Two spaces that already found their geometer in the thirties

TL;DR

This paper compares Giorgio Parisi's recent ideas on continuous dimension with Von Neumann's earlier work, highlighting historical and conceptual connections in the understanding of geometric spaces.

Contribution

It provides a comparative analysis of Parisi's and Von Neumann's approaches to the concept of continuous dimension in geometry.

Findings

Parisi's speculations relate to classical ideas by Von Neumann.

The paper clarifies conceptual differences and similarities.

It situates recent ideas within historical mathematical context.

Abstract

Giorgio Parisi's recent speculations on the concept of continuous dimension (cond-mat/0207334) are compared with Von Neumann's serious work.