The New Structure of Mathematics

Our blogs will now become somewhat specialized.

Huffington Post will be a general site...Harmony.

This blog, Mathematical Universe, will deal with the underlying mathematics of Harmonious Universe...truth.

Quantum Universe will deal with the underlying science...beauty.

The Art of Hardball will deal with the underlying politics and economics...justice.

The new structure of mathematics will build up from the deep structures of pure and particle mathematics through the cobbled structures of economics, finance and actuarial science.

The unifying structures will be those of complexity science. At it s most basic level, complexity science is the application of the most advanced computer and analytical structures to the most advanced problems of society.

It is the structure which emerges when the best scientists apply their deepest wisdom to the deep problems they attack.

No one will have to go back to school to follow this blog. A major point of the new structure of mathematics is that it be coherent to a general audience.

That doesn't mean sacrificing analytical robustness. It merely means organizing and explaining the tools better.

The new structure itself naturally starts with pure mathmatics. This involves mathematical structures that don't necessarily relate to anything we observe.

It should be noted that much of what is originally considered pure mathematics is ultimately found to apply to real problems. Similarly, much applied math (ie. that being developed in string theory) is often found to be pure.

The first level of mathematics beyond pure math is that being used in particle physics. One doesn't have to be able to manipulate Lagrangians, Hamiltonians. Hermitians, Laguerre's, Legendre's, Fouriers, Path Integrals, Hilbert Spaces, Lie Groups, Topologies, or Tensors to know that Schrodinger Waves, Dirac Seas, Feynman Diagrams, Pauli Exclusions, Planck Lengths, Heisenberg Uncertainties, and Maxwell's Equations help us understand how fundamental particles waves and fields become atoms, molecules and us.

The mathematics of particle physics points us to the mathematics of chemistry which in turn points us to biology. Neurology and psychology are on the same trajectory . Now society itself is in view mathematically.

This is where complexity science really shines. Along with some of the structures of chaos theory (fractals, universality...), complexity science is cobbling together a mathematics of everything.

Skeptics will say that humanity and its institutions are too complicated to approach mathmatically. There is some wisdom in that skepticism if not taken to far.

Remember that if we don't use the best math, we will use an inferior one, like the math behind the models which have missed all the recent global meltdowns.

What we are saying is that complexity science gives us a conceptual framework by which to combine the best math and computer science being used in the labs and universities with that being used in business and government. By considering connections among econometric, actuarial and financial models with those of Quantum Mechanics, String Theory and Relativity we will find better ways of connecting mathematics and our realities.

That will put us in a better position to anticipate problems and resolve them so as to optimize human welfare.

Is that not a worthy goal?

The journey begins.

Lee