Last modified on 19 May 2011, at 11:54

A Lecture on the Limits of Human Knowledge


Ever since Pierre-Simon Laplace envisioned the Hypothetical "Laplace's Demon" in 1814, an entity with infinite computing power that knows the exact location and velocity of every particle in the universe, there has been speculation that if one had such abilities, the past, present, and future of the universe can be predicted. However, there are limits to even this kind of knowledge, and it may very well be impossible for mankind to ever find the much sought-after "Theory of Everything". Does Laplace's Demon hold proof of Predestination? Could it even exist? We will examine these questions shortly.

Laplace's Demon and PredestinationEdit

Let us assume, for one moment, that Laplace's Demon not only could exist, but it is real. The entity is sitting in a laboratory, doing computations, and feeding scientists data about the future of the universe. This scenario could be thought of as absolute proof that free will is an illusion, and that predestination rules the universe. As the Demon simulates particles ricocheting off of each other, forming atoms, cooling down, then gradually forming stars several billion years ago, it watches matter spin, gravity attract material; Earth forms, then life forms, then Humans slowly evolve, it predicts the chemical reactions going on inside our brains, it knows what we will do, what we will think, and what we will feel. For the processes of our brain are no different, no less certain than the boiling of water or the constant flickering of minute switches in the circuitry of a computer. Neurons fire, some adrenaline is released there, some dopamine here, and you get a human thought. What we perceive as free will is merely routine chemical processes occurring within our brains, and we are no more than clumps of matter floating around in the universe like the coldest space rock, as time moves only forward, and the universe expands outward. and nothing- nothing is uncertain in the mind of the Demon.

A Counter to Laplace's DemonEdit

According to chemical engineer Robert Ulanowicz, in his 1986 book Growth and Development, Laplace's demon met its end with early 19th century developments of the concepts of irreversibility, entropy, and the second law of thermodynamics. In other words, Laplace's demon was based on the premise of reversibility and classical mechanics; thermodynamics, i.e. real processes, however, are, under current theory, thought to be irreversible. There has recently been proposed a limit on the computational power of the universe, specifically the ability of Laplace's Demon to process an infinite amount of information. The limit is based on the maximum entropy of the universe, the speed of light, and the minimum amount of time taken to move information across the Planck length, and the figure was shown to be about 10120 bits.[1]

Accordingly, anything that requires more than this amount of data cannot be computed in the amount of time that has lapsed so far in the universe. So not only could Laplace's Demon in the literal sense never exist, but due to the second law of thermodynamics, its principle of predestination is also invalid.

Also, Laplace's Demon's knowledge is limited by the fact that it is in and of itself a part of the universe it is observing. To the question, "Will you answer this question to be true or false?", Laplace's Demon can never accurately determine the answer. This is similar to trying to determine the truth of the statement, "The next sentence is true. The previous sentence is false." Any object in the universe is limited in computing power by itself being a part of that universe, Therefore, it is impossible for the human mind to comprehend a true "Theory of Everything".

Elementary Chaos TheoryEdit

To predict whether a baseball heading towards a house will fall short, smash through the window, or pass overhead -- we look at the location and velocity of that baseball, and we can get a rough estimate of where it will land with a simple estimate. With a bit more information about the wind, we can get an even better estimate of where it will land. There are infinite other factors, for example, the tiny aerodynamic imperfections of the surface of the ball, the gravity of the ball and all objects surrounding it, and other such data that each subtly contribute to the velocity and impact site of the ball, and when they all add together, they can change the trajectory of the ball drastically.

Some kinds of uncertainty are "linear" -- if my measurement of the horizontal velocity of the baseball is 10% too low, then the baseball will probably land about 10% further than my estimate. Other kinds of uncertainty are "exponentially growing" ("deterministic chaos").

ConclusionEdit

In spite of all these things, we can still learn something from Laplace's Demon. For example, the more data that you have about the universe, the more accurate and long range your predictions can be. According to chaos theory, very small factors can alter and influence large and complex systems over time. A butterfly flapping its wings in the Amazon could potentially cause a hurricane in the Gulf coast a week later; e.g. the "Butterfly Effect". However, the more "butterflies" you factor in, the longer the range of your weather predictions could be. Perhaps, one day a vast network of quantum computers, being fed data about micro-climate systems across the planet and planetary systems, the temperature over all regions of the sun, and other data, long-range interplanetary weather- forecasting may not be impossible. However, humans will never be able to predict the future state of the universe accurately.

Further readingEdit