4.4 Scientific Theories and Mathematical Models
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| Milton Visiting Galileo by Granger, 1638 |
Scientific Theories
Scientific theories (henceforth just theories) are beliefs about physical phenomena [1]. These beliefs try to explain the hows, whats and whys regarding the phenomena. For example, the theory of gravity tries to explain the attraction of masses. The belief here is that there is something called gravity that is pulling objects with some property called mass. The concepts - gravity and mass are mere assumptions, beliefs.
Obviously, theories are very useful. Once we have the concepts of gravity, mass etc, say, we can deduce equations, relations, behaviours from experimentation and mathematics and can build buildings, airplanes, boats, send people to the Moon and what not. So why would any sane person call theories an affliction? They become an affliction only when we forget that they are just beliefs, and take them as fact and nothing but fact. I’m sure most of the “educated” folk think that the ideas like gravity, electromagnetism, fundamental particles etc are nothing but truths. After all that’s what their textbooks taught them.
Why does that happen? Usually the educational standards are so low that textbooks do not include the definition of a theory, not even in fine print. No mention is made of scientific method. Philosophy and history of science are fringe subjects (perhaps they don’t land good jobs and make you rich). Students are taught theories (and “laws”) as if they are written in stone. It escapes many, even the intelligent and so called “scientists” that theory is a synonym for belief. Perhaps your school is a better one and did a good job in this case, but only a few get it. Tabloids (aka science magazines) never mention that scientists are simply stating their beliefs when they are describing something about a directly observed phenomenon.
I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called a hypothesis, and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.
- Isaac Newton
When a phenomenon is observed, its explanation starts with the description of its direct observation, how to replicate it and how to measure it. This is pure experimental science (aka Empirical science) and is closest to the truth, but is not the truth, Science does not deal with truths, period. Truth is a philosophical concept, that is, a made up thing, there are no truths, just experiences (we have discussed this in detail earlier). However, there are logical truths, which simply means that some description of an experience/experiment is consistent when seen objectively. Not going again into the nitty-gritty of truths, I’d just say that the relation of a phenomenon with truth ends at empirical observation. After that, its all just theory, concepts, beliefs.
Next, a hypothesis is proposed to explain the phenomenon. A Hypothesis is just a minimum set of assumptions. There can be many hypotheses (E.g. the phenomenon of light can be hypothesized as tiny particles , EM waves or quantum objects called photons, all merely assumptions). A good hypothesis is the one that minimizes the number of assumptions or entities. The hypotheses are then tested via experimentation, and when a hypothesis gathers some evidence it is promoted to the rank of a theory. A theory adds logical statements, equations and predictions to the whole idea. Engineers take up these ideas and implement them in practice, creating new devices, things that work and are useful, providing further support to the theory. No matter how successful a theory is, it never becomes a truth, it remains as a belief.
It is a good morning exercise for a research scientist to discard a pet hypothesis every day before breakfast. It keeps him young.
- Konrad Lorenz
Science progresses by continuously replacing the old theories with new ones. The new ones are better, more elegant and encompass a wider range of phenomena. This alone shows that a theory is just a description, and is totally disposable. In fact discarding theories and promoting a wide variety of them is encouraged in Science. This ensures fresh ideas keep coming in and stale ones go out of favour. Science is very dynamic, ever changing, ever evolving.
So where does it all go wrong? Scientists are just humans and come with all the fears, ego issues, beliefs, biases and stupidities just like any other person. Just because someone is a scientist does not magically make his Mind free of all afflictions. Some scientists (I prefer to call them science-workers) are trained as a scientist due to their education or job, and they grow up into a dogmatic personality full of beliefs. Science is just another religion for them. These people derive their bread and butter from the skills they learnt from the books or such. So any idea of their “knowledge” being incorrect makes them tremble with fear, fear of losing their jobs, losing their credibility or public image. Clearly they have made their survival dependent on scientific views that are in fashion in their days. When the views change (as they must), these science-workers are first to oppose the change. They hold on to their dear beliefs, as their destruction would mean the person’s obsolescence. Pride also pays a major role here besides survival. Some science-workers gain a position of authority based on their old expertise on the subject, and when newcomers throw the old off, they are threatened, they find ways to keep their false pride intact. Finally some politics, cunningness, competition, greed, funding dependencies, desire for fame, jealously etc are other reasons science-workers don’t want science to change or improve and don’t like their beliefs questioned [2].
I’m going to write another article on corruption in science to discuss the sorry state of things in the scientific fields. Science is as good as the person practicing it. So is it all bad? Obviously no. There are real Scientists (with capital S) that arrive on the scene occasionally and throw off the old dogmas through their superior genius. These are the deviant kinds, they have creativity, intelligence and many more qualities a true Scientist should have to make sweeping changes and improvements in their scientific field. Major discoveries, inventions are done by these people. Others, especially the science-workers merely follow them. True Scientists are the ones that push the whole humanity a few notches up, they are the people who actually contribute to the knowledge. They are real sages. Sometimes even these people fall as their contributions are swept away in the coming tide of new ideas in Science, and they become fossilized, opposing any changes. The power of beliefs is not be underestimated.
This is the way nature works. If You don't like it, go somewhere else!
