Is our idea of Artificial Intelligence incorrect?
First we need to know what our idea of natural intelligence is, and so far, there is no unified answer. The closest thing we have is the Turing test, but that has several holes in it and is disputed by many. Even using John Searle's definition of Strong AI, there is still a lot of room for interpretation. In short we don't know yet what exactly needs to be achieved for us to say that we have successful strong AI (Emotional intelligence? Creativity? The ability to see beyond Godel's theorem?). But we are making definite progress, even if we haven't completely defined the target.
But this isn't how our minds operate. When we teach a child what a broken window is, a visual comparison is not the only tool we use. In fact, we could probably teach someone what a broken window is without ever showing them what one looks like, and they will know what it is when they do see it.
Actually, humans don't operate the way you described. A lot of people would recognize a broken window despite never having seen one because they have seen a broken plate or a broken flower pot, and are extrapolating the information that they learned into the new situation of a broken window. They are not performing some form of structural analysis of the surface based on internalized laws of physics or anything like that. In fact, if one were to find someone who has led such a sheltered life that they never saw any broken surface before, they would not recognize that the window is broken and they would cut themselves.
Here the issue you are pointing to is the question of GOFAI (or symbolic AI - solving problems by applying rules of logic) vs connectionism and pattern recognition (solving problems by learning from examples). If anything humans seem to do more learning by example than computers do. Consider the development of automatic language translators. For years people were trying to implement rule based language translation software and the results were terrible (remember how bad those 90s translations devices were, how comical babblefish was?). Then Google came along and started using pattern recognition technics (by learning from the millions of already translated texts it had access to in its network), and Google translate final started providing workable (if still far from perfect) machine language translation.
In John Searle's classification, pattern recognition and connectionism based software fall under weak AI. In this we have been very successful, and I strongly disagree with Cort Ammon's reply, we have been making noticeable progress in the last twenty years in all forms of pattern recognition, including in image recognition. An example: if you use Facebook, you will notice now that when you upload the picture of a friend, Facebook will correctly recognize that person based on other photos, even though it has never seen the new photo, and suggest whether you want to tag that person or not. Ask any AI researcher from the 50s and 60s whether that constitutes successful AI (Or at least a spectacular improvement since their time), and the answer will be a resounding "Yes!". Or better still ask them if a talking phone which can give you directions to the mall is a significant improvement in AI or not.
The output of Watson in a lot of cases will be identical to that of an intelligent human, but the knowledge is different. Is our definition of intelligence determined by how the answerer comes up with their answer, or just that the answer is correct?
This is the most philosophically interesting part of your question. The answer of whether "how" matters or not depends on who you ask, although the current consensus is that it doesn't matter, and as long as a computer can perform the same functions as a person, we have succeeded in achieving AI. This position is know in the philosophy of mind as functionalism: Mental states are defined by their functional properties, and it doesn't matter how they are implemented on a human brain, a robot brain, or a completely novel alien mental architecture from another planet.
The common analogy given is with poisons: It doesn't matter what the molecular structure of a poison is, or how it acts on a body, a poison is defined by the function is has of making animals and humans sick or killing them. Similarly, mental states such "pain" or "believing that it will rain tomorrow" are defined in terms of their function, i.e. there usefulness in predicting future behavior, and their relationship with other mental states. How these states are implemented doesn't matter. Recent advances in pattern recognition support this position. For a long time people tried to perform machine learning using neural networks (simulations of human neurons) and the results were mixed. When people abandoned neural network architectures and started using support vector machines and random forests, which are based on purely statistical considerations and do not have any biological basis whatsoever, the results were much better.
Other schools might disagree. Type-identity theorists would say that things such as pain and love can only be implemented in human neurons. There aren't that many type-identity proponents left. Most who object to functionalism do so on the grounds that a systems that functionally reproduces human mental behavior still wouldn't achieve consciousness, see for example Ned Block's China brain.
To recap:
- We can't really speak to our idea of artificial intelligence, because we haven't yet defined what natural intelligence is.
- That being said, definite progress is being made in AI, even if the long term targets aren't clear.
- Humans learn mostly from examples, not just from rules. Successful AI will eventually incorporate both rules based problem solving and pattern recognition. Pattern recognition is much more powerful and successful than people realize.
- Different schools of thought have different answers, but for the current dominant school of philosophy of mind, functionalism, it does not matter how the results are achieved as long as they are functionally equivalent to those that can be achieved by a human.