Attention: to Threat and to Efficacy

Attention and Inattention are modeled to have a distortionary effect on an entity’s overall valuation toward the fulfillment of a purpose.  Here I will present three different, though similarly structured, setups for modeling attention in the functions.  Because of the chosen structures for the two equations, Attention will be used for the Avoidance of Pain function and Inattention will be used for the Pursuit of Pleasure function.  With some tweaking, however, either could be used.  Additionally, the x-variable, Time, can be implemented into the function properly for the Avoidance of Pain functions (Half-Life of Attention) and for the Pursuit of Pleasure functions (Doubling-Time of Inattention).  Although none of the three forms presented here model valuation extinction (i.e., the entity is still considered to exist to the individual even if ignored indefinitely), valuation extinction could be modeled by also placing Attention as a coefficient at the base of the equation alongside Existence if desired.

1. Form one will model Attention with exponential decay and without error for the Half-Life of Attention (if the Half-Life of Attention is considered to be a constant value).  Form one uses the theoretical Attentional Unit for the Avoidance of Pain function and the Inattentional Unit for the Pursuit of Pleasure function.  This would be the standard model for attention and is most useful for modeling short-term memory and working memory. [*Note, this form is form IV in the print version of the book]
2. Form two will model Attention with exponential decay and with error for the Half-Life of Attention (if the Half-Life of Attention is considered to be a constant value).  Form two is used throughout the book primarily to avoid the inconvenience of dealing with excessively large values in the exponent.  The Attentional Unit and the Inattentional Unit are turned into a ratio instead.  This model is useful to the same extent that form one is, but it can used more easily without a calculator, as Attentional Units could number in the millions or billions.
3. Form three will model Attention with valuation resilience.  Although form three makes use of the same ratio as Form Two, it models attention as being completely under volitional control.  Entities that are ignored have their valuations actively suppressed, or if they are abnormally elevated then they are passively permitted to return to their original state.  Entities that have their valuations attuned to are either passively permitted to surge to their original state, or are they may have their valuations actively elevated.  This model of attention would be most useful for depicting memories that force themselves into consciousness (e.g., in the event of trauma), long-term memory, modeling affect with computers, and for modeling the activities of individuals with exceptional autobiographical memories (i.e., those with the condition of hyperthymesia).

The Attentional Unit and Inattentional Unit vs. Attention/Inattention as a Ratio of Awareness to Neglect 

The theoretical Attentional Unit may be thought of as the minimum quantity of attentional neurons whose activation is required to maintain the base firing-rate of a specific component at its initial value (at the onset of the stimulus) over a given time frame.  If an individual were 100% attuned to a feature, then the maximum number of Attentional Units in an individual’s body would be a finite whole number (e.g., 1,000 or possible 10,000,000,000).  For instance, if an individual had a maximum potential of 1,000 Attentional Units to devote to a feature, but only 750 of them are attuned to the particular feature, then 75% of the individual’s total attentional resources are devoted to it and 25% are not.  The remaining 250 of the 1,000 that are not be attuned to the feature would be labeled Inattentional Units.

Attentional Units and Inattentional Units are calculated at the onset of a stimulus, that is, when the individual first experiences the stimulus. The calculation may fluctuate as long as the stimulus is available, but once it is gone from perception the Attention and Inattention devoted to it will change unless held constant by Reasoning.  Reasoning is described with the Half-Life of Attention and the Doubling-Time of Inattention.

Form One:

The sum of the Attentional Units and Inattentional Units would always equal an individual’s maximum attentional capacity, which in the above example is 1,000.  As both concepts would be derived from the same pool of neurons, the user of the function could employ whichever one he or she felt comfortable using by modifying the function accordingly.

• The Attentional Units that are attuned to a feature are said to be aware of it.
• The Inattentional Units that are not attuned to a feature are said to be neglecting it.

Forms Two and Three:

When Attention and Inattention are modeled as a Ratio of Awareness to Neglect, or vice-versa, a few extra steps are required and a few restrictions apply.

• Awareness is modeled as the number of Attentional Units attuned to a feature divided by the total number of attentional resources (the maximum number of Attentional Units that could attune to the feature if 100% of attentional resources were devoted to it).
• Neglect is modeled as the number of Inattentional Units (not attuned to a feature) divided by the total number of attentional resources.
• Awareness and Neglect are both fractions that when added together always equals one.  Awareness + Neglect
• Awareness can never be more than one-half (.5) for more than two separate features.  Neglect has no such restriction.
• Neither Awareness nor Neglect can equal one nor zero (cannot divide by zero) for any particular feature.

For forms two and three in the examples that follow, Attention is modeled as Awareness divided by Neglect.  This is used for the Avoidance of Pain functions in the examples demonstrated here.  In the above example, with 750 Attentional Units out of 1000 being used, Attention would be the following:

Attention = Awareness ÷ Neglect = ( 750 / 1000 ) ÷ ( 250 / 1000 ) = ( . 75 ) ÷ ( .25 ) = an Attention level of 3

Inattention, in contrast, is modeled as Neglect divided by Awareness.  This is used for the Pursuit of Pleasure functions in the examples demonstrated here.  In the above example, with 250 Inattentional Units out of 1000 being used, Inattention would be the following:

Inattention = Neglect ÷ Awareness = ( 250 / 1000 ) ÷ ( 750 / 1000 ) = ( .25 ) ÷ ( .75 ) = an Inattention level of 1 / 3

Defining Attention and Inattention as a ratio of Awareness to Neglect simply an optional matter of convenience that scales the numbers down so that large values requiring large computations do not have to be input. The downside to this, however, is that if a constant value is used for the Half-Life of Attention or the Doubling Time of Inattention, then changes in Awareness and Neglect at the extreme ends of the spectrum are given more significance than those in the middle of the spectrum.

Form One with Exponential Decay and No Error for the Half-Life of Attention

Form Two with Exponential Decay and Error for the Half-Life of Attention

Form Three with Valuation Resilience

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