- Richard Feynman (QED Lecture at University of Auckland)
How should one get rid of scientific beliefs? If you are in the field of science, just realize that Science deals with observation and theory (aka beliefs, ideas). The concept of truths is beyond the scope of science, there are just explanations, models and clever descriptions. Nothing is true in Science, and nothing is false. A Scientist is a true Agnostic, open minded critical thinker. It should take only a few minutes for a Scientist to realize what a theory is. However, if you are a science-worker or non-scientist, you need to educate yourself first. See how Science works, how theories evolve. When you have no idea what Science is, you will obviously form wrong notions about it. You will be subjected to manipulation by people who use science as a shield and as a weapon to rule. You will have no choice but to obey the so called scientists. Once you see that Science is only a way to gather knowledge, you will see all its advantages and disadvantages yourself and can judge it better.
Isn’t everything that is unscientific (not based on Scientific Method) just fantasy, woo-woo, mumbo-jumbo? Most of the Science is also fantasy, woo-woo and mumbo-jumbo. One only needs to take a look at the history of Science to see how much mumbo-jumbo it had. One need not assume that it is totally purified these days, it is surely better these days, because it is natural for Science to progress. But most of the Science is founded in fantasy. This is because theory has gained favour over direct Empirical observation for some reasons. Anything new that does not conform to an "established theory" is thrown away. Its a strange upside-down behaviour that has more to do with sociology and psychology than Science itself. However, it remains the best tool that humans ever invented to study the physical universe. That is one part of the answer, the other part is, there is nothing preventing you from applying Scientific Method yourself to the so called woo-woo stuff. Experiment, hypothesize, theorize and publish it to the community, you are most welcome. How many people do that? Almost none, reason – bias, fears (of ridicule, harm to career etc) and hardened beliefs. Beliefs that Science must deal with only material things. There are no material things. Says who? Science.
Science today is locked into paradigms. Every avenue is blocked by beliefs that are wrong, and if you try to get anything published by a journal today, you will run against a paradigm and the editors will turn it down.
- Sir Fred Hoyle
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| A page from Lilavati by Bhaskara, 1150 AD |
Mathematical Models
A mathematical model (henceforth model) is a description of a physical phenomenon using mathematics, numbers and logic. It is simulation of the actual experience of the phenomenon. The simulation resides in the mind, on paper or in a computer. A model is often based on experimental data, but can be totally made up to fit an experiment. An experiment may conform to a model more or less, and that decides the success of the model in explaining it. All models need not describe a phenomenon or any phenomenon, some are just purely mathematical and correspond to no phenomenon at all.
Some example of the models are force/mass/acceleration model of a body (object) which is simply written as F=ma. Another one is V=IR, which is a relation between voltage and current in an electrical circuit. These are very simple models and of course there can be very complex ones such as Maxwell’s equations or Schrodinger equations. The more closely a model mimics the observations, the more favour it gains, and more predictions can be made using calculations. This makes the model useful for developing new technologies and forming new theories.
Wonderful! Science at its best. So why are we dealing with models in mental afflictions section? A model becomes an affliction in the Mind of a scientist or a student of science when it takes on a form of reality. Some people with shallow knowledge of Science (aka indirect knowledge) often take the model as actual phenomenon it is describing. A model is not your experience of the phenomenon, it is a mathematical simulation.
In above stated examples, the mathematical entities viz. force, mass, current, and voltage etc are not experiential entities and do not exist except as concepts. Shocking, isn’t it? Even the scientific beliefs get solidified with time and mechanical repetition, so much so, that ordinary people believe that the modelled entities are “real” things. As it turns out, majority of theoretical science deals with nothing but imaginary entities (aka mathematical objects). These entities are purely mental and correspond more or less with the observations. They are very useful, but are just ideas, beliefs. It is ok as long as ordinary people are concerned, they wouldn’t know any better anyway without devoting their lives in the study of theoretical sciences. But when you are on a path of knowledge, it becomes necessary to dig deeper…deeper than even the most capable Scientist can go [3]. It becomes necessary to realize that the models, whether related to physical or non-physical phenomena, are just simulations, and your experience of the phenomena, if any, will be totally different.
As one can see, the models keep changing, they evolve, some are discarded. Some take centuries and some crumble in a few years. New entities are introduced and old are forgotten. With so much change, one would expect that a scientist would know the difference between observed phenomenon and its model, but no, this is only an ideal case. Science-workers take models literally and so do some Scientists. Ordinary folk simply follow whatever they are told, not their fault, Science is difficult, beliefs are easy.
Notes:
[1] Theories can be created for other kind of experiences too, besides the physical kind. Many would hesitate to call them "scientific" though, because of the strong belief that the "science" (whatever that is) must deal only with the physical.
[2] Even though the science-workers are dogmatic and full of beliefs, they are an important part of the society. They are the ones that enable schools, universities, industries, research labs and many more organizations to function properly. They are usually wiser than any other kind of workers and do contribute to the advancement of Science and technology in an incremental way, by constantly improvising the existing knowledge. Occasionally a science-worker discovers or invents something awesome, which even the best Scientist can only dream of. So I'm very grateful to them for their excellent contributions.
[3] A Scientist is also a seeker, albeit he stops at the level of physical. Reason - beliefs. Where do engineers stand in regard to beliefs? Don't they simply assume the science behind their devices and machines as truth? I've seen that an engineer is generally not bothered very much by what is true, as long as it works. They resemble yogis and seekers when it comes to the matter of usefulness vs truth. In my experience, I've encountered more engineers traveling on a spiritual path as compared to scientists.
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