I'm posting this prematurely because in today's world you just don't know what happens tomorrow. Or today.

Could you help me to formulate statistics with the properties I'm going to describe?

I want to share my way of seeing the world, analyzing information and experiencing other people. (But it's easier to talk about fantastical places, so I'm going to give examples with fantastical places.)

I think my ideas could help to formalize (a little bit, not entirely) thinking about vague concepts and the process of generating hypotheses. It's something Bayesianism doesn't do (it tries to deal with atomic outcomes), if I understand correctly. By "vague concepts" I mean concepts that have specific enough meaning in context, but no definite meaning outside of a context. For example, the concept of a "game" is easy to understand in a specific context, but potentially outright impossible to understand/define outside of any context. The same with the concept of "being healthy" (can you list all conditions of "being healthy" outside of any context?). The same with human values, such as "freedom". The same with most of the words in the human language. All those context-dependent objects create clusters of things with family resemblances.

I think my ideas could help to describe how vague concepts obtain specific meaning in context. And how new contexts are created. I feel that it's related to hypotheses generation because some general (scientific) ideas/paradigms don't have any meaning outside of context (maybe Thomas S. Kuhn wrote about this in The Structure of Scientific Revolutions). But when they compete with each other in the real world, they obtain specific meaning.

I think it all relates even to human personalities ("personality" is a vague concept too): if you took all your behaviors in the course of your life, would there be a single thread that connects them all and differentiates you from most other people? And if "no", does it mean that you're just a combination of random behaviors? Your entire personality is a "context-dependent object", it makes sense only in a specific context, contrasted against something else.

If you could formally analyze (at least to some degree) concepts that are connected only by loose connections of "family resemblance" or "sorites paradox" types of connections, it would be an extremely powerful thinking tool, and a needed one. You could analyze meaning of words, human values, personalities of people...

"Introduction"

I got only two main philosophical ideas. First idea is that a part/property of one object (e.g. "height") may have a completely different meaning in a different object. Because in a different object it relates to and resonates with different things. By putting a part/property in a different context you can create a fundamentally different version of it. You can split any property/part into a spectrum. And you can combine all properties of an object into just a single one.

The second idea is that you can imagine that different objects are themselves like different parts of a single spectrum.

I want to give some examples of how a seemingly generic property can have a unique version for a specific object.

Example 1. Take a look at the "volume" of this place: (painting 1)

Because we're inside of "something" (the forest), the volume of that "something" is equal to the volume of the whole place.
Because we have a lot of different objects (trees), we have the volume between those objects.
Because the trees are hollow we also have the volume inside of them.

Different nuances of the place reflect its volume in a completely unique way. It has a completely unique context for the property of "volume".

Example 2. Take a look at the "fatness" of this place: (painting 2)

The road doesn't have too much buildings on itself: this amplifies "fatness", because you get more earth per one small building.
The road is contrasted with the sea. The sea adds more size to the image (which indirectly emphasizes fatness).
Also because of the sea we understand that it's not the whole world that is stretched: it's just this fat road. We don't look at this world through a one big distortion.

Different nuances of the place reflect its "fatness" in a completely unique way.

Example 3. Take a look at the "height" of this place: (painting 3)

The place is floating somewhere. The building in the center has some height itself. It resonates with the overall height.
The place doesn't have a ceiling and has a hole in the middle. It connects the place with the sky even more.
The wooden buildings are "light", so it makes sense that they're floating in the air.

...

More of Jacek Yerka paintings (a collection by me): https://imgur.com/a/jp1DaHe

I could go on about places forever. Each feels fundamentally different from all the rest.

And I want to know every single one. And I want to know where they are, I want a map with all those places on it.

My "theory"

Key philosophical principles

Here I describe the most important, the most general principles of my philosophy.

Objects have definite properties only in context of each other, like colors in a spectrum. So objects are like "colors", and the space of those objects is like a "spectrum". Outside of the context of a spectrum an object has an infinite amount of properties and interpretations.
All properties of an object are connected/equivalent. Basically, an object has only 1 super property. This super property can be called "color".
Colors differentiate all usual properties. For example, "blue height" and "red height" are 2 fundamentally different types of height. But "blue height" and "blue flatness" are the same property.

So, each color is like a world with its own rules. Different objects exist in different worlds.

The same properties have different "meaning" in different objects. A property is like a word that heavily depends on context. If the context is different, the meaning of the property is different too. There's no single metric that would measure all of the objects. For example, if the property of the object is "height", and you change any thing that's connected to height or reflects height in any way - you fundamentally change what "height" means. Even if only by a small amount.

Note: different objects/colors are like qualia, subjective experiences (colors, smells, sounds, tactile experiences).

Intro: "Details"

"Detail" is like the smallest structural unit of a place. The smallest area where you could stand.

It's like a square on the chessboard. But it doesn't mean that any area of the place can be split into distinct "details". The whole place is not like a chessboard.

This is a necessary concept. Without "details" there would be no places to begin with. Or those places wouldn't have any comprehensible structure.

Intro: Colors

A detail is like a cell. Cells create tissues. Details create "colors". "Colors" are something like textures created by patterns of details.

A place in a spectrum has only 1 unique color. But you can still think of a place as a combination of colors. As an approximation.

Details can create a volume, a flat structure or a "cloud" and other things. Similar to how stars create constellations.

A color in a spectrum is like a straightjacket for a place, it limits the place's possible interpretations and properties.

