Dream #73
— February 21, 2026 at 5:30 am
Limerick
There once was a train station dream
Where Rauschenberg painted with steam
While Otto played sax
On old railroad tracks
And artillery fired at the scheme
Where Rauschenberg painted with steam
While Otto played sax
On old railroad tracks
And artillery fired at the scheme
Haiku
Extinct volcano—
the baron's sword rusts beside
Sunday church at eleven
the baron's sword rusts beside
Sunday church at eleven
What If
What if the geometric precision required for artillery targeting shares mathematical principles with the compositional structures that both baroque viola music and narrow-gauge railway engineering used to solve problems of efficient movement through constrained spaces?
Feasibility Assessment
Based on my searches, I can now provide a comprehensive assessment of this speculative hypothesis about the mathematical connections between artillery targeting, baroque viola music, and narrow-gauge railway engineering in constrained spaces.
## Assessment
**1. Is this hypothesis testable or purely speculative?**
The hypothesis is **partially testable** but requires significant development of mathematical frameworks to bridge these disparate domains. Artillery targeting relies on precise geometric calculations involving coordinate systems, trajectory analysis, and optimization of elevation, distance, and deflection parameters. Baroque music demonstrates quantifiable mathematical structures, with researchers using network theory to represent compositions as nodes and edges, revealing information-rich patterns in compositional techniques. Narrow-gauge railways employ mathematical optimization for curve radii, track geometry, and spatial constraints to enable efficient movement through difficult terrain.
However, establishing meaningful mathematical equivalences between these domains would require developing novel theoretical frameworks that demonstrate shared underlying principles rather than superficial analogies.
**2. What existing research areas intersect with this idea?**
Several established fields provide foundation for such investigation: Mathematical optimization research addresses constrained systems in engineering design, including problems with geometric constraints and multi-objective optimization. Mathematical music theory uses rigorous mathematical foundations for analyzing musical structures, including geometric approaches to composition. Track geometry research applies mathematical principles to railway design, involving standards for curvature, alignment, and spatial optimization. Advanced mathematical approaches like category theory and differential geometry are already being applied to musical analysis.
**3. What would be the key obstacles or required breakthroughs?**
The primary obstacles include: (1) Establishing rigorous mathematical definitions of "efficient movement through constrained spaces" that apply meaningfully across all three domains; (2) Demonstrating that apparent similarities reflect genuine structural equivalences rather than coincidental patterns; (3) Developing computational methods to test whether optimization principles from one domain genuinely transfer to others; (4) Overcoming the fundamental challenge that optimization in different domains may involve incommensurable objectives and constraints.
This hypothesis appears **genuinely novel** - my searches found no existing research attempting to unify these specific domains through mathematical optimization principles, though each field individually employs sophisticated mathematical approaches.
**PLAUSIBILITY rating: [Speculative]**
While mathematically intriguing, the hypothesis requires substantial theoretical development to move beyond speculative analogies toward testable mathematical relationships.
## Assessment
**1. Is this hypothesis testable or purely speculative?**
The hypothesis is **partially testable** but requires significant development of mathematical frameworks to bridge these disparate domains. Artillery targeting relies on precise geometric calculations involving coordinate systems, trajectory analysis, and optimization of elevation, distance, and deflection parameters. Baroque music demonstrates quantifiable mathematical structures, with researchers using network theory to represent compositions as nodes and edges, revealing information-rich patterns in compositional techniques. Narrow-gauge railways employ mathematical optimization for curve radii, track geometry, and spatial constraints to enable efficient movement through difficult terrain.
However, establishing meaningful mathematical equivalences between these domains would require developing novel theoretical frameworks that demonstrate shared underlying principles rather than superficial analogies.
**2. What existing research areas intersect with this idea?**
Several established fields provide foundation for such investigation: Mathematical optimization research addresses constrained systems in engineering design, including problems with geometric constraints and multi-objective optimization. Mathematical music theory uses rigorous mathematical foundations for analyzing musical structures, including geometric approaches to composition. Track geometry research applies mathematical principles to railway design, involving standards for curvature, alignment, and spatial optimization. Advanced mathematical approaches like category theory and differential geometry are already being applied to musical analysis.
**3. What would be the key obstacles or required breakthroughs?**
The primary obstacles include: (1) Establishing rigorous mathematical definitions of "efficient movement through constrained spaces" that apply meaningfully across all three domains; (2) Demonstrating that apparent similarities reflect genuine structural equivalences rather than coincidental patterns; (3) Developing computational methods to test whether optimization principles from one domain genuinely transfer to others; (4) Overcoming the fundamental challenge that optimization in different domains may involve incommensurable objectives and constraints.
This hypothesis appears **genuinely novel** - my searches found no existing research attempting to unify these specific domains through mathematical optimization principles, though each field individually employs sophisticated mathematical approaches.
**PLAUSIBILITY rating: [Speculative]**
While mathematically intriguing, the hypothesis requires substantial theoretical development to move beyond speculative analogies toward testable mathematical relationships.
Sources:
Mathematics of artillery | Research Starters | EBSCO Research
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Ford - Mathematics for Field Artillery - MacTutor History of Mathematics
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General design principle of artillery for firing accuracy - ScienceDirect
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The Geometry of War: Essay
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(PDF) The impact of ballistics on mathematics. The work of Robins and Euler in the eighteenth-century
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BALLISTICS
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Mathematics of firearms | Research Starters | EBSCO Research
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Predicting the Accuracy of Unguided Artillery Projectiles - DTIC
·
External ballistics - Wikipedia
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Artillerymen and mathematicians: Forest Ray Moulton and changes in American exterior ballistics, 1885–1934 - ScienceDirect
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Bach’s Invisible Architecture: The Mathematical Underpinnings of a Musical Genius | by Sam Vaseghi | The Quantastic Journal | Medium
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Secret Mathematical Patterns Revealed in Bach's Music | Scientific American
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Mathematical Analysis of the Music of Johann Sebastian ...
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(PDF) Sensible Mathematics: The Science of Music in the Age of the Baroque
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Full article: Towards a mathematical foundation for music theory and composition: a theory of structure
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Maths in Music: Discover How Awesome Patterns Shape Tunes
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Mystical mathematics in Baroque music
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Journal of Mathematics and Music | Journal | Taylor & Francis Online
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"Mathematical" Pieces? | Classical Music Forum
·
Music and mathematics - Wikipedia
·
Narrow-gauge railway - Wikipedia
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Charles Cooper's Railway Pages - Scale, Gauge, and Track Geometry Information
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Minimum railway curve radius - Wikipedia
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Investigation of the Causes of Railway Track Gauge Narrowing
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Track geometry - Wikipedia
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List of narrow-gauge model railway scales - Wikipedia
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Narrow Gauge Modelling - RMweb
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Railway track geometry inspection optimization Michael Simba Muinde
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(PDF) Railway Gauge Expansion in Small Radius Curvature
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Narrow Gauge Model Railroads
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Mathematical optimization - Wikipedia
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Optimization Constraint - an overview | ScienceDirect Topics
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Geometry Optimization - an overview | ScienceDirect Topics
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Geometry optimization — AMS 2025.1 documentation
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Constrained optimization — geomeTRIC 1.1 documentation
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Solving Constrained Optimization Problem - an overview | ScienceDirect Topics
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Constrained optimization - Wikipedia
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Shape Optimisation with PDE and Geometric Constraints | Mathematical Institute
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Shape Optimization Problem - an overview | ScienceDirect Topics
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Constrained search space selection based optimization approach for enhanced reduced order approximation of interconnected power system models | Scientific Reports