Part III
Penrose-Hameroff theory (final part)
Summary of parts I and II
An integrate-and-fire brain neuron is a cell held together by its
cytoskeleton which is formed among other things by microtubules.
The cytoskeleton is effectively a cellular nervous system (Sherrington, 1957).
The neurons are cells which do not undergo mitosis (cell division) and therefore their microtubules are very stable.
The dendritic and somatic microtubules in particular are the most suitable for long term information encoding and memory.
A microtubule is a cylindrical skew hexagonal lattice composed from 13
longitudinal protofilaments of tubulins with helical winding pathways
(in the A-lattice) repeating according to the Fibonacci sequence
(3,5,8,...).
Each tubulin can be in two conformational states (open or closed).
These are supposed to be quantum states analogous to the spin states (up and down).
The quantum forces are either London forces (instantaneous
dipole-induced dipole attractions between electron clouds) or magnetic
dipoles due to electron spin enabling spin-flip alternating currents in
microtubules.
Thus, a tubulin can exist in an infinite number of
superposed states and thus it acts as the quantum bit or qbit of
microtubules information processing.
There are 10^9 tubulins per
neuron which are switching at 10 MHz which gives a 10^16 operations per
second per neuron relevant for qualitative consciousness.
In
contrast, the brain consists of 10^11 neurons and each neuron contains
10^3 synapses and each synapses performs 10^2 transmission per second.
This gives 10^16 operations per second for the entire brain performing
classical computations relevant for functional consciousness.
The
information processing of microtubules relevant for quantum computations
(qualitative consciousness) far exceeds that of neurons relevant for
classical computations which is based on axonal firings and synaptic
transmissions (functional consciousness).
Thus, microtubule-level
quantum information processing and quantum computation lie perhaps at
the origin of neuron-level classical information processing and
classical computation in the brain.
And perhaps, consciousness
resides in microtubules and not neurons. For example, anesthetic are
seen to act in microtubules and not in neurons.
The tubulins in microtubules across many neurons should act coherently through quantum entanglement.
In 2009 Bandyopadhyay's group in Japan showed that microtubules at biological temperatures may indeed enjoy quantum properties.
Orch OR:
In the Diósi–Penrose interpretation an objective reduction of the
quantum state (collapse of the wave function) occurs objectively, i.e.
dynamically, when a threshold is reached of the order of the lifetime of
quantum superposed states which is determined by quantum gravity
effects on the spacetime geometry.
This should be understood as a
proposed solution for the measurement problem (of why we dont see
quantum superposed states and the conflict between processes I and II of
von Neumann) which runs effectively opposite to the Copenhagen-von
Neumann-Wigner interpretation.
Since in the Penrose interpretation
the collapse is effectively an instant of conscious experience whereas
in the Wigner interpretation it is the conscious experience that causes
collapse.
Thus, in the OR interpretation the collapse of the wave
function is an actual independent physical effect arising from quantum
gravity (which is the strongest proposal of this proposal in our view)
and the bridge between the classical and the quantum is quantum gravity
and not environment or many-worlds or consciousness.
According to
Penrose, if we assume that the quantum superposition contains for
simplicity two stationary states, then the objective reduction of this
superposition will occur at a random instant with an average lifetime
scale (similar to radioactive decay) τ equal \hbar/E_G where \hbar is
Planck's constant and E_G is the gravitational self-energy of the
difference between the two stationary mass distributions involved in the
superposition.
For rigid mass distributions E_G is the energy
required to move one of the distributions in the gravitational field of
the other.
The quantum superposition corresponds to a superposition
of two spacetime geometries caused respectively by the two stationary
mass distributions.
In other words, each mass distribution generates a slightly different spacetime metric.
When the spacetime separation (given in terms of symplectic measure on
the space of 4-dimensional metrics) between the two spacetime manifolds
reaches a critical amount one of the spacetimes decays instantaneously
according to OR and the other one emerges as the actual classical
spacetime geometry.
The critical spacetime separation is a product
of time separation T and a space separation S which is of order 1 in
natural units.
Thus, for small S (such as an electron) τ=T is very
large. An electron in a superposed state may reach the OR threshold
after thousands of years.
But, for small τ=T the space separation S
is very large. Thus a Schrodinger's cat which has large S may reach the
OR threshold after only 10^{-43}s (Planck's time).
