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While it is correct, this oversimplifies the point. The finding was that certain wheather patterns can be modelled better than before by using a quantum