
## 2.2 No Brain Without A Body / Ai Becoming A Formal Science

Heuristic approaches will continue to play an important role in many AI applications, to the extent they empirically outperform competing methods. But like with all young sciences at the transition point between an early intuition-dominated and a later formal era, the importance of mathematical optimality theorems is growing quickly. Progress in the formal era, however, is and will be driven by a different breed of researchers, a fact that is not necessarily universally enjoyed and welcomed by all the earlier pioneers.

Today the importance of embodied, embedded AI is almost universally acknowledged (e. g., [20]), as obvious from frequently overheard remarks such as "let the physics compute" and "no brain without a body." Many present AI researchers focus on real robots living in real physical environments. To some of them the title of this subsection may seem oxymoronic: the extension of AI into the realm of the physical body seems to be a step away from formalism. But the new millennium's formal point of view is actually taking this step into account in a very general way, through the first mathematical theory of universal embedded AI, combining "old" theoretical computer science and "ancient" probability theory to derive optimal behavior for embedded, embodied rational agents living in unknown but learnable environments. More on this below.

## 2.3 What'S The I In Ai? What Is Life? Etc.

Before we proceed, let us clarify what we are talking about. Shouldn't researchers on Artificial Intelligence (AI) and Artificial Life (AL) agree on basic questions such as:
What is Intelligence? What is Life? Interestingly they don't.

Are Cars Alive? For example, AL researchers often offer definitions of life such as: it must reproduce, evolve, etc. Cars are alive, too, according to most of these definitions. For example, cars evolve and multiply. They need complex environments with car factories to do so, but living animals also need complex environments full of chemicals and other animals to reproduce - the DNA information by itself does not suffice. There is no obvious fundamental difference between an organism whose self-replication information is stored in its DNA, and a car whose self-replication information is stored in a car builder's manual in the glove compartment. To copy itself, the organism needs its mothers womb plus numerous other objects and living beings in its environment (such as trillions of bacteria inside and outside of the mother's body). The car needs iron mines and car part factories and human workers.

What is Intelligence? If we cannot agree on what's life, or, for that matter, love, or consciousness (another fashionable topic), how can there be any hope to define intelligence? Turing's definition (1950, 19 years after G¨odel's paper) was totally subjective:
intelligent is what convinces me that it is intelligent while I am interacting with it. Fortunately, however, there are more formal and less subjective definitions.

## 2.4 Formal Ai Definitions

Popper said: all life is problem solving [21]. Instead of defining intelligence in Turing's rather vague and subjective way we define intelligence with respect to the abilities of