Nelle Backstory
Fifteen years ago, a group of us at the MIT Media Lab published a mathematical model relating emotions to learning. This paper, which debuted an innovative research project funded by the National Science Foundation's Research on Learning and Education (ROLE) Directorate, won the Best Theory Paper Award at ICALT-2001 (International Conference on Advanced Learning Technologies).
Here is a succinct summary of that research on the role of emotions in learning.
A "mathematical" model. Didn't see any mathematics, just some graphics. The problem that we have is that the structure of "emotion-space" is simply too vague at present to be understood mathematically. We have simple models of "intelligent agents" that have scalar functions associated to their utility, and more sophisticated (normed) vector valued versions of utility functions are possible, but it is unclear what if anything these algorithms have to do with the human brain, and where the analogues of this processing are to be found in the biological strata. That's why I tend to stay away from psychological analyses like these; they are almost certainly misleading at best, and wrong at worst.
The key mathematical idea is summarized in Table 1, in which emotions are modeled as the second and third time-derivative the learning curve. See especially the Phase Plane Diagram of Figure 6, which is adapted straight away from Newtonian Calculus.
There is also a key theorem presented in Figure 9. This theorem (named for Tom Clancy), is the extension of classical results in Game Theory to the domain of Drama Theory.
The section on Multiple Interlinked Economies adopts a model inspired by Maxwell's Equations (in which flows and fluctuations in one parameter induce fluctuations and flows in a related parameter).
Notice that all the mathematics in these models are analogies adapted directly from well-established mathematics in Newtonian Calculus, Game Theory, and Electromagnetic Field Theory.
Concerning table 1, you say that emotions are time derivatives of "learning" or second derivatives of knowledge. Really? Why do you think that? And doesn't it seem a bit odd....if I take this literally, you'd be saying that if I suddenly increased the pace at which I learn....something....I'd feel an emotion? Doesn't seem plausible to me. Unless "learning" is metaphorical. Overall, I find it hard to take this hypothesis seriously.
Concerning "Clancys theorem" my only response is....need more math. From your presentation alone, there is very little information, very few definitions, and not even the outline of a proof. So I can't really say if this is a theorem or just excited speculation.
Concerning "multiple interlinked economies"...at this point, I do have to commend you for your command of words. Every slide seems to be a reservoir of neologisms...now if only there was content to back it up. You mention a lot of "its" but it's not at all clear what you're trying to say. Is this just vague, feel good "connectioney" stuff, or is this concept critical to your theory somehow? And please beware of analogies to Maxwells equations unless you really have an analogy here. Maxwells equations have a very specific mathematical structure (far more rich than simple "flows") encoded by the U(1) lie group, so unless there's a specific correspondence, i'd avoid making the analogy.
Overall, I think this presentation is high on verbiage and low on actual content. If this is meant to be science, it verges perilously close to pseudoscience, and unintelligible nonsense. If it's just literary metaphor, then by all means, metaphorize! (is that a word?) but don't drag mathematics into this.
Your skepticism is a fairly typical response to initial exposure to this model. My colleagues at MIT were similarly skeptical the first time I presented this model at the MIT Media Lab. One of my closest professional colleagues at MIT is Professor Rosalind Picard, whom I have known for 30 years. When I first disclosed this model to her, back in the early 90s, she also thought it couldn't be right, especially given there was no prior literature supporting it.
It took almost five years before Picard became convinced that the model had merit, after which she marveled at her own process of reversal. During that time, she took the initiative to scour the scientific literature, looking for any evidence to support or refute the model (or to demonstrate that it was already present in the literature and therefore not a novel theory). She not only concluded that this was a novel model, unprecedented in the literature, but that the entire field of research on emotions and learning was largely devoid of any substantive computational models at all.
After completing her literature search, Picard wrote up a summary of what she did find in a seminal 1995 paper entitled "Affective Computing." A year later, she decided to expand that brief paper into a book (also entitled Affective Computing) which came out in 1997.
And thus the field of Affective Computing was born.
So how did I come up with this model in the first place, and why did I think it had enough merit to share with my colleagues in academia?
