Is the level stretched vertically or horizontally?
Is the level easy to separate into similar square-like pieces or not? (like a patchwork)
The levels go from “vertical and separable” to “horizontal and not separable”.
But to see this you need to note:
Level 1 is very vertical: it’s just a vertical wall. So it “takes away” verticality from levels 2 and 3.
From levels 1-3, level 3 is the most horizontal. Because it’s the least similar to the level 1.
Levels 4-6 repeat the same logic, but now levels are harder to separate into similar square-like pieces. Why? Because levels 1 and 2 are very easy to separate (they have repeating patterns on the walls), so they “take away” separability from all other levels.
Any question about any property of any level is answered by another question: is this property already “occupied” by some other level?
Can the place fit inside a box-like space? (not too big, not too small)
Is the place inside or outside of something small?
The places go from “box-like and outside” to “not box-like and inside”.
But to see this you need to note:
Place 1 could be interpreted as being inside of a town. But similar Place 5 is inside a single road. So it takes away “inside-ness” from Place 1.
Place 2 is more “outside” than it seems. Because similar Place 6 fits inside an area with small tiles. So it takes away “inside-ness” from Place 2.
Place 3 is not so tall as it seems. Because similar Place 6 is very tall. So it takes away height from Place 3.
If you feel this relativity of places’ properties, then you understand how I think about places. You don’t need to understand a specific order of places perfectly.
Does the space create a 3D space (box-like, not too big, not too small) or 2D space (flat surface) or 0D space (shapeless, cloud-like)?
Levels go from 3D to 2D to 0D.
But to see this you need to note:
Levels 6 and 7 are less box-like than they seem. Because similar levels 1 and 2 already create small box-like spaces. So they take away “box-like” feature from levels 6 and 7.
Level 3 is more box-like than it seems. Because levels 4 and 5 create more dense flat surfaces. So they take away flatness of Level 3.
Each level is described by all other levels. This recursive logic determines what features of the levels matter.
Negative objects
When objects take their properties from a single pool of properties, there may appear “negative objects”. It happens when objects A and B take away opposite properties from a third object C (with equal force). For example, A may take away height from C. But B takes away shortness (anti-height) from C. So, “negative objects” are like contradictions. You can’t fit a negative object anywhere in the order of positive objects.
Let’s get back to Crash Bandicoot 3 and add two levels: image. Videos of the levels: Level −2, Level −1
Take a look at Level −2. It’s too empty for levels 6 and 7 (and too box-like). But it’s too big and shapeless for levels 1 and 2. And it’s obviously not a flat surface. So, it doesn’t fit anywhere. Maybe it’s just better to place it in its own order.
Similar thing is true for Level −1. It’s too different from levels 6 and 7 and it’s too small for levels 1 and 2.
Levels −2 and −1 are also both inside some kind of structures. This adds confusion when you compare them to other levels.
Note that negative levels are still connected with all the other levels anyway: their properties are still determined by properties of all other levels, just in a more complicated way.
You can order negative levels by using the metrics for positive levels. In the case above, you can do it like this:
Take negative levels. Cut out their larger parts. Now they’re just like the positive levels.
Order them the same way you ordered positive levels.
Hyper objects
There are also “hyper objects” (hyper positive and hyper negative objects). Such objects take “too much” or “too little” from the common pool of properties compared to normal objects.
How do hyper objects appear? I may not be able to explain it. Maybe a hyper object appears when an object takes a property (equally strong) from objects with very different amounts of that property. This was very confusing and vague, so here’s an analogy: imagine a number that’s very-very, but equally far away from the numbers 2 and 5. It has distance 10 from both 2 and 5. How can this be? This number should go somewhere “sideways”… it must be a complex number. So, you can compare hyper objects to complex numbers.
“Bye Bye Blimps” is like a flat surface, but utterly gigantic. But it’s also shapeless like levels 6 and 7, yet bigger than them/equally big, but in a different way.
“N. Gin” is identical to “Bye Bye Blimps” in this regard.
Theory
How is this related to anything?
You may be asking “How can ordering things be related to anything?” Prepare for a little bit abstract argument.
