For some time I wanted to apply the idea of probabilistic thinking (used for predicting things) to describing things, making analogies between things. This is important because your hypotheses (predictions) depend on the way you see the world. If you could combine predicting and describing into a single process, you would unify cognition.
Fuzzy logic and fuzzy sets is one way to do it. The idea is that something can be partially true (e.g. “humans are ethical” is somewhat true) or partially belong to a class (e.g. a dog is somewhat like a human, but not 100%). Note that “fuzzy” and “probable” are different concepts. But fuzzy logic isn’t enough to unify predicting and describing. Because it doesn’t tell us much about how we should/could describe the world. No new ideas.
I have a different principle for unifying probability and description. Here it is:
Properties of objects aren’t contained in specific objects. Instead, there’s a common pool that contains all possible properties. Objects take their properties from this pool. But the pool isn’t infinite. If one object takes 80% of a certain property from the pool, other objects can take only 20% of that property (e.g. “height”). Socialism for properties: it’s not your “height”, it’s our “height”.
How can an object “take away” properties of other objects? For example, how can a tall object “steal” height from other objects? Well, imagine there are multiple interpretations of each object. Interpretation of one object affects interpretation of all other objects. It’s just a weird axiom. Like a Non-Euclidean geometry.
This sounds strange, but this connects probability and description. And this is new. I think this principle can be used in classification and argumentation. Before showing how to use it I want to explain it a little bit more with some analogies.
Connected houses
Imagine two houses, A and B. Those houses are connected in a specific way.
When one house turns on the light at 80%, the other turns on the light only at 20%.
When one house uses 60% of the heat, the other uses only 40% of the heat.
(When one house turns on the red light, the other turns on the blue light. When one house is burning, the other is freezing.)
Those houses take electricity and heat from a common pool. And this pool doesn’t have infinite energy.
Kindness
Usually people think about qualities as something binary: you either has it or not. For example, a person can be either kind or not.
For me an abstract property such as “kindness” is like the white light. Different people have different colors of “kindness” (blue kindness, green kindness...). Every person has kindness of some color. But nobody has all colors of kindness.
Abstract kindness is the common pool (of all ways to express it). Different people take different parts of that pool.
Some more analogies
Theism analogy. You can compare the common pool of properties to the “God object”, a perfect object. All other objects are just different parts of the perfect object. You also can check out Monadology by Gottfried Leibniz.
Spectrum analogy. You can compare the common pool of properties to the spectrum of colors. Objects are just colors of a single spectrum.
Ethics analogy. Imagine that all your good qualities also belong (to a degree) to all other people. And all bad qualities of other people also belong (to a degree) to you. As if people take their qualities from a single common pool.
Buddhism analogy. Imagine that all your desires and urges come (to a degree) from all other people. And desires and urges of all other people come (to a degree) from you. There’s a single common pool of desire. This is somewhat similar to karma. In rationality there’s also a concept of “values handshakes”: when different beings decide to share each other’s values.
Quantum analogy. See quantum entanglement. When particles become entangled, they take their properties from a single common pool (quantum state).
Fractalanalogy. “All objects in the Universe are just different versions of a single object.”
Subdivisionanalogy. Check out Finite subdivision rule. You can compare the initial polygone to the common pool of properties. And different objects are just pieces of that polygone.
Connection with recursion
Recursion. If objects take their properties from the common pool, it means they don’t really have (separate) identities. It also means that a property (X) of an object is described in terms of all other objects. So, the property (X) is recursive, it calls itself to define itself.
For example, imagine we have objects A, B and C. We want to know their heights. In order to do this we may need to evaluate those functions:
A(height), B(height), C(height)
A(B(height)), A(C(height)) …
A(B(C(height))), A(C(B(height))) …
A priori assumptions about objects should allow us to simplify this and avoid cycles.
Fractals. See Coastline paradox. You can treat a fractal as an object with multiple interpretations (where an interpretation depends on the scale). Objects taking their properties from the common pool = fractals taking different scales from the common range.
Classification
To explain how to classify objects using my principle, I need to explain how to order them with it.
