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, my way of experiencing other people. (But it’s easier to talk about fantastical places and videogame levels, so I’m going to give examples with places/levels.)
If you want to read more about my motivation, check out “part 3”.
Part 1: Theory
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 “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 “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.
...
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.
I think my ideas may be important because they may lead to some new mathematical concepts.
Sometimes studying a simple idea or mechanic leads to a new mathematical concept which leads to completely unexpected applications.
For example, a simple toy with six sides (dice) may lead to saving people and major progress in science. Connecting points with lines (graphs) may lead to algorithms, data structures and new ways to find the optimal option or check/verify something.
Not any simple thing is guaranteed to lead to a new math concept. But I just want you to consider this possibility. And maybe ask questions answers to which could rise the probability of this possibility.
A new type of probability?
I think my ideas may be related to:
Probability and statistics.
Ways to describe vague things.
Ways to describe vague arguments or vague reasoning, thinking in context. For example arguments about “bodily autonomy”
Maybe those ideas describe a new type of probability:
You can compare classic probability to a pie made of a uniform and known dough. When you assign probabilities to outcomes and ideas you share the pie and you know what you’re sharing.
And in my idea you have a pie made of different types of dough (colors) and those types may change dynamically. You don’t know what you’re sharing when you share this pie.
This new type of probability is supposed to be applicable to things that have family resemblance, polyphyly or “cluster properties” (here’s an explanation of the latter in a Philosophy Tube video).
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.
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 experience. I believe everyone’s experience contains objective and important information.
Meta subjective knowledge
If you can get knowledge from/about subjective experience itself, it means there exists some completely unexplored type of knowledge. I want to “prove” that there does exist such type of knowledge.
Such knowledge would be important because it would be a new fundamental type of knowledge.
And such knowledge may be the most abstract: if you have knowledge about subjective experience itself, you have knowledge that’s true for any being with subjective experience.
People
I’m amazed how different people are. If nothing else, just look at the faces: completely different proportions and shapes and flavors of emotions. And it seems like those proportions and shapes can’t be encountered anywhere else. They don’t feel exactly like geometrical shapes. They are so incredibly alien and incomprehensible, and yet so familiar. But… nobody cares. Nobody seems surprised or too interested, nobody notices how inadequate our concepts are at describing stuff like that. And this is just the faces, but there are also voices, ways to speak, characters… all different in ways I absolutely can’t comprehend/verbalize.
I believe that if we (people) were able to share the way we experience each other, it would change us. It would make us respect each other 10 times more, remember each other 10 times better, learn 10 times more from each other.
It pains me every day that I can’t share my experience of other people (accumulated over the years I thought about this). My memory about other people. I don’t have the concepts, the language for this. Can’t figure it out. This feels so unfair! All the more unfair that it doesn’t seem to bother anyone else.
This state of the world feels like a prison. This prison was created by specific injustices, but the wound grew deeper, cutting something fundamental. Vivid experiences of qualia (other people, fantastic worlds) feel like a small window out of this prison. But together we could crush the prison wall completely.
Here I describe the most important, the most general principles of my philosophy.
Objects exist 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”.
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). Or you could say they’re somewhat similar to Gottfried Leibniz’s “monads”: simple substances without physical properties.
The objects I want to talk about are “places”: fantastical worlds or videogame levels. For example, fantastical worlds of Jacek Yerka.
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.
Colors
“Details” are like cells. Cells make up different types of tissues. “Details” make up colors. You can compare colors to textures or materials.
(The places I’m talking about are not physical. So the example below is just an analogy.)
Imagine that you have small toys in the shape of 3D solids. You’re interested in their volume. They have very clear sides, you study their volume with simple formulas.
Then you think: what is the volume of the giant cloud behind my window? What is a “side” of a cloud? Do clouds even have “real” shapes? What would be the formula for the volume of a cloud, would it be the size of a book?
The volume of the cloud has a different color. Because the context around the “volume” changed completely. Because clouds are made of a different type of “tissue”. (compared to toys)
OK, we resolved one question, but our problems don’t end here. Now we encounter an object that looks like a mix between a cloud and a simple shape. Are we allowed to simplify it into a simple shape? Are we supposed to mix both volumes? In what proportions and in what way?
