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Dynamical systems theory as it is used in the context of developmental psychology, and by some psychoanalysts as in this article or in this video by the first speaker can be described as an attempt to introduce mathematical concepts in the study of psychological phenomena. Unlike other applications of dynamical systems theory, the above seem to use terms like "attractor" in an abstract or metaphorical sense, that is, outside of a formal mathematical context.

  • Is this kind of application useful or just a bunch of preety words, stripped of their real meaning ?
  • Do we have a better understanding of psychological phenomena through such a framework?
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    $\begingroup$ This seems like a very broad question likely to elicit opinions more than factual answers, and as such seems off-topic to me. It could be rewritten a bit to ask for instances of applying these theories or something more specific to avoid that, I think, if it would answer your need. $\endgroup$ – Krysta Nov 3 '14 at 18:49
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    $\begingroup$ Thanks for pointing that out. I 'll think a bit about which section would be better to focus on and then I will edit it to a more precise question. $\endgroup$ – Lazaros Mitskopoulos Nov 3 '14 at 19:16
  • $\begingroup$ I'm worried that your question is too broad and subjective. To further improve the question, you could modify it in a reference-request and perhaps narrow it down to a specific mathematical theory and how it applies to a specific domain of psychology. $\endgroup$ – Seanny123 Nov 4 '14 at 2:43
  • $\begingroup$ Quite related: Does neurodynamics have any relation to psychodynamics? $\endgroup$ – Ooker Jul 5 '18 at 7:59
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Like all models and modeling frameworks, the utility of the approach is often tied to how much it increases our understanding of the phenomena of interest. As summarized nicely by Smith & Thelen (2003), there are developmental questions that are better conceptualized through the framework of DST than through alternative modeling frameworks due to the richly interactive and multi-causal structure of the phenomena.

You'll also find that applications of DST in Developmental Psychology are not just appealing to the metaphorical use of DST. There are rigorous mathematical uses of the tools of DST to explain developmental phenomena. One of the most cited examples is Thelen et al. (2001), who modeled the A-not-B error. There is a lot of similarly inspired modeling work being done throughout the field.

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  • $\begingroup$ I didn't know about the actual mathematical uses of DST in developmental psychology. I am glad to hear about them, because I often get the impression that metaphorical imports of concepts used in the natural sciences, intend to impress rather than actually provide a useful framework. I guess I was wrong this time. $\endgroup$ – Lazaros Mitskopoulos Nov 5 '14 at 13:48
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Dynamical systems models is commonly used in the domain of perception and action. See Warren, 2006 for a comprehensive review. This work uses the mathematical formalism of dynamics and not just the metaphorical concepts. An exploration of the references of Warren's paper, as well as of papers that have cited it, will find many examples of dynamical models of perception and action.

For another example of dynamical modeling in perception-action research (with moves toward more "cognitive" models as well), I recommend Scott Kelos' Book Dynamic Patterns. This is an accessible overview (10 years before Warren's paper) that makes very explicit the connection between the metaphors and actual models.

I will also add that there are close theoretical and methodological links between Warren, Thelen/Smith, and Kelso that go beyond merely the use of dynamical systems models. For example, they all draw links between dynamical systems methods and the possibility of a non-representational ontology of mind.

All that said, even within perception-action, there are many researchers who use the metaphorical concepts of dynamical systems theory inexactly. A chapter of my Ph.D. thesis will be on incorrect use of the terms "attractor" and "bifurcation", etc., in the literature. (playing fast and loose with fixed points vs. nullclines, state variables vs. parameters, etc.)

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  • $\begingroup$ It's actually excellent form to answer old questions! Welcome to CogSci.SE! $\endgroup$ – Seanny123 Jan 1 '16 at 17:49
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The premise of this answer is that if math can be applied to accurately used for psychic phenomena than meta use of math can be applied accurately as well.

Psychoanalysis is a tricky subject. Unlike cognitive behavioural psychotherapy its goal isn't expressly to teach a new behavior but to find a source of a stimulus. If strands of thought based on rational movement and happenings were a line then the human condition certainly would be nonlinear because so much of what we do is a reflection of our training and associations from the past both conscious and subconscious. Though we know not the exact equation of consciousness we can accurately theorize that human intelligence is reflected in the artificial intelligences we have created. For instance some decisions can be mapped out as a proposition logical equation simular to a decision tree. Other decisions are based purely on instinct like neural networks and some come from recognizing and finding things that please and displease us like SVMs. Some of those equations would have random variables of course but much of what we do has been predetermined.

Something like this decision tree probabilities and truth values of situations contribute to the end result:

or this:

Other decisions can only be explained in terms of an equation of neurons firing and pleasure or goodness derived from each neuron like an SVM or Neural Net.

SVMs create linear and nonlinear discriminants which is a line that tells groups apart based on features. They can be quite complex in their ability to discriminate between pleasure and pain or classify an object.

Neural networks work based on several input senses which are weighted then ran through a function to determine if a pathway is activated.

The equation for sexual position of greatest preference might include things from past experiences, prejudices and preferences for pornography actors who were in that position, feelings associated with bending and flexing that way. Then as Freud acuaratly pointed out seeming random things from childhood that logically should be completely separate from sexuality but because we are connected individuals built systematically.

So yes using math especially those related to artificial intelligence, time series and propositional logic are useful methods in describing psychic phenomena. Simplifications of the aforementioned sometimes contributes to misunderstanding of how humans think but can be implemented in ways that facilitate understanding for those of less experience or education.

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  • $\begingroup$ This answer didn't address the question I asked, but maybe it's my fault for making it too broad, as others pointed out. I am not asking if mathematics can be applied in psychology. I am asking if the metaphorical use of mathematical terms by some psychologists is anything more than just pretty words. Anyway, I will soon edit my question to make it more precise and then if you want you can write a different answer. $\endgroup$ – Lazaros Mitskopoulos Nov 4 '14 at 16:03
  • $\begingroup$ I don't know if I agree with the premise. If a mathematical model is useful in describing certain behaviours, it does not necesserily follow that a metaphorical use of its terms also applies. A metaphor can stretch the meaning of a word in various degrees, and in some cases where a term has a precise definition in a certain context, the same term can become meaningless in a different context. $\endgroup$ – Lazaros Mitskopoulos Nov 5 '14 at 11:53
  • $\begingroup$ @LarryM. If you can describe a model with a mathematical fact which has a physical representation like 75mph then all less accurate metaphors and similes like as fast as cars in Texas but slower than cars in Germany are accurate enough to explain to someone who has no concept of miles or hours as long as they have traveled in Texas and Germany by car. The same can be said 20x faster than a walk or etc. $\endgroup$ – user6939 Nov 5 '14 at 17:03
  • $\begingroup$ The trick is in understanding the topic and audience well enough to create accurate metaphors $\endgroup$ – user6939 Nov 5 '14 at 17:04

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