In my last post of 2013, I gave a problem that provides part of the plot of my ebook novel Athene's Prophecy: how could a Roman prove the heliocentric theory? Before doing that, however, I have to go on a diversion to discuss how you actually prove a theory. Yes, I know, you usually see people write, you can never prove a scientific theory; all you can do is falsify it. That is actually wrong. Let us suppose you have a theory A that predicts the set of observations P if experiment E is carried out. Equally, we could have theory B that predicts the set of observations Q if experiment E is carried out. We carry out E and observe O. There are several possibilities: O can be an element of either P or Q, or of both, or of neither. If both, the experiment is irrelevant in terms of being definitive, if neither both theories are wrong, and if one but not the other, the other is wrong. Under this circumstance, no theory is proven. To prove a theory, it must be of the form, if and only if theory A is correct, then we shall see the set of observations P if experiment E is carried out. The problem, of course, is to justify the "only if" part, so that is what has to be done by my Roman to prove the heliocentric theory.
 
In practice, there is more to it. The first step to overturning a theory, which is what had to be done here, is to review the literature. Personally, I find classical science to be quite interesting because it shows some very interesting issues that apply today just as then, and further, if you look carefully, what we read today about the ancients is really not fair to them, and in the next series of posts, I hope to illustrate that point.
 
Now, there are two ways of reviewing the literature. The first is to read what is there, accept it, and try to work out how to develop what from it. I believe that is the common practice today and most scientists are quite happy to accept the literature explanations and use them to solve more puzzles, in the spirit of Kuhn's "normal science". The second way is to deeply question certain issues, to be sure the theory is on sound ground. In my opinion, this is done only too infrequently. How many current scientists have ever really questioned something of fundamental nature given by authority? Throughout history, everybody seems to think "they are on the right track". We know classical science was not, but how many think we are currently more or less correct? Quantum electrodynamics is regarded by many as the most accurate theory ever in science, but it can be regarded as a subset of quantum field theory. The vacuum energy predicted by quantum field theory appears to be wrong by a factor of at least 10^107. That is an enormous difference, in fact one could say it is well outside any experimental error! But how many scientists actually think quantum field theory might be wrong in some way? More importantly for you, how many theories or explanations in chemistry have you ever thought could be wrong? If the answer is more than zero, what did you do about it? Why not?
 
That last question gets to the heart of the matter: the reviewer has to have an urge to overturn something. The "official" line is, that urge is provided by observations that do not fit the theory, however I think that is wrong. The vacuum energy error mentioned above is an example. The fit with theory is appalling but there is no attempt to overthrow the theory because quantum electrodynamics makes some absolutely remarkably accurate predictions elsewhere. When the theory works much of the time, as Kuhn noted, awkward results tend to be placed in the drawer and forgotten. The average scientist does not wish to overturn the apple cart. The reason for not wishing to do this are clear: most of the time he believes he will not get anywhere, and spend a lot of time not getting there. Einstein spent over fifteen years trying to get relativity in order, and how many scientists have his ability? With promotions, funding and general standing in the scientific community at stake, who wants to spend years not getting anywhere, getting publications rejected, or being regarded as a curiosity? In classical times, the problem would have been worse because if you succeeded, who would care? People work for reward, and for most scientists, reward means, acknowledgement by your peers. You do not get that by trying to show they are wrong. In classical times, most of the time you had no peers. Archimedes made his discovery not to unravel nature, but to solve a problem given to him. There would be no reward for a Roman to prove the heliocentric theory, because current theory did everything that was required of it.
 
Finally, I promise I shall get to the issue, but not next post, because it is time for a review of planetary formation theory.