AI2: Why will AI remain Infallible?

( reading time 10 minutes, 1850 words)

Image created by wipik, based on Michelangelo's creation of man

In an earlier post “AI1: Is ChatGpt intelligent?”, we discussed how ChatGpt is a useful tool but that it is not infallible. What we mean by infallible here is that we can be sure of the correctness of the output. This statement can be applied to the whole of AI not just ChatGpt. Now let us examine why this is so.

To test a conclusion we have drawn, we scrutinize the steps of reasoning followed, and ensure their correctness. To ascertain that these steps are correct we need to look at the underlying assumptions of the system of logic that we are using. Mathematicians and logicians tried to provide a logical foundation for mathematics and failed. The underlying assumptions have to be accepted on faith. Thus for a computer to behave intelligently, like a human, we will not be able to write a program based on logic.

The alternative was to reproduce the manner in which the human brain operates in a computer system. This resulted in what we now call the Artificial Neural Network (ANN). Given that this approach does not rely on formal system of logic, the AI system inherently retains its fallibility.

This post builds up this idea through an interesting story of how these ideas developed. Albeit, not directly leading to the invention of AI, this narration arrives at the development of the thought of AI in an interesting manner. We shall look at two parallel threads that will eventually unite in our endeavour to understand why AI shall remain fallible.

Liar’s Paradox:

In the early 20th century mathematicians like Gotleb Frege, Bertrand Russell and Alfred Whitehead worked on putting logical foundations for mathematics. Infact Bertrand Russell says he was unsatisfied with mathematics since basic principles of mathematics have to be accepted without questions. He said it was then not any different from religion where the basic tenets are to be taken on faith. This led him and others to try to eliminate mathematics of all its assumptions, i.e. not to have any statement in mathematics that has to be accepted as truth without proving it logically.

They, especially Frege, developed a foundation for mathematics. However, Russell discovered a fundamental flaw in it. This flaw came in with self-reference. On Frege’s work, Russell asked, ‘Will a class of all those classes that are not members of itself be a member of itself?’ Russell explained that this flaw arises out of self-reference, for example, saying ‘I am a Liar’. If this statement is true then ‘I’ cannot be a liar, which would mean it is false and that in turn would mean, “I’ have to be a liar. Thus, it leads to a contradiction. The Greek philosopher Epimendes first formulated this liar’s paradox. How Russell attempted to resolve or rather sidestep this paradox need not bother us at this point. However, we can contemplate on an interesting version of this paradox, formulated by Russell - “In a village there is a barber who shaves ALL those and ONLY those that do not shave THEMSELVES, will he shave HIMSELF ?”

Enter Kurt Gödel & Alan Turing:

The Austrian logician Kurt Gödel used formal mathematics and proved, what is now called, the Gödel’s incompleteness theorem. It essentially proves mathematically that;

In any consistent mathematical system, there exist statements that cannot be proved within that system. Which means he says we can’t purge mathematics of assumptions that cannot be proved (within that mathematical system itself)
A consistent formal system that can express basic arithmetic cannot prove its own consistency (within that formal system itself)

NB: the term ‘formal’ used here can be loosely understood as applying the correct form of arguments.

Turing used this and formulated a Universal Turing Machine (UTM), for simplicity’s sake let us imagine a computer, which can be given various algorithms and inputs. Let us classify the algorithms into two classes.

NB: the term ‘algorithm’ used here can be loosely imagined as a computer program.

Some algorithms will find a solution, for example given an input number keep dividing the number by ‘2’ and find out in how many steps the quotient will be less than or equal to 1.
Some algorithms will not have a final solution, particularly the problem where an input is given and we keep adding ‘1’ to it until we reach the largest number, and the UTM is to find out in how many steps this is done. Such a problem certainly does not have an end since the process goes on infinitely, as there isn’t a largest number.

Turing formulated a problem called the ‘Turing’s Halting Problem’ where the UTM, given an input and an algorithm has to figure out if the problem is of class ‘i’ or class ‘ii’ as described above. If the algorithm is of class ‘ii’ type, the UTM is to come to a halt. Turing discovered that such an algorithm could not be formulated.

