This is a very brief outline of some of the problems with Popper's refutation of LaPlace's demon. Two analogies are offered as evidence that Popper was mistaken.
In Karl Popper’s The Open Universe: An Argument for Indeterminism he makes reference to LaPlace’s hypothetical demon, which has the knowledge of the entire universe at its conception and knowledge of causal relationships. This demon, with the knowledge at his disposal, would be able to predict the state of the universe at any given time, assuming that determinism were true. Popper refutes this argument by saying that, in order for the demon to have this predictive ability, he would have to be more complicated than the universe itself and thus would not be of the universe. He also goes on to say that scientific determinism cannot be proven until all other scientific questions have been answered. Coupled with his dismissal of LaPlace’s demon this would mean that we could never prove determinism.
We will try to refute Popper’s disbelief that any such being could exist in our universe through a few analogies. Popper’s statement that a being such as the demon could not exist in our universe because he would be more complex than the universe itself is incorrect. The first analogy we’ll examine is concerned with computer programming in the real world. It is not very hard to create a function within a program that could give you the results of any other function from the program. It would take some forethought on the programmers, such as making the function call to other functions through the variables plugged into it. This function would still be able to give you any answer to a question within the limits of the program, and yet would still be part of the program. Not only that, but the “universal function”, as we’ll call it, would actually be relatively easy to create. There is no real reason that LaPlace’s demon couldn’t exist as a sub-function of the universe which could call to any other physical law or relationship in the universe and figure out what the result would be at any given time.
Our second analogy comes from computer production. Today the most advanced computer hardware is no longer designed by humans, but by computers themselves. Computers are used to develop new hardware which is more advanced then the computers that designed it. These pieces of hardware, with their new processing power, can later be implemented into the very machines that designed them. Granted, this is example is on a very small scale, but since it is obviously possible for one object to create an object more complicated than itself, and later combine with I fail to see why such an occurrence could not also have happened on a greater scale with the universe. The universe created something more complicated then itself, maybe to increase its productivity, and merged with it to increase itself.