esoteriic.com

It is about time I returned to the main idea that inspired me to create this website. While I enjoy writing for the sake of it there was one idea that really wanted to share and hence became the impetus for creating a website and writing many articles. This idea concerned the possibility of expressing opinion in a logical and rational form, but in a way that was indisputably consistent with the hope of finding (or constructing) a system that allowed one to express opinion in an invariant way. Two of the major inspirations behind this idea was the Political Compass and the notion of invariance in physics. While I haven't said much, if anything, about physical invariance on this website I have at least written a brief article on the Political Compass in 2009. It wasn't supposed to take this long to get to this article. Read on...

2006

The year was 2006. A year when I was a lowly physics undergraduate with a keen interest in philosophy and debate. These days I'm less interested in debate and haven't read as much philosophy as I used to. At many points in my undergraduate studies I was confronted by the topic of physical invariance and how certain physical variables can have an absolute measure. That is to say that these variables are the same regardless of where you are standing or how fast you are going. Obviously, these sort of issues are not something that anyone worries about while taking a train but in physics there are consequences associated with making measurements. On the one hand there are effects due to relativity (due to an observer moving) and also due to inherent uncertainty from quantum mechanics. Invariance is (as far as I know) really only used when relativistic effects are a concern.

Given my keenness to engage in philosophical debates  (or almost any debate) I often came up against people with very good debating skills but also (more commonly) against people with very poor debating skills. For example, anyone that uses ad hominem arguments falls into the later category. Soon I realised that debates often started from a misunderstanding or a miscommunication of definitions, and further to this many people started from the same premise but came to different conclusions. Debates often became heated and lead to insults and the usual drama. So naively I wondered if there was a way to avoid unnecessary heated arguments that lead to drama and just stick to a logical debate where people can agree upon the answer. If physics has a notion of invariance then surely debates could have a notion of invariance too.

This was the start of my idea which I conceived in 2006 and have returned to at various points in the last 6 years but never really putting my ideas out into a public forum. Even the very few friends that I tried to the idea with didn't give me a lot of feedback. The concept sounded impressive and with interesting considerations but unfortunately no further help was forthcoming.

First attempt

The initial attempt at making this whole idea work was based upon simple drawings where geometric perspective was key. I tried to relate two symbols to each other by where the sat relative to each other on a piece of paper. Most of this involved scribbling symbols unto paper and then drawing lines between them to see if there was anything obvious that would guide me towards a greater understanding. As already mentioned the idea of invariance was related to observation and so it should be related to geometry. It seemed like a natural first attempt. I coined this first attempt "Geometry of Opinion", it is terminology that I've kept even into my final creation.

The political compass was also known to me at this time and it seemed to me that the political compass was an attempt to be objective about how we (as people) understand politics. It seemed like a natural ally in my attempt to make all debates objective. Soon after my first attempt I tried to do a very similar thing but this time with some inspiration from the political compass. I knew that the idea of dimensionality was important; there was something in the extra dimension that was both important but not quite faithfully constructed in the political compass.

Second attempt

My second attempt involved drawing symbols with lines between them, as before, but this time to consider an arbitrary point in the middle as the observer. There had to be some special importance to this centre point in order for this new attempt to make any sense. So far the first and second attempts sound very similar; however, with some inspiration from the political compass I put the symbols onto a graph and tried to consider what each of the dimensions could mean. A symbol could be a point, which is zero dimensional and the line between two points is one dimensional. I tried to reason that there was a link between the symbols and dimensionality, that is to say that there was a definite link between one's perspective and the dimensionality of the representation. If one thinks about something, or looks at something, in a one dimensional way then we can represent this graphically as a one dimensional object. In this second attempt I hadn't quite fully grasped how this would be done.

One thing that I did realise was that there should be a logical way to ascend or descend the dimensions as necessary. While some ideas are very simple there ought to be a way of building more complex ideas from something very simple. Conversely, there should be a way of taking something very complex and simplifying it down to its core elements. Where this attempt ultimately failed was that I focussed too much on the geometrical perspective (as with the first attempt). I created many pictures that involved lines with symbols at either end, both in one and two dimensions, and that this was somehow meaningful.

One idea was to consider what would happen if the symbols was looked at from a distance, then surely the positions of the symbols would not be distinguishable from one another. Looking at that another way: the further away something is then the smaller it looks. Or in a another way: the distance between two objects looks smaller the further away you get. The key here was perspective: was the observer close or far away? I tried to force a lot of meaning into these drawings but couldn't quite do it.

Third attempt

My latest attempt, or the latest version of this attempt, started down a bit of a different path from the other previous two attempts. In order for this project to make any sense and ultimately be consistent it needed a solid base from which to start: the rules had to be clear, the notation concise and the process of construction had to be logically intuitive. A lot of the ideas that went into the third attempt came from the notes of the second attempt. What I managed in the third attempt was to determine which of the ideas made sense and could be kept, and which ideas were just malformed.

The key difference in this attempt was the use of algebraic notation. So I devised my own notation that is loosely based upon set theory but incorporated many of my own conventions in order to make progress. Now the graphical part (the geometric element) was a secondary feature and not even wholly necessary. The visualization is nice and is much more friendly than looking at tables of numbers. So my new name for this system of expression is aptly: the Algebra and Geometry of Opinion (AGO).

The hope is that this system of expression enables clearer communication of ideas when there are questions of ambiguity. It is thus a starting point for cleaning up debates, as form of evidence, to make them more logical and rational although it isn't a system of rules for creating logical debates. It can also be used to check whether there is agreement between two statements or entities: if two entities begin with the same premise and follow the same argument then both will end with the same conclusion.

Slowness

So it has taken from 2006 until 2012 to get my ideas from raw thoughts into a semi-published form (in a public place). Part of this slowness has been the desire to create something that complete, although a major factor has been the lack of feedback and hence not knowing whether what I was doing actually made any sense or whether I was delusional. Once I finally hit upon something good in 2008 (the start of the latest version: AGO) I felt like I had come upon something that felt more complete but needed a lot of effort to work through various scenarios. Some of the the conclusions I began to draw seemed obvious and I feared that what I had created was redundant, and essentially offering nothing new in terms of economy of thought. Eventually I discovered a few subtleties in this work that I hadn't, and still haven't come across anywhere else. These subtleties implied further inconsistencies and deficiencies within the political compass.

Ultimately, I haven't achieved what I had hoped to do in the first place which was to provide a method of invariant expression but it is at least a step towards. But the strength of this system of expression has lead to numerous insights, and is something to be proud of. That was back in 2009 and was, as mentioned, the impetus for creating this website. After 3 years of being fearful of unveiling the ideas I will now present the idea as a series of articles.

The Algebra and Geometry of Opinion [under construction]

Here is a list of the (proposed) topics I will cover in order to expound my AGO idea and hence try to make major inroads to an invariant system for comparing opinions.

Flaws of the Political Compass

Measuring Agreement

From the beginning: the zeroth dimension of AGO.

Beyond dualism: one dimension.

The Political Compass: Two dimensions.

N-dimensional AGO.