Indeed, for weak
gravitational fields E_G is given by the gravitational self-energy of
the difference between the mass distributions of the two superposed
states. We get E_G=S and T=τ and hence T=τ=\hbar/E_G=\hbar/S.
In
most cases E_G gets most of its contributions from the environment and
as a consequence OR becomes indistinguishable from the usual R operation
(process I) of Copenhagen caused by environmental decoherence.
Thus, the quantum superposition should be kept isolated from the
environment (i.e. it should only be allowed to evolve unitarily under
the Schrodinger equation or process II also called process U by Penrose)
until the time τ of OR if the reduction is to be due to the system and
caused by quantum gravity and not due to the random effect of the
environment.
The orchestrated (or tuned) objective reduction
proposal or Orch OR is OR with the further assumption that each OR event
produces an element of consciousness called proto-consciousness.
Thus, it is required in Orch OR that isolation from the non-orchestrated
random environment is achieved so that only orchestrated reductions
(not fully random as in Copenhagen but depends on the new quantum
gravity physics) are allowed which can support quantum computations,
integration, cognition and consciousness.
The R and OR effects are
fundamentally non-computable (as opposed to U) and therefore they are
associated with the non-computatble aspects of the mental such as
understanding and qualia and free will, etc.
Indeed, according to
Penrose consciousness is a bilogical quantum computation in the brain in
microtubules (in the A-lattice) terminating by objective reductions OR
when tiny space-time differences reach the Planck level.
Strictly
speaking the unitary quantum evolution corresponds to pre-consciousness ,
unconsciousness, non-consciousness and functional consciousness while
the reduction is what corresponds exactly to consciousness proper.
The OR process is non-computable, non-detreminstic, irreversible and
random in some sense (the instant when it occurs) but not completely
random as in the Copenhagen since it is guided by Planck-scale geometry.
The location for coherent microtubule Orch OR and consciousness is in
post-synaptic dendrites and soma during integration phases in
integrate-and-fire brain neurons.
Synaptic inputs orchestrate
tubulin superposition in vast numbers of microtubules all involved
quantum-coherently together in a large-scale quantum state where
entanglement and quantum computation take place during integration.
This quantum computation is terminated by OR at the end of integration
where appropriate microtubule states are selected which will then
control the axons firing, i.e. conscious behavior.
Quantum entanglement of superposed microtubule is what allows unity and binding of conscious content.
And 1) isolation against environment decoherence (using some bilogical
mechanisms such as ordered water and and topological quantum error
correction) and 2) orchestration via entanglement and tunneling (through
gap junctions) between the microtubules are what yields consciousness
at the end of this gravitational OR.
Otherwise without orchestration
and isolation we have elementary quanta of consciousness without
necessarily any meaningful consciousness.
Thus, proto-consciousness is widespread in the Universe as widespread as elementary particles.
And in the same way that particles are governed by U process these proto-conscious occasions/moments are governed by R.
And in the same way that particles sometimes give rise to bodies but
not always these proto-concsious moments can give rise to consciousness.
OR acts instantaneously with respect to the physical time but it creates itself the conscious time.
References:
Sherrington CS. Man on his nature. 2nd edition. Cambridge (MA): Cambridge University Press; 1957.
Penrose R. The emperor’s new mind: concerning computers, minds, and the laws of physics. Oxford: Oxford University Press; 1989.
Penrose R. Shadows of the mind: an approach to the missing science of consciousness. Oxford: Oxford University Press; 1994.
Penrose R. On gravity’s role in quantum state reduction. Gen Relativ Gravit 1996;28:581–600.
Penrose R. Wavefunction collapse as a real gravitational effect. In:
Fokas A, Kibble TWB, Grigouriou A, Zegarlinski B, editors. Mathematical
physics. London: Imperial College Press; 2000. p. 266–82.
Diósi L. A universal master equation for the gravitational violation of quantum mechanics. Phys Lett A 1987;120(8):377–81.
Diósi L. Models for universal reduction of macroscopic quantum fluctuations. Phys Rev A 1989;40:1165–74.
Sahu S, Ghosh S, Ghosh B, Aswani K, Hirata K, Fujita D, et al. Atomic
water channel controlling remarkable properties of a single brain
microtubule: correlating single protein to its supramolecular assembly.
Biosens Bioelectron 2013;47:141–8.
