The topology of truth

This is a post about how we think about others' opinions. We inevitably imagine that we are right and others wrong, and that others are more wrong the more their opinions differ from ours. That's not quite right.

https://medium.com/the-weird-politics-review/covid-19-beyond-caution-and-normality-ad3985dc368b

I was set to thinking about this again by this article describing two different ways of seeing the current situation. Each viewpoint is reasonable if you accept its set of values, but each has illogical extremes, and this gives a good example of a general problem. I have been in many arguments and discussions in my life, and for many people truth feels like a straight line gradient: I’m over here, further down the path to truth, and every ideological direction seems to be higher up. So that person further away is extremely wrong. I’ve drawn this in this first picture

We all know the different points that can be made about the things close to us, and within our own range of understanding we are reasonably sure that we’ve made the right judgements.

It’s all very much like the energy states of a protein when the amino acids are folding up, or the energy state of a collection of chemicals. At school we learn that chemicals naturally progress to the lowest energy state of a system: if by reacting the resultant mix of chemicals are more stable, the reaction will progress.

We can model that as a graph of energy. Below is an open source example of combustion (burning).

But, as with protein folding and chemical energy states, the lowest current energy state isn’t the absolute lowest. Sometimes the local minimum is only local: with some activation energy, the system can be pushed over a boundary and then drop even further.

That’s shown in the above picture: you need to put in the energy to reach the transition state, like rolling a boulder over a hummock before it can roll all the way down the hill.

If we return to our article about two different opinions, we can draw a little map of these two different approaches that looks similar to our energy graphs for chemical reactions.

There are two local minima in this little part of our world. Someone at point B, for example, can see people at points A and C and think ‘those people are wrong; it makes more sense to think like me’. Someone at point E will think the same of those people he can see at D and F.

And, of course, B and E can extrapolate from that knowledge to assume, as we saw right at the beginning, that someone with even more different opinions is even more wrong. And, if the people at A and F are the really newsworthy people doing very stupid things, they will confirm that assumption.
So when B and E meet, each will say “Oh, you’re like F/A; you’re very wrong. You should slide towards the truth just like D/C should”.

I experience this a lot. I make an effort to look broadly at an issue and consider all opinions. In our topology of opinion, I range widely over the map, unafraid of hills and keen to look beyond them. I want to understand the terrain and work out what really is the truth.

I regard myself as the ‘E’ in the above example, but an E who knows not only about position B but also that it’s more wrong than E. But the Bs of the world don’t like to listen; we often argue across each other, with them trying to persuade me that positions F and D are wrong and me trying to explain that E is lower than B.

I’m not the only one who imagines that I’m right, but I hope that the picture above helps people argue their cases better with others. You have to understand someone’s position before you assume that, because it’s more extreme than D, or almost as extreme as F, it’s therefore a bit more wrong than D, or only a bit less wrong than F. Sometimes there really is a local minimum that from a certain perspective seems pretty right. After all, if you’re the E and I’m B, you won’t persuade me by telling me that A and C are wrong and that I’m in the middle. I know I’m in the middle, and I also know that logic should slide them both to me. You are making assumptions about how the world looks over here and making yourself seem ignorant and wrong as a consequence.

And then there’s the ‘split-the-difference’ debaters like C and D. I don’t know if it’s an emotional need for everyone to win and all to have prizes or a blissful inability to recognise truth, but some people see how strongly those in troughs B and E are stuck in their ruts and decide to please everyone by being more wrong than either. I can understand if you start on the left side you might slide down to B, even though E is lower. I can understand that there are forces in the world (external and internal) radicalising people, pushing them to A and F. But C and D really seem plain old stupid: based on the idea in the first picture that there is only one minimum and no bumps or obstacles. So if B is better than A, and E is better than F, surely going to the middle and B and E must be even better?

This is not how the world works. I might prefer to be in London than in Watford, and on holiday in Madrid rather than the Sahara Desert, but the middle of London and Madrid is probably in the ocean in the Bay of Biscay, and that’s not very comfortable either. C and D are positions that come from looking far away but not bothering to judge the position on its own merits, and a failure of self-reflection is a pretty big failure.

It’s also interesting to note that convex curves obscure the peak. Anyone who’s done much mountain-climbing will know that when you climb a gently curving hill you can’t see the top; the curve gets in the way. People at the bottom of a slope can have a very restricted vision of what’s around them. I don’t think we need to stop our analogy there, though.

So I’ve drawn one last map of opinions that illustrates a few possibilities. First of all, it’s possible to hold the same opinion for different reasons, which can be more or less correct.

So someone at P has the same final answer as someone at O, but is nonetheless more wrong. If you’ve met someone at L and you assume that everyone at L, O, P and even H and g are basically the same, you are going to annoy those Os a lot. And fail to persuade them at all. They know that P is above them, but they also know that they’ve come to their opinion via an entirely different route. They’ve gone caving from over at N, and sometimes you need to retrace the route to get them out of whatever dead end they’re in.

Then there’s the example of the people at Q. Someone at Q might be mightily pleased with themselves for finding a narrow gap in all the obstacles and delving deep towards the truth. They know it was hard to see Q from any distance, and are therefore very unwilling to listen; either to those they think are at L or R.

And then there are the successive steps between M and I. Each position is more in-depth than most of the rest of the range of opinion; it’s taken careful thought and some effort to get that far. But even now, there are two attitudes people can take. You can look behind, or look ahead. You might find that almost everyone you meet is an L or R, mixed with extremists at g and U, and a bit like the Qs, you give up and start treating others as dolts if they don’t drop down the mine shaft to N with you.

Or, having got to N, you can remain open to help. People calling from J can help you find your way from N to more truth. The problem is that people calling from H might seem very similar and as the cacophony intensifies you might not have the time or the ability to separate a good signal from all the rest.

I aim to be a J and I, really much closer to the truth than you might think, especially if you do a rough survey from above. Pollsters might ask everyone’s opinions to try to plot them out on a line, but if pollsters don’t understand the cave structures underneath the surface then they will misunderstand what people really think. They might assume that the I-Os are all Ls (or Hs), fitting them onto a blander, less fine map of thought.

When we realize how complex the terrain of thought is, we also realize how important it is to be able to move around and find your way. Navigation, the mental fitness and agility to climb hills, and light to show the way, are all much more important than your starting location. Someone calling to you could be wrong, or could be right, and the more right you are, the likelier it is to be misleading and the harder it is to trust well-meaning advice.

And I haven’t really addressed density yet! There will be a whole city of people collected at R (or E on a previous picture) telling each other that they’re right. The voices from the few cavers (‘experts’) in the depths of J-O will be lost unless people make a conscious decision to listen to them. But they might hear voices from S reassuring them that if they bothered to spend more time on it they’d not change their opinions much; that they are definitely more right than the mass of people over at L.

One final thought: we might see that people over at T clearly haven’t explored much, but they’ve found a nice local minimum. They can see the world in the broad map of people at g and U, and imagine that the centre is that little bump next to them. After all, if they meet a truly central opinion it’ll seem to be about as true as that bump next to them. They’ve taken the red pill and discovered the hidden truth in its little valley. Maybe they haven’t discovered as much truth as they think…

Maybe I’m not at J or even I. Maybe I got stuck in the dead end at O; my musings have taken me down a bad dead end. But if you assume that everyone is up top on our map of A-F, you might mostly be right, but you will never get me to move. Truth, and argument, comes in layers. If you go too deep, someone up top might not follow you. But not deep enough and those people who’ve already delved will dismiss you and feel insulted.