by: Paul Martin

We want to understand the universe. We want to be able to make predictions about what will happen in certain circumstances. We come up with theories that predict things. If the predictions are accurate and we are able to comprehend and describe the theory, then that is called 'science' and we say we understand the universe to the extent that the theory covers phenomena.

Theories have traditionally been discovered by first speculating on, or guessing at, some predictive rule, then using the rule to make predictions for certain experimental circumstances, and finally to observe the results of the experiment to verify the predictions of the theory. This is the basic method of science and it has proved to be extremely successful.

The question was posed by Einstein and by Hilbert asking what, if anything, can we know about the universe in the absence of any observed data. In other words, can any conditions or constraints on what is possible to exist in reality be derived and demonstrated mathematically? Dick Stafford has answered the question in the affirmative and shown how to derive a constraint which implies most of the laws of physics.

One assumption is made at the outset that the universe, or at least the part we are interested in, is communicable. That is, it is describable to the degree that the descriptions can be communicated from one human-like mind to another. Since we find that our universe is describable in that way, the assumption is not vacuous. If there are other universes, or aspects of our own or any other, which cannot be referred to, the constraints discovered by Dick do not apply to them.

Dick approached the problem by examining a completely arbitrary set of numbers. He discovered that it is always possible to augment the set of numbers with "unknowable" data in such a way that a rule will exist allowing the unknowable data to yield the original set, or "knowable" data. This fact represents a constraint on the augmented set, i.e. the "knowable data" plus the "unknowable" data, while the original set of "knowable" data remains completely unconstrained.

Since the universe is describable, all physical facts, patterns among those facts, and concepts involving the facts and patterns, can all be described. These descriptions can be represented by sets of numbers.

Since the set of numbers was completely general, the constraint he found applies to any set of numbers, including the set described above as representing descriptions of physical facts and patterns and concepts involving those facts. This means that the physical facts themselves and the patterns and concepts all fall under the constraints Dick discovered. Sure enough, when solutions to the equation stating the constraints were found, they turned out to be the familiar laws of physics.

To bring this a little closer to home, think of the original set of numbers, i.e. the "knowable data", as having any and all information available to us from the universe (reality). Think of the "unknowable data" as the explanation or theory we have come up with to explain or describe the universe (reality). The conclusion is that no matter what true "reality" actually is, it is possible to interpret the information from it that is available to us in such a way that the familiar laws of physics will hold.

Previous introductory essay
Next introductory essay
Links to introductory essays