Perez Hourglass (Sablier de Perez)
The Perez Hourglass (Sablier de Perez in French) is a mathematical structure discovered by French mathematician Jean-Claude Perez, a former IBM researcher and collaborator of Nobel laureate Luc Montagnier. This fractal, hourglass-shaped structure emerges from a transformation of Pascal’s Triangle and represents a unique integration of the golden ratio (φ) and Fibonacci sequences.
Mathematical Foundation
Origin from Pascal’s Triangle
The Perez Hourglass emerges from applying a specific transformation to Pascal’s Triangle:
- Northern Hemisphere: Maintains the traditional additive pattern of Pascal’s Triangle
- Southern Hemisphere: Uses subtraction instead of addition, creating negative values
- Result: A symmetric, hourglass-shaped fractal pattern
Key Properties
- Fractal Nature: The structure repeats at all scales
- Symmetry: Perfect bilateral symmetry around the central axis
- Golden Ratio Integration: The number φ (≈1.618) is concentrated at the structure’s core
- Extended Fibonacci Sequences: The structure is associated with a mirror-symmetric Fibonacci-like sequence around zero, described as “numerical antimatter” to Pascal’s Triangle
Theoretical Applications
1. PHAM - Perez Hourglass Associative Memory
The Perez Hourglass could revolutionize artificial intelligence through PHAM (Perez Hourglass Associative Memory), a theoretical memory system with remarkable properties:
- Error Tolerance: Capable of recovering data even with >40% corruption or loss
- Instantaneous Retrieval: Uses fractal topology for immediate pattern reconstruction
- Superior Performance: Theoretically more efficient than existing Hopfield networks
2. Quantum Computing Applications
In quantum computing, the Perez Hourglass offers:
- Fibonacci-based Error Correction: Novel approach to qubit decoherence problems
- Computational Speed: Potential to reduce complex calculations (e.g., climate simulations) from years to minutes
- Timeline: Theoretical stability achievable by 2027-2035
3. Post-Quantum Cryptography
The structure provides cryptographic advantages:
- Infinite One-Time Pad: Unbreakable encryption through infinite key generation
- Diffie-Hellman Hourglass: Quantum-resistant key exchange mechanism
- Security: Keys impossible to predict even with quantum supercomputers
Distinction from Neural Network Hourglasses
Important: The Perez Hourglass should not be confused with the “hourglass phenomenon” in neural networks:
| Perez Hourglass | Neural Network Hourglass |
|---|---|
| Mathematical structure from Pascal’s Triangle | Network architecture bottleneck |
| Theoretical discovery | Observed technical limitation |
| Fractal, symmetric pattern | Information concentration in central layers |
| Potential technological applications | Performance constraint in AI models |
| Still in theoretical stage | Documented problem in practice |
Scientific Context
Jean-Claude Perez, former IBM researcher, has been developing this concept since 1997. The discovery is presented as:
- A “fractal digital codex” based on golden ratio and Fibonacci sequences
- A potential universal language connecting biology, physics, and computer science
- A “mirror of the universe” reflecting a holistic mathematical vision
Current Status
As of December 2025, Perez has published a series of scientific papers highlighting potential high-tech applications. However, these applications remain:
- Theoretical: Mathematical concepts awaiting practical implementation
- Under Evaluation: Require rigorous scientific validation
- Promising: Potentially revolutionary if successfully implemented
Related Concepts
- Golden Ratio: The mathematical constant φ at the heart of the structure
- Fibonacci Sequences: Extended sequences integrated into the hourglass
- Fractals: Self-repeating patterns at multiple scales
- Quantum Computing: Potential application domain
- Cryptography: Post-quantum security applications
- Artificial Intelligence Memory Systems: PHAM implementation
References
- Perez, J.C. (2025). Series of scientific publications on Perez Hourglass applications
- Original discovery: 1997
- Collaborative work with Luc Montagnier, Nobel laureate
Note: This entry documents a theoretical mathematical structure. Applications mentioned are based on published theoretical frameworks and require further scientific validation.