I’ll explain it using fantastical places and videogame levels, because those things are formal and objective enough (they are 3D shapes). But I believe the same classification method can be applied to any objects, concepts and even experiences.
Basically, this is an unusual model of contextual thinking. If we can formalize this specific type of contextual thinking, then maybe we can formalize contextual thinking in general. This topic will sound very esoteric, but it’s the direct application of the principle explained above.
Intro
(I interpret paintings as “real places”: something that can be modeled as a 3D shape. If a painting is surreal, I simplify it a bit in my mind.)
Let’s compare 2 of them: image. Let’s say we want to know the “height” of those places. We don’t have a universal scale to compare the places. Different interpretations of the height are possible.
If we’re calling a place “very tall”—we need to understand the epithet “very tall” in probabilistic terms, such as “70-90% tall”—and we need to imagine that this probability is taken away from all other places. We can’t have two different “very tall” places. Probability should add up to 100%.
Now take a look at another place (A): image(I ignore the cosmos to simplify it). Let’s say we want to know how enclosed it is. In one interpretation, it is massively enclosed by trees. In another interpretation, trees are just a decorative detail and can be ignored. Let’s add some more places for context: image. They are definitely more open than the initial place, so we should update towards more enclosed interpretation of (A). All interpretations should be correlated and “compatible”. It’s as if we’re solving a puzzle.
You can say that properties of places are “expandable”. Any place contains a seed of any possible property and that seed can be expanded by a context. “Very tall place” may mean Mt. Everest or a molehill depending on context. You can compare it to a fractal: every small piece of a fractal can be expanded into the entire thing. And I think it’s also very similar to how human language, human concepts work.
You also may call it “amplification of evidence”: any smallest piece of evidence (or even absence of any evidence) can be expanded into very strong evidence by context. We have a situation like in the Raven paradox, but even worse.
Is the space of the place “box-like” and small or not?
Is the place enclosed or open?
The places go from “box-like and enclosed” to “not box-like and open” in my ordering.
But to see this you need to look at the places in a certain way, reason about them in a certain way:
Place 1 is smaller than it seems. Because Place 5 is similar and “takes away” its size.
Place 2 is more box-like than it seems. Because similar places 4 and 6 are less box-like.
Place 3 is more enclosed than it seems. Because similar places 4 and 6 “take away” its openness.
Place 5 is more open than it seems. Because similar places 1 and 2 “take away” its closedness.
Almost any property of any specific place can be “illusory”. But when you look at places in the context you can deduce their properties vie the process of elimination.
You can apply the same idea (about the “common pool”) to hypotheses and argumentation:
You can describe a hypothesis in terms of any other hypothesis. You also can simplify it along the way (let’s call it “regularization”). Recursion and circularity is possible in reasoning.
Truth isn’t attached to a specific hypothesis. Instead there’s a common “pool of truth”. Different hypotheses take different parts of the whole truth. The question isn’t “Is the hypothesis true?”, the question is “How true is the hypothesis compared to others?” And if the hypotheses are regularized it can’t be too wrong.
Alternatively: “implications” of a specific hypothesis aren’t attached to it. Instead there’s a common “pool of implications”. Different hypotheses take different parts of “implications”.
Conservation of implications: if implications of a hypothesis are simple enough, they remain true/likely even if the hypothesis is wrong. You can shift the implications to a different hypothesis, but you’re very unlikely to completely dissolve them.
In usual rationality (hypotheses don’t share truth) you try to get the most accurate opinions about every single thing in the world. You’re “greedy”. But in this approach (hypotheses do share truth) it doesn’t matter how wrong you are about everything unless you’re right about “the most important thing”. But once you’re proven right about “the most important thing”, you know everything. A billion wrongs can make a right. Because any wrong opinion is correlated with the ultimate true opinion, the pool of the entire truth.
You can’t prove a hypothesis to be “too bad” because it would harm all other hypotheses. Because all hypotheses are correlated, created by each other. When you keep proving something wrong the harm to other hypotheses grows exponentially.
