The analogy between physical crystallization and the process of forming a knowledge structure is excellent, but it shouldn’t be overstated. Experimental data show how much entropy actually decreases during the crystallization of substances, and it’s not as dramatic as you suggest—for example, for gold ΔS ≈ 9.3 J/(mol·K) at a melting temperature of 1337 K, and there are even lower values. For liquid ³He, it is actually negative! In this case, the liquid is more ordered than the solid.
It is important to give the correct definition of a crystal: a crystal is a state of matter exhibiting long-range order, in addition to the short-range order already present in the liquid and absent in the gas. In an infinite ideal crystal, long-range order is usually understood as translational symmetry along a lattice vector. I don’t think one can draw such a simple analogy to knowledge structures.
The crystal analogy overlooks the fact that it obeys the law of mass conservation—a crystal grows at the expense of a solution or by dissolving another smaller crystal.
If we consider the structural units of a crystal as facts, knowledge as the result of crystallizing facts, an elementary act of cognition as docking a fact into the crystalline structure of knowledge, and rethinking as transferring a fact from one microcrystal to another, then why can’t I embed the same fact into different knowledge systems? This is called doublethink, and I can do it easily.
I will admit to not being the most well-versed in crystals so that might be true. I’m wondering if there’s some sort of thing where you can think about a specific ontology of the world as one structure and another ontology as another structure?
For example, we know that there are incompatible world views in the world and an easy example is politics. The ground state of news is the same (enthropic solution) and the view that you pick up of that base state is going to be different dependent on how you process it?
Processing information is therefore kind of taking a soup of information and crystallizing it?
I like to think about utility functions and these crystalline surfaces and stuff as interpretaive frames. I think it is within chapter 6 of Godel Escher Bach that he talks about a jukebox and how it only knows how to play a specific disc by being preprogrammed with a tape reader. I think these crystals are the same and that it is some sort of combination of value function and ontology that creates a way of thinking.It is a way of interpreting information that comes in and it can only be shown through the specific type of crystalline structure that appears?
I think there’s something interesting here from an information theory perspective but I might just be overinterpreting and analogising a connection that isn’t there.
There is a rational idea in your analogy—the idea of knowledge crystallizing simultaneously around several centers of growth can be illustrated with a quite viable example of a child living in a totalitarian state and having a loving father. As the child accumulates knowledge, they understand how their father is an example of an intelligent and purposeful person for them, while the totalitarian state persecutes dissidents by sending them to concentration camps, and this knowledge crystallizes around two different centers, until the child learns that their father is the commandant of one of such camps. What kind of remelting can align the child’s knowledge in this situation? It might seem that the problem is about growing up, but for example, religious dogmas and geocentrism also once collided with astronomical observations and the laws of planetary motion. I remember they even burned someone at the stake there. But when we studied this in Soviet school, everything was calibrated down to the smallest detail—the church was an example of obscurantism, while astronomy shed true light on the state of things in the universe. Therefore, this is not a problem of teaching at all, but a problem of curriculum design.
I translated this into English using an LLM, so it might appear to be LLM-generated, therefore I’m warning you in advance.
The analogy between physical crystallization and the process of forming a knowledge structure is excellent, but it shouldn’t be overstated. Experimental data show how much entropy actually decreases during the crystallization of substances, and it’s not as dramatic as you suggest—for example, for gold ΔS ≈ 9.3 J/(mol·K) at a melting temperature of 1337 K, and there are even lower values. For liquid ³He, it is actually negative! In this case, the liquid is more ordered than the solid.
It is important to give the correct definition of a crystal: a crystal is a state of matter exhibiting long-range order, in addition to the short-range order already present in the liquid and absent in the gas. In an infinite ideal crystal, long-range order is usually understood as translational symmetry along a lattice vector. I don’t think one can draw such a simple analogy to knowledge structures.
The crystal analogy overlooks the fact that it obeys the law of mass conservation—a crystal grows at the expense of a solution or by dissolving another smaller crystal.
If we consider the structural units of a crystal as facts, knowledge as the result of crystallizing facts, an elementary act of cognition as docking a fact into the crystalline structure of knowledge, and rethinking as transferring a fact from one microcrystal to another, then why can’t I embed the same fact into different knowledge systems? This is called doublethink, and I can do it easily.
Interesting points!
I will admit to not being the most well-versed in crystals so that might be true. I’m wondering if there’s some sort of thing where you can think about a specific ontology of the world as one structure and another ontology as another structure?
For example, we know that there are incompatible world views in the world and an easy example is politics. The ground state of news is the same (enthropic solution) and the view that you pick up of that base state is going to be different dependent on how you process it?
Processing information is therefore kind of taking a soup of information and crystallizing it?
I like to think about utility functions and these crystalline surfaces and stuff as interpretaive frames. I think it is within chapter 6 of Godel Escher Bach that he talks about a jukebox and how it only knows how to play a specific disc by being preprogrammed with a tape reader. I think these crystals are the same and that it is some sort of combination of value function and ontology that creates a way of thinking.It is a way of interpreting information that comes in and it can only be shown through the specific type of crystalline structure that appears?
I think there’s something interesting here from an information theory perspective but I might just be overinterpreting and analogising a connection that isn’t there.
There is a rational idea in your analogy—the idea of knowledge crystallizing simultaneously around several centers of growth can be illustrated with a quite viable example of a child living in a totalitarian state and having a loving father. As the child accumulates knowledge, they understand how their father is an example of an intelligent and purposeful person for them, while the totalitarian state persecutes dissidents by sending them to concentration camps, and this knowledge crystallizes around two different centers, until the child learns that their father is the commandant of one of such camps. What kind of remelting can align the child’s knowledge in this situation? It might seem that the problem is about growing up, but for example, religious dogmas and geocentrism also once collided with astronomical observations and the laws of planetary motion.
I remember they even burned someone at the stake there. But when we studied this in Soviet school, everything was calibrated down to the smallest detail—the church was an example of obscurantism, while astronomy shed true light on the state of things in the universe. Therefore, this is not a problem of teaching at all, but a problem of curriculum design.
I translated this into English using an LLM, so it might appear to be LLM-generated, therefore I’m warning you in advance.