The illustration above is of a tokamak. That is a device scientists have been working with for decades to make nuclear fusion possible. So far surprisingly few positive results but it may still work in the end. Part of the way it works is to concentrate a electromagnetic field with external coils formed into a toroidal shape.
In How Squishy Math Is Revealing Doughnuts in the Brain by Kelsey Houston-Edwards writes of some new neuroscience research has “found that certain brain cells use a torus, the mathematical name for the surface of a doughnut, to map their environment”.
Typically the brain is represented as flattened diagram showing connections between neurons somewhat like a circuit diagram. The brain actually exists in three physical dimensions. Accounting to this new research when the temporal firings are mapped geometrical forms emerge that are up to seven dimensions. These are not actual physical dimensions but mathematical dimensions required to express the complexity of the patterns.
Immediately after receiving the stimulus, the simplicial complexes grew like a massive Lego construction, adding in pieces of higher and higher dimensions until the sculpture reached the maximum of three or four dimensions, depending on the stimulus. Then the whole thing rapidly disappeared. “You have these increasingly complex structures that are being created by the stimulus until it just all collapses,” Hess says.
In this topological analysis, the firing data gets mapped temporally and spatially at different levels of granularity. “‘At every scale you’re going to have a different snapshot of what that complex looks like,’ says Ranthony Edmonds, a mathematician at the Ohio State University”.
Topologists study this spectrum of shapes—recording, in particular, the number of holes in each dimension. They are especially interested in holes that persist through many different scales. Some holes briefly appear and then disappear, but the stubborn holes—those that survive through a range of scales—point to the most essential features of the data. TDA can thus reduce a complex mess of data to a simple list of stubborn holes, in much the way that a JPEG photo file compresses an image. “It’s a way of paring down the data to the stuff that really matters so that we have something much more workable,” Ghrist says.
Sometimes the holes identified in this way have direct interpretations. Mathematician Jose Perea of Northeastern University and a team of computational biologists used persistent homology to find periodic biological processes—those that repeat at regular intervals. Examples include the metabolic cycle of yeast or a mouse’s circadian clock. “What is recurrence or repetition?” Perea asks. “Geometrically it should be like you’re traversing some sort of loop in the space of the thing that you’re looking at.
Is any chance that the “holes”, especially the persistent ones, might be where electromagnetic fields generated by the firings are concentrated? Maybe the “fusion” of consciousness isn’t found directly in the firings but in the holes where the neurons don’t fire.
Making certain a wing and fuselage design in a new airplane works as expected is critical before the airplane flies. It also isn’t easy. The dynamics of air flow is complicated and the number of variables so enormous that the computation of fluid dynamics for plane has been beyond the capacity of most computers. Simulations of this sort generally had to be undertaken on government super-computers until recently. The Wright Brothers solved this problem by flying models of their airplane tethered to the ground over many years and many designs until they perfected the wings used in first powered flight in 1903. Before the Wright Brothers in 1871 a British engineer Frank Wenham invented the first wind tunnel to perform the same kind of testing on a small scale, a 3.7-meter-long square tube that sent air through at speeds up to forty miles per hour. A miniature model of the plane or wing could be placed in the tunnel and measurements made of its aerodynamic performance. A smoke gun could also color the air and permit visualization of the air flows. The wind tunnel became to the go-to method for testing wing and airplane aerodynamics for almost every plane designed and flown since. Even with the advances in the computational dynamics and computer power, wind tunnels are still in use. NASA has one over 430 meters long.[1]
Aeronautical engineers without computers and with a partial understanding of aerodynamics solved the problem of designing planes that could fly by creating a model. It was an exceedingly practical approach to a complex problem. Instead of doing basic science until achieving a full understanding fluid dynamics, then inventing supercomputers to do the calculations, engineers tried their models out to see how they worked. Could the evolution of consciousness be a similar exceedingly practical solution to a complex problem – the problem of surviving and thriving in a complicated world?
Brain waves were discovered over a hundred years ago and first measured crudely with an electroencephalogram in 1924. We know the brain is always active, even during sleep, and the patterns of activity change with our conscious state.
