Tuesday, January 29, 2013

Computational Neurology

A Partial Mathematical and Conceptual theory

1. Nodes (soma), connections, associations (dendrites and axons).

The below image depicts convergence and divergence, a fundamental process occuring in neurons, their nodes and their connections.

This image is hardly any different than the process that is going on in the brain. Information is stored with in the neurons, and than it is either distributed/scattered outward or inward.

Sensory information is an input, where as imagination can be both output and input, in areas of the brain.

A visual out put of a candle, mentally, can be the cause the output of the word candle. So we see there is information being output from the visual cortex into the audio cortex.

The sound association with the visual information depends on what is called word-to-visual association frequency. The association frequency strengthens a link between the two nodes, word(s) and visual(s).

Association laws:
A) Sound-visual association : λS + Vi = sSa : Frequency of sound with visual information equals strength of sound association.
B) Visual-visual association : λVstimuli = sVa : Frequency of visual input equals strength of visual association (convergence of input with output).

From input and out put we realize there are signals going out and signals coming in. Input signals is a stimuli that means (equates to) there are efferent nerves carrying signal to away from a soma.

Connection Laws:
A) (O<)n/μ = ξ-ζn : Number of outputs per node equals number of potential efferent unactive neuron connections (ζ).
B) (I>)n/μ = α-ζn : Number of inputs per node equals number of potential afferent neuron connections.

Activation law:
A) s(stimuli+ass) = pἄ Association strength equals probability of activation.

2. Reductionism
Every node may contain what is called a category. So a node of "a candle" will be a category (node), than we can use gestalt psychology to understand that every node can have other nodes, which equate to the parts of the thing. The brain has a whole (whole nodes) which can than form a connection with its parts (part nodes).

A thought experiment for this is, a candle stick. It consists of a candle holder, candle stick, and wick. This is the process as described above.

Structuralism  laws:
A) W = nP, whole equals number of parts.
B) W+(c) = nP, the wholes connections are equal to the number of parts. This being true in the part-reductionism, as a function.
C) nῥ. = P or W, properties (ῥ) can equal part or whole.

Properties : A) Phenomenal properties are, color, shape, velocity, measurement/size (angles/outlines), state (Ex: liquid, fear), texture (feels like), part of whole, language, aroma, temperature, and pleasure/pain & emotional value, need, desire, nutritional value/health value. So in this we get that each thing can be viewed with 15 different translations, and that there is a one in 15translations possible in temporal order of consciousness of properties.

T = 1:15p thought of thing equals a particular property of a whole.

Each property must have a gate-node, an inner opening of neuronetworks that allows for input of information and detects according to its gate/receptor (color receptors, size receptors).

Reducing things to their 15 particulars, having 0 or a number of different features (n), is total phenomenal-property level reductionism. When a thing is said to have 0 features, than there is another property which exists that can be added on into the system of recognition (input of stimulation, output of idea), or it factually consists of no information for the receptors.

Property reductionism: 
15:14p = Total (Ppreduction), in this we can also know that a thing is equal to its parts, or number of mental reactions, which can increase the total number of outcomes in property reductionism (structuralism).

*I do not know if this is all the properties an intelligence can detect (as in complexity which might equal a degree of the number of parts of a thing).

If we imagine, there are 15 total properties possible to extract or input into an idea of thing. When the thing is recepted, and it is lacking properties, it will be thought of as the whole thing. These properties can be have subproperties, as in the property color being red, as in the color temperature having a specific rough measurement.

There is a difference between extraction of properties and imputation of properties.

Linguistic programming, for reductionism - We understand that all things have physical properties, that can be expressed through a word, as in an adjective. The whole of the thing, can be expressed in the form of a noun, or a adjective noun conjunction (baked bread, red car, simple man).

Structuralism Node Laws:
A) nP = nμ or nC The number of properties of a thing, equates to the number of nodes, and gives us the number of neuron connections necessary (not always visible) to account for the cohesion of the whole.
B) nP(W) = -ζn number of properties of a thing, in the inactivate state.
C) λPartAss(W) = W Property association frequency (property of x, equals color y, therefore x is z) equals the probability of the thing being thought of as a whole. This equates to the idea that an extraction of a property consciously is all that is require to identify a thing at whole.

This algorithm as a thought function can have an error margin, that can be reduced with a total parts or properties reduction to equate to whole thing. This is also what is called the Induction problem, where a universal is taken to describe or be a property of all x's, when it is only true that all x's have a particular distribution of the property (as in, all people are mean, therefore x will be mean). The particular solves the problem of universal induction.

3. Functionalism

A things function is equal to the number results that can occur for it.

This brings us to a simple equation that everything can have an end, and that the number of ends it can be thought to have can take up end-nodes. Numerous end-nodes, create a sequence of events, which is what is probably going on with even the most minute actions.

Functionalism Laws:
A) E of x = nC : ends of x equal number of connections possible.
B) Frequency of e of x = pἄ
C) Thought of e of x = pἄ
D) As the number of ends is decreased in a t1 or decision-state, the ends take on a greater probability of activation.

Conscious-threshold :
The existence of being aware must exist as a threshold frequency, that can be determined through calculations. The lower frequencies, that are making things happen in the body, or to the body, can cross over the conscious-threshold. Therefore, states of the body must exist in a steady state activation, which can be sensed when their activation is interrupted and when that interruption crosses over the conscious-threshold.

4. Neurogenesis

Since we know that ever object can be observed in its, properties, parts, and functions, we than realize that neurogenesis CAN take place when any novel property, part, of function is input. If there is no neurogenesis upon a novel end, property, or part-whoe, than there is a connections with previously existing information nodes. Similar functions, properties, and parts, only cause the activity of connections and nodes that are already in place.

5. Pain/pleasure

There most be a pain and pleasure threshold, which exists, where signals are activated to pleasure or pain centers, and the state can be stimulated into excitement by a corresponding threshold. Since each part of the body can be triggered into pain or pleasure, than there must be as many neuron clusters to account for the number of input-sources.

6. Expectation

Expectation is equate to association, meaning we expect things to be the way they are because of are frequency with the stimuli that is presented in the environment. When it comes to expecting the future, there is a greater equation for this kind of convergent thinking mechanism.

Expectation is also equate to the ends of a thing in thinking of them, and the strength or likelihood of the expectation depends on its activation.

Interference problem: Imagination can interfere with the reductionism of a thing, and cause the idea to take on properties or functions not contained in the observed thing. For accurate or semi-accurate internal recognition to take place, the output of non-existing properties in the input-source, must be inhibited.

Identification of Unknown -
1. A thing contains a property that has no primed gate. (No-priming)
2. There is no gate or receptor for the information. (No receptor)
3. A thing is observed and a property of it can not be receptive. (Limited field of property-sense)
4. There is no temporal cohesion between cause and effect (no temporal gates or connections).
5. A thing is observed and the end or cause of it can not be receptive. (Limited cause-sense, limited effect-sense).
6. The properties or functions of the thing are imperceptible because of size and limited observation (imperceptibility_ as in atomic makeup).
7. No cc-connections between things or ideas (no contrast-compartive connections made between two or more things).

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