# Thread: What does the word arbitrary mean in this definition?

1. I'm a lay person with no scientific education whatsoever. I'm reading Stephen Hawking's A Brief History of Time, and I have question about the following definition that appears in it: A theory is a good theory if it satisfies two requirements: It must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations.

My question is about why the definition makes a point of saying "a few arbitrary elements." Why do they need to be arbitrary?I'm assuming that maybe, this refers to the way observations may be explained through the use of many different kinds of elements or concepts, and the scientist needs to pick and choose a few for his theory, given that a perfect, all-encompassing theory that explains all possible data isn't realistic. There's no real reason why he should pick one concept over the other, other than his gut instinct. For instance, an ancient scientist may have attempted to explain why a stone falls to the ground by pointing to data to do with a concept such as the weight of the atmosphere above pushing it down. Newton, though, chose to use concepts such as mass and gravity. The types of concepts each scientist chose to base his theory on was nothing but a personal preference or instinctive idea, and therefore "arbitrary".

This is how I understand it. Am I correct? Thank you for your help.

2.

3. It seems to me that Hawking expressed himself badly.
A good theory should contain as few arbitrary elements as possible.
I.e. "arbitrary elements" are not desirable, but, lacking total information, we have little choice but to include them. Especially in the initial stages.
You have to start somewhere, pick an arbitrary start point and test it against reality...

4. I think an example of this would be Newton's law of universal gravitation which states that bodies attract each other in proportion to the product of their masses and inversely proportional to the square of the distance between them. Starting with this "arbitrary" relationship you can explain the elliptical orbits of the planets, Kepler's laws, and also the effect of gravity on bodies on earth. This is a big improvement over earlier models such as the idea that the planets were guided in their orbits by hordes of angels beating their wings, each of which was acting independently in an arbitrary fashion.

Newton's law of universal gravitation is "arbitrary" in that it doesn't seem to be based on anything more fundamental. It just works.

5. Originally Posted by Harold14370
I think an example of this would be Newton's law of universal gravitation which states that bodies attract each other in proportion to the product of their masses and inversely proportional to the square of the distance between them. Starting with this "arbitrary" relationship you can explain the elliptical orbits of the planets, Kepler's laws, and also the effect of gravity on bodies on earth. This is a big improvement over earlier models such as the idea that the planets were guided in their orbits by hordes of angels beating their wings, each of which was acting independently in an arbitrary fashion.

Newton's law of universal gravitation is "arbitrary" in that it doesn't seem to be based on anything more fundamental. It just works.
I don't think the inverse square part is arbitrary. It embodies the way the intensity of something emanating from the surface of a sphere becomes attenuated as it spreads out with increasing distance, other examples being light intensity and the strength of electric or magnetic fields. And the idea of a force proportional to mass is fairly evident from the observed weight of objects, isn't it?