A few recent studies have shed additional light on the patterns of firing of neurons. The way neurons fire has been compared to the wave in stadium where the firings seem to move in spatial patterns. A recent study found:
Neural oscillations are evident across cortex but their spatial structure is not well- explored. Are oscillations stationary or do they form “traveling waves”, i.e., spatially organized patterns whose peaks and troughs move sequentially across cortex? Here, we show that oscillations in the prefrontal cortex (PFC) organized as traveling waves in the theta (4-8Hz), alpha (8-12Hz) and beta (12-30Hz) bands. Some traveling waves were planar but most rotated. The waves were modulated during performance of a working memory task. During baseline conditions, waves flowed bidirectionally along a specific axis of orientation. Waves in different frequency bands could travel in different directions. During task performance, there was an increase in waves in one direction over the other, especially in the beta band.
The rotational nature of waves may be critical for working memory. An article explaining the study notes: “A stationary wave (one in which all the neurons involved were “on” or “off” in unison) would mean that information could be unavailable when activity was off across the whole group. With a rotating traveling wave there is always activity somewhere around the circle—just like how in a stadium of fans doing “the wave,” the next section stands up as soon as the preceding one sits down”.
A different study found that the firing of neurons of rats navigating an environment were mapped on a toroidal manifold. A torus is a doughnut shape.
A study of administration of the anesthetic propofol shows it alters the spatial pattern of neural firings.
Oscillatory dynamics in cortex seem to organize into traveling waves that serve a variety of functions. Recent studies show that propofol, a widely used anesthetic, dramatically alters cortical oscillations by increasing slow-delta oscillatory power and coherence. It is not known how this affects traveling waves. We compared traveling waves across the cortex of non-human primates before, during, and after propofol-induced loss of consciousness (LOC). After LOC, traveling waves in the slow-delta (∼1 Hz) range increased, grew more organized, and traveled in different directions relative to the awake state. Higher frequency (8–30 Hz) traveling waves, by contrast, decreased, lost structure, and switched to directions where the slow-delta waves were less frequent. The results suggest that LOC may be due, in part, to increases in the strength and direction of slow-delta traveling waves that, in turn, alter and disrupt traveling waves in the higher frequencies associated with cognition.
An article describes the pattern changes: “Whereas conscious brains exhibit a mixture of waves of various frequencies rotating or traveling straight in various directions, brains under propofol anesthesia became dominated by powerful, very low frequency “delta” waves that roll straight outward in opposite directions instead of slowly rotating around central points as they do during consciousness“.
The view emerging from these studies is that the spatial organization of neural firings may be a critical component of the neural computation the brain performs. The traditional view of neural computation has been that of information passed sequentially from one neuron to other neurons as it moves through stages of processing, This new view augments the traditional view with spatial patterns and interactions carrying information. A researcher compares this difference to wave-particle duality in physics:
“The traditional view of brain function describes brain activity as an interaction of neurons. Since every neuron is confined to a specific location, this view is akin to the description of light as a particle,” says Gepshtein, director of Salk’s Collaboratory for Adaptive Sensory Technologies. “We’ve found that in some situations, brain activity is better described as interaction of waves, which is similar to the description of light as a wave. Both views are needed for understanding the brain.”
The best way to explain how the neurons were behaving, they discovered, was through interaction of microscopic waves of activity rather than interaction of individual neurons. Rather than a flash of light activating specialized sensory cells, the researchers showed how it creates distributed patterns: waves of activity across many neighboring cells, with alternating peaks and troughs of activation—like ocean waves.
When these waves are being simultaneously generated in different places in the brain, they inevitably crash into one another. If two peaks of activity meet, they generate an even higher activity, while if a trough of low activity meets a peak, it might cancel it out. This process is called wave interference.
“When you’re out in the world, there are many, many inputs and so all these different waves are generated,” says Albright. “The net response of the brain to the world around you has to do with how all these waves interact.”
In addition to the improved understanding of biological computation, concepts of neural wave interference show much promise for developing new methods of “analog computation, including artificial intelligence (AI) systems. Previous approaches to AI largely relied on artificial neural networks that learn by changing the strengths of connections between neurons. In contrast to this mainstream paradigm, spiking neural networks and oscillator-based computing use the system’s rich repertoire of evolving dynamical states to perform computations that offer significant energy savings (since spiking affords remarkably low expenditure of energy).
