Miguel Ángel Sebastián (National Autonomous University of Mexico) & Manolo Martínez (Universitat de Barcelona), "Gradualism, Bifurcation, and Fading Qualia"

Analysis, 2024

The Gradualist Assumption & Why It Might Skid Off Track

By Miguel Ángel Sebastián & Manolo Martínez

Imagine you're out for a ride on your motorcycle, taking in the scenery and enjoying the feel of the road beneath you. As you gently twist the throttle, you anticipate a smooth increase in speed. And naturally, if you ease off, you'd expect the bike to slow down in a predictable manner. This intuitive understanding, that a small action will result in a proportionate reaction, is what we refer to as the gradualist assumption. It's the belief that if two variables, like speed and throttle twist, are connected by a continuous function, one won't drastically change without the other doing the same. This concept isn't just limited to motorcycles; it's a foundational idea in many philosophical discussions.

However, there's a phenomenon that challenges this assumption, called subcritical bifurcations. Think of it as the unexpected twist in our story: sometimes, minor changes can lead to significant and unpredictable outcomes.

To illustrate, let's shift gears and think of water flowing through a pipe. When the flow is gentle, the water moves smoothly, akin to motorcycles driving orderly on a highway. This is known as laminar flow. But increase the pressure, and suddenly water starts swirling chaotically, entering what we call turbulent flow. Here's where stable points come into play. Think of them as the "cruising speeds" for water flow, where everything feels just right. But if conditions change, say pressure increases, that cruising speed might shift. Interestingly, if you then reduce the pressure, hoping for water to return to its laminar state, it doesn't always comply immediately. It might linger on its turbulent state for a while before settling down. This delay in returning to its original state, even when conditions are reversed, is known as hysteresis, and it’s common in subcritical bifurcations.

You might have been wondering for a while, how is this relevant to philosophy? In our paper, we explore some possible implications of the gradualist assumption using Chalmers’ fading qualia argument as an example.  Here's the gist: Chalmers champions the idea that if you took a conscious being (like us humans) and started replacing brain neurons with tiny computer-like units, as long as they had the same input-output behavior, our conscious experiences would remain unchanged. Think of it as swapping out a part in a machine and expecting it to run just as smoothly. He argues that merely replacing one neuron shouldn't just switch off our consciousness. That would be like removing a single piece from a puzzle and expecting the entire picture to disappear. Moreover, if you were to toggle that neuron on and off, our consciousness would seemingly flicker, yet we'd act as if all's normal.  That doesn’t seem plausible at all.

Here's where things get interesting: Chalmers might have overlooked  the possibility of subcritical bifurcations. If our experiences hinge on the stable points of a cognitive system (a brain, say), and the presence of these points depends on the number of neurons, then a single neuron change could indeed disrupt our conscious flow, because there can be abrupt changes in the stability points, driven by a bifurcation. And the kicker?  Once the music stops, just plugging that neuron back in need not start the party again. Once flow is disrupted, merely restoring that neuron doesn't necessarily set things right---hysteresis might prevent that. You'd need to replace back a lot more, kinda like how our dancing water in the pipe doesn't calm down immediately.

In conclusion, the next time someone suggests that changes occur in a predictable, step-by-step manner, you might want to introduce them to the concept of subcritical bifurcations, stability points, and hysteresis. It's a reminder that the world, much like our motorcycle ride, can sometimes be full of unexpected twists and turns.