We need rules to interpret objects (rules to assign importance to different parts or “layers” of an object before mixing them into a single substance). We need rules to mix colors. We need rules to infer intermediate colors.
Spectrum(s)
There are different spectrums. (Maybe they’re all parts of one giant spectrum. And maybe one of those spectrums contains our world.)
Often I imagine a spectrum as something similar to the visible spectrum: a simple order of places, from the first to the last.
A spectrum gives you the rules to interpret places and to create colors. How to make a spectrum?
You take a bunch of places. Make some loose assumptions about them. You assume where “details” in the places are and may be.
Based on the similarities between the places, you come up with the most important “colors” (“materials”) these places may be made of.
You come up with rules that tell you how to assign the colors to the places. Or how to modify the colors so that they fit the places.
The colors you came up with have an order:
The farther you go in a spectrum, the more details dissolve. First you have distinct groups of details that create volume. Then you have “flat”/stretched groups of details. Then you have “cloud-like” groups of details.
But those colors are not assigned to the places immediately. We’ve ordered abstract concepts, but haven’t ordered the specific places. Here’re some of the rules that allow you to assign the colors to the places:
When you evaluate a place, the smaller-scale structures matter more. For example, if the the smaller-scale structure has a clear shape and the larger-scale structure doesn’t have a clear shape, the former structure matters more in defining the place.
The opposite is true for “negative places”: the larger scale structures contribute more. 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 call those “normalization principles”. But we need more.
The principle of explosion/vanishing
Two places with different enough detail patterns can’t have the same color. Because a color is the detail pattern.
One of the two places have to get a bigger or a smaller (by a magnitude) color. But this may lead to an “explosion” (the place becomes unbelievably big/too distant from all the other places) or to a “vanishing” (the place becomes unbelievably microscopic/too distant).
This is bad because you can’t allow so much uncertainty about the places’ positions. It’s also bad because it completely violates all of your initial assumptions about the places. You can’t allow infinite uncertainty.
When you have a very small amount of places in a spectrum, they have a lot of room to move around. You’re unsure about their positions. But when you have more places, due to the domino effect you may start getting “explosions” and “vanishings”. They will allow you to rule out wrong positions, wrong rankings.
Overlay (superposition)
We also need a principle that would help us to sort places with the “same” color.
I feel it goes something like this:
Take places with the same color. Let’s say this color is “groups of details that create volume”.
If the places have no secondary important colors mixed in:
Overlay (superimpose) those places over each other.
Ask: if I take a random piece of a volume, what’s the probability that this piece is from the place X? Sort the places by such probabilities.
If the places do have some secondary important colors mixed in:
Overlay (superimpose) those places over each other.
Ask: how hard is it to get from the place’s main color to the place’s secondary color? (Maybe mix and redistribute the secondary colors of the places.) Sort places by that.
For example, let’s say the secondary color is “groups of details that create a surface that covers the entire place” (the main one is “groups of details that create volume”). Then you ask: how hard is it to get from the volume to that surface?
Note: I feel it might be related to Homeostatic Property Clusters. I learned the concept from a Philosophy Tube video. It reminded me of “family resemblance” popularized by Ludwig Wittgenstein.
Thought: places by themselves are incomparable. They can be compared only inside of a spectrum.
3 cats (a slight tangent/bonus)
Imagine a simple drawing of a cat. And a simple cat sculpture. And a real cat. Do they feel different?
If “yes”, then you experience a difference between various qualia. You feel some meta knowledge about qualia. You feel qualia “between” qualia.
You look at the same thing in different contexts. And so you look at 3 versions of it through 3 different lenses. If you looked at everything through the same lens, you would recognize only a single object.
If you understand what I’m talking about here, then you understand what I’m trying to describe about “colors”. Colors are different lenses, different contexts.
(Drafts of a future post.)
