Some offer us a sleek view: the brain as computer.

We have not mastered the brain, the way we have the computer. Some bits of the physics on which a computer runs are not fully grasped, perhaps. But they are known to the degree that they will conduct streams of electrons down circuits in a regular pattern and that these patterns will hold state information. We designed the computer, first on paper, and then in silicon, in a way that we could say that a electromagnetic state mapped to a state in the design.

Nobody designed the brain, they tell us. And on the testing goes. Meanwhile, engineers have designed machines to compute and have proved them Turing Complete—or ready to compute any number of problems. And in making a scheme and store for a set of instructions, made the machines flexible computation machines, by rejecting designs that locked the engineer in to one problem per computer.

We have mastered the computer, because we built it. It wouldn’t be here if we didn’t know what it was doing. Not so the brain, apparently.

We can imagine the brain as a computer, but that doesn’t make it one. The brain-as-computer model helps us make concrete observations about thought and computation. But taking the brain as a computer just doesn’t hold the value that people tend to think it does.

The computer is limited. It has bounds; it has a problem domain. The trick is to figure out how to convert your task, into a similar task that can be solved in the problem domain.

It is by numbers and lookup tables that a machine deals with characters. Characters comprise text and the contents of text provide the machines interpretation of the user’s purpose in providing these characters. It stores “cat” as the sequence 67, 65, 104. It doesn’t relate that string to anything other than what some other software will tell it to relate to it. It cannot even paint those letters on your screen unless some pre-designed scheme tells it how to draw something based on that number. Needless to say, we’ve done that work.

Every problem that lies outside the given problem domain of the computer will need to have a set of designed steps which tells the computer how to transform each part of the problem into the problem domain of the computer. Needless to say, we’ve done a lot of work there.

Now, as much as I have been schooled in computer architecture and computability theory, I do not hold every scrap of knowledge about the computer. Very few application designers know the instruction set of a machine anymore. It is almost impossible to understand the high-level view of software, by thinking in terms of machine instructions.

It is better that a compiler handles these details and that our minds are set free to recall how to turn boxes that we drew on the page into patterns of text called “source code”. The compiler will then use the text to create instructions. I should not have to know how an “object” is composed in memory in order to design objects. All computers these days will need some scheme to represent the “object” so the charge to the compiler designer is “Thou shalt represent objects!”

So a computer doesn’t even begin to solve your problem, until you solve the problem of how it’s going to represent the state of your problem. The brain, on the other hand, solves problems—or so we think that’s what it is doing. We don’t know for sure.

The computer is sometimes called a Turing Machine, This term names the mathematical model of an algorithm (set of computational steps). But more specifically, the computer is more properly an example of a Universal Turing Machine. Programs, like your web browser, are also a type of Turing Machine, only more specific to the problem of retrieving text from the web and displaying it to you. The Universal Turing Machine takes a mathematical representation of another Turing Machine and processes it with an input. That is the universal TM (computer) takes the code for a specific TM (browser) and processes your input.

Now, in the field of Turing Machines (TMs) we have a thing called Halting Problem, which roughly says that there is no definite way for a universal TM (computer) to decide whether the input TM (program) will completely process a given input or even stop.

As well as having no precise specification of the brain or how my the sight of my mouse is “input” into my brain. But were there such a representation, we have no way of knowing whether the brain would have definitively processed, say the input of the eyes. And the shadow of Rice’s Theorem suggest that a non-trivial property, say “sight-processing” can never be determined by an exact algorithm—including, perhaps the algorithm the Brain-TM uses to analyze TMs.

So were the brain a TM, Computability Theory tells us that stating on-trivial properties of that TM are impossible by algorithm, which is all that the brain as TM can do. We come to a place where the brain either is a TM and if the universe is computable, then the TM cannot say non-trivial things about the universe with any certainty that could be checked by another algorithm.

Thus objectivity breaks down.

Take it in this way: We take the Universe-TM as input and we process it within our Universal TM. Provided that we could specify exactly the process we came up with to process the computable universe, no one could ever check our math” with an algorithm, that is their brain. They could not “run” our brain and pass the universe in as input and conclude any fixed thing. Nor could it be computed that we should ever fix any one things about the brain by following the steps of our brain.

In fact to say we could ever verify the statement brain1 = brain2 is to remove our mooring to fact. And again, with Rice’s Theorem, “processes like brainx” is non-trivial and remains problematic for a brain or a computer to decide this.

Next: The Black Box Brain II