring fascinating facts and ideas. Brain Food, Not Brain Rot. What is Intellect Plus?
Related
More in Mathematicians · More in Science · Latest · A–Z · All topics
