Is there a proper name of learning by experience (i.e. feeling something subconsciously)?

Question

We all know about these two ways of learning:

1. Rote learning (by mechanically repeating something to remember it).
2. Learning by understanding (by understanding the logic behind something).

But I strongly believe, that one more way of learning exists - learning by feeling. But do we have a term or some explanation for this type of learning?

Some examples:

1. you can learn the formula for least-count of device by:
   • repeating it to remember it whenever required;
   • understanding it to derive it whenever required;
   • by feeling it, i.e. using the device for some time, to enable us to put that formula in our subconscious mind;
2. (better example) in chemistry, we can learn the effect of $NO_2$ on benzene, the following ways:
   • repeating it;
   • understanding its chemical nature, its structure and then concluding the results;
   • by seeing examples of its reactions and feeling that that is its behavior, to happen like this.

Answer 1

Maybe what you are looking for is tacit knowledge:

Tacit knowledge is the kind of knowledge that is difficult to transfer to another person by means of writing it down or verbalizing it. For example, that London is in the United Kingdom is a piece of explicit knowledge that can be written down, transmitted, and understood by a recipient. However, the ability to speak a language, ride a bicycle, knead dough, play a musical instrument, or design and use complex equipment requires all sorts of knowledge that is not always known explicitly, even by expert practitioners, and which is difficult or impossible to explicitly transfer to other people.

With tacit knowledge, people are not often aware of the knowledge they possess or how it can be valuable to others. Effective transfer of tacit knowledge generally requires extensive personal contact, regular interaction and trust. This kind of knowledge can only be revealed through practice in a particular context and transmitted through social networks. To some extent it is "captured" when the knowledge holder joins a network or a community of practice.

Another word that may suit your description is intuition:

Intuition is the ability to acquire knowledge without proof, evidence, or conscious reasoning, or without understanding how the knowledge was acquired. Different writers give the word "intuition" a great variety of different meanings, ranging from direct access to unconscious knowledge, unconscious cognition, inner sensing, inner insight to unconscious pattern-recognition and the ability to understand something instinctively, without the need for conscious reasoning.

Instinct is often misinterpreted as intuition and its reliability considered to be dependent on past knowledge and occurrences in a specific area. For example, someone who has had more experiences with children will tend to have a better instinct about what they should do in certain situations with them. This is not to say that one with a great amount of experience is always going to have an accurate intuition.