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, my way of experiencing other people. (But it’s easier to talk about fantastical places and videogame levels, so I’m going to give examples with places/levels.)
If you want to read more about my motivation, check out “part 3”.
Part 1: Theory
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 “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 “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.
...
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.
Part 2: Examples
Part 3: Motivation
I think my ideas may be important because they may lead to some new mathematical concepts.
Sometimes studying a simple idea or mechanic leads to a new mathematical concept which leads to completely unexpected applications.
For example, a simple toy with six sides (dice) may lead to saving people and major progress in science. Connecting points with lines (graphs) may lead to algorithms, data structures and new ways to find the optimal option or check/verify something.
Not any simple thing is guaranteed to lead to a new math concept. But I just want you to consider this possibility. And maybe ask questions answers to which could rise the probability of this possibility.
A new type of probability?
I think my ideas may be related to:
Probability and statistics.
Ways to describe vague things.
Ways to describe vague arguments or vague reasoning, thinking in context. For example arguments about “bodily autonomy”
Maybe those ideas describe a new type of probability:
You can compare classic probability to a pie made of a uniform and known dough. When you assign probabilities to outcomes and ideas you share the pie and you know what you’re sharing.
And in my idea you have a pie made of different types of dough (colors) and those types may change dynamically. You don’t know what you’re sharing when you share this pie.
This new type of probability is supposed to be applicable to things that have family resemblance, polyphyly or “cluster properties” (here’s an explanation of the latter in a Philosophy Tube video).
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 experience. I believe everyone’s experience contains objective and important information.
Meta subjective knowledge
If you can get knowledge from/about subjective experience itself, it means there exists some completely unexplored type of knowledge. I want to “prove” that there does exist such type of knowledge.
Such knowledge would be important because it would be a new fundamental type of knowledge.
And such knowledge may be the most abstract: if you have knowledge about subjective experience itself, you have knowledge that’s true for any being with subjective experience.
People
I’m amazed how different people are. If nothing else, just look at the faces: completely different proportions and shapes and flavors of emotions. And it seems like those proportions and shapes can’t be encountered anywhere else. They don’t feel exactly like geometrical shapes. They are so incredibly alien and incomprehensible, and yet so familiar. But… nobody cares. Nobody seems surprised or too interested, nobody notices how inadequate our concepts are at describing stuff like that. And this is just the faces, but there are also voices, ways to speak, characters… all different in ways I absolutely can’t comprehend/verbalize.
I believe that if we (people) were able to share the way we experience each other, it would change us. It would make us respect each other 10 times more, remember each other 10 times better, learn 10 times more from each other.
It pains me every day that I can’t share my experience of other people (accumulated over the years I thought about this). My memory about other people. I don’t have the concepts, the language for this. Can’t figure it out. This feels so unfair! All the more unfair that it doesn’t seem to bother anyone else.
This state of the world feels like a prison. This prison was created by specific injustices, but the wound grew deeper, cutting something fundamental. Vivid experiences of qualia (other people, fantastic worlds) feel like a small window out of this prison. But together we could crush the prison wall completely.
Key philosophical principles
Here I describe the most important, the most general principles of my philosophy.
Objects exist 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”.
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). Or you could say they’re somewhat similar to Gottfried Leibniz’s “monads”: simple substances without physical properties.
The objects I want to talk about are “places”: fantastical worlds or videogame levels. For example, fantastical worlds of Jacek Yerka.
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.
Colors
“Details” are like cells. Cells make up different types of tissues. “Details” make up colors. You can compare colors to textures or materials.
(The places I’m talking about are not physical. So the example below is just an analogy.)
Imagine that you have small toys in the shape of 3D solids. You’re interested in their volume. They have very clear sides, you study their volume with simple formulas.
Then you think: what is the volume of the giant cloud behind my window? What is a “side” of a cloud? Do clouds even have “real” shapes? What would be the formula for the volume of a cloud, would it be the size of a book?
The volume of the cloud has a different color. Because the context around the “volume” changed completely. Because clouds are made of a different type of “tissue”. (compared to toys)
OK, we resolved one question, but our problems don’t end here. Now we encounter an object that looks like a mix between a cloud and a simple shape. Are we allowed to simplify it into a simple shape? Are we supposed to mix both volumes? In what proportions and in what way?