Motivated reasoning is valid: truth of a hypothesis depends on context, on the range of interests you choose. Your choice affects the truth.
Any theory is the best (or even “the only one possible”) on its level of reality. For example, on a certain level of reality modern physics doesn’t explain weather better than gods of weather.
In a way it means that specific hypotheses/beliefs just don’t exist, they’re melted into a single landscape. It may sound insane (“everything is true at the same time and never proven wrong” and also relative!). But human language, emotions, learning, pattern-matching and research programs often work like this. It’s just a consequence of ideas (1) not being atomic statements about the world and (2) not being focused on causal reasoning, causal modeling. And it’s rational to not start with atomic predictions when you don’t have enough evidence to locate atomic hypotheses.
Causal rationality, Descriptive rationality
You can split rationality into 2 components. The second component isn’t explored. My idea describes the second component:
Causal rationality. Focused on atomic independent hypotheses about the world. On causal explanations, causal models. Answers “WHY this happens?”. Goal: to describe a specific reality in terms of outcomes.
Descriptive rationality. Focused on fuzzy and correlated hypotheses about the world. On patterns and analogies. Answers “HOW this happens?”. Goal: to describe all possible (and impossible) realities in terms of each other.
Causal and Descriptive rationality work according to different rules. Causal uses Bayesian updating. Descriptive uses “the common pool of properties + Bayesian updating”, maybe.
“Map is not the territory” is true for Causal rationality. It’s wrong for Descriptive rationality: every map is a layer of reality.
“Uncertainty and confusion is a part of the map, not the territory”. True for Causal rationality. Wrong for Descriptive rationality: the possibility of an uncertainty/confusion is a property of reality.
“Details make something less likely, not more” (Conjunction fallacy). True for Causal rationality. Wrong for Descriptive rationality: details are not true or false by themselves, they “host” kernels of truth, more details may accumulate more truth.
For Causal rationality, math is the ideal of specificity. For Descriptive rationality, math has nothing to do with specificity: an idea may have different specificity on different layers of reality.
In Causal rationality, hypotheses should constrain outcomes, shouldn’t explain any possible outcome. In Descriptive rationality… constraining depends on context.
Causal rationality often conflicts with people. Descriptive rationality tries to minimize the conflict. I believe it’s closer to how humans think.
Causal rationality assumes that describing reality is trivial and should be abandoned as soon as possible. Only (new) predictions matter.
In Descriptive rationality, a hypothesis is somewhat equivalent to the explained phenomenon. You can’t destroy a hypothesis too much without destroying your knowledge about the phenomenon itself. It’s like hitting a nail so hard that you destroy the Earth.
Example:Vitalism. It was proven wrong in causal terms. But in descriptive terms it’s almost entirely true. Living matter does behave very differently from non-living matter. Living matter does have a “force” that non-living matter doesn’t have (it’s just not a fundamental force). Many truths of vitalism were simply split into different branches of science: living matter is made out of special components (biology/microbiology) including nanomachines/computers!!! (DNA, genetics), can have cognition (psychology/neuroscience), can be a computer (computer science), can evolve (evolutionary biology), can do something like “decreasing entropy” (an idea by Erwin Schrödinger, see entropy and life). On the other hand, maybe it’s bad that vitalism got split into so many different pieces. Maybe it’s bad that vitalism failed to predict reductionism. However, behaviorism did get overshadowed by cognitive science (living matter did turn out to be more special than it could be). Our judgement of vitalism depends on our choices, but at worst vitalism is just the second best idea. Or the third best idea compared to some other version of itself… Absolute death of vitalism is astronomically unlikely and it would cause most of reductionism and causality to die too along with most of our knowledge about the world. Vitalism partially just restates our knowledge (“living matter is different from non-living”), so it’s strange to simply call it wrong. It’s easier to make vitalism better than to disprove it.
