Human creativity, free will and consciousness

Jonathan Mason

Mathematical Institute, University of Oxford, UK

This contribution summarises the talk of the same title given at the celebratory symposium for Prof. Tim Palmer on 6th December 2022 at Oxford. It was a great pleasure to be an invited speaker and to celebrate Tim’s many contributions to science. The talk is based on the last three chapters of Tim’s book The Primacy of Doubt (Palmer, 2022), which touch on themes in the field of Mathematical Consciousness Science. ^{1, 2, 3}

One of Tim’s pivotal contributions to the field of weather and climate modelling is the introduction of stochastic parametrisations in simulators. This research, and techniques such as stochastic rounding, also lead Tim to consider the potential benefits of stochasticity in the brain.

The human brain only uses 20W, and evolution has favoured miniaturisation of neurons, including axons, in order to accommodate some 80Bn neurons in the brain. This leads to noisy neurons. Moreover (Summhammer et al., 2018), action potentials propagating along slender axons are boosted by the flow of ions along ion channels in the neuronal membrane. The speed of ion flows through the channels favour quantum models over classical, indicating that quantum (1ps) effects may play a role in the brain and may produce quantum generated noise.

Semiconductors in integrated circuits become noisy when the power level drops too low. Unlike such systems, the brain is robust to a certain level of noise and, given noise can be useful, evolution may have found uses for it. In particular, Tim expands on Kahneman’s fast and slow brain modes. During the relaxed fast mode, when the brain uses heuristics and is able to undertake many tasks at once, the 20W is distributed widely and, potentially, stochasticity is increased. This may help us to be more creative by allowing the brain to explore a wider range of ideas than would be possible using the slow mode alone during which the 20W is concentrated within fewer brain regions resulting in more deterministic and algorithmic processing. Therefore, the slow-fast thinking cycle can also be thought of as a deterministic- stochastic thinking cycle. There is evidence (Palmer, 2022), that mathematicians use such a thinking cycle and that their creative breakthroughs come during the relaxed, fast, stochastic mode. Tim has also compared the cycle to the Simulated Annealing algorithm in optimisation.

Beyond this, Tim also suggests links between his Invariant Set Postulate (Palmer, 2009), quantum noise in the brain, free will and consciousness. He openly admits these ideas are speculative, but they are all the more interesting for that.

The Invariant Set Postulate: “Cosmological states of physical reality belong to a non-computable fractal state space geometry “I”, invariant under the action of some subordinate deterministic causal dynamics” (i.e. unchanging in time). Every point in Tim’s cosmological state space specifies a state of the whole universe. The state space is divided in to “real” and “unreal” subspaces that exhibit a fractal geometry that corresponds to the effect of chaos in nature. The theory aims to resolve various issues in quantum mechanics; see Tim’s ideas on superdeterminism, (Palmer 2022, Chapter 11). Two key properties for us are:

1. All points are equally responsible for determining the fractal geometry.

2. Each point lies within a neighbourhood of counterfactual worlds.

Property 1) has potential relevance to free will. Instead of us all being slave to the initial conditions of the big bang and the laws of nature, all points are equally responsible for determining the fractal geometry of the invariant set and therefore on what happens and what does not happen. Just like the geometry of space-time tells matter how to move and matter tells space-time how to curve, every point in the invariant set determines its geometry.

Property 2) has potential relevance to consciousness. Tim suggests that we may be aware of the existence of objects by their counterfactual alternative configurations in nearby trajectories on the invariant set that are weakly present for us, like a sixth sense, due to quantum effects in the brain. See (Palmer 2022; Palmer 2020) and Figure 1.

Thank you Tim for your stimulating ideas, and for what may be yet to come.

¹ https://wiki.amcs.science/index.php?title=Mathematical_Consciousness_Science

² https://amcs-community.org

³ https://omcan.web.ox.ac.uk