#39. The 1950 Ramp [population, evolutionary psychology, engineering, neuroscience]

PO   EN   EP   NE

Red, theory; black, fact

A schematic of a simple rate-of-increase controller mechanism

Historical 

Since about 1950, the world population has been increasing along a remarkably steady ramp function with no slackening in the rate of increase yet apparent, although one cycle of oscillation in the slope occurred during the Sixties. Malthusian reasoning predicts an exponential increase, which this is not. Several lines of evidence point to the idea that humans have a subconscious population controller in their heads, and yet such a controller would have leveled out the increase by now. Until now, no theory has sufficed to explain the facts.

Human Population is Being Controlled for Endless Trouble

The natural population curve for humans in good times may be a saw-tooth waveform, with population ramps alternating with political convulsions that result in a large group being expelled permanently, resulting in the precipitous but limited drop in local population density that ends the saw-tooth cycle. This cycle accomplishes the ecological dispersal function. The population must ramp up for a time to sustainably create the numbers needed for the expulsions. The WHO population curve shows only a ramp because it is a worldwide figure and therefore population losses in expelling regions are balanced by population increases in welcoming regions. This also implies that human population has been increasing in a way unrestrained by food or resource availability or any other external constraint since 1950, to now.

Clearly, human population is being controlled; not to a constant absolute density, but to a constant rate of increase. Population density would go up along the much faster, steeper, and more disastrous exponential curve of Malthus if there were actually no controller.

Neuroscience Aspects

Researchers should look first for such a controller in the hypothalamus, already known to control other variables, such as temperature, by feedback principles.

"Nature does not reinvent the wheel" [quote from my old Professor], which I understand to mean that once a brain structure evolves to serve a particular computational function, it will be tapped for all future needs for such a calculation. This process may make it grow larger or develop sub-nuclei, but additional, independent nuclei for the same computation will never evolve.

Engineering Aspects 

The population controller may contain a conventional PID controller. To make it control rate of increase rather than absolute population density, you put a differentiator in the feedback pathway. If you are of the opinion that human population control is urgent, then you must knock out this differentiator and replace it with a simple feed-through connection. 

Back to Neuroscience 

Fortunately, one common way for evolution to implement differentiation in mammals is to begin with such a feed-through connection and supplement it with an inhibitory, slow, parallel feed-forward connection. If this is the case here, then you  inhibit the feed-forward pathway pharmacologically with sufficient specificity and the job is done. Subjectively, the effect of such a drug would be to take away people's ability to get used to higher population density in deciding how many children to have. An increased propensity to riot should not occur.

The political convulsions that produce dispersal would be triggered by the value on the integrator of the PID controller rising above a threshold. The amygdala of the brain may mediate this. Consistent with this, bilateral removal of the amygdala and hippocampus in monkeys is known to have a profound taming effect accompanied by hypersexuality, known as the Kluver-Bucy syndrome.

#27. The Origin of Consciousness [neuroscience]

NE

Red, theory; black, fact

We begin life conscious only of our own emotions. Then the process of classical conditioning, first studied in animals, brings more and more of our environment into the circle of our consciousness, causing the contents of consciousness to become enriched in spatial and temporal detail. Thus, you are now able to be conscious of these words of mine on the screen. However, each stroke of each letter of each word of mine that now reaches your consciousness does so because, subjectively, it is "made of" pure emotion, and that emotion is yours.

Some analogies come to mind. Emotion as the molten tin that the typesetter pours into the mold, the casting process being classical conditioning and the copy the environmental data reported by our sense organs. Emotion as the area on one side of a fractal line and sensory data the area on the other side. Emotion as an intricately ramifying tree-like structure by which sensory details can send excitation down to the hypothalamus at the root and thus enter consciousness.

The status of "in consciousness" can in principle affect the cerebral cortex via the projections to cortex from the histaminergic tuberomamillary nucleus of the hypothalamus. Histamine is known to have an alerting effect on cortex, but to call it "alerting" may be to grossly undersell its significance. It may carry a consolidation signal  for declarative, episodic, and flash memory. Not for a second do I suppose all of that to be packed into the hippocampus, rather than being located in the only logical place for it: the vast expanse of the human cerebral cortex.

#13. The Neural Code, Part II: the Thalamus [neuroscience, engineering]

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Red, theory; black, fact

Schematic of thalamus circuits

Thalamic processing as Laplace transform

The thalamus may perform a Laplace transform (LT). All the connections shown are established anatomical facts, and are based on the summary diagram of lateral geniculate nucleus circuitry of Steriade et al. (Steriade, M., Jones E. G. and McCormick, D. A. (1997) Thalamus, 2 Vols. Amsterdam: Elsevier).  I have added feedback from cortex as a context-sensitive enabling signal for the analytical process.

Thalamic electrophysiology

The thalamic low-threshold spike (LTS) is a slow calcium spike that triggers further spiking that appears in extracellular recordings as a distinctive cluster of four or five sodium spikes. The thalamus also has an alternative response mode consisting of fast single spikes, which is observed at relatively depolarized membrane potentials.