Perhaps you could call the old version of vitalism “too specific given the information about the world”: why should “life-like force” be beyond laws of physics? But even this would be debatable at the time. By the way, the old sentiment “Science is too weak to explain living things” can be considered partially confirmed: 19th century science lacked a bunch of conceptual breakthroughs. And “only organisms can make the components of living things” is partially just a fact of reality: skin and meat don’t randomly appear in nature. This fact was partially weakened, but also partially strengthened with time. The discovery of DNA strengthened it in some ways. It’s easy to overlook all of those things.
In Descriptive rationality, an idea is like a river. You can split it, but you can’t stop it. And it doesn’t make sense to fight the river with your fists: just let it flow around you. However, if you did manage to split the river into independent atoms, you get Causal rationality.
2 types of rationality should be connected
I think causal rationality has some problems and those problems show that it has a missing component:
Rationality is criticized for dealing with atomic hypotheses about the world. For not saying how to generate new hypotheses and obtain new knowledge. Example: critique by nostalgebraist. See “8. The problem of new ideas”
You can’t use causal rationality to be critical of causal rationality. In theory you should be able to do it, but in practice people often don’t do it. And causal rationality doesn’t model argumentation, even for the most important topics such as AI safety. So we end up arguing like anyone argues.
Doomsday argument, Pascal’s mugging. Probability starts to behave weird when we add large numbers of (irrelevant) things to our world.
The problem of modesty. Should you assume that you’re just an average person?
Causal rationality doesn’t give/justify an ethical theory. Doesn’t say how to find it if you want to find it.
Causal rationality doesn’t give/justify a decision theory. There’s a problem with logical uncertainty (uncertainty about implications of beliefs).
I’m not saying that all of this is impossible to solve with Causal rationality. I’m saying that Causal rationality doesn’t give any motivation to solve all of this. When you’re trying to solve it without motivation you kind of don’t know what you’re doing. It’s like trying to write a program in bytecode without having high-level concepts even in your mind. Or like trying to ride an alien device in the dark: you don’t know what you’re doing and you don’t know where you’re doing.
What and where are we doing when we’re trying to fix rationality?
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.
For some time I wanted to apply the idea of probabilistic thinking (used for predicting things) to describing things, making analogies between things. This is important because your hypotheses (predictions) depend on the way you see the world. If you could combine predicting and describing into a single process, you would unify cognition.
Fuzzy logic and fuzzy sets is one way to do it. The idea is that something can be partially true (e.g. “humans are ethical” is somewhat true) or partially belong to a class (e.g. a dog is somewhat like a human, but not 100%). Note that “fuzzy” and “probable” are different concepts. But fuzzy logic isn’t enough to unify predicting and describing. Because it doesn’t tell us much about how we should/could describe the world. No new ideas.
I have a different principle for unifying probability and description. Here it is:
Properties of objects aren’t contained in specific objects. Instead, there’s a common pool that contains all possible properties. Objects take their properties from this pool. But the pool isn’t infinite. If one object takes 80% of a certain property from the pool, other objects can take only 20% of that property (e.g. “height”). Socialism for properties: it’s not your “height”, it’s our “height”.
How can an object “take away” properties of other objects? For example, how can a tall object “steal” height from other objects? Well, imagine there are multiple interpretations of each object. Interpretation of one object affects interpretation of all other objects. It’s just a weird axiom. Like a Non-Euclidean geometry.
This sounds strange, but this connects probability and description. And this is new. I think this principle can be used in classification and argumentation. Before showing how to use it I want to explain it a little bit more with some analogies.
Connected houses
Imagine two houses, A and B. Those houses are connected in a specific way.
When one house turns on the light at 80%, the other turns on the light only at 20%.
When one house uses 60% of the heat, the other uses only 40% of the heat.
(When one house turns on the red light, the other turns on the blue light. When one house is burning, the other is freezing.)
Those houses take electricity and heat from a common pool. And this pool doesn’t have infinite energy.
Kindness
Usually people think about qualities as something binary: you either has it or not. For example, a person can be either kind or not.
For me an abstract property such as “kindness” is like the white light. Different people have different colors of “kindness” (blue kindness, green kindness...). Every person has kindness of some color. But nobody has all colors of kindness.
Abstract kindness is the common pool (of all ways to express it). Different people take different parts of that pool.