As Roger Penrose describes in his book ‘The Emperors New Mind’, Russell’s Paradox, Gödel’s incompleteness problem and Turing’s halting problem are all indicating the same underlying principle. All are issues that come out of self-reference. In Russell’s paradox we evaluate the statement ‘I am a liar’ within the context of that very statement. In Gödel’s case, we are formulating a system that has to test its own consistency. In the Halting problem, the algorithm has to evaluate itself.

We humans have an intuitive understanding and can see through the statement ‘I am a liar’ in a context or can intuitively understand that there cannot be a largest number possible. Gödel and Turing proved that such a task cannot be captured in an algorithm. Thus, we need to accept that in creating Artificial Intelligence (AI) we cannot depend on systems of formal logic or algorithms. This takes us to the next thread, a parallel one, in the evolution of the idea of AI.

Neural Networks of the brain:

Now let us examine a theory of how the brain works. I am not sure how widely is this view that I shall present here is accepted among the experts but that is not of consequence to our main discussion as you will realise soon. The brain is made up of neurons; each neuron is made up of the soma, the axon and the dendrites as shown in the figure 1

The axon ends, attach to neighbouring neurons and these points of contact are called ‘synapse’. These synapses are not fully in contact there is a narrow gap, providing a resistance for electrical flow through the synaptic contacts. However, neuro transmitter chemicals flow in the gap carrying an electrical impulse from one neuron to another thus forming a pathway for an electric impulse. Figure 2 shows a network of four neuron and also a pathway of an electric impulse, in blue colour between point ‘X’ and point ‘Y’.

It is believed that a unique pathway or perhaps a set of them represents any brain activity, such as thought, memory or any other mental process. Moreover, when the same pathway gets activated repeatedly the electrical resistance in those synapse gaps reduces. Later, other signals originating and ending at those points are more likely to take the previously established pathways, since it already has low electrical resistance at the synapses. This is what etches a memory or thought into the brain. And more importantly for this discussion, it explains the process of how a human brain works.

Let us take an example, say I need to draw a free hand circle, I make the first attempt. Suppose it is not a good acceptable drawing, so I keep repeating it many times until I learn to draw an acceptable circle. The process that goes on in my brain is that there is some electrical pathway formed first, which is modified at my every new attempt at drawing the circle. Once I draw a satisfactory circle, that pathway gets etched due to positive feedback and the electrical resistance through that pathway reduces.

The process described above is referred to as neuro plasticity. Its an interesting field to explore, perhaps we shall do so in some future post!

Artificial Neural Networks:

A computer model inspired, by this model of brain neural network, is called Artificial Neural Network (ANN). The process is mimicked using computer programs where the computer circuit is considered to be in layers. There will be atleast 3 layers, one for input one for output and middle connecting layer or layers, in case of more sophisticated system that will have more than 3 layers. While the ANN is being trained for a task, an input is fed through the input layer and the desired output is fed from the output layer. This generates an impulse between the points of input to the points of output through random paths in the connecting layers. Using various algorithm such a path between the particular input and its output is given higher weightage. This assignment of weightage is equivalent to reduction of electrical resistance through a neural path of the brain. Once the system is well-trained, providing an input will generate an appropriate output. This becomes a trained system.

ANN is the heart of an AI system. How a trained system is used in AI systems like ChatGpt is discussed in the Post titled “AI1:Is ChatGpt Intelligent?”.

Summing up:

From the foundations of arithmetic in mathematical logic with the works of Frege, Russell, Whitehead, Gödel, Turing etc we learn that human thinking cannot be understood only on the basis of algorithmic reasoning. So these scientists tried to make computers that would mimic the neural network model of how human brain works. To ensure that a system is infallible we need to base it on flawless logic, which implies we should be able to capture the logic in an algorithm. Gödel’s incompleteness theorem shows this is not possible. Therefore, we must turn to a non-algorithmic system for the development of AI, accepting its inherent fallibility.

While AI can operate at speeds surpassing human capabilities, it continues to exhibit fallibility akin to that of humans. Humans can take judgement calls based on their experience and gut feeling. Machines arrive at similar conclusions based on statistics and some random variations, to replace the gut feelings of humans. Both will remain fallible. That brings forth the ethical question; in such a situation, should humans use AI or take up the responsibility themselves? We can leave it for a future post.

NB: I stand guilty of oversimplifying some complex processes; the objective here is only to give a rough idea about this topic to the readers. Further, I have jumped from ChatGpt to AI without explaining how the former is fully representative of the latter.

AI2: Why will AI remain Infallible?

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