Does the mind work with unconscious mathematical underpinnings?

Question

That is, is our mind geared to use math without our knowledge?

Reading academic writings from the biological and social sciences, I observed patterns of methods widely used in maths/statistics such as clustering, classifiers, variable concept and making use of variables to make comparisons.

I would like to formalise these observations since this would be useful to semi-automate the writing process.

Example:
- Hi Paul! How are you?
- Fine, thank you Lisa!

Lisa is asking a simple question, but seems she is trying make Paul to summarise her answer in only one word (Fine). In fact, Lisa is asking an open question, involving a lot of variables since Paul life has a ton of variables, e.g. If food was OK at work or if today was sunny. Paul has the ability to sum up all day variables in only one, that we can define as nominal and binary, being 'Fine' and 'so-so' the possibilities. Seems Lisa and Paul unconsciously have the ability to do some kind of PCA analysis, a common information reduction method. Since Paul is a shy guy, conversation stops here, but if Paul would be me, I will start talking about some of the day variables in order to have a more pleasant conversation.

Although not much elaborated, this example is simple and includes some mathematical concepts.

Answer 1

I once read a popular maths book that declared an ant which is moving along the edge of a ruler was doing trigonometry when it decides to cross the breadth of it in a diagonal manner.

Ants don't do trigonometry; the author is simply confusing how we might model the situation with the doings of an ant and how it might be thinking.

When Paul sums up his day by the word 'fine'; doesn't mean that he is doing addition, or integration as a mathematician is doing a sum or an integration; he may be saying 'no worse than when I saw you last', or 'nothing significant has happened in the intervening interval' or even 'something significant has happened, and obviously you're nosing around to find out exactly what, but I don't trust you so I am keeping quiet'.

None of this is mathematical on any sense - but thinking, feeling and emotion.

Answer 2

You should check out the literature of embodied theories of cognition- George Lakoff, Mark Johnson, Rafael Nunez, et al., (Where Mathematics Comes From, The Metaphors We Live By, Philosophy in the Flesh, etc.). In particular you should look at the work of Nunez. If these guys are right, then the basic underlying mechanics of how the mind works, is not dictated by “unconscious mathematical underpinnings”- it’s very much the other way around. Nunez (et al.) would have us believe that mathematical cognition has its basis in primitive sensory-motor routines and patterns; and is built up successively of layers of metaphor ultimately derived from this grounding in ‘primitive’ aspects ordinary experience/perception and motor activity.

Answer 3

I would give the same answer that I have given to slightly different questions: https://philosophy.stackexchange.com/a/23190/9166 or https://philosophy.stackexchange.com/a/23276/9166

In short, I believe the notions of category and 'form of intuition' in Kant imply that he definitely thought this, and I think he overstated it a bit, but is basically right.

To slightly overstate Kant on the other side, I also believe that math is a branch of psychology -- it is the study of the bases and boundaries of human abstraction. So 'unconscious underpinnings' are what math is studying. It is just trying to make them a little less unconscious.

If you look at math as 'handmaiden of the sciences', it asks the same question that drives many therapists "How can I help you think about your own chosen problem better?"

From that perspective, the kinds of methods you see deployed recur all the time because they are things that we have observed our own thoughts doing, and we have decided to try doing them less unconsciously.

Answer 4

I would dispute that in the example you gave, Paul is doing any form of aggregating or dimensionality reduction. While many factors influence his wellbeing (money, sex life, world peace,…), his wellbeing itself is a simple fact, and when replying to Lisa he is directly answering the question about that simple fact, not summing up the totality of facts that led to it.

That being said, you are correct in your general premise that the human mind is performing some advanced pattern recognition and clustering on sensory inputs (including speech), and sorting and aggregating them to a higher symbolic level such that it can process them using formal logic.

Indeed, this is the starting assumption that AI and machine learning specialists work off of: The mind is already performing such calculations, the challenge is to reproduce those processes in digital computers.

The real question, is how much of these pattern recognition processes are innate and how much are acquired? That’s where Kant comes in, and where I am no longer qualified to discuss the topic.