Part II
The
claim of most modern science and philosophy is that consciousness
emerges from the classical computation of neural networks in the brain
which are composed of neurons (the basic units of information in the
brain similar to transistors in computers ) and synapses (which play the
role of wires connecting transistors/neurons).
These neurons are
effectively integrate-and-fire logic devices in which the synaptic
inputs reaching the various dendrites are integrated into a membrane
potential which is then compared to the threshold potential at axon
initiation segment or AIS.
If the AIS threshold is reached then an
all-or-none action potential is triggered as output and we say that the
neuron has fired.
This all-or-nothing situation is precisely what
happens also in computers where either there is a signal down a wire
(true/1) or there is not (false/0).
So the neurons either they fire
or they dont and as a consequence all computations that they can perform
is classical computations which -on the account of some- can not
capture the aspects of qualia or free feell (compatibility to be
accurate) of consciousness.
Some claim (Chalmers and Nagel for
example) that qualitative subjective consciousness cannot in principle
be captured by any function either based on classical structure or
quantum structure.
But others (Stapp and Penrose for example) claim
that quantum mechanics will be able to capture those aspects of
consciousness that resists classical functional description.
However, they contend, that in order to be able to do that we need to go
from the larger scales of classical neurons to the nano scales of
microtubules which could potentially support quantum effects.
Microtubules play in cytoskeletons the same role that neurons play in the brain.
In fact the cytoskeleton can be thought of as the brain of the neuron.
This is the idea originally championed by Hemeroff since the early
1980's.
The cytoskeleton of a neuron (or of any eukaryotic cell for
that matter) is a framework which holds the cell in shape and acts as
its control system.
It consists of a protein network of microtubules
(MT's), microtubule-associated proteins (MAPs), actin, and intermediate
filaments.
The micrtotubules in particular are very crucial to us
because they are cylindrical lattices composed of the so-called tubulins
which act as our quantum bits in the same way that neurons in neural
networks act as classical bits.
Description of Microtubules and Tubulins:
Microtubules are hollow cylindrical tubes with an outside diameter
equal 25 nm and an inside diamater equal 14 nm with variable lengths
from few hundred nm up to meters in long nerve axons.
See first illustration.
The microtubules are in fact protein polymer constructed out of peanut-shaped tubulin proteins.
Each tubulin is a dimer consisting of two separate monomers called α-tubulin and β-tubulin.
And each monomer is composed from a 450 amino acids.
The dimer is about 8nm x 4nm x 4nm in size with an atomic number about 11x10^4.
The microtubule is organized from a 13 columns or protofilaments of tubulin dimers.
The lateral connections of these 13 protofilaments give rise to two
types of hexagonal lattices (the A-lattice and the B-lattice).
These
are hexagonal lattices because each tubulin has six nearest neighbors
since the protofilaments shift in relation to their neighbors by 3
monomers.
The number 13 is one of the Fibonacci numbers:
0,1,1,2,3,5,8,13,21,..
where each number is the sum of the previous two.
The skew hexagonal A-lattice defines a pattern of microtubules made up
of 5 right-handed and 8 left-handed helical arrangements.
We remark that both 5 and 8 are Fibonacci numbers and 13=8+5.
Thus, tubulins are arranged vertically in protofilaments but they also
follow helical winding patterns with regular repeat intervals according
to the Fibonacci series.
See illustrations 2 and 3.
Each of the tubulins is an electric dipole and therefore the microtubules are lattices of oriented dipoles.
The tubulin units are thought of to represent quantum informational bit states.
Indeed, each tubulin dimer can exist in two geometrical configurations
(states) called conformations which correspond to two different states
of the dimer's electric polarization.
In one of these conformations the tubulins bend to 30 degree to the direction of the microtubule.
See iIlustration 1.
These two different conformational states arise from the displacement
of an electron centrally placed in the α-tubulin/β-tubulin juncture.
Aletrnatively, the α-tubulin can be thought of as - while the β-tubulin can be thought of as +.
In the A-lattice the lateral associations of protofilaments occur
between adjacent α and β-tubulin subunits in such a way that an
α-tubulin subunit from one protofilament interacts with a β-tubulin
subunit from an adjacent protofilament.
Thus, in a protofilament one
end will have α-tubulin exposed and therefore it is - while the other
end will have β-tubulin exposed and therefore it is +.
