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To illustrate the mathematical calculations employed in a PCT simulation, consider a pursuit tracking task in which the participant keeps a mouse cursor aligned with a moving target on a computer monitor.
The model assumes that a perceptual signal within the participant represents the magnitude of the input quantity ''q<sub>i</sub>''. (This has been demonstrated to be a rate of firing in a neuron, at least at the lowest levels.)<ref name=Powers73>{{cite book| title=Behavior: The Control of Perception| year=1973| first=William T.| last=Powers| isbn=978-0-7045-0092-1| title-link=Behavior: The Control of Perception| publisher=Wildwood House}}</ref><ref name=Yin.BG2014>{{cite journal | last =Yin | first =Henry H. | title =How Basal Ganglia Outputs Generate Behavior | journal =Advances in Neuroscience | volume =2014 | issue =768313 | pages =1–28 | date =18 November 2014 | doi =10.1155/2014/768313 | doi-access =free }}</ref> In the tracking task, the input quantity is the vertical distance between the target position ''T'' and the cursor position ''C'', and the random variation of the target position acts as the disturbance ''d'' of that input quantity. This suggests that the perceptual signal ''p'' quantitatively represents the cursor position ''C'' minus the target position T, as expressed in the equation ''p''=''C''–''T''.
Between the perception of target and cursor and the construction of the signal representing the distance between them there is a delay of ''τ'' milliseconds, so that the working perceptual signal at time ''t'' represents the target-to-cursor distance at a prior time, ''t'' – ''τ''. Consequently, the equation used in the model is
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This "reorganization system" is proposed to be part of the inherited structure of the organism. It changes the underlying parameters and connectivity of the control hierarchy in a random-walk manner. There is a basic continuous rate of change in intrinsic variables which proceeds at a speed set by the total error (and stops at zero error), punctuated by random changes in direction in a hyperspace with as many dimensions as there are critical variables. This is a more or less direct adaptation of Ashby's "[[homeostat]]", first adopted into PCT in the 1960 paper<ref name=PCM1960 /> and then changed to use E. coli's method of navigating up gradients of nutrients, as described by Koshland (1980).<ref>Koshland, Daniel. (1980). ''Bacterial chemotaxis as a model behavioral system''. New York: Raven Press.</ref>
Reorganization may occur at any level when loss of control at that level causes intrinsic (essential) variables to deviate from genetically determined set points. This is the basic mechanism that is involved in trial-and-error learning, which leads to the acquisition of more systematic kinds of learning processes.<ref name="Cziko 1995">{{cite book| title=Without Miracles| year=1995| first=Gary| last=Cziko| isbn=978-0-262-03232-2| title-link=Without Miracles| publisher=MIT Press}}.</ref>
==Psychotherapy: the method of levels (MOL)==
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Perceptual control theory has not been widely accepted in mainstream psychology, but has been effectively used in a considerable range of domains<ref>{{Cite web | url=https://thepsychologist.bps.org.uk/volume-28/november-2015/perceptual-control-revolution |title = A perceptual control revolution? |website=The Psychologist}}</ref><ref name="IJHCS">The June 1999 Issue of ''The International Journal of Human-Computer Studies'' contained papers ranging from tracking through cockpit layout to self-image and crowd dynamics.</ref> in human factors,<ref name="CBUT">PCT lies at the foundation of [[Component-Based Usability Testing]].</ref> clinical psychology, and psychotherapy (the "[[Method of Levels]]"), it is the basis for a considerable body of research in sociology,<ref>For example: McClelland, Kent A. and Thomas J. Fararo, eds. 2006, ''Purpose, Meaning and Action: Control Systems Theories in Sociology'', New York: Palgrave Macmillan. (McClelland is co-author of Chapter 1, "Control Systems Thinking in Sociological Theory," and author of Chapter 2, "Understanding Collective Control Processes."). McClelland, Kent, 2004, "Collective Control of Perception: Constructing Order from Conflict", ''International Journal of Human-Computer Studies'' 60:65-99. McPhail, Clark. 1991, ''The myth of the madding crowd'' New York: Aldine de Gruyter.</ref> and it has formed the conceptual foundation for the reference model used by a succession of [[NATO]] research study groups.<ref name="IST">volume-28november-2015 Reports of these groups are available from the [[NATO Research and Technology Administration]] publications page: {{cite web |url=http://www.rta.nato.int/Abstracts.aspx |title=NATO Research & Technology Organisation Scientific Publications |access-date=2010-05-15 |url-status=dead |archive-url=https://web.archive.org/web/20100623055236/http://www.rta.nato.int/abstracts.aspx |archive-date=2010-06-23 }}> under the titles RTO-TR-030, RTO-TR-IST-021, and RTO-TR-IST-059.</ref> It is being taught in several universities worldwide and is the subject of a number of PhD dissertations.<ref>{{cite web |last=Heylighen |first=Francis |title=The Economy as a Distributed, Learning Control System |url=http://pespmc1.vub.ac.be/Papers/MarketCo.html}}</ref>
Recent approaches use principles of perceptual control theory to provide new algorithmic foundations for [[artificial intelligence]] and [[machine learning]].<ref>{{cite journal |last1=Monaco |first1=Joseph D. |last2=Hwang |first2=Grace M. |title=Neurodynamical Computing at the Information Boundaries of Intelligent Systems |journal=Cognitive Computation |date=27 December 2022 |volume=16 |issue=5 |pages=1–13 |doi=10.1007/s12559-022-10081-9|s2cid=255222711 |doi-access=free |pmid=39129840 |pmc=11306504 }}</ref>
==Selected bibliography==
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