Science after the 18th century was based upon deductive and inductive logic and traditions of rationalism. Mathematics is not the “imposition” of defined quantities onto nature, but rather the representation of this deductive/inductive logic and rationalism.
Prior to this, such expressions were indeed derived from observation and experiment. From then on, this was not the case. Science became progressively theoretical, with new theories being derived from logical principles preceding it.
I have done my dissertation on this subject. Western science uses the hypothetical-deductive method. This is neither rationalism or empiricism. It is based on making your hypothesis sound rational. You make an observation, you develop a theoretical model to explain the observation, and then your model is used to make predictions. However, your model is just a model, and in the future new observations are made which falsify the previous model.
It is not that simple though, because new observations do not lead to an immediate falsification of the model. When a new observation is made which falsifies the old model, the observation is either rejected as an outlier or normalized to fit the model. When the data becomes statistically significant the model is falsified and a new model is created.
This is what your mathematical formalism is. It is nothing but a model which attempts to explain and predict physical events. The equations are just attempts at explanation. Newtonian Mechanics, for example, gives you a set of equations to explain and predict mechanistic behaviour. However, these equations do not work under relativistic conditions such as objects approaching the speed of light , they give wrong results. This is because the world does not at all behave as the Newtonian model predicts. Thus a new model was created, the General relativity model. This involved the complete revamping of the old Newtonian model and introducing new variables such as space-time. However, these equations do not work when explaining and predicing microscopic phenomenon, they give wrong results. Thus a new model was created, the quantum mechnical model which uses statistical probability to predict where an electron will appear. This too does not explain or predict what is really happening, so now they have created the superstring model, which introduces new variables of n number of dimensions.
In this way models come and go in science. So mathematical formalism does not tell us anything other than how we think things are working. A bunch of equations only represent our model. Nothing more and nothing less. Today, science is in crisis, because they cannot explain what is happening at the fundamental level of reality. So there are several models and interpretations of models.
In Hindu science there are no models because Hindu science does not use the hypothetical-deductive method. In fact any kind of hypothetical thinking is considered an invalid means of knowledge, because all hypothesis as modern philosophers of science also argue, is based on assumptions. Your models are all based on assumptions you make. They do not tell you about reality, but rather how you interpret reality. So Hindu science uses a different method: inferential reasoning. You must demonstrate that two premises are invariably concomitant, such that if p is true, then q is also true. If there is x kind of smoke, then there is y kind of fire. This is always true. If there is no relationship of invariable concomitance between two premises, then that is invalid knowledge. Theoretical models are invalid knowledge, because they can be falsified.
In Vaiseshika darsana through pure inferential reasoning they demonstrate that an object will not move until a force is applied, because nothing ever happens without a cause. Thus a relationship of invariable concomitance is established. An object will only move when a force is applied in proportion to the force. Then the next inference is made that an object which is falling must have an invisible force acting down on it. This is because you have established through inference that no object will move without applying a force, therefore to explain the falling of an object you must posit a invisible force that acts down on the object.
This method uses no theoretical models. There is no attempt at creating an explanation of what that force is as in the Newtonian model, because this will only tell us what we think that force is. Newton thought it was an actual quantity. Einstein changed that to a distortion in space-time. The Hindu method does not make any such statements about what that force ontologically is, it simply describes its effects without making any truth claims about what it is.
This is where Western science ties itself into knots. It tries to explain what something is by making several assumptions and claims to explain how it will behave through equations. There are no such knots in Hindu science, because Hindu science is descriptive. It simply says it as it. Yes, there is an effect called gravity, but why there is gravity and what gravity really is adrishya(unknown and unseen)
Hindu science knows that the cause of anything is not simple and cannot be isolated. You can only describe effects, not causes. Thus in Hindu science they use two words to describe causality: adrishya and gunas. Nothing arises independently, everything is of dependent origin. It relies on a infinite network of causes in relation to one another. Thus no equations will ever be able to describe what is going on. You cannot measure anything. But what you can do is describe effects.
Another thing Hindu science teaches is that it is impossible to know the cause of anything through any kind of empirical measurement. That is there are limits to empirical knowledge. Your senses, mind, language and ego are the limits of your world. If you want to go beyond these limits, then you must transcend the senses, mind, language and ego. Therefore Hindu sciences shows that the only method via which one can go beyond these limits is through exploration of consciousness. This is exactly the same conclusion quantum physics has arrived at. If we want to go beyond the quantum barrier it is only possible if we explore the structures of consciousness. No amount of measurement will tell us anything about the world beyond.
So Hindu science went beyond empirical sciences into the spiritual sciences. It uses explorations of consciousness to directly experience the realities beyond the quantum barrier in a controlled observation of mind. It made extensive maps of these realities; mapping out the energy body, the mental body, the causal body and exploring how they interrelate. It has explored the entire mind-matter continnum. This knowledge is unknown by Western science, because it is stuck at the quantum barrier. It does not know how to go beyond it.
The higher sciences pranic sciences and mental sciences completely elude Western science. This is why I am saying Hindu science is ahead. We are past the quantum barrier, while Western science is stuck at it. This is why Hindu scientists have not bothered too much about cultivating material science and technology, for them what is more important is going beyond the physical and transforming oneself completely.
There is a vast continuum of reality out there which one needs to explore. If you isolated yourself in the physical sensory world, you are missing out. Hindu science is all about equipping you with knowledge and methods to directly experience this vast universe and take you beyond your limited view. This is the objective Hindu science serves. If Western science does not adopt Hindu methods, it will never go beyond the quantum barrier. The future of Western science is Hindu science.
I’ve told you we are ahead. You are foolish to think Western science has pulled ahead of us. We are are far ahead of them. This is why Western scientists are looking at our sciences, so they can catch up with us.
Surya Deva, if you study the history of mathematics and science, you can see that all civilizations, had they been left to their own fate, would have developed the same “things” as Europeans did. The same traditions of rationalism, inductive and deductive logic can easily be found in Indian traditions. It was simply a matter of time before someone took up the mantle all civilizations held prior to this, and the toss of the coin landed in favor of the Europeans.
Now, the mantle is once again shifting back to the East.
Nope, that is completely false. If this is true, why did the Africans, Australian aborgines, Native Americans not develop science, philosophy and mathematics, or even literature for that matter? This is because, they were not developed civilisations. All of science, philosophy and mathematics has been developed by three civilisations: Hindu, European and Chinese. Of these the Hindus have been the most superior. We initiated the studies in the sciences because our culture was based on knowledge. We then transmitted these sciences to other cultures. The Greeks were the first to learn from us, then the Arabs and finally the Europeans. They did not develop on our knowledge at all. If our knowledge was in need of development, then why would modern scientists continue to look back on our very ancient knowledge? In the youtube link where the theoretical physicist talks about the Vedic tradition, it mentions how physicists have made it a point to study Vedic knowledge. Why would they if their knowledge was superior?
We are very far ahead in every area. We have served the role of teachers on this planet for 10,000 years. If we were not here, the world would have remained in a primitive stage like Africa. We are the reason there is any science and philosophy at all. There is nothing ethnocentric about this. It is a pure fact. It has been widely acknowledged by all cultures that we were the masters of science and philosophy. We still are. Indian people may not be able to appreciate this, because they have gone gaga over materialism, but many Western people appreciate this. The very great Western scientists you just mentioned like Schrodinger appreciated it. This is why it is a shame that you cannot appreciate your own gems.
. so can india fullfil its potential and become a superpower in more important ways other than cricket (without doing it in a western way?).