We are all interconnected.
Every living being on Earth is a part of a huge web and what affects one part will
ultimately affect every other part. Bet your maths textbook never taught you that! Well,
that’s exactly what the mathematics of complexity is all about. |
It
includes fractal geometry (you’ve already read about that) and the chaos theory
(which you’ll read in the coming pages).
But mathematics of "complexity"? Isn’t maths complex enough in the first
place? Not really, new mathematics is a fascinating journey of relationships and patterns
and covers everything under the universe. But before we get on to exactly what this means,
let us see the limitations of old mathematics.
The Greeks thought that every problem in the world could be solved using classical
geometry. Galileo carried this further and used it to explain the solar system. By the
time Newton explained his laws of motion, everyone was convinced that the world was like a
mechanical clock and if you knew all of the initial conditions and how the it worked you
could predict what would happen at any point in time. Science assumed that everything
could be known and eventually predicted. The Universe was ruled by a detailed system of
unchanging laws.
The "cosmic clock image" first began to shatter at the turn of the nineteenth
century when physicists found that at the behaviour of the atom and individual electron
could not be predicted. This gave birth to quantum physics decades later, but this,
however, developed independent of the physics Newton came up with.
NEWTON, OLDHAT
Taking another example, you may have studied that Newton’s laws of gravitation work
extremely well if we take two bodies into account. Take three bodies and it’s quite
difficult, and beyond that the equations are so complicated that even a supercomputer
cannot solve it. So science was already finding it difficult to explain complex systems.
But no one had articulated a different view to replace the one that existed.
In fact, Mathematics prided itself in its detached, abstract isolation, completely
apart from the real world — particularly nature — breathing instead the refined
and pure air of its own self-contained universe of number. In the last century it even
divorced itself from physics, its sister science for centuries.
CHAOS REIGNS
But now mathematics is making a comeback in a new avatar, totally shedding the image of
the world as a cosmic clock with unchanging laws.
Now this is not to say that laws don’t govern nature and the universe at all, but
the laws are of a different kind than previously thought. The real world is fundamentally
disordered, free. Chaos reigns over predictability. The world is an astonishingly complex
pattern, which is actually a sum of simple ones. And all its elements are self-organising
and inter-connected, where the whole is more than the sum of its components. (Something
that would be abhorred by old mathematics)
In fact, the thrust is now from linear to non-linear. In the linear world, small
changes result in small deviations and large changes result in large deviations (like you
study in your mathematics equations). However in the real non-linear world, a small change
in the initial conditions can have cataclysmic results and large changes may result in
minor deviations. (Confused? Read "Law and Disorder on page 74). In fact, simple,
linear systems are the exception in the Universe, not the rule.
New mathematics found that science had been fooling itself for centuries by ignoring
tiny deviations in its data and experiments. If a number was slightly off what the causal
laws predicted, the scientists simply assumed there was an error in measurement in order
to uphold the sanctity of the law itself. And even computers can push a linear model so
far.
The nineteenth century was the last century where classical science ruled. In the
twentieth, it co-existed with the new school of thought. The twenty-first century on the
other hand, may just be the century of the mathematics of complexity.
The real world
is fundamentally disordered, free. |
New
mathematics has found that science has been fooling itself for centuries |
|
