Computer manufacturers have worked in recent years to wean us off the speed metric for their chips and systems. No longer do they scream out GHz values, but use chip brands like atom, core duo, and quad core, or just give up altogether and sell on other features. They don't really have much to crow about, since chip speed increases have slowed with the increasing difficulty of cramming more elements and heat into ever smaller areas. The current state of the art is about 3 GHz, (far below predictions from 2001), on four cores in one computer, meaning that computations are spread over four different processors, which each run at 0.3 nanosecond per computation cycle.
The division of CPUs into different cores hasn't been a matter of choice, and it hasn't been well-supported by software, most of which continues to conceived and written in linear fashion, with the top-level computer system doling out whole programs to the different processors, now that we typically have several things going on at once on our computers. Each program sends its instructions in linear order through one processor/core, in soda-straw fashion. Ever-higher clock speeds, allowing more rapid progress through the straw, still remain critical for getting more work done.
Our brains take a rather different approach to cores, clock speeds, and parallel processing, however. They operate at variable clock speeds between 5 and 500 Hertz. No Giga here, or Mega or even Kilo. Brain waves, whose relationship to computation remains somewhat mysterious, are very slow, ranging from the delta (sleep) waves of 0-4 Hz through theta, alpha, beta, and gamma waves at 30-100+ Hz which are energetically most costly and may correlate with attention / consciousness.
On the other hand, the brain has about 1e15 synapses, making it analogous to five million contemporary 200 million transistor chip "cores". Needless to say, the brain takes a massively parallel approach to computation. Signals run through millions of parallel nerve fibers from, say, the eye, (1.2 million in each optic nerve), through massive brain regions where each signal traverses only perhaps ten to twenty nerves in any serial path, while branching out in millions of directions as the data is sliced, diced, and re-assembled into vision. If you are interested in visual pathways, I would recommend Christof Koch's Quest for Consciousness, whose treatment of visual pathways is better than its treatment of other topics.
Unlike transistors, neurons are intrinsically rhythmic to various degrees due to their ion channel complements that govern firing and refractory/recovery times. So external "clocking" is not always needed to make them run, though the present articles deal with one such case. Neurons can spontaneously generate synchrony in large numbers due to their intrinsic rhythmicity.
Nor are neurons passive input-output integrators of whatever hits their dendrites, as early theories had them. Instead, they spontaneously generate cycles and noise, which enhances their sensitivity to external signals, and their ability to act collectively. They are also subject to many other influences like hormones and local non-neural glial cells. A great deal of integration happens at the synapse and regional multi-synapse levels, long before the cell body or axon is activated. This is why the synapse count is a better analog to transistor counts on chips than the neuron count. If you are interested in the topics of noise and rhythmicity, I would recommend the outstanding and advanced book by Gyorgy Buzsaki, Rhythms of the Brain. Without buying a book, you can read Buzsaki's take on consciousness.
Two recent articles (Brandon et al., Koenig et al.) provide a small advance in this field of figuring out how brain rhythms connect with computation. Two groups seem to have had the same idea and did very similar experiments to show that a specific type of spatial computation in a brain area called the medial entorhinal cortex (mEC) near the hippocampus depends on theta rhythm clocking from a loosely connected area called the medial septum (MS). (In-depth essay on alcohol, blackouts, memory formation, the medial septum, and hippocampus, with a helpful anatomical drawing).
Damage to the MS (situated just below the corpus collosum that connects the two brain hemispheres) was known to have a variety of effects on functions not located in the MS, but in the hippocampus and mEC, like loss of spatial memory, slowed learning of simple aversive associations, and altered patterns of food and water intake.
The hippocampus and allied areas like the mEC are one of the best-investigated areas of the brain, along with the visual system. They mediate most short-term memory, especially spatial memory (i.e rats running in mazes). The spatial system as understood so far has several types of cells:
Head direction cells, which know which way the head is pointed (some of them fire when the head points at one angle, others fire at other angles.
Grid cells, which are sensitive to an abstract grid in space covering the ambient environment. Some of these cells fire when the rat is on one of the grid boundaries. So we literally have a latitude/logitude-style map in our heads, which may be why map-making comes so naturally to humans.
Border cells, which fire when the rat is close to a wall.
Place cells, which respond to specific locations in the ambient space- not periodically like grid cells, but typically to one place only.
Spatial view cells, which fire when the rat is looking at a particular location, rather than when it is in that location. They also respond, as do the other cells above, when a location is being recalled rather than experienced.
