Validating theories

After more than a month of architectural redesign in the software product I am working on, I reluctantly took a couple of days off to attend a cousin’s wedding (which was interesting enough to merit a post of its own… coming soon…). The last pieces of the redesign are left and this morning, I intended to resume and finish them off. Instead, I just ended up sitting in front of my computer for several hours staring at the screen blankly. Surprised at this, I constructed a theory that being the introvert that I am, the two days of social interaction had taken so much out of me that my mind had hibernated and needed to reload all the stuff needed to think about work from the hard disk. (Perhaps, as a programmer, I can’t help thinking about everything in computing related analogies) The theory tied in nicely with what programmers call being “in the zone” (Look for Paul Graham’s essay on the topic – if I am not mistaken).

A few hours later I discovered that I had an upset stomach and a slight fever. So much for my theory! I need to be more careful.

Science and philosophy – 2

I just finished reading “dreams of a final theory” by Steven Weinberg. The book is somewhat less technical than I had expected. Despite having a chapter titled “Against Philosophy”, Weinberg deals with several issues that have more to do with the methodology of science than with its content, such as reductionism, “aesthetics” in science, positivism, belief in God etc. Overall, the book is quite enjoyable. I am interested in developing a better understanding of several of the issues Weinberg discusses, so this book has given me a lot of starting material.

To me, the most interesting arguement that Weinberg makes is that “aesthetics” has played a significant role in the formulation as well as the acceptance of several of the theories that have been developed in the last century. I had encountered similar claims before but had not taken them very seriously. But Weinberg makes his case quite convincingly. He argues that validating a theory by means of experiment is not as simple as it may seem. There can be any number of reasons for an anomaly in experimenal results. In judging whether a theory may be valid, whether it is worth trying to validate, physicists necessarily rely on “aesthetic” judgements. As an example, he argues that physicists were more or less certain of Einstein’s theory of general relativity before it was conclusively validated by experiment. As another example, he argues that physicists were sceptical of the theory of quantum electro-dynamics although it was in agreement with experimental results because some calculations based on it involved “ugly” infinities in intermediate steps. He writes that part of this “beauty” lies in simplicity – not the simplicity of the equations but of ideas. Another part of this beauty lies in what he calls logical isolation or rigidity. For example, he writes that no one has yet found a way to make a small modification in the principles of quantum mechanics without destroying the theory altogether. It would make little difference in Newton’s inverse square law of gravitational force if the exponent were changed to 2.01 instead of 2, but even the introduction of a small non-linear term in the linear equations of quantum mechanics produces nonsensical results. Such a theory does not explains why it should be correct but it explains why it cannot be just a little wrong. Concluding a chapter titled “Beautiful Theories” Weinberg writes

We believe that, if we ask why the world is the way it is and then ask why that answer is the way it is, at the end of this chain of explanations we shall find a few simple principles of compelling beauty… the beauty of present theories is an anticipation, a premonition, of the beauty of the final theory. And in any case, we would not accept any theory as final unless it were beautiful. (emphasis mine)

The last sentence in that excerpt sums up most of what Weinberg is saying about beauty. If one keeps asking why as Weinberg does, there will come a point where one will have to stop. How does one decide what that point is? For Weinberg that point will have been reached when we have a simple and logically isolated theory that “explains” everything including the values of what we call universal constants.

In my next post in this series, I will try to present my own thoughts on what it means for a theory to explain something and on beauty.

Science and philosophy – 1

A couple of days back, in a comment on this video, I wrote

Unfortunately because of the philosophy of logical positivism, most scientists today are afraid or unwilling to accept the necessity of metaphysics at all.

Today, I started reading a book “dreams of a final theory” by Steven Weinberg. Early on in the book, he writes

Speaking of a final theory, a thousand questions and clarifications crowd into the mind. What do we mean by one scientific principle ‘explaining’ another? How do we know that there is a common starting point for all such explanations? Will we ever discover that point? How close are we now? What will the final theory be like? What will it say about life and consciousness? And, when we have our final theory, what will happen to science and to the human spirit?

A few pages later, explaining what the pursuit of a final theory means, he starts with “Chalk is white. Why?” Some answers (light, wavelengths etc.) and then another “why”. Some more answers (atomic structure, energy levels etc.) and then another “why” and so on until he comes to a point where he does not know the answers. Finally, he writes,

Even so, it is a tricky business to say exactly what one is doing when one answers such a question. Fortunately, it is not really necessary.

and then, a few paragraphs later,

Ludwig Wittgenstein, denying even the possibility of explaining any fact on the basis of any other fact, warned that ‘at the basis of the whole modern view of the world lies the illusion that the so-called laws of nature are the explanations of natural phenomena.’ Such warnings leave me cold. To tell a physicist that the laws of nature are not explanations of natural phenomena is like telling a tiger stalking prey that all flesh is grass. The fact that we scientists do not know how to state in a way that philosophers would approve what it is that we are doing in searching for scientific explanations does not mean that we are not doing something worthwhile. We could use help from professional philosophers in understanding what it is that we are doing, but with or without their help we shall keep at it.

As an engineer, I can certainly sympathize with what Weinberg is saying. Philosophers such as Wittgenstein have betrayed science (and philosophy). But that is not a good enough reason for scientists to abandon philosophy. Proper science needs a solid base in philosophy. I dare say that without an explicit (philosophical) understanding of what “searching for scienific explanations” means, scientists will not discover a final theory. I think science has reached a level (based on some reading of quantum mechanics) from where it cannot proceed without answering some fundamental questions that are not just scientific.

Anyhow this is a fascinating subject, and I will return to it often. I have been fascinated by this subject for about an year now, and have been reading some books off and on when I find time. So far I have not written on this subject, because I do not like to write unless I have a clear idea of what I am writing. But it seems unlikely that I will find answers to questions like this without a lot of thinking. So I intend to think by putting my thoughts on this blog instead of doing it before going to sleep.

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