Well, marcus, you may be right that there was no battle at all, but I belive there was sometimes a battle, or at least passionated discussions regarding the role of quantitative methods for the understanding of nature. I think the origin of these can be traced to Plato and Aristotle, with the different roles of sensorial experience in knowledge. Anyway, I am not an expert in history of science and I cannot be more profound here.
On the other hand may be you misunderstood me. I was not talking about life, but about science. Of course nobody thinks about mathematical models when swiming in the sea or being in the beach, but, note: no scientific theory relies today on physical feelings, or on anykind of role of the subject when explaining something.
For example: as you probably know, the ancient greeks postulated the world to be made of earth, fire, water and air. We may laugh about that from our quantitative and analitic way of thinking, but it is subtle: it depends only on which point of the distance between object and subject you are focusing. Their focus was near the subject and they thought that the different categories of sensorial feeling shoud determinate, or at least give clear hints about the nature of the objects. The next step is obvious: just look in yourself and find out which categories of sensorial feeling you may experience and then try to extrapolate to reality.
I am confident that something like this is definitely lost in the occidental culture, means a different kind of relation between subject and knowledge, a different weighting. Whether this can be regarded to be more intuitive than modern physics is another question. In my oppinion it may, it depends what we understand under the term intuition.