[Being Human Series 1/n] Introspection and the cusp of not knowing

Background: The Introspection

I’ve recently completed a 4 day silent meditation retreat, had a couple of days to finish off delayed coursework, and then a family camping trip to the wonderful Verdon National Park.

During the Meditation retreat we were asked not to keep notes, which I did except for one need to write a list of outstanding tasks, I’ve a habit of writing those down to allow me to stop thinking of them - it works! 🤷🏼‍♂️

As a result this is the second reflective piece I’ve written since returning 8 days ago. The first is not yet refined, was about non-verbal thinking, specifically acknowledging it and giving it space. This one is about being in the cusp of knowing. They relate though I’m yet not fully sure I know how (spoiler alert, I do link them by writing this).

Discovering What I Don’t Know

When I left for the retreat I had been highly focused on collating what I understood of reasoning, mainly Symbolic and Probabilistic (see here). However my focus was clouded by (what I am currently calling) non-verbal thoughts, basically as yet defined ideas.

It came about via a miscategorisation on my part - Embeddings and Transformers are not considered Probabilistic Reasoning.

I was considering, and to a certain extent still do, the output of a transformer to be Probabilistic (rather than Statistical). I viewed the output as a distribution that represented the “beliefs” stored in an LLM, beliefs shaped by various aspects of the training. Though that is a detail for another day, as my original goal was to address Probabilistic Reasoning, as defined by society at large, rather than synthesising something from my personal understanding.

What occurred though was arriving at what I thought would be a “knowledge way point” and realising that I was only highlighting what I didn’t yet understand.

A Bit More Background: The Bayesian Revelation

This quest for new knowledge dates back to a chance conversation on Eurostar last summer. Long story short; both Comp Sci students of University of Bath, played sports there, worked in finance, and the conversation turned to a mix of all. As I’m highlighting how I enjoy betting as I view it as a calculation of the perceived probabilities involved, Sam points out I need to learn about the Bayesian view of Probability.

He was very right, when I finally studied the Bayesian view of Probability it blew my mind.

Now I have a mathematical notation and theories to describe what I’ve been doing, not only looking at the odds of an event but evaluating priors and betting if those seem out of place. The terms prior and posterior hit home and I get them, however, in the past week or so, I learnt that I haven’t fully internalised the implications.

The other bit that really hit home was that they can be used to represent beliefs, also beliefs that conflict and do not add up to one (which links to my view on LLMs).

Uncertainty: The Experiential Nature of Not Quite Knowing

This was quite an interesting mental state to observe whilst on retreat. I mean interesting in that ambiguous British polite way of saying it wasn’t particularly pleasant (rather than it being curious and fun to investigate).

I’m sitting in a meditation hall, focused on my breath, and sitting with a feeling of ill-at-ease. I am pondering the question “Why can I not make peace with my current situation?”.

There was definitely a real world distraction, a bird outside the meditation hall would not shut up! I’m sensitive to sounds, particularly short sounds that don’t overlap, so I ended up doing a lot of walking meditation and found a great spot by a river (that sound is magic).

That’s when I start to get a bit more insight into this apparently physical nagging sensation.

Practical Application vs Theory and Synthesis

As a reminder I felt like I knew something, and that has not changed. What has changed isy ability to express it.

What I’ve come to see is that I can, and have been with success, practically apply Bayes Theorem (basically having more informed priors than the bookies or market).

Yet I wasn’t able to explain that or use it in other circumstances, not least because there are other non-verbal concepts that are technically adjacent but occupy my thinking. When I tried to write down what I understand (I believe that Penguins cannot fly with P(not fly | Penguin) = 0.999…) and how we can reason other than with Bayes Theorem P(A|B) = (P(B|A) · P(A))/P(B), I started to “see” logic in high dimensional space. 🤦🏼‍♂️

(Side note: For the record I’m about P(logic | embeddings) = 0.8, that is there being an applicable logic to a robust semantic space, but that needs more time to increase (or decrease) that P value. ).

In watching my mind grasp for understanding what it was not I noticed multiple forces.

As a human we have many skills that are used with varying levels of consciousness, awareness, and definable and indefinable knowledge. I use the words specifically, it appears we can use these skills without being able to communicate what it is we know. The actions can be conscious or subconscious, with varying levels of awareness, and completely indefinable in a language that is common to another human.

Person 1: Why did you do that?

Person 2: 🤷🏼‍♂️ It was the right thing to do…

(Another side note: so this is where I see it linking up to non-verbal thinking - maybe non-language is a better term - and I mean thinking that we cannot easily define with language).

What Have I Learnt or Affirmed?

It’s with a high level of confidence that I see not all thinking as verbal or language based. I believe this is widely accepted (though maybe forgotten when talking of reasoning LLMs…)

Two other things jump out at me:

1. On reflection, I’m possibly talking around the subjective experiences that mean the objective scientific method is such a great tool for civilizations. Humans are complex, our ability to communicate beliefs and knowledge is restricted by the channel of communication.

2. We have an internal mechanism that motivates us in terms of understanding the world around us. I haven’t got clarity on that emotion, I believe the sound of the deadlines whooshing past has been too distracting to understand if the core emotion is a light, positive intrigue or a darker, fearful pressure. I like to think it is the former but experienced more of the latter. Yin and Yang I guess!

And with that, I am open more towards knowledge being a potentially conscious emotional state where you can apply (infer) what you know for a given situation. It is very temporal, i.e. it might not be knowledge before or after the application (inference) in a situation.

Including my previous exploration of why symbolic logic fails, I find the term “knowledge representation” a misnomer. These entities are purely information stores, we can only use the term knowledge in the correct application of the stored information. This is a broad statement that doesn’t have clear definitions of knowledge or information yet, however it is a key element of what I’m investigating and opens up to a wider question of what are they! Here is my start on what Knowledge Representation, Logic, and Reasoning are.

I have spent some time reflecting on the non-verbal aspects and differentiate these feelings from a general fear of not knowing or missing out. My current view is that the ill-at-ease I was experiencing was due to me being aware of inconsistencies in my information store but not able to articulate them. Writing appears to be a great way to flush them out, a lot better than reading. Possibly due to the outward nature of the ill-at-ease; fix, don’t add! 🤓

Looking Forward

I’m left wondering:

• Can we define, maybe in acceptable Mathematical notation, systems that distinguish between information storage and genuine knowledge states?
• What relevance do temporal context and uncertainty have in this system?

I’m sure there’s more, for now I’ll be focusing on uncertainty, specifically uncertainty around future events and how to bring that into Probabilistic Reasoning - which will include code. 🤓