Some more analogies
Theism analogy. You can compare the common pool of properties to the “God object”, a perfect object. All other objects are just different parts of the perfect object. You also can check out Monadology by Gottfried Leibniz.
Spectrum analogy. You can compare the common pool of properties to the spectrum of colors. Objects are just colors of a single spectrum.
Ethics analogy. Imagine that all your good qualities also belong (to a degree) to all other people. And all bad qualities of other people also belong (to a degree) to you. As if people take their qualities from a single common pool.
Buddhism analogy. Imagine that all your desires and urges come (to a degree) from all other people. And desires and urges of all other people come (to a degree) from you. There’s a single common pool of desire. This is somewhat similar to karma. In rationality there’s also a concept of “values handshakes”: when different beings decide to share each other’s values.
Quantum analogy. See quantum entanglement. When particles become entangled, they take their properties from a single common pool (quantum state).
Fractal analogy. “All objects in the Universe are just different versions of a single object.”
Subdivision analogy. Check out Finite subdivision rule. You can compare the initial polygone to the common pool of properties. And different objects are just pieces of that polygone.
Connection with recursion
Recursion. If objects take their properties from the common pool, it means they don’t really have (separate) identities. It also means that a property (X) of an object is described in terms of all other objects. So, the property (X) is recursive, it calls itself to define itself.
For example, imagine we have objects A, B and C. We want to know their heights. In order to do this we may need to evaluate those functions:
A(height), B(height), C(height)
A(B(height)), A(C(height)) …
A(B(C(height))), A(C(B(height))) …
A priori assumptions about objects should allow us to simplify this and avoid cycles.
Fractals. See Coastline paradox. You can treat a fractal as an object with multiple interpretations (where an interpretation depends on the scale). Objects taking their properties from the common pool = fractals taking different scales from the common range.
Classification
To explain how to classify objects using my principle, I need to explain how to order them with it.
I’ll explain it using fantastical places and videogame levels, because those things are formal and objective enough (they are 3D shapes). But I believe the same classification method can be applied to any objects, concepts and even experiences.
Basically, this is an unusual model of contextual thinking. If we can formalize this specific type of contextual thinking, then maybe we can formalize contextual thinking in general. This topic will sound very esoteric, but it’s the direct application of the principle explained above.
Intro
(I interpret paintings as “real places”: something that can be modeled as a 3D shape. If a painting is surreal, I simplify it a bit in my mind.)
Take a look at those places: image.
Let’s compare 2 of them: image. Let’s say we want to know the “height” of those places. We don’t have a universal scale to compare the places. Different interpretations of the height are possible.
If we’re calling a place “very tall”—we need to understand the epithet “very tall” in probabilistic terms, such as “70-90% tall”—and we need to imagine that this probability is taken away from all other places. We can’t have two different “very tall” places. Probability should add up to 100%.
Now take a look at another place (A): image (I ignore the cosmos to simplify it). Let’s say we want to know how enclosed it is. In one interpretation, it is massively enclosed by trees. In another interpretation, trees are just a decorative detail and can be ignored. Let’s add some more places for context: image. They are definitely more open than the initial place, so we should update towards more enclosed interpretation of (A). All interpretations should be correlated and “compatible”. It’s as if we’re solving a puzzle.
You can say that properties of places are “expandable”. Any place contains a seed of any possible property and that seed can be expanded by a context. “Very tall place” may mean Mt. Everest or a molehill depending on context. You can compare it to a fractal: every small piece of a fractal can be expanded into the entire thing. And I think it’s also very similar to how human language, human concepts work.
You also may call it “amplification of evidence”: any smallest piece of evidence (or even absence of any evidence) can be expanded into very strong evidence by context. We have a situation like in the Raven paradox, but even worse.
Rob Gonsalves
(I interpret paintings as “real” places.)
Places in random order: image.
My ordering of places: image.
I used 2 metrics to evaluate the places:
Is the space of the place “box-like” and small or not?
Is the place enclosed or open?
The places go from “box-like and enclosed” to “not box-like and open” in my ordering.
