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Mathematics

The violin has taught me much about Mathematics. The only way to master the complexities and difficulties of the violin is to work from the simplest first principles. In my experience, the same is true for mathematics. In the mid-1970's I relearned the fundamentals of violin playing following the method of Yehudi Menuhin, where the symmetry of the human body is transformed to create a dynamic asymmetry between the violin and the bow. This experience impressed upon me the power of simplicity.

Similarly, in the application of mathematics I have learned to work back to first principles, which then become the focus of the structured development of solutions. If and when flashes of insight occur, they occur within the context of this process.

Another lesson learned from music is the value of a global appreciation of human achievement and endeavor in a given field. Having learned from Menuhin how to draw the bow across an open violin string, it is revelatory to hear Menuhin perform the Bach "D minor Chaconne." Then, one may also follow Menuhin a step further into the music of India, and beyond to the music of the entire planet.

In mathematics too, first principles and global appreciation are together the basis for sustained motivation and inspiration. My personal and professional experience has validated this approach through successful application in fields as diverse as algorithm/software development, network troubleshooting, musical performance and composition, and education for the gifted.

   

'First Principles' Example: A Lattice is a non-empty set and two binary operations, ("join"), and ("meet"), that satisfy the 4 identity-pairs to the left. This simple structural basis applies directly to the {"OR","AND"} of propositional logic, as well as to the {"LCM,"GCD"} of elementary number theory. The further development of this structure includes the vector lattice, with which the Daniell Integral may be defined, as well as the orthomodular lattice, which provides a basis for quantum logic.

 

'Global Appreciation' Example: The Euler Product form of the Riemann Zeta Function is a stunningly beautiful example of deep mathematical insight, reaching back to the beginnings of numerical reasoning, and forward through analytic number theory to the Riemann Conjecture and the hypothetical application of P-adic Valuation to Planck-scale physics. In the field of music, one might point to comparable achievement in Bach's unfinished Contrapunctus 14 of The Art of the Fugue, or in Ustad Ali Akbar Khan's profound sarod music - perfected through 18 hours practice a day for twenty years. What distinguishes mathematics is the capacity to encapsulate deep universal insight into a few pencil strokes

   
   

 

 

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Last Updated: 2004-07-15     2003 by Ramsey Ameen and Resolution Corp.      All rights Reserved