We need rules to interpret objects (rules to assign importance to different parts or “layers” of an object before mixing them into a single substance). We need rules to mix colors. We need rules to infer intermediate colors.
Spectrum(s)
There are different spectrums. (Maybe they’re all parts of one giant spectrum. And maybe one of those spectrums contains our world.)
Often I imagine a spectrum as something similar to the visible spectrum: a simple order of places, from the first to the last.
A spectrum gives you the rules to interpret places and to create colors. How to make a spectrum?
You take a bunch of places. Make some loose assumptions about them. You assume where “details” in the places are and may be.
Based on the similarities between the places, you come up with the most important “colors” (“materials”) these places may be made of.
You come up with rules that tell you how to assign the colors to the places. Or how to modify the colors so that they fit the places.
The colors you came up with have an order:
The farther you go in a spectrum, the more details dissolve. First you have distinct groups of details that create volume. Then you have “flat”/stretched groups of details. Then you have “cloud-like” groups of details.
But those colors are not assigned to the places immediately. We’ve ordered abstract concepts, but haven’t ordered the specific places. Here’re some of the rules that allow you to assign the colors to the places:
When you evaluate a place, the smaller-scale structures matter more. For example, if the the smaller-scale structure has a clear shape and the larger-scale structure doesn’t have a clear shape, the former structure matters more in defining the place.
The opposite is true for “negative places”: the larger scale structures contribute more. 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 call those “normalization principles”. But we need more.
The principle of explosion/vanishing
Two places with different enough detail patterns can’t have the same color. Because a color is the detail pattern.
One of the two places have to get a bigger or a smaller (by a magnitude) color. But this may lead to an “explosion” (the place becomes unbelievably big/too distant from all the other places) or to a “vanishing” (the place becomes unbelievably microscopic/too distant).
This is bad because you can’t allow so much uncertainty about the places’ positions. It’s also bad because it completely violates all of your initial assumptions about the places. You can’t allow infinite uncertainty.
When you have a very small amount of places in a spectrum, they have a lot of room to move around. You’re unsure about their positions. But when you have more places, due to the domino effect you may start getting “explosions” and “vanishings”. They will allow you to rule out wrong positions, wrong rankings.
Overlay (superposition)
We also need a principle that would help us to sort places with the “same” color.
I feel it goes something like this:
Take places with the same color. Let’s say this color is “groups of details that create volume”.
If the places have no secondary important colors mixed in:
Overlay (superimpose) those places over each other.
Ask: if I take a random piece of a volume, what’s the probability that this piece is from the place X? Sort the places by such probabilities.
If the places do have some secondary important colors mixed in:
Overlay (superimpose) those places over each other.
Ask: how hard is it to get from the place’s main color to the place’s secondary color? (Maybe mix and redistribute the secondary colors of the places.) Sort places by that.
For example, let’s say the secondary color is “groups of details that create a surface that covers the entire place” (the main one is “groups of details that create volume”). Then you ask: how hard is it to get from the volume to that surface?
Note: I feel it might be related to Homeostatic Property Clusters. I learned the concept from a Philosophy Tube video. It reminded me of “family resemblance” popularized by Ludwig Wittgenstein.
Note 2: https://imgur.com/a/F5Vq8tN. Some examples I’m going to write about later.
Thought: places by themselves are incomparable. They can be compared only inside of a spectrum.
3 cats (a slight tangent/bonus)
Imagine a simple drawing of a cat. And a simple cat sculpture. And a real cat. Do they feel different?
If “yes”, then you experience a difference between various qualia. You feel some meta knowledge about qualia. You feel qualia “between” qualia.
You look at the same thing in different contexts. And so you look at 3 versions of it through 3 different lenses. If you looked at everything through the same lens, you would recognize only a single object.
If you understand what I’m talking about here, then you understand what I’m trying to describe about “colors”. Colors are different lenses, different contexts.