How AI Neural Networks Show That the Mind Is Not the Brain
Recently, I’ve been arguing (here and here, for example) that we can use artificial neural networks (ANNs) to prove that the mind is not the brain. To recap, here is the logic of my argument:
Premise A: neural networks can learn better than the brain Premise B: the human mind can learn better than a neural network Conclusion: the human mind can learn better than the brain, therefore it is not the brain
This means if we can conclusively show the human mind can learn better than a neural network, then the mind is not the brain.
For Premise A, I’ve argued that the differentiable neural network is a superior learning model compared to the brain neuron’s “all or nothing principle”. The neural network has a “hot” or “cold” signal that it can learn from iteratively, whereas the neuron has a binary “yes” or “no” signal that does not allow for gradual improvement, making learning impossible for brain neurons.
This brings us to Premise B, where I will show that, nonetheless, the human mind can learn better than a neural network.
Let’s return to the original puzzle that Marvin Minsky (1927–2016) identified for the perceptron: learning the simple XOR function shown below. A simple perceptron fails this puzzle, but the XOR function can be learned, in a sense, with multiple layers of perceptrons, which we call an artificial neural network (ANN).
However, what is going on under the hood is quite messy and, as we shall see, that leads to a fundamental problem down the road.
Before we dive into all that, let’s look more closely at the XOR function and then consider what it means for a neural network to learn it.
Basic logic functions include AND, OR, and NOT. Logic functions are applied to logical variables, and we can represent them using truth tables.
Here is an example of the AND function on the two logic variables A and B in a truth table. T and F stand for True and False:
The AND function should be true only when both A and B are true.
Although we don’t often stop to think about it, we all use this idea in everyday speech (which depends on logic). The sentence “Jane is a medical doctor and a lawyer” is True only if Jane is both a medical doctor and a lawyer. Thus, there are three ways that the sentence can be False and only one way that it can be True.
The logic table expresses this basic idea in logic. Thus, if we look at the table, we see there is only one T under the “A AND B” column: in the fourth row, where both A and B are T. In other words, the logic function A AND B can only be true when both A and B are true.
But now, let’s look at the truth table for the XOR function:
Examining the truth table, you’ll see that the “A XOR B” column is only true when either A or B is true but not when both are true. XOR stands for “exclusive or,” which means that A and B exclude each other. That’s why we only see the function register as True when either A or B is True, but not both at the same time.
For example, let’s say John and Harry are in a close race for Congress. Either could win (True) but both can’t win (False). Nor, under normal circumstances, can neither man win (False).
At first, it is not obvious. Marvin Minsky showed that a simple perceptron could not do it. That is because neural networks learn numbers, not logic. How can such a network be tweaked to learn a table of logic?
What if we replace logic with numbers so that the network doesn’t have to think, just add?
To get from here to there, we need a quick mind tweak: We represent True and False by the numbers 1 and 0. Hey presto! By representing logic as numbers, a neural network can now learn logic functions.
We can also draw the logic function on a 2D graph. Here is a 2D graph of the XOR function. You can see that it is divided into four quadrants, and the number 1 only shows up in a quadrant when one variable is 1 and the other is 0.
We can go one step further, and use colors. Let’s color 0 black, and 1 red.