The inspiration for this model came in 1985, when I happened to be mentoring an adult in her mid-30s who had gone back to the local community college in Monmouth County NJ to obtain a Masters in Education, so as to advance her career. I'll call her "Nelle" (not her real name). At the time, Nelle was teaching First Grade. She disclosed to me that she had Dyslexia which seriously interfered with her ability to read. As a result, she learned very little from reading, relying mostly on direct experience and face-to-face interactions with other people. One other characteristic of this individual was that she was emotionally volatile, often exhibiting perplexing outbursts of anger that seemingly came out of nowhere.
One of the required courses in Nelle's curriculum at Monmouth College was "Statistics for Education." By my standards this was a fairly elementary introduction to the subject. But Nelle had math anxiety the likes of which I had never seen before. When she came to Chapter 4, "Hypothesis Testing," her level of math anxiety was utterly debilitating, if not downright chilling. I suggested we begin with the first problem at the end of the chapter. This was a word problem in which the Principal of an elementary school surveys the children and observes that some of the children are raising their hands to recite in class, while others are reticent and holding back. The Principal notices that the children who are willing to recite are earning high grades, while the children who are holding back are earning lower grades. So the Principal forms an hypothesis, that being verbal causes high grades. And he proposes to mandate a course in public speaking, so that the children can learn to be more verbal and thus get higher grades. The objective of this problem is to critique the Principal's hypothesis.
Nelle is utterly stuck. She has no idea how to proceed to think about this homework problem. So I begin using the Socratic Method (as is my custom when mentoring math) to help her think through the problem. In the Socratic Method, one asks carefully crafted questions to lead the student, step by step, to think their way through the problem. But I'm getting nowhere with Nelle. Now in the Socratic Method, if you ask a question that proves to be too hard for the student, you ask progressively simpler questions. In this case I got all the way down to what I call the "atomic question" where you basically lay out the possible answers in the body of the question, such that one of the answers is obviously correct.
And so I put it to Nelle, "Would you say that being verbal causes high grades? Or would you say that it's the other way around -- that getting high grades causes students to be verbal? Or could it be just a coincidence? Or could something else, like studying the night before and knowing the answer cause both?" I laid out for Nelle four plausible possibilities for the "arrow of causality" to see if I could spark her thinking on the question.
Well, I didn't just get a spark. I got a lightning bolt. Nelle suddenly exploded with uncharacteristic positive emotion, screaming, "This seems to be a very important idea!" And she furiously begins writing it down in her notebook. I started to reinforce the idea and she screamed, "Shut up! Shut up! I have to write this down before I lose it!"
Now up until that point, I had seen many comparable outbursts of negative valence emotions (typically anger), but this was the first time I witnessed a comparably intense positive emotion. And I was there at the Moment of Epiphany. Indeed I had personally midwifed the epiphany by use of the Maieutic Method of Socrates.
This anecdotal observation, linking an intense emotional outburst to an increment in learning was so startling to me that I reflected on it for days and weeks, wondering why I had never before noticed (or hypothesized) a systematic link between emotions and learning.
Eventually, I translated that singular observation into an evolving theoretical model relating emotions to learning, building up the details of the model for the next 15 or 20 years, and testing it by a variety of methods which I won't delineate here, as they are comprehensively documented elsewhere.
Last week, Leonard Nimoy died, reminding us of his iconic character, Mr. Spock, who was commonly considered to be without emotion. Although Spock was nominally portrayed as logical and unemotional, he demonstrated the classical emotions of a scientist: curiosity, fascination, puzzlement, skepticism, and insight.
And that brings us full circle to why I (and many of my professional colleagues in academia) think this model has merit. On page 93 of her seminal 1997 book on Affective Computing, Rosalind Picard invokes the fascinating character of Spock to introduce her chapter on Applications of Affective Computing and the role of emotions in learning.
Today there is a substantial body of literature on all aspects of Affective Computing, including a fairly modest section on a variety of models relating emotions to learning. I invite you to dive into that literature if you wish to dig deeper than the level of summary found in the article that I originally crafted for Google Knol, where it became a top-rated article on the site.
I'll point out that the work summarized in that article won 7 years of funding from the National Science Foundation, during which time our team at MIT collaborated with similar teams from Carnegie-Mellon and the University of Memphis. And you will note that our very first paper, presented in 2001 at ICALT (International Conference on Advanced Learning Technologies) won the Best Theory Paper Prize.