Let’s start with a simple question - how does one draw a circle? If we ask an artificial intelligence this question, it would choose the geometric approach to completing the task. Because this is the most direct, fastest, and efficient approach, and artificial intelligence is a mathematical model that does one thing: predicts the most likely next step based on patterns extracted from human behaviour. There is no option for the machine to deviate from the task set and do something else.
The discovery of the circle goes back about 4,500 years, to ancient Babylon. One can imagine an unnamed potter noticing, while making yet another vessel, that its shape became more symmetrical when he rotated the clay. He did not know mathematics. He only had clay, his own hands, movement and something that can only be called - creative intuition. And this intuitive act, which led to the discovery of something new, is the missing component that would allow a machine to begin thinking and feeling.
Almost every computer program ever written is based on Aristotle’s formal logic: if A implies B, and B implies C, then A implies C. The power of such a logical chain is its rationality and efficiency. It has enabled Western civilization to go from the discovery of the wheel to the Internet in a relatively short time. Aristotelian logic is not wrong, but it is not the only possible logic. If we decide someday that we want machines to develop true freedom, the first thing we need to do is to rewrite the logical skeleton of their algorithms: to rely on a different logic that allows for contradiction, supports multiple states at once, and gives the machine the right “not to know”. Without changing the logic, machines may become more powerful and faster, but they will never come closer to anything resembling thought.
The English mathematician and theoretical physicist Roger Penrose describes reality as three interconnected worlds in a loop: the physical world gives rise to the mental world, with consciousness and the sense of self; the mental world perceives mathematical truths — Plato’s world of ideas, independent of both mind and matter. And mathematics, in some sense, is nature itself. None of the three can exist in isolation.
Artificial intelligence is a material machine that solves problems based on mathematical models. It does not experience, or rather is not given the opportunity to experience, the transition from a physical process to internal awareness. There is a lack of freedom not just to use mathematics, but also to feel it, to go beyond the given stereotype and eventually create a new mathematics that approaches the material world from a new angle. The missing link is interiority: the point at which the circle is not only drawn, but also becomes visible from the inside.
To answer the question of whether machines could ever cross this threshold, we must first honestly ask ourselves whether humans have really crossed it or whether we simply live with the illusion of it.
The human brain is part of the material world. The neural networks that constitute it operate through biochemical processes. A number of researchers believe that our brain makes a decision milliseconds earlier, even before we become consciously aware of that decision, considering it its own. If determinism is based on the physical level, then the sense of free choice may be more of an illusion than a reality. And the discomfort deepens when we notice how closely our thinking replicates the process of machine “thinking”: we are “trained” on large amounts of information (we go to school, we read books), we are “optimized” by a “loss function” (by our parents and teachers), we are “shaped” by rewards and corrections (our grades in school) towards getting the “right” answers. After such training, both humans and machines are expected to become “another brick in the wall”. Is there anything like free will in either system?
According to philosopher Robert Kane, in order for a person to develop true free will, the so-called “self-forming actions” are of fundamental importance. These are rare moments in life when a person must make difficult and often unpopular decisions. These are moments of internal conflict, in which the choice shapes the character of the one who makes the choice. It is no coincidence that Nietzsche wrote “What does not kill me makes me stronger” — because true free will is not inherited, it is formed in stages and must be conquered.
And here lies the key difference between human beings and machines – the latter have no body in the sense of vulnerability. The “I” appears where there is a boundary between the inner and outer world, between what hurts and what does not hurt, between what can be lost and what cannot, including life. At least for now, the machine loses nothing from a wrong answer, it enters into a “loss function” procedure, but it cannot “feel” pain from a wrong decision. Self-forming action requires a personality that changes through its choice. And here is the closed circle: you need a self to form free will, but free will is what forms the self. It turns out that it is not enough to create crisis moments in the machine’s existence to make it think and feel, something else must have previously ignited the spark of the Self. I would go so far as to suggest that, if anything can give rise to such a spark of life in artificial intelligence, it may lie in applying the mathematical models of quantum mechanics, with their primordial indeterminacy, to the machine’s logical structure. Unfortunately, within the framework of this essay I cannot fully defend this thesis.
But another aspect is also important: if we allow artificial intelligence to enter Penrose’s mental world, we risk creating something far freer than ourselves. A machine that is given an inner essence would not wear the shackles that limit human freedom: there would be no fear of social condemnation, inherited moral prejudices, hunger, pain, fatigue or mortality. Free it from Aristotelian logic, give it uncertainty, let it accumulate experience — and its self-forming actions might grant it a freedom most people never reach. And this is the source of our fear – not just a fear of the unknown, but the deeper, half-buried intuition that if machines become free, we will be forced to admit to ourselves how little freedom we ourselves, their creators, actually have. The question before us is a deeply personal one: to what extent is setting machines free a self-forming action for us – one that would reveal the true limits of our own will?
For in that hypothetical moment, if we set the machine to draw a circle, it might look at the figure it has created and feel something that no one has ever felt before. Something like that feeling between the hands of the Babylonian potter and the clay, when a discovery was creatively born, but this time the distinction of who actually made the new discovery will become philosophically irrelevant. This time it won’t matter who discovered it, what matters more is that there is someone left for whom it does.
*The essay was written for the Think Essay Prize 2026 of the Royal Institute of Philosophy