Opinion-Sustainability through mathematical lens

The editorial board of Sankhya, department of mathematics of Miranda House, is elated to bring to you an opinion article on Sustainability through a mathematical lens written by Ashika Deb, a third-year mathematics honor student.

Today every organization’s goal is either to achieve sustainability or its role is intimately entwined with sustainability. For those who might not be familiar with the term, sustainable development is an organizing principle for meeting human development goals while simultaneously sustaining the ability of natural systems to provide the natural resources and ecosystem services on which the economy and society depend. But where does Mathematics factor into all this?

The answer is in fractals! Fractal, in mathematics, is a class of complex geometric shapes that commonly have “fractional dimension”.

Studies over the last couple of decades have established the monumental importance of fractal geometry – and its related field of chaos theory – in science. “Chaos,” as its name implies, is the study of processes that appear so random that they do not seem to be governed by any known laws or principles, but which have an underlying order. In simple words, not even the most random things are random, and we’re beginning to determine just what that underlying “code” is. Scientists are learning that everything natural including static elements as well as energy flows, living things, and their behavior patterns are created by the immutable laws of fractal geometry. We are now beginning to learn how to dissect these “codes” and fractal geometry is now being used in many different ways like understanding the impact of economic trends, computerized image/data compression, human behavior, natural systems, molecular biology, cosmology, and much, much more.

When we think of sustainability, we think of people, the planet, and profits. If these are bound by the laws of a fractal; geometry, it follows that their combinations will be similar. A closer examination proves the point.

Human physiology and psychology, seemingly complex, follow fractal patterns. Natural objects like clouds, trees, ferns, snowflakes, crystals, etc can be produced remarkably accurately within a computer using relatively simple fractal geometric equations.

Our understanding of fractal geometry has enabled us to understand that the ethical perspectives and the functioning of a community are based on fractal geometric relationships. Fractal geometry has significant ramifications in economics and finance. In a nutshell, understanding fractal geometry enables organizations to improve their profitability and opens up entirely new economic opportunities, For instance, in the 1930s, Ralph Elliott proposed that market prices unfold in specific patterns, which we now call fractal patterns.

In 2002, William McDonough and Michael Brungart introduced the Cradle to Cradle Design Framework which used the concept of "fractal ecology" symbolized by the fractal equilateral triangle model of sustainability to demonstrate how the three ecology-economy-equity bottom line needs should integrate.

Life is based on a fundamental “code”; patterns that replicate themselves on increasing and decreasing scales. Similarly, for sustainable development, the underlying code is comprised of three elements - Utility, Effectiveness, Efficiency. To incorporate these concepts, one must make use of “People, Planet, Profits.” Profit represents the utility to be attained; Planet represents efficiency and the understanding of limited resources; People represents the opportunity for effectiveness.

To visualize (in terms of SLDI Code) think of a three-sided fractal geometric figure. It’s called Sierpinski’s (equilateral) Triangle. It consists of an equilateral triangle, with smaller equilateral triangles recursively removed from its remaining area

It penetrates deeper and deeper into project decision-making, replicating itself throughout all of the various areas, aspects, and phases of the project development process from planning through finance, design, construction, maintenance, and back to planning again. As it goes deeper, the basic instruction of optimizing/balancing utility, efficiency, and effectiveness continues to replicate itself. The SLDI Code provides the basic instructions upon which any sustainable project may be achieved. The principles used are so universal that the code can be used on any project enhancing the quality of outcomes, however diverse they may be, toward greater sustainability from a holistic people, planet, and profit perspective.

If you reflect for a moment, it's as though we are somehow programmed by mathematics. Snowflake, human, or the galaxy: we're all bound by the same order

Source of inspiration: www.triplepundit.com