Wednesday, July 27, 2011

But what use is it anyway?

Basic researchers of every stripe have to answer this question to every one from funding agencies to the neighbours' school-going kids. While all these enquiring minds have every right to ask this question, every right thinking researcher has to suppress, for reasons of politeness and practicality, the primitive urge to snap and say `does everything have to be useful?'. The Nature issue of 14th July has carried out an admirable job of answering this question. Peter Rowlett has produced seven tales, both little known, and well known, which provide the answer, viz. `theoretical work may lead to practical applications, but it can't be forced and it can take centuries.' The original link is here, but needs a subscription to Nature.

For those who don't have access to the journal, here is a quick summary: Mathematics displays the astonishing quality of being able to provide an effective toolbox for researchers trying to solve practical problems.The surprising thing about this, is that the mathematicians who invented the toolbox, sometimes centuries earlier, neither knew nor cared about the applicability of the results. The strength of the mathematical result lies in the fact that it is proven for all time, once a rigorous proof is provided, within its range of assumptions, unlike the physical sciences, which constantly need to be re-evaluated, in the light of new experimental evidence. Not only do mathematicians not worry about applicability, they push ideas to the limit of abstraction, with no particular regard for the constraints of the `real' world. The applicability of mathematics arises when suddenly, an abstraction provides an amazing fit to a practical situation.

Rowlett provides some interesting examples. These include the use of quarternions in applications to robotics, computer vision and graphics programming (Lara Croft, no less!); Riemannian geometries for cosmological models, the mathematics of sphere packing for modern communications, such as channel coding and error codes; the applicability of the Parrondo paradox to the Brownian ratchet which models directed molecular motion; the use of probability theory and the law of large numbers in actuarial mathematics; applications of topology, like knot theory for understanding DNA structure, braids for quantum computing, Mobius strips for conveyor belts; Hilbert spaces for quantum mechanics, and Fourier series everywhere. Practicing scientists and engineers will obviously find numerous others. The British Society for the History of Mathematics has asked readers to contribute examples known to them (see It would also be really nice if readers of this blog would share their examples here. We look forward to your response.

This blog post is by Neelima Gupte and Sumathi Rao.


vbalki said...

Here are a few, not necessarily as profund as, say, the connection between linear spaces and quantum mechanics, or Riemannian geometry and space-time: Topology (homotopy) and defects in condensed matter; Ito calculus and financial markets; random walks amd electrical networks; Monte Carlo simulatins and a huge number of applications; functional calculus and numerous applications (quantum field theory, polymer dynamics); prime factorization and encryptation algorithms.

Neelima said...

Thanks, Bala. There's also the connection between moving space curves, Heisenberg spin chains, soliton equations and numerous other systems, but I'm not the right person to comment on those.

Rahul Basu said...

Here is an interesting link on learning mathematics.