The Penrose Microtubule Anomaly, Buckyball Clathrins and Consciousness

Based upon his anesthesia research, Stuart Hameroff suggested that microtubules were involved in the emergence of consciousness at the level of quantum computation. Microtubules are self-assembling polymers (i.e. large scale, macro-molecules composed of repeating structural units) located in the cytoskeleton within neurons (and many other cells, both mammal and plant). In his 1994 book, Shadows of the Mind, a Search for the Missing Science of Consciousness, [53] Sir Roger Penrose posed the important “puzzling question,” or anomaly: “Why do Fibonacci numbers appear in microtubules?”

Microtubules have Fibonacci structure with 13 protofilaments that align side-by-side, forming spiral patterns that are similar to a pinecone or sunflower, with 8 spirals winding in one direction and 5 spirals in the opposite direction (see Figure 3) [72]. Occasionally so-called double-microtubules form with (not 26, twice 13) but 21 protofilaments, 13 spiraling in one direction and 8 in the other! When looking more closely for an abductive answer or explanation, we notice that the ratios of adjacent Fibonaccis (i.e. 21:13, 13:8 and 8:5) are each approximating the underlying golden ratio, and therefore, are explicate order expressions of the enfolded implicate order’s golden mean number system. And in fact, the proportional “geometric mean” sequences of 13:8:5 and 21:13:8 are unfolded numerical approximations of the golden mean proportion itself, namely, Φ:1:ϕ. We argue that this golden mean proportion emerges at the outset of the universe in the primordial first act – the ontological asymmetric cut or golden section that leads to the inherent golden proportional symmetry, Φ:1::1:ϕ.

In their 1995 paper, “Quantum computing in microtubules: self-collapse as a possible mechanism for consciousness,” [79] Penrose and Hameroff proposed that consciousness can be explained by quantum computations orchestrated through groups of microtubules in the neurons of the brain. They argued that the microtubules in a quantum coherent state could orchestrate an objective reduction or self-collapse of the quantum wave function thereby producing consciousness. Of course, in the alternative Copenhagen interpretation of Quantum Mechanics it is consciousness in the subjective act of observation or measurement that collapses the wave function. Whatever the explanation, consciousness is intimately tied to the collapse of the wave function where, as indicated in E-Infinity theory, the ϕ2 pre-quantum wave (Empty set) collapses [whether under “local” subjective observation or measurement, or the “nonlocal” objective self-collapse due to the “entire ensemble”] into its corresponding ϕ pre-quantum particle (Zero set)1 [5,54,95].

Provocative research in 2003 began to demonstrate that quantum coherence occurs even in warm biological systems, including “bird brain” navigation, DNA, protein folding, biological water and microtubules. But Max Tegmark objected, claiming that microtubules would be incapable of doing quantum computing because decoherence in the warm, wet and noisy environment of the brain would prevent it. Thus, the microtubule quantum coherence debate between Hameroff and Penrose on the one side, and Tegmark on the other had begun.

In 2011 Penrose and Hameroff wrote that the “multiple winding patterns… matching the Fibonacci series found widely in nature and possessing a helical symmetry, [are] suggestively sympathetic to large-scale quantum processes.” [80] As part of the cytoskeleton, the microtubules establish cell shape, direct growth, and organize cellular functions, “defining cell architecture like girders and beams in a building.” (Ibid.) But their lattice structure can be compared to computational systems. Penrose and Hameroff see them as biomolecular quantum computers. This of course means there can be entanglement, superposition (being in two places at once), and immediate “nonlocal connection” even when appearing to be “locally” separated. The present authors’ position, simply stated, is that this is a reflection of the inherent golden mean number system infused into nature that gives rise to life and the resonant expansion of states of consciousness.

Penrose and Hameroff had responded to the earlier Tegmark decoherence objection, arguing that Frohlich coherence in pumped dissipative systems could provide a physical basis for warm quantum systems like microtubules. Frohlich coherence in microtubules has now been effectively established by Anirban Bandyopadhyay and his team, thus rebutting the Tegmark objection. The group demonstrated that microtubules stabilize as non-equilibrium Frohlich coherent systems when certain external frequencies are pumped into them, resulting in long range collective phenomena. In the abstract of their paper they explain what they observed: “As we bring tubulin protein molecules one by one into the vicinity, they self-assemble and the entire event we capture live via quantum tunneling. We observe how these molecules form a linear chain and then chains self-assemble into 2D sheets, an essential for microtubules, fundamental [for] nano-tubes in a cellular form….” [99]

Clathrins, located at the tips of microtubules in the axon’s synaptic boutons, are buckyball shaped proteins that selectively sort cargo at the cell membranes. As truncated icosahedra, they have internal rectangles constructed in the ratio ٣Φ:١. During mitosis the clathrins bind directly to the microtubules (or microtubule-associated proteins called MAPS). But most importantly, together with microtubules the clathrins regulate synaptic activity. Our suggestion is that their “golden in-phase resonance” and attendant aesthetics hold a central key to the mystery of consciousness. Hence, beauty, function and illumination appear to be intimately interrelated! [5]

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