Statistics for vague concepts and “Colors” of places

[Q Home]

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.

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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

1. We need to take a bunch of places. Come up with “main colors” for them. Those colors are already ranked.

2. We need to assign the colors to the places.

3. 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.

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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”.

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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”.

[Q Home]

I want to share a part of a conversation I had in order to explain my post better:

“Vague concepts”

A game is clearly defined in any context. What do you mean that it is impossible to understand outside of “any context”?

Sorry for not making it more clear, I was just referring to this idea:

https://​​en.wikipedia.org/​​wiki/​​Family_resemblance

It argues that things which could be thought to be connected by one essential common feature may in fact be connected by a series of overlapping similarities, where no one feature is common to all of the things. Games, which Wittgenstein used as an example to explain the notion, have become the paradigmatic example of a group that is related by family resemblances.

The idea is that when you consider a bunch of “games”, it’s easy to see the common features. But when you consider more and more “games” and things that are sometimes called “games”, it turns out that everything can be a game.

And yet no matter how you stretch the concept (e.g. say something like “love is just a game”), in a specific context the meaning is clear enough.

You can also call concepts like this “cluster properties” (explanation in Philosophy Tube video). Or even the (in)famous “social constructs”. In the text form:

Even more interestingly, Harris’ idea is an accidental ripoff of a theory developed by philosopher Richard Boyd in 1982, called: ‘The Homeostatic Cluster Property Theory of Metaethical Naturalism’ Sexy title. Boyd thought that words like ‘good’ and ‘evil’ refer to real properties out there in the material world, and that therefore statements like ‘Murder is bad’ are capable of being objectively true, or at least true in the same way as scientific statements are. Which prompts the question, “To what exactly do these words refer?”

Boyd’s answer is that they are cluster properties—groups of things that tend to go together. The example he uses is actually the same one Harris does—health. There are all kinds of things we would want to include in a definition of the word “healthy,” like your heart should be beating and you should be able to breathe, but do you have to be a certain size in order to be healthy? Do you have to not be in pain? Can you have a beating heart and be unhealthy? There’s a cluster of properties here somewhere that makes up the definition of the word health but we’re never going to pin down a definite list because that’s just not how the concept works. Despite that vagueness it’s still very obviously useful and meaningful.

Similarly Boyd thinks that a word like ‘good’ refers to a cluster of things that are non-morally good for humans, like sharing friendship, sharing love, having fun, watching quality YouTube videos, but just like with health, you’re never going to be able to pin down a full list because the concept just isn’t like that.

And here’s the big takeaway—if we say ‘John is healthy’ we could be talking about any number of things in the cluster of health—whether he a has disease, whether he works out, whether he has a good relationship with his mother—all of which are objective—but whether the sentence ‘John is healthy’ is true will still depend on what aspect of his health we’re talking about. It will be relative to the context in which we’re saying it.

...

So, I call clusters like this (games, health, goodness) “vague concept”: those concepts obtain specific meaning in a specific context, but they can’t be defined outside of context.

How to understand a vague concept? You can try to memorize all contexts (that you know of) in which it’s used. Or you can learn to infer its meaning in new contexts and learn to create new contexts for this concept yourself. This is what I meant by “creating new contexts”.

I feel that it’s related to hypotheses generation because some general (scientific) ideas/​paradigms don’t have any meaning outside of context

You could imagine a hypothesis based on vague concepts, for example “healthy people earn more money than unhealthy people” or “people who love games earn more money”. In their most abstract form, those theories can’t be falsified. But it’s easy to generate specific falsifiable hypotheses based on those ideas.

Scientific theories, too, can have an unfalsifiable core. This is Imre Lakatos’ model of scientific progress:

https://​​en.wikipedia.org/​​wiki/​​Imre_Lakatos#Research_programmes

Lakatos’s second major contribution to the philosophy of science was his model of the “research programme”,[19] which he formulated in an attempt to resolve the perceived conflict between Popper’s falsificationism and the revolutionary structure of science described by Kuhn. Popper’s standard of falsificationism was widely taken to imply that a theory should be abandoned as soon as any evidence appears to challenge it, while Kuhn’s descriptions of scientific activity were taken to imply that science is most fruitful during periods in which popular, or “normal”, theories are supported despite known anomalies. Lakatos’ model of the research programme aims to combine Popper’s adherence to empirical validity with Kuhn’s appreciation for conventional consistency.

A Lakatosian research programme[20] is based on a hard core of theoretical assumptions that cannot be abandoned or altered without abandoning the programme altogether. More modest and specific theories that are formulated in order to explain evidence that threatens the “hard core” are termed auxiliary hypotheses. Auxiliary hypotheses are considered expendable by the adherents of the research programme—they may be altered or abandoned as empirical discoveries require in order to “protect” the “hard core”. Whereas Popper was generally read as hostile toward such ad hoc theoretical amendments, Lakatos argued that they can be progressive, i.e. productive, when they enhance the programme’s explanatory and/​or predictive power, and that they are at least permissible until some better system of theories is devised and the research programme is replaced entirely.