But to see this you need to look at the places in a certain way, reason about them in a certain way:
Place 1 is smaller than it seems. Because Place 5 is similar and “takes away” its size.
Place 2 is more box-like than it seems. Because similar places 4 and 6 are less box-like.
Place 3 is more enclosed than it seems. Because similar places 4 and 6 “take away” its openness.
Place 5 is more open than it seems. Because similar places 1 and 2 “take away” its closedness.
Almost any property of any specific place can be “illusory”. But when you look at places in the context you can deduce their properties vie the process of elimination.
Argumentation, hypotheses
You can apply the same idea (about the “common pool”) to hypotheses and argumentation:
You can describe a hypothesis in terms of any other hypothesis. You also can simplify it along the way (let’s call it “regularization”). Recursion and circularity is possible in reasoning.
Truth isn’t attached to a specific hypothesis. Instead there’s a common “pool of truth”. Different hypotheses take different parts of the whole truth. The question isn’t “Is the hypothesis true?”, the question is “How true is the hypothesis compared to others?” And if the hypotheses are regularized it can’t be too wrong.
Alternatively: “implications” of a specific hypothesis aren’t attached to it. Instead there’s a common “pool of implications”. Different hypotheses take different parts of “implications”.
Conservation of implications: if implications of a hypothesis are simple enough, they remain true/likely even if the hypothesis is wrong. You can shift the implications to a different hypothesis, but you’re very unlikely to completely dissolve them.
In usual rationality (hypotheses don’t share truth) you try to get the most accurate opinions about every single thing in the world. You’re “greedy”. But in this approach (hypotheses do share truth) it doesn’t matter how wrong you are about everything unless you’re right about “the most important thing”. But once you’re proven right about “the most important thing”, you know everything. A billion wrongs can make a right. Because any wrong opinion is correlated with the ultimate true opinion, the pool of the entire truth.
You can’t prove a hypothesis to be “too bad” because it would harm all other hypotheses. Because all hypotheses are correlated, created by each other. When you keep proving something wrong the harm to other hypotheses grows exponentially.
Motivated reasoning is valid: truth of a hypothesis depends on context, on the range of interests you choose. Your choice affects the truth.
Any theory is the best (or even “the only one possible”) on its level of reality. For example, on a certain level of reality modern physics doesn’t explain weather better than gods of weather.
In a way it means that specific hypotheses/beliefs just don’t exist, they’re melted into a single landscape. It may sound insane (“everything is true at the same time and never proven wrong” and also relative!). But human language, emotions, learning, pattern-matching and research programs often work like this. It’s just a consequence of ideas (1) not being atomic statements about the world and (2) not being focused on causal reasoning, causal modeling. And it’s rational to not start with atomic predictions when you don’t have enough evidence to locate atomic hypotheses.
Causal rationality, Descriptive rationality
You can split rationality into 2 components. The second component isn’t explored. My idea describes the second component:
Causal rationality. Focused on atomic independent hypotheses about the world. On causal explanations, causal models. Answers “WHY this happens?”. Goal: to describe a specific reality in terms of outcomes.
Descriptive rationality. Focused on fuzzy and correlated hypotheses about the world. On patterns and analogies. Answers “HOW this happens?”. Goal: to describe all possible (and impossible) realities in terms of each other.
Causal and Descriptive rationality work according to different rules. Causal uses Bayesian updating. Descriptive uses “the common pool of properties + Bayesian updating”, maybe.
“Map is not the territory” is true for Causal rationality. It’s wrong for Descriptive rationality: every map is a layer of reality.
“Uncertainty and confusion is a part of the map, not the territory”. True for Causal rationality. Wrong for Descriptive rationality: the possibility of an uncertainty/confusion is a property of reality.
“Details make something less likely, not more” (Conjunction fallacy). True for Causal rationality. Wrong for Descriptive rationality: details are not true or false by themselves, they “host” kernels of truth, more details may accumulate more truth.
For Causal rationality, math is the ideal of specificity. For Descriptive rationality, math has nothing to do with specificity: an idea may have different specificity on different layers of reality.