Clearly, once these cells all network together, a rather detailed self-orientation system is possible, based on high-level input from various senses (vestibular, whiskers, vision, touch). The role of rhythm is complicated in this system. For instance, the phase relation of place cell firing versus the underlying theta rhythm, (leading or following it, in a sort of syncopation), indicates closely where the animal is within the place cell's region as movement occurs. Upon entry, firing begins at the peak of the theta wave, but then precesses to the trough of the theta wave as the animal reaches the exit. Combined over many adjacent and overlapping place fields, this could conceptually provide very high precision to the animal's sense of position.
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| One rat's repeated tracks in a closed maze, mapped versus firing patterns of several of its place cells, each given a different color. |
We are eavesdropping here on the unconscious processes of an animal, which it could not itself really articulate even if it wished and had language to do so. The grid and place fields are not conscious at all, but enormously intricate mechanisms that underlie implicit mapping. The animal has a "sense" of its position, (projecting a bit from our own experience), which is critical to many of its further decisions, but the details don't necessarily reach consciousness.
The current papers deal not with place cells, which still fire in a place-specifc way without the theta rhythm, but with grid cells, whose "gridness" appears to depend strongly on the theta rhythm. The real-life fields of rat grid cells have a honeycomb-like hexagonal shape with diameters ranging from 40 to 90cm, ordered in systematic fashion from top to bottom within the mEC anatomy. The theta rhythm frequency they respond to also varies along the same axis, from 10 to 4 Hz. These values stretch and vary with the environment the animal finds itself in.
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| Field size of grid cells, plotted against anatomical depth in the mEC. |
The current papers ask a simple question: do the grid cells of the mEC depend on the theta rhythm supplied from the MS, as has long been suspected from work with mEC lesions, or do they work independently and generate their own rhythm(s)?
This was investigated by the expedient of injecting anaesthetics into the MC to temporarily stop its theta wave generation, and then polling electrodes stuck into the mEC for their grid firing characteristics as the rats were freely moving around. The grid cells still fired, but lost their spatial coherence, firing without regard to where the rat was or was going physically (see bottom trajectory maps). Spatial mapping was lost when the clock-like rhythm was lost.
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| One experimental sequence. Top is the schematic of what was done. Rate map shows the firing rate of the target grid cells in a sampled 3cm square, with m=mean rate, and p=peak rate. Spatial autocorrelation shows how spatially periodic the rate map data is, and at what interval. Gridness is an abstract metric of how spatially periodic the cells fire. Trajectory shows the rat's physical paths during free behavior, overlaid with the grid cell firing data. |
"These data support the hypothesized role of theta rhythm oscillations in the generation of grid cell spatial periodicity or at least a role of MS input. The loss of grid cell spatial periodicity could contribute to the spatial memory impairments caused by lesions or inactivation of the MS."This is somewhat reminiscent of an artificial computer system, where computation ceases (here it becomes chaotic) when clocking ceases. Brain systems are clearly much more robust, breaking down more gracefully and not being as heavily dependent on clocking of this kind, not to mention being capable of generating most rhythms endogenously. But a similar phenomenon happens more generally, of course, during anesthesia, where the controlled long-range chaos of the gamma oscillation ceases along with attention and consciousness.
It might be worth adding that brain waves have no particular connection with rhythmic sensory inputs like sound waves, some of which come in the same frequency range, at least at the very low end. The transduction of sound through the cochlea into neural impulses encodes them in a much more sophisticated way than simply reproducing their frequency in electrical form, and leads to wonders of computational processing such as perfect pitch, speech interpretation, and echolocation.
Clearly, these are still early days in the effort to know how computation takes place in the brain. There is a highly mysterious bundling of widely varying timing/clocking rhythms with messy anatomy and complex content flowing through. But we also understand a lot- far more with each successive decade of work and with advancing technologies. For a few systems, (vision, position, some forms of emotion), we can track much of the circuitry from sensation to high-level processing, such as the level of face recognition. Consciousness remains unexplained, but scientists are definitely knocking at the door.
- Subjective time, with David Eagleman.
- A philosophy bite with Eagleman, on free will.
- Lies, trickle-down economics, and more lies.
- Double-dip is quite possible, yet austerity is "in".
- Economics quotes of the week, from Krugman:
"As I’ve often written, we’re in a strange state now where people who actually take textbook economics and simple arithmetic seriously are seen as dangerously radical and irresponsible, while people who believe in invisible bond vigilantes and confidence fairies, who claim to know what the market will want even though there’s no sign of that desire in current asset prices, are viewed as Very Serious."
- and Bill Mitchell:
"... many readers have been writing in asking me about price manipulation in international commodity markets – which is aka how financial markets caused a jump in world starvation and death."
