Title: Chaos, order and regularities
Course: UGQuants (SSPS) > Section: Probability

Chaos, order and regularities

A useful place to start is chaos. If everything in the world, natural or social, varied randomly or occurred purely by chance, then we would live in a state of absolute disorder that was neither knowable nor predictable. There would be no regularities in the past that we could remember and describe to help us understand the present, nor would we have any way of conceptualising or predicting anything about the future.

Life, however, is not completely random or chaotic: it has order. This is easiest to see in the natural world. We know that if we throw something up in the air, it will – unless something intervenes - come down again. We know that if we hold a mirror up to a source of light, the mirror will reflect it. We know that a cube of ice immersed in hot water will melt. We know that each day, at dawn, the sun rises (unless you live in Scotland).

These kinds of order can be thought of as the existence of regular or stable relationships between variables. For example, in the case of water, if the variable temperature takes the value 10 degrees Celsius, then we can confidently predict that the value of the variable state of matter will be 'liquid'. Likewise, at 110 degrees Celsius the value would be ‘gas’.  Physics describes some important relationships in terms of 'Laws', which are better thought of as well-established theories: such as Newton's laws of motion.

Like our theories about the social world, such theories are falsifiable (that is to say, they are open to criticism, testing and retesting, and thus improvement) and have indeed changed as new evidence has been gathered and new theories developed. Thus Einstein's theories about time and space led to a revision of Newtonian physics and later the development of quantum physics in which the ‘Laws’ are quite different.