Vague concepts lead to vague hypotheses (“research programmes”). Vague hypotheses work the same way vague concepts do. (part ¹⁄₂)

[Q Home]

Properties, differences

What do you mean by “meaning” here? How does an attribute of size have inherent meaning?

It is absolutely unclear what you mean by this. What does “height” relate to and resonate with, and why does that change with object? What do you even mean by “relate and resonate”?

What do you mean by “part/​property”? Something like “height”? How do you put “height” into a different context? “You can create a [...] different version of it”? What do you mean by “fundamentally different”? A version of what? Of “height”?

I tried to give 3 examples there (with paintings). But here’s a simpler example:

• Imagine a cube and a tree. Think about their heights. Cube’s height has a different “meaning” because it’s the same thing as its width and length.

You may need to make a leap of faith/​understanding here somewhere, it’s a new concept or perspective. I may try explaining it in different ways and analogies, but I can’t reduce this idea to simpler ideas.

For example, I could make an analogy with homology in biology:

https://​​en.wikipedia.org/​​wiki/​​Evolutionary_developmental_biology#The_control_of_body_structure

Roughly spherical eggs of different animals give rise to unique morphologies, from jellyfish to lobsters, butterflies to elephants. Many of these organisms share the same structural genes for body-building proteins like collagen and enzymes, but biologists had expected that each group of animals would have its own rules of development. The surprise of evo-devo is that the shaping of bodies is controlled by a rather small percentage of genes, and that these regulatory genes are ancient, shared by all animals. The giraffe does not have a gene for a long neck, any more than the elephant has a gene for a big body. Their bodies are patterned by a system of switching which causes development of different features to begin earlier or later, to occur in this or that part of the embryo, and to continue for more or less time.[7]

Those topics talk about the ways animals’ parts and properties get differentiated.

And you can combine all properties of an object into just a single one.

I tried to give 3 examples of this. It’s some type of holism: “you should view a part in the context of the whole”, “a whole is greater than the sum of its parts”.

I give this idea a fractal spin: “any part of a thing is equivalent to the whole”. The most similar philosophical idea I know of is Gottfried Leibniz’s Monadology, for example:

https://​​en.wikipedia.org/​​wiki/​​Monadology

(III) Composite substances or matter are “actually sub-divided without end” and have the properties of their infinitesimal parts (§65). A notorious passage (§67) explains that “each portion of matter can be conceived as like a garden full of plants, or like a pond full of fish. But each branch of a plant, each organ of an animal, each drop of its bodily fluids is also a similar garden or a similar pond”.

You can compare colors to monads and spectrums to the “supreme monad” (God).

So you are describing art theory! That is something learned in 10th grade art. Contrast /​homo-/​heterogenity of form, color etc.

I don’t think it’s art theory. Not 10th grade.

No idea what you are getting at. Why are you calling your new super property “color” when you are also discussing classical form and color? This makes confusing these terms incredibly likely.

I believe I don’t discuss classical “color”. I only mention it in a single analogy (and one more time when I mention qualia).

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My goal

I guess you are talking about categorizing arbitrary qualia properties and their relations, but that is a matter of art theory. How do you even propose to objectively study something inherently subjective? It does seem that what you describe is covered by artists. Beyond that it is incredibly unclear what you are talking about.

I can explain my goal with a story. I didn’t include it in the post to not make it too big, but maybe I should have:

Blind men and an elephant

Imagine a world where people don’t know the concept of a “circle”. People do see round things, but can’t consciously pick out the property of roundness. (Any object has a lot of other properties.)

Some people say “the Moon is like a face”. Other say “the Moon is like a flower”. Weirder people say “the Moon is like a tree trunk” or “the Moon is like an embrace”. The weirdest people say “the Moon is like a day” or “the Moon is like going for a walk and returning back home”. Nobody agrees with each other, nobody understands each other.

Then one person comes up and says: “All of you are right. Opinions of everyone contain objective and useful information.”

People are shocked: at least someone has got to be wrong? If everyone is right, how can the information be objective and useful?

The concept of a “circle” is explained. Suddenly it’s extremely easy to understand each other. Like 2 and 2. And suddenly there’s nothing to argue about. People begin to share their knowledge and this knowledge finds completely unexpected applications.

https://​​en.wikipedia.org/​​wiki/​​Blind_men_and_an_elephant

The situation was just like in the story about blind men and an elephant, but even more ironic, since this time everyone was touching the same “shape”.

With my story I wanted to explain my opinions and goals:

• I want to share my subjective experience.

• I believe that it contains objective and important information.

• I want to share a way to share subjective experiences. I believe everyone’s experience contains objective and important information.

(part ²⁄₂)