In Causal rationality, hypotheses should constrain outcomes, shouldn’t explain any possible outcome. In Descriptive rationality… constraining depends on context.
Causal rationality often conflicts with people. Descriptive rationality tries to minimize the conflict. I believe it’s closer to how humans think.
Causal rationality assumes that describing reality is trivial and should be abandoned as soon as possible. Only (new) predictions matter.
In Descriptive rationality, a hypothesis is somewhat equivalent to the explained phenomenon. You can’t destroy a hypothesis too much without destroying your knowledge about the phenomenon itself. It’s like hitting a nail so hard that you destroy the Earth.
Example: Vitalism. It was proven wrong in causal terms. But in descriptive terms it’s almost entirely true. Living matter does behave very differently from non-living matter. Living matter does have a “force” that non-living matter doesn’t have (it’s just not a fundamental force). Many truths of vitalism were simply split into different branches of science: living matter is made out of special components (biology/microbiology) including nanomachines/computers!!! (DNA, genetics), can have cognition (psychology/neuroscience), can be a computer (computer science), can evolve (evolutionary biology), can do something like “decreasing entropy” (an idea by Erwin Schrödinger, see entropy and life). On the other hand, maybe it’s bad that vitalism got split into so many different pieces. Maybe it’s bad that vitalism failed to predict reductionism. However, behaviorism did get overshadowed by cognitive science (living matter did turn out to be more special than it could be). Our judgement of vitalism depends on our choices, but at worst vitalism is just the second best idea. Or the third best idea compared to some other version of itself… Absolute death of vitalism is astronomically unlikely and it would cause most of reductionism and causality to die too along with most of our knowledge about the world. Vitalism partially just restates our knowledge (“living matter is different from non-living”), so it’s strange to simply call it wrong. It’s easier to make vitalism better than to disprove it.
Perhaps you could call the old version of vitalism “too specific given the information about the world”: why should “life-like force” be beyond laws of physics? But even this would be debatable at the time. By the way, the old sentiment “Science is too weak to explain living things” can be considered partially confirmed: 19th century science lacked a bunch of conceptual breakthroughs. And “only organisms can make the components of living things” is partially just a fact of reality: skin and meat don’t randomly appear in nature. This fact was partially weakened, but also partially strengthened with time. The discovery of DNA strengthened it in some ways. It’s easy to overlook all of those things.
In Descriptive rationality, an idea is like a river. You can split it, but you can’t stop it. And it doesn’t make sense to fight the river with your fists: just let it flow around you. However, if you did manage to split the river into independent atoms, you get Causal rationality.
2 types of rationality should be connected
I think causal rationality has some problems and those problems show that it has a missing component:
Rationality is criticized for dealing with atomic hypotheses about the world. For not saying how to generate new hypotheses and obtain new knowledge. Example: critique by nostalgebraist. See “8. The problem of new ideas”
You can’t use causal rationality to be critical of causal rationality. In theory you should be able to do it, but in practice people often don’t do it. And causal rationality doesn’t model argumentation, even for the most important topics such as AI safety. So we end up arguing like anyone argues.
Doomsday argument, Pascal’s mugging. Probability starts to behave weird when we add large numbers of (irrelevant) things to our world.
The problem of modesty. Should you assume that you’re just an average person?
Weird addition in ethics. Repugnant conclusion, “Torture vs. Dust Specks”.
Causal rationality doesn’t give/justify an ethical theory. Doesn’t say how to find it if you want to find it.
Causal rationality doesn’t give/justify a decision theory. There’s a problem with logical uncertainty (uncertainty about implications of beliefs).
I’m not saying that all of this is impossible to solve with Causal rationality. I’m saying that Causal rationality doesn’t give any motivation to solve all of this. When you’re trying to solve it without motivation you kind of don’t know what you’re doing. It’s like trying to write a program in bytecode without having high-level concepts even in your mind. Or like trying to ride an alien device in the dark: you don’t know what you’re doing and you don’t know where you’re doing.
What and where are we doing when we’re trying to fix rationality?
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.