Sunday, June 24, 2007

Truth and Verification

There may be many positions on truth in this installment I will focus on two the Hegelian and the existentialist. The Hegelian view holds that there exists a God-like point of view from which it is possible to reason about the world, in other words, absolute truth is possible. The existentialist holds that we are finite beings as such a God-like point of view is not possible. Both are right but, the reason why is contained in neither.

I think Karl Popper gave us an answer. Karl Popper believed that humans are capable of attaining absolute truth but, the problem is verifying that a statement is true. This statement shows that both the Hegelian and the existentialist view are correct and both incorrect.

I suppose a Hegelian could argue that a God-like point of a view presupposes a God-like method of verification, in which case the Hegelian must show that such a method of verification is accessible to finite beings (like us). Until such time we must accept some tenets of the existentialist view, our methods of verification are finite as we are finite beings.

Let us apply the above to physics. The above statements imply that though we may have the ideas and theories that will turn out to be true or close to true, we will not be able to verify that they are true or close to true, ahead of time.

Friday, June 15, 2007

Necessary But Not Sufficient Part III

I don't want to give the impression that any theoretical physicist is doomed to failure rather I wanted to give an explanation as to why progress in science is not linear and why only a couple of physicists make breakthroughs. Also I wanted to make clear that it has nothing to do with competency, simply because you ended up working on a theory that turned out to be false doesn't mean you are an incompetent physicist.

Once again I must reiterate the probability of making a breakthrough is higher if you try than if you don't try. In lieu of future knowledge as to which ideas or theories will turn out to be correct the best we can do is use critical thinking to determine which theories or directions have a higher probability of being correct. In the very least we can determine which theories or directions that we think will be fruitful. Not every paper will lead to a breakthrough but it will clarify some point of contention or simply show what can be done with certain starting assumptions. On the positive side, someone may have already published a paper with an idea that one day will work.

I take Edison's philosophy to heart after failing nearly 10,000 times to find a light bulb filament that won't burn some news reporter asked him, "how does it feel to fail 10,000 times" Edison said "I haven't failed 10,000 times, I have successfully found 10,000 ways that won't work". Later on he found a way to not burn the filament and yet have the filament glow. We have many physicists who have successfully found ways that either won't work, have trouble working, or one day will work. All in all each paper serves a purpose and each is our best effort to find the truth, or an approximation thereof.

Thursday, June 14, 2007

Necessary But Not Sufficient Part II

Sometimes people believe that sheer intelligence will yield a correct theory in physics, people believe that intelligence gives people the ability to "derive" or "see" the correct theory of physics.

Though ability does help, the biggest problem with this belief is that there are many internally consistent, plausible, and complex theories that can describe or hopefully describe the same phenomena and yet can recover the classical theories of physics. Sometimes plausible theories require much work to develop, sometimes they are developed to the point where an insurmountable problem arises or a contradiction arises, this is another problem. Sometimes the theories yield falsifiable predictions which require new technologies or funding to test. As one can see without the benefit of future knowledge as to which theory will lead to correct predictions, even the most intelligent person on earth can spend his/her days working on a theory that will turn out to be false.

If there was only one logically, mathematically possible theory, it would be easier to develop the "right" theory. The problem is that we tend to view progress in science as a linear process where each proceeding theory is seen, in a loose manner, as obvious and as the only theory logically consistent with the older theory. So we fall under the impression that nearly every theory was obvious, if only the people back then could "reason" or "think" correctly. This is only possible with hindsight for the criteria for correct reasoning, in a certain field, is constrained by the knowledge/insights/results available at the time. The reason the "correct" path was not obvious to people of the past is that at the time what was considered obvious was completely different.

John G.

Thursday, June 07, 2007

P.S, P.S.

As a post script to post script I would like to say, that there are no guaretees but there are probabilities. Some people might reason that if there isn't a guarantee of a breakthrough then why should they make an effort to study theoretical physics? The reason is that the probability of making a breakthrough is much higher if you do try than if you don't try. The probability that you will make a breakthrough is higher if you study hard and go to a good university, the probabilities are higher if you try to develop new ideas or at least new directions.

Sometimes the physical concepts, mathematical concepts, and the technology are available to make a breakthrough, someone simply has to reorient their thinking to see it. Sometimes neither the physical concepts, mathematical concepts, nor the technology is available, the problem is that we as people, constrained by results/insights/knowledge of our time, cannot determine which of the two scenarios obtains. This is why it is crucial that we try, for our attempts and our mini-breakthroughs will eventually add up possibly allowing someone in the future to make a major breakthrough.