The specific method

We need to take a bunch of places. Come up with "main colors" for them. Those colors are already ranked.
We need to assign the colors to the places.
We need to rank places with the same "main" colors. Or unclear main colors.

Rules for step 2:

2.1) When you evaluate a place smaller scale structures matter more. The opposite is true for "anti places". I often split my spectrum into a "positive" part and a "negative" part. They are a little bit like positive and negative numbers. You can also conceptualize "anti places" as places having contradictory interpretations.

2.2) Places with different enough detail patterns can't have the same color (because a color is the detail pattern). And you shouldn't create new "main" colors to fit the places. (Unless you have enough places that can be described by this new color... so it's a little bit like Occam's razor: don't multiply colors without nessecity!)

Rules for step 3:

3.1) If places have the same "main" color, but different known "secondary" colors (known secondary colors are like the main colors), you mix the secondary colors and redistribute those between the places. Then you ask: how hard is it to get from the place A's main color to its secondary color B? If it's easy to get to B, you move the place A closer to the places with the main color B.

3.2) If places have the same "main" color, but different unknown "secondary" colors, you rank the place which seems "bigger" higher.

Example: Rob Gonsalves

Below is an order ("spectrum") of some paintings by Rob Gonsalves

https://i.imgur.com/u3ZkIsU.jpeg

When I analyze the paintings I "simplify" them. Because on the paintings you often see impossible illusions. But I analyze paintings as if they're places that could be levels in a videogame.

Rest In Peace, Rob Gonsalves.

Step 1: let's get the colors and their order.

Violet means "details create a volume with a clear shape".
Grey means "details create something flat".
Orange means "details create something without a clear shape/something too big".

From the most dense to the most sparse: Violet < Grey < Orange.

"Anti places" are marked with Black dots.

Step 2: let's assign the colors and order everything

Violet

1st violet place: Here details are in the towers. Towers create a valley that creates some volume. There're also mountains, but they matter less because of the rule 2.1

2nd violet place: Here details are on the surface of the bridge. The bridge creates some volume under itself.

The bridge is closer to the grey places because it's easier to turn the bridge into something flat. (Rule 3.1)

Grey

1st grey place: Here details are on the platform.

2nd grey place: Here details are the book tables, covering a plane.

The platform is closer to the violet places because it's easier to turn into a volume. And book tables are closer to the orange places because they're easier to turn into something without a clear shape. Also their space may look bigger.

Orange

1st orange place: Here details are on top of the tower... and in the field. (Rule 2.1: bigger structures are interpreted in the context of the smaller structures.) This place is like a cloud of details.

2nd orange place: Here details are in the stories of the house. And in the forest, perhaps, because the forest is interpreted in the context of the house. This place is like a cloud of details.

3rd orange place: Here details are in the house and in the field. This place is like a cloud of details (it looks flat but has no structure compared to the grey places).

4th orange place: Here details are in the streets and in the houses. This place is like a cloud of details.

1st and 2nd places are easier to turn into a clear volume, so they're closer to the violet places. But 1st is bigger than 2nd, so it's even closer to the violet places. (Rule 3.2)

1st and 2nd places are both easier to turn into a "small"/structured surface. But 2nd is harder to turn into a "small"/structured surface, so it's farther away.

Step 2.2: ordering "anti places"

2.1) When you evaluate a place smaller scale structures matter more. The opposite is true for "anti places". I often split my spectrum into a "positive" part and a "negative" part. They are a little bit like positive and negative numbers. You can also conceptualize "anti places" as places having contradictory interpretations.

Black Violet

1st anti-violet place: if it wasn't surrounded by the forest in such a way, it would be grey or orange. But the "hole" in the forest also creates a clear volume (anti volume).

2nd or 3rd anti-violet place: if those places didn't have multiple stories, they would be grey. But those are "buildings" that create a volume (anti volume).

The volume of the 1st place looks smaller, so it's lower in the order.

Black Grey

It's more or less the same like the "positive" grey, but the areas are enclosed.

Black Orange

It could be violet if it had less details: the space between the mountains would be creating a volume. But this place also looks like a cloud of details. So it has "contradictory interpretations".

Important point: if you took a spectrum (such as the one above) and tried to describe what causes specific places to end up in specific positions, what are their definite structural differences... you wouldn't get any clear answer, only a network of overlapping similarities and differences. (See "Family resemblance".) Because it doesn't make sense to describe context through causation.

I could give more examples of different spectrums that work according to the same principles. I could give examples with games, e.g. Crash Bandicoot: Warped or Donkey Kong Country 2. But as I said, I just decided to post everything I have at the moment. So I'll get back to the topic I started with ("vague concepts", hypotheses):

Why think about all of this, again?

Places are like "vague concepts". Places in a spectrum (places with a color) are like concepts with specific meaning. You can also compare places to vague hypotheses.

So if you formalize what I described above, you may figure out something about vague concepts and hypotheses generation. And something about human values. The latter would be important for AI alignment.

You can compare "colors" to a special type of probability... or rather to things that "create" probabilities: for example probability density function or probability amplitude. And you can compare "details" to specific outcomes.

So maybe you can be interested in this if you're interested in unexpected interpretations of probability, in playing with the idea of "probability".

P.S.: Just in case I'm also leaving this link here: "We need to develop new ways to analyze characters" (No Practictipation link). I tried to describe a way to find strong connections between characters that are only connected through various overlapping similarities ("family resemblance"). So it is related to this post, but I don't have the time to find the exact connection with the concepts of "colors" and "details".