The idea of that consciousness is involved with spatial and analog computation is probably familiar to anyone who has been reading this blog. McFadden in his cemi theory of consciousness argues that the brain performs both digital and analog computations. The digital computations involve information transmitted from one neuron to the next. The analog computations involve the electromagnetic field that neural circuits create.Spiking is critical in McFadden’s theory since it magnifies the strength of the EM field and makes additional neurons teetering on the edge of firing to commit to firing.
Is it possible the spatial patterns perform critical functions for consciousness? Let’s begin with the idea that the spatial forms are complex and may work in many different ways, including ones not involving consciousness. Aside from that, rotating patterns of firings might assist in creating and sustaining elements of consciousness by concentrating the EM field. Planar patterns might serve to create a ground state or as an erasure or reset mechanism needed to remove or repaint elements of consciousness. Recall the propofol study mentioned above where delta waves roll straight outward in opposite directions to provide the ultimate erasure of anesthesia.
I first encountered the researcher John Smythies when I was reading about Aldous Huxley, Humphry Osmond, and The Doors of Perception. Smythies was a researcher who worked with Humphry Osmond to investigate the effects of mescaline in London in the early modern study of psychedelics. He collaborated with Russell Brain on an early attempt to bridge the gap between materialism and idealism called extended materialism in the The Analysis of Perception. Smythies among a small group gradually came to the view that consciousness is a different kind of matter that exists in a different physical space – another dimension. This is a form of dualism but one in which the material of mind exists in a space outside 3+1 spacetime.
In Space, Time, and Consciousness he draws on the work of Andre Linde who has argued that the world consists of space-time, matter and consciousness. Smythies concludes:
Linde’s theory of consciousness suggests that, in a comprehensive physical theory of the Universe, space-time, matter and consciousness will all become ontologically equal partners in a single over-riding physical reality in a multidimensional hyperspace. Linde himself does not discuss what the nature of consciousness might be other than its independent ontology. Nor does he comment on what might be the nature of the relations between a consciousness and its brain. However, some of the details of this hypothesis have been filled in by the people quoted such as Price, Broad, Russell and myself. My own contribution to this theory is to present the case that a consciousness may have its own space–time system and its own system of ontologically independent and spatiotemporally organized events sensations and images) that have as much right to be called ‘material’ as do protons and electrons. Price (1953) and I also have suggested that the relations between a consciousness and its brain are causal.
So the new formulation of reality might consist of the following ontologically equal partners — (A) physical space-time (10 or more dimensions) containing physical matter (protons, electrons, etc.); (B) phenomenal space (3 more dimensions of a parallel universe) containing mind stuff (sensations and images); and (C) real time (time 2). A and B are in relative motion along the time 1 axis in time 2. Their contents are in causal relations via the brain. The psychological ‘now’ of time marks the point of contact of the two systems.
The idea may seem initially a little far-fetched to some; however, the idea of additional dimensions to our familiar 3+1 isn’t new to physics. There are numerous contemporary theories involving extra dimensions. As Lisa Randall points out in The case for extra dimensions, Theodor Kaluza suggested an extra dimension in 1919 to unify electrodynamics and relativity. Kaluza noticed that when he solved Albert Einstein’s equations for general relativity using five dimensions, then Maxwellian equations for electromagnetism emerged spontaneously (from Wikipedia). Oskar Klein suggested in 1926 that the extra dimension would be extraordinarily small and, hence, unable to be detected. The Kaluza-Klein theory as is known became a precursor to string theory and so far is unproven but not also not disproven. Ultimately the problem is how to detect additional dimensions in a world that consists of our apparent 3+1 dimensions.
The linking of an extra dimension to electromagnetics in the Kaluza-Klein theory and the linking of electromagnetics to consciousness in McFadden’s cemi theory creates an intriguing hypothesis that consciousness has a location where its stuff exists but it is not in the three dimensional space of the brain but rather in an additional physical dimension. Consciousness itself may be a sort of folding of 3+1 spacetime as information embedded in an additional dimension mediated by an electromagnetic field. The spatial patterns of neural firings essentially encode the qualia into the additional dimension.
This is all very speculative but it is interesting to see the idea of extra dimensions relating to consciousness being considered. A recent article by Peter Sjöstedt-Hughes on The Institute of Art and Ideas argues that extra spatial dimensions may be the key to solving the hard problem of consciousness. Whether it completely answers the hard problem, I doubt, but it might get us close enough to the answer that the difference is meaningless.
Broad Speculations 