1. Computational Theory
2. Representation and Algorithm
3. Hardware Implementation

Computational Theory 应当试图理解和定义 Vision 这个 Information Processing System 做了什么样的 computation，以及为什么要做这样的计算。他在书里用算术做为例子，比如说关于加法的理论应当是，比如，我们需要加法是为了计算我们在超市买东西的时候计算总价用，那么这个操作应该满足交换率，因为我的总价不应该和我选择物品的顺序相关；比如如果我拿了一件东西但是又不想买了，拿到 refund 之后我的钱应该不增不减，于是要求存在逆元（当然可能还需要先定义零元）等等。这些就是“加法”的 Theory，他和我们的数字怎么表示（罗马数字、二进制数字）以及我们怎么去做具体的计算都是无关的。那么回到 Vision，亚里士多德说的是“to see, is to know what is where by looking”。可是，说到头，Vision 到底是在做什么呢？

Chomsky 举了一个例子：你通过一扇窗户观察到外面的世界，然后你可以用统计模型和大量的观察数据得到一个外面的世界的 approximation，可能在许多时候他甚至能给出相当精确的窗户里将会看到的景象的预测。但是如果我们的目的是要做科学（而不只是工程）的话，这样做是不行的，因为通过这样的方法我们没有办法去理解事物的本质或者法则，比如通过这样的方法我们不可能去抽象出小球在无摩擦的光滑平面上运动的理想情况来（这样的情况在真实世界中是无法观察到的），也不会得出相关的各种运动定律等等。当然，物理里所研究的系统从某种意义上来说比生物智能系统要简单许多，所以这样的比喻也不一定是很恰当 (Chomsky 自己也打趣说之所以众多科学领域里物理似乎是最硕果累累的，其实是因为物理学家们只研究简单的问题，问题一复杂就归到其他领域里去了。比如说分子大了之后就丢给化学家们，各种分子组成复杂的细胞之后再丢给生物学家们，细胞啊神经啊之类的连接在一起神奇地产生了智能系统，于是又被丢给 Cognitive Scientists……)，万一智能系统就是如此复杂不存在一个干净的简单的抽象模型呢？

Finally, let me comment on the problem of learning, which is an intriguing and interesting omission in Marr’s Vision quest to understand intelligence and the brain, especially because learning was the focus of his famous papers (1969, 1970) on the cerebellum and the neocortex. I am sure that this omission would have been corrected had Marr had the time… I have been arguing for the last two decades that the problem of learning is at the core of the problem of intelligence and of understanding the brain. Learning, I think, should have been included explicitly in Turing’s operational definition of intelligence – his famous Turing test. Not surprisingly, the language of modern statistical learning, including regularization, SVMs, graphical models, hierarchical Bayesian models, is permeating various areas of computer science and is also a key component of today’s computational neuroscience. I am not sure that Marr would agree, but I am tempted to add learning as the very top level of understanding, above the computational level. We need to understand not only what are the goals and the constraints of a computation are but also how a child could learn it and what the role of nature and nurture is in its development. Only then may we be able to build intelligent machines that could learn to see – and think – without the need to be programmed to do it.