The thalamic low-threshold spike as triggered by a hyperpolarization due to a negative electric current pulse injected into the neuron through the recording electrode. ACSF, normal conditions; TTX, sodium spikes deleted pharmacologically. From my thesis, page 167.

Network relationships of the thalamus

Depolarizing input to thalamus from cortex is conjectured to be a further requirement for the LTS-burst complex. This depolarization is conjectured to take the form of a pattern of spots, each representing a mask to detect a specific pole of the stimulus that the attentional system is looking for in that context.

The complex frequency plane is where LTs are graphed, usually as a collection of points. Some of these are "poles," where gain goes to infinity, and others are "zeroes," where gain goes to zero. I assume that the cerebral cortex-thalamus system takes care of the poles, while the superior and inferior colliculi take care of the zeroes. 

If this stimulus is found, the pattern of poles must still be recognized. This may be accomplished through a cortical AND-element wired up on Hebbian principles among cortical neurons. These neurons synapse on each other by extensive recurrent collaterals, which might be the anatomical substrate of the conjectured AND-elements. Explosive activation of the AND network would then be the signal that the expected stimulus has been recognized, as Hebb proposed long ago, and the signal would then be sent forward in the brain via white matter tracts to the motor cortex, which would output a collection of excitation spots representing the LT of the desired response.

Presumably, a reverse LT is then applied, possibly by the spinal grey, which I have long considered theoretically underemployed in light of its considerable volume. If we assume that the cerebral cortex is highly specialized for representing LTs, then motor outputs from cerebellum and internal globus pallidus would also have to be transformed to enable the cortex to represent them. In agreement with this, the motor cortex is innervated by prominent motor thalami, the ventrolateral (for cerebellar inputs) and the ventroanterior (for pallidal inputs).

Brain representation of Laplace transforms

The difficulty is to see how a two-dimensional complex plane can be represented on a two-dimensional cerebral cortex without contradicting the results of receptive field studies, which clearly show that the two long dimensions of the cortex represent space in egocentric coordinates. This just leaves the depth dimension for representing the two dimensions of complex frequency.

A simple solution is that the complex frequency plane is tiled by the catchment basins of discrete, canonical poles, and all poles in a catchment basin are represented approximately by the nearest canonical pole. It then becomes possible to distinguish the canonical poles in the cerebral cortex by the labelled-line mechanism (i.e., by employing different cell-surface adhesion molecules to control synapse formation.)

Layer 1 of cortex is mostly processes, which leaves us with five cortical cell layers not yet assigned to functions. Four of them might correspond to the four quadrants of  the complex frequency plane, which differ qualitatively in the motions they represent. The two granule-cell layers 2 and 4 are interleaved with the two pyramidal-cell layers 3 and 5. The two granule layers might be the top and bottom halves of the left half-plane, which represent decaying, stabilized motions. The two pyramidal layers might represent the top and bottom halves of the right half-plane, which represent dangerously growing, unstable motions. Since the latter represent emergency conditions, the signal must be processed especially fast, requiring fast, large-diameter axons. Producing and maintaining such axons requires correspondingly large cell bodies. This is why I assign the relatively large pyramidal cells to the right half-plane.

Intra-thalamic operations

The brain may calculate the Laplace transform just the way it is defined: the integral of the product of the input time-domain function and an exponentially decaying or growing sinusoid (eigenfunction). A pole would be recognized after a finite integration time as the integrand rising above a threshold. This thresholding is plausibly done in cortical layer 4, against a background of elevated inhibition controlled by the recurrent layer-6 collaterals that blocks intermediate calculation results from propagating further into the cortex. The direct projections from layer 6 down to thalamus would serve to trigger the analysis and rescale eigenfunction tempo to compensate for changes in behavioural tempo. Alternation of LTS-bursting activity between thalamic reticular neurons and thalamic principal neurons would be the basis of the oscillatory activity involved in implementing the eigenfunctions. This alternation or ping-ponging is precedented by the spindling mechanism of light sleep and thalamic oscillation is further precedented by the phenomenon of Parkinsonian tremor cells, which are in the thalamus. Furthermore, when you are recording it in real time, the thalamic LTS has a bouncy look.

Mutual inhibition of reticular thalamic neurons (established but not shown in my schematic) would be the basis of the integrator, and multiplication of functions would be done by silent inhibition in the triadic synapses via the known disinhibitory pathway from the reticular thalamus through the thalamic inhibitory interneurons. These interneurons are not shown in the schematic. (Still unaccounted for is direct participation of the reticular thalamic afferents in triadic synapses, which my schematic shows.)

A negative feedback system will be necessary to dynamically rejig the thalamus so that the same pole maps to the same spot despite changes in tempo. Some of the corticothalamic cells (layer 6) could be part of this system (layer 6 cells are of two quite different types).

