I did a maths and physics degree, and even though I have forgotten much of it after 36 years, my brain is still oriented in that direction and I sometimes have maths dreams. Last night I had another, where I realized I’ve never heard of a branch of mathematics to describe emotions or emotional interactions. As the dream progressed, it became increasingly obvious that the most suited part of maths for doing so would be field theory, and given the multi-dimensional nature of emotions, tensor field theory would be ideal. I’m guessing that tensor field theory isn’t on most university’s psychology syllabus. I could barely cope with it on a maths syllabus. However, I note that one branch of Google’s AI R&D resulted in a computer architecture called tensor flow, presumably designed specifically for such multidimensional problems, and presumably being used to analyse marketing data. Again, I haven’t yet heard any mention of it being used for emotion studies, so this is clearly a large hole in maths research that might be perfectly filled by AI. It would be fantastic if AI can deliver a whole new branch of maths. AI got into trouble inventing new languages but mathematics is really just a way of describing logical reasoning about numbers or patterns in formal language that is self-consistent and reproducible. It is ideal for describing scientific theories, engineering and logical reasoning.
Checking Google today, there are a few articles out there describing simple emotional interactions using superficial equations, but nothing with the level of sophistication needed.
an example from this:
Disappointment = Expectations – Reality
is certainly an equation, but it is too superficial and incomplete. It takes no account of how you feel otherwise – whether you are jealous or angry or in love or a thousand other things. So there is some discussion on using maths to describe emotions, but I’d say it is extremely superficial and embryonic and perfect for deeper study.
Emotions often behave like fields. We use field-like descriptions in everyday expressions – envy is a green fog, anger is a red mist or we see a beloved through rose-tinted spectacles. These are classic fields, and maths could easily describe them in this way and use them in equations that describe behaviors affected by those emotions. I’ve often used the concept of magentic fields in some of my machine consciousness work. (If I am using an optical processing gel, then shining a colored beam of light into a particular ‘brain’ region could bias the neurons in that region in a particular direction in the same way an emotion does in the human brain. ‘Magentic’ is just a playful pun given the processing mechanism is light (e.g. magenta, rather than electrics that would be better affected by magnetic fields.
Some emotions interact and some don’t, so that gives us nice orthogonal dimensions to play in. You can be calm or excited pretty much independently of being jealous. Others very much interact. It is hard to be happy while angry. Maths allows interacting fields to be described using shared dimensions, while having others that don’t interact on other dimensions. This is where it starts to get more interesting and more suited to AI than people. Given large databases of emotionally affected interactions, an AI could derive hypotheses that appear to describe these interactions between emotions, picking out where they seem to interact and where they seem to be independent.
Not being emotionally involved itself, it is better suited to draw such conclusions. A human researcher however might find it hard to draw neat boundaries around emotions and describe them so clearly. It may be obvious that being both calm and angry doesn’t easily fit with human experience, but what about being terrified and happy? Terrified sounds very negative at first glance, so first impressions aren’t favorable for twinning them, but when you think about it, that pretty much describes the entire roller-coaster or extreme sports markets. Many other emotions interact somewhat, and deriving the equations would be extremely hard for humans, but I’m guessing, relatively easy for AI.
These kinds of equations fall very easily into tensor field theory, with types and degrees of interactions of fields along alternative dimensions readily describable.
Some interactions act like transforms. Fear might transform the ways that jealousy is expressed. Love alters the expression of happiness or sadness.
Some things seem to add or subtract, others multiply, others act more like exponential or partial derivatives or integrations, other interact periodically or instantly or over time. Maths seems to hold innumerable tools to describe emotions, but first-person involvement and experience make it extremely difficult for humans to derive such equations. The example equation above is easy to understand, but there are so many emotions available, and so many different circumstances, that this entire problem looks like it was designed to challenge a big data mining plant. Maybe a big company involved in AI, big data, advertising and that knows about tensor field theory would be a perfect research candidate. Google, Amazon, Facebook, Samsung….. Has all the potential for a race.
AI, meet emotions. You speak different languages, so you’ll need to work hard to get to know one another. Here are some books on field theory. Now get on with it, I expect a thesis on emotional field theory by end of term.