And since all
protofilaments are parallel the resulting microtubule is also polar
with one end positive and the other end negative.
The basic unit of information is therefore the tubulin (analogous to spin).
In fact the tubulin function as a quantum bit or qbit.
A model of protein conformational switching is given in the 4th illustration.
We imagine a pair of electrons in the juncture coupled by London forces (which are quantum forces).
The coupled electrons in the tubulin dimer can exist in the open
conformational state or in the closed conformational state or in any
linear superposition thereof because of quantum coherence.
Quantum
computation in the tubulin dimer is therefore possible by allowing the
tubulin to exist in the coherent linear superposition, evolving it
unitarily in time according to the Schrodinger equation, and then
performing a measurement which will collapse the state to one of the two
classical conformational configurations (open or closed).
References:
1-Stuart Hameroff, Ultimate Computing: Biomolecular Consciousness and NanoTechnology, 1987.
2-S.Hameroff, R.Penrose, Consciousness in the universe
A review of the ‘Orch OR’ theory, Physics of Life Reviews 11 (2014) 39–78.
3-S.Hameroff , A. Nip, M. Porter, J. Tuszynski, Conduction pathways in
microtubules, biological quantum computation, and consciousness,
BioSystems 64 (2002) 149–168.
4-R.Penrose, Shadows of the Mind, Oxford University Press, 1994.
Neurons and synapses in the brain perform classical computations
similar to those performed in computers with transistors (neurons) and
wires (synapses).
This is the standard picture due originally to McCullogh and Pitts back in 1943.
Therefore the neurons are the fundamental information units and
consciousness emerges from complex classical computations in neural
networks consisting of neurons and synapses. This is precisely the
statement of physicalism and functionalism the dominant forces in
science today.
On the other hand, others maintains that neuronal
networks can only correspond to functional consciousness, i.e.
consciousness without any associated qualia.
This is effectively
the hypothesis of the hard problem of consciousness. In other words, the
hypothesis that phenomenal consciousness (which is conscious states
associated with qualia) lies outside the realm of function and
possibly structure (Chalmers).
1-A soma or cell body (trunk of the tree): This is the nucleus where the cell resides.
2-A dendrites (branches of the tree): This is where input from axons of other neurons is received via synapses.
The surface of the dendrites are characterized by small protrusions
(called spines) which are effectively the post-synaptic contact sites
with synapses.
3-An axon (roots of the tree): This is a long thin
structure where an electric signal called an action potential is
generated signalling that the neuron is active.
The action
potential propagates along the axon and causes the release of
neurotransmitters into the synapse (more precisely into the synaptic
clef) which then allows communication with other neurons.
Of course,
the axon normally bifurcate into separate strands each terminating at a
different synapse. Hence the action potential signalling that the
neuron is active (or that the neuron has fired) is transmitted to all
other neurons.
In biological neuronal networks synapses play a crucial role as important as that of neurons.
Some synapses are excitatory (excites the neuron's firing and
contributes positively to the synaptic action) whereas others are
inhibitory (inhibits the neuron's firing and contributes negatively to
the synaptic action) and they add up to obtain an integrated action
potential and then compared to a certain threshold at the axon
initiation segment (AIS).
If the AIS threshold is reached then an
all-or-none action potential firing is triggered as output and the next
neuron will fire.
This picture is effectively that of the original
Hodgkin and Huxley model (1953) for which the authors won the Nobel
prize in medicine in 1963.
This neuron-synapse picture of the brain
can be emulated relatively easily in connectionist models of artificial
neural networks.
These emulation take also into account the
so-called brain plasticity, i.e. the fact that synapses in the brain are
continually changing, by giving appropriate computational rules
governing synaptic changes such as Hebb's procedure.
However,
all this computation, no matter how complex, remains in a very obvious
sense classical and therefore very deterministic (no room for free will)
and very objective (no room for phenomenal consciousness) according to
Chalmers, Penrose and Hameroff and others.
McCulloch W, Pitts W. A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 2013;5(9943):115–33.
Hodgkin A, Huxley A. A quantitative description of membrane current and
its application to conduction and excitation in nerve. J Physiol
1952;117:500–44.
Hebb DO. Organization of behavior: a neuropsychological theory. New York (NY): John Wiley and Sons; 1949.
The Hodgkin-Huxley Model: Its Extensions, Analysis and Numerics, Ryan Siciliano, 2012.