Consequences for object recognition

The foregoing system could be used to extract objects from the incoming data by in effect assuming that the elements or features of an object always share the same motion and therefore will be represented by the same set of poles. An automatic process of object extraction may therefore be implemented as a tendency for Hebbian plasticity to involve the same canonical pole at two different cortical locations that are connected by recurrent axon collaterals.

#12. The Neural Code, Part I: the Hippocampus [neuroscience, engineering]

EN   NE

Red, theory; black, fact

Santiago Ramón y Cajal (1911) [1909] Histologie du Système nerveux de l'Homme et des Vertébrés, Paris: A. Maloine. The French copyright expired in 2004.

"Context information" is often invoked in neuroscience theory as an address for storing more specific data in memory, such as whatever climbing fibers carry into the cerebellar cortex (Marr theory), but what exactly is context, as a practical matter?

Requirements for a Learning Context Signal

First, it must change on a much longer timescale than whatever it addresses. Second, it must be accessible to a moving organism that follows habitual, repetitive pathways in patrolling its territory.

The Fourier Transform as Context Signal

Consideration of the mainstream theory that the hippocampus (see illustration) prepares a cognitive map of the organism's spatial environment suggests that context is a set of landmarks. It seems that a landmark will be any stimulus that appears repetitively. Since only rhythmically repeating functions have a classical discrete-frequency Fourier transform, the attempt to calculate such a transform could be considered a filter for extracting rhythmic signals from the sensory input. 

From Repeating to Rhythmic 

However, this is not enough for a landmark extractor because landmark signals are only repetitive, not rhythmic. Let us suppose, however, that variations in the intervals between arrivals at a given landmark are due entirely to programmed, adaptive variations in the overall tempo of the organism's behavior. A tempo increase will upscale all incoming frequencies by the same factor, and a tempo decrease will downscale them all by the same factor. Since these variations originate within the organism, the organism could send a "tempo efference copy" to the neuronal device that calculates the discrete Fourier transform, to slide the frequency axis left or right to compensate for tempo variations. 

Thus, the same landmark will always transform to the same set of activated spots in the frequency-amplitude-phase volume. 

A Possible Neuronal Mechanism

I conjecture that the hippocampus calculates a discrete-frequency Fourier transform of all incoming sensory data, with lowest frequency represented ventrally and highest dorsally, and a with a linear temporal spectrum represented between. 

Tempo Compensation 

The negative feedback device that compensates tempo variations would be the loop through medial septum. The septum is the central hub of the network in which the EEG theta rhythm can be detected. This rhythm may be a central clock of unvarying frequency that serves as a reference for measuring tempo variations, possibly by a beat-frequency principle. 

Fourier Transform by Re-entrant Calculation 

The hippocampus could calculate the Fourier transform by exploiting the mathematical fact that a sinusoidal function differentiated four times in succession gives exactly the starting function, if its amplitude and frequency are both numerically equal to one. This could be done by the five-synapse loop from dentate gyrus (DG) to hippocampal CA3 to hippocampal CA1 to subiculum (sub) to entorhinal cortex (EC), and back to dentate gyrus. The dentate gyrus looks anatomically unlike the others and may be the input site where amplitude standardization operations are performed, while the other four stages would be the actual differentiators. 

Differentiation would occur by the mechanism of a parallel shunt pathway through slowly-responding inhibitory interneurons, known to be present throughout the hippocampus.

The two long spatial dimensions of the hippocampus would represent frequency and amplitude by setting up gradients in the gain of the differentiators. A given spot in the hippocampal array would map the input function to itself only for one particular combination of frequency and amplitude. 

The self-mapping sets up a positive feedback around the loop that makes the spot stand out functionally. All the concurrently active spots would constitute the context. This context could in principle reach the entire cerebral cortex via the fimbria fornix, mammillary bodies, and tuberomamillary nucleus of the hypothalamus, the latter being histaminergic.

Learning and Novelty 

The cortex may contain a novelty-detection function, source of the well-documented mismatch negativity found in oddball evoked-potential experiments. A stimulus found to be novel would go into a short term memory store in cortex. If a crisis develops while it is there, it is changed into a flash memory and wired up to the amygdala, which mediates visceral fear responses. In this way, a conditioned fear stimulus could be created. If a reward registers while the stimulus is in short term memory, it could be converted to a conditioned appetitive stimulus by a similar mechanism.

It Gets Bigger

I conjecture that all a person's declarative and episodic memories together are nothing more nor less than the context data that were instrumental in conferring conditioned status on particular stimuli.

Context is Required for Novelty

To become such a memory, a stimulus must first be found to be novel, and this is much less likely in the absence of a context signal; to put it another way, it is the combination of the context signal and the sensory stimulus that is found to be novel. Absent the context, and almost no simple stimulus will be novel. This may be the reason why at least one hippocampus must be functioning if declarative or episodic memories are to be formed.