Tuesday, June 05, 2007


As a postscript I should mention that not all ideas are equal, some ideas have a higher probability of being closer to truth than others. My point is that we must strike a balance between complete stifling of free thought and treating all ideas and theories as equal. This is why it is so difficult to develop something new, the idea must be "irrational" enough to be new but "rational" enough to be plausible.

Monday, June 04, 2007

Necessary but Not Sufficient

People often believe that by simply mastering existing theories and concepts that somehow they will assuredly discover or create something new. Though mastering previous theories and concepts is necessary, it is not sufficient for developing something new. It is one thing to master that which already has been done, it is quite another to discovery/create something new.

The problem is that it is not possible to rigorously derive new theories from old theories, in other words it is not possible to discover/create something new thinking strictly in terms of old structures of thought. For example it is not possible to rigorously derive Quantum Mechanics or General Relativity from Classical Mechanics, though it is possible to derive Classical Mechanics from QM and GR. So, the process of discovery/creation can't be too rigorous simply because the new theory contains ideas and concepts not contained in the old; you can't extract concepts that are not implicit in the fundamental assumptions of the old theory. Sometimes these new ideas may appear irrational, if reasoned from the perspective of the old ideas. A strange inversion occurs the old ideas become irrational when the new ideas are shown to be valid. On the other hand, the reasoning can't be too loose, it must be possible to extract the old theory from the new. This is why high intelligence does not guarantee discoveries/progress; the path to the new theory is not simply a complex derivation from the old, in other words it is not linear. To be fair innate ability does help, though lack of innate ability doesn't imply a lack of discoveries/progress.

Obviously this implies risk because the ideas have not been shown to be valid, the chances you will turn out to be wrong are high. The reason why we take this risk is because the old theories sometimes prove to be inadequate, this is not because previous physicists were incompetent rather, it is because we have information/results/insights they didn't have. Sometimes the new information/results/insights shows there is a problem with their theory. There may be elements of truth in the old theory, but these elements are constrained by the information available to their creators.

Another problem is that people may not want to question old ideas/theories on the basis that old ideas/theories have worked so well and are so well reasoned that they must be true. Sometimes people don't question old ideas/theories on the basis that if people "smarter" than themselves couldn't improve upon the theory, neither could they. At other times people believe that everything that could ever be thought of has already been thought, so what's the use? Sometimes people believe something to be impossible hence they don't consider it further. Some people believe it is not their position in life to develop something new, that is left to "special" people. Others simply don't want to make the effort. Finally any new idea brings the risk of the unknown and of being shown wrong hence, many people do not want to take the risk. The entire paradigm of thought weighs heavy on people's shoulders any attempt to cast it off is difficult.

Many people wish for a life or career of guarantees; guaranteed success, guaranteed position, guaranteed wealth, and for the physicists, guaranteed truth (or approximation thereof). The problem is that there is none; you may spend your entire life working on a theory only to have it turn out to be wrong, you may be the most intelligent person on earth working on what appears to be the correct direction for a new theory only to have it destroyed in an instant.

These prospects sometimes lead people and sometimes entire cultures to rarely take risks, to rarely think of something new, or to even pursue new avenues of thought. According to them, it is much safer to work with theories and ideas that are already established, especially if one desires guaranteed results or success. Sometimes entire societies inadvertently stifle free thought, especially if the cultural structures of thought implicitly impair the development of new ideas. This usually takes form as a belief in certain unquestioned assumptions that may or may not be evident, sometimes it is a belief that every idea must be rational (in common parlance it must make sense), the only problem is that what is considered rational is constrained by available information/insights/results.

To sum up it is necessary to master established theories but it is not sufficient to make new discoveries.

Saturday, June 02, 2007

Study Time

People often get the mistaken impression that by simply sending a child to SAT prep courses or intensive study courses, in any subject, that somehow, magically, the child will show significant improvements in performance. The problem is that 1 or 2 hours of intensive study per week cannot substitute for 1 or 2 hours of intensive study over an extended period of time.

The child may show some improvement if he/she studies 1 or 2 hours per week but, if you desire your child to show significant improvement, he/she must study intensely everyday. In addition your child should strive to improve their study technique in comparison to the previous day. They should strive to understand more or understand things more deeply, they should strive to identify their weak spots and work on them until they become strong. They should strive to understand the logic behind the subject, to understand the subject from a broader perspective, and finally they should strive to improve the very way they improve their study technique.

As you well know sports is my favorite analogy; how can you expect to become a better baseball, soccer, or tennis player if you only practice intensely 1 or 2 hours a week? Also, when you do practice you don't practice with the intent of practicing better than you did last time? Eventually you will reach a plateau of performance that has nothing to do with genes or talent. The only way to break through that "wall" is by pushing yourself to be better than you were last time, to constantly seek ways to practice better, and finally to realize that practicing intensely everyday yields far better results than practicing intensely once or twice a week.