Hofstadter puts a lot of effort into unraveling the steps behind problem solving. He notes that there are two main approaches to attacking a problem, which he discusses continually throughout his book, but only for a brief moment mentions by name. The ideas of both bottom-up and top-down problem solving can be applied to many different fields and sciences. Psychologists, philosophers, computer and cognitive scientists, and even detectives analyze things from these two differing perspectives, as do most people without ever being aware of the processes. A great example of top-down thinking, also known as deductive reasoning, is that which Sherlock Holmes is famous for.
The idea of top-down thinking is that you are given a clue, or an idea, and through the process of reasoning you work downwards from the general towards the very specific. This kind of reasoning gives you a definitive “valid” or “invalid” conclusion. Sherlock Holmes may have known that the murderer left behind boot marks at the crime scene and that only 12 people at the party that night wore boots. He moved from having a general idea that it was someone at the party, to a shorter, more specific, list of 12 suspects. Eventually through deductive reasoning one will come to a conclusion that is either valid or invalid, there is no in-between. Think of an upside-down pyramid with clues at the top, and a conclusion at bottom. In this way, one works from the top of the pyramid where ideas are very general, towards a very specific point at the bottom.
Bottom-up causation, on the other hand, also known as inductive reasoning can also be thought of as existing on this upside down pyramid. Given some data and starting at the bottom one can work their way up from the specific towards the more general; however, this can only yield a probabilistic certainty. For example, if Sherlock Holmes thought it was John Grady he could gather more evidence against him, and with each new set of evidence come closer to a probabilistic estimation of his guilt.
Philosophers and cognitive scientists use these theories of bottom-up and top-down causation when musing over the concept of “mind over matter”. This idea, known as mind-body dualism, argues that there is a separation between consciousness (the mind) and the physical brain. There is a dichotomy among philosophers and scientists as to whether this separation is real; with some arguing that the brain simply generates the mind. This is bottom-up causation. Inversely, proponents of top-down causation of the mind argue that the mind can alter the brain, and there is some interesting “evidence” to argue this.
Hofstadter mentions these ideas of top-down and bottom-up thinking when discussing his machine for solving number sequences. His idea is to create a machine that starts from the bottom (with specific data) and uses these clues to work in a top down manner (from theories). We may not be aware of it as humans, but we run through similar processes all the time.
-James