Any thought/experience is about multiple things coexisting in your mental state. So, any thought/experience is about direct or indirect comparison between things. And any comparison can be described by an order or multiple orders.
If compared things don’t share properties, then you can order them using “arithmetic” (absolute measurements, uncorrelated properties). In this case everything happening in your mental state is absolutely separated, it’s a degenerate case.
If compared things 100% share properties, then you can order them using my method (pool of properties, absolutely correlated properties). In this case everything happening in your mental state is mixed into a single process.
If compared things partially share properties, then you can use a mix between “arithmetic” and my method. In this case everything happening in your mental state partially breaks down into separate processes.
So, “my orders + arithmetic orders” is something like a Turing machine: a universal model that can describe any thought/experience, any mental state. Of course, a Turing machine can describe anything my method can describe, but my method is more high-level.
Formalization
I know that what I described above doesn’t automatically specify a mathematical model. But I think we should be able to formalize my idea easily enough. If not, then my idea is wrong.
We have those hints for formalization:
The idea about the common pool of properties. Connection with probability.
Connection with recursion.
The idea of “negative objects” and “hyper objects”. Connection with superrationality/splitting resources.
We can test the formalization on comparing 3D shapes (maybe even 2D shapes). Easy to model and formalize.
Connection to hypotheses, rationality. To Bayes’ rule. (See below.)
We can try a special type of brainstorming/spitballing based on my idea. (See below.)
To be honest, I’m bad at math. I based my theory on synesthesia-like experiences and conceptual ideas. But if the information above isn’t enough, I can try to give more. I have experience of making my idea more specific, so I could guess how to make the idea even more specific (if we encounter a problem). Please, help me with formalizing this idea.
Crash Bandicoot 1
Crash Bandicoot N. Sane Trilogy
My ordering of some levels: image. Videos of the levels: Level 1, Level 2, Level 3, Level 4, Level 5, Level 6.
I used 2 metrics to evaluate the levels:
Is the level stretched vertically or horizontally?
Is the level easy to separate into similar square-like pieces or not? (like a patchwork)
The levels go from “vertical and separable” to “horizontal and not separable”.
But to see this you need to note:
Level 1 is very vertical: it’s just a vertical wall. So it “takes away” verticality from levels 2 and 3.
From levels 1-3, level 3 is the most horizontal. Because it’s the least similar to the level 1.
Levels 4-6 repeat the same logic, but now levels are harder to separate into similar square-like pieces. Why? Because levels 1 and 2 are very easy to separate (they have repeating patterns on the walls), so they “take away” separability from all other levels.
Any question about any property of any level is answered by another question: is this property already “occupied” by some other level?
Jacek Yerka
Jacek Yerka
Places in random order: image.
My ordering of places: image.
I used 2 metrics to evaluate the places:
Can the place fit inside a box-like space? (not too big, not too small)
Is the place inside or outside of something small?
The places go from “box-like and outside” to “not box-like and inside”.
But to see this you need to note:
Place 1 could be interpreted as being inside of a town. But similar Place 5 is inside a single road. So it takes away “inside-ness” from Place 1.
Place 2 is more “outside” than it seems. Because similar Place 6 fits inside an area with small tiles. So it takes away “inside-ness” from Place 2.
Place 3 is not so tall as it seems. Because similar Place 6 is very tall. So it takes away height from Place 3.
If you feel this relativity of places’ properties, then you understand how I think about places. You don’t need to understand a specific order of places perfectly.
Crash Bandicoot 3
My ordering of some levels: image. Videos of the levels: Level 1, Level 2, Level 3, Level 4, Level 5, Level 6, Level 7
I used 1 metrics to evaluate the levels:
Does the space create a 3D space (box-like, not too big, not too small) or 2D space (flat surface) or 0D space (shapeless, cloud-like)?
Levels go from 3D to 2D to 0D.
But to see this you need to note:
Levels 6 and 7 are less box-like than they seem. Because similar levels 1 and 2 already create small box-like spaces. So they take away “box-like” feature from levels 6 and 7.
Level 3 is more box-like than it seems. Because levels 4 and 5 create more dense flat surfaces. So they take away flatness of Level 3.
Each level is described by all other levels. This recursive logic determines what features of the levels matter.
Negative objects
When objects take their properties from a single pool of properties, there may appear “negative objects”. It happens when objects A and B take away opposite properties from a third object C (with equal force). For example, A may take away height from C. But B takes away shortness (anti-height) from C. So, “negative objects” are like contradictions. You can’t fit a negative object anywhere in the order of positive objects.
Let’s get back to Crash Bandicoot 3 and add two levels: image. Videos of the levels: Level −2, Level −1
Take a look at Level −2. It’s too empty for levels 6 and 7 (and too box-like). But it’s too big and shapeless for levels 1 and 2. And it’s obviously not a flat surface. So, it doesn’t fit anywhere. Maybe it’s just better to place it in its own order.
Similar thing is true for Level −1. It’s too different from levels 6 and 7 and it’s too small for levels 1 and 2.
Levels −2 and −1 are also both inside some kind of structures. This adds confusion when you compare them to other levels.
Note that negative levels are still connected with all the other levels anyway: their properties are still determined by properties of all other levels, just in a more complicated way.
You can order negative levels by using the metrics for positive levels. In the case above, you can do it like this:
Take negative levels. Cut out their larger parts. Now they’re just like the positive levels.
Order them the same way you ordered positive levels.
Hyper objects
There are also “hyper objects” (hyper positive and hyper negative objects). Such objects take “too much” or “too little” from the common pool of properties compared to normal objects.
How do hyper objects appear? I may not be able to explain it. Maybe a hyper object appears when an object takes a property (equally strong) from objects with very different amounts of that property. This was very confusing and vague, so here’s an analogy: imagine a number that’s very-very, but equally far away from the numbers 2 and 5. It has distance 10 from both 2 and 5. How can this be? This number should go somewhere “sideways”… it must be a complex number. So, you can compare hyper objects to complex numbers.
An example of hyper levels for Crash Bandicoot 3: image. Video of the levels: “Bye Bye Blimps”, “N. Gin”
“Bye Bye Blimps” is like a flat surface, but utterly gigantic. But it’s also shapeless like levels 6 and 7, yet bigger than them/equally big, but in a different way.
“N. Gin” is identical to “Bye Bye Blimps” in this regard.
Theory
How is this related to anything?
You may be asking “How can ordering things be related to anything?” Prepare for a little bit abstract argument.
Any thought/experience is about multiple things coexisting in your mental state. So, any thought/experience is about direct or indirect comparison between things. And any comparison can be described by an order or multiple orders.
If compared things don’t share properties, then you can order them using “arithmetic” (absolute measurements, uncorrelated properties). In this case everything happening in your mental state is absolutely separated, it’s a degenerate case.
If compared things 100% share properties, then you can order them using my method (pool of properties, absolutely correlated properties). In this case everything happening in your mental state is mixed into a single process.
If compared things partially share properties, then you can use a mix between “arithmetic” and my method. In this case everything happening in your mental state partially breaks down into separate processes.
So, “my orders + arithmetic orders” is something like a Turing machine: a universal model that can describe any thought/experience, any mental state. Of course, a Turing machine can describe anything my method can describe, but my method is more high-level.
Formalization
I know that what I described above doesn’t automatically specify a mathematical model. But I think we should be able to formalize my idea easily enough. If not, then my idea is wrong.
We have those hints for formalization:
The idea about the common pool of properties. Connection with probability.
Connection with recursion.
The idea of “negative objects” and “hyper objects”. Connection with superrationality/splitting resources.
We can test the formalization on comparing 3D shapes (maybe even 2D shapes). Easy to model and formalize.
Connection to hypotheses, rationality. To Bayes’ rule. (See below.)
We can try a special type of brainstorming/spitballing based on my idea. (See below.)
To be honest, I’m bad at math. I based my theory on synesthesia-like experiences and conceptual ideas. But if the information above isn’t enough, I can try to give more. I have experience of making my idea more specific, so I could guess how to make the idea even more specific (if we encounter a problem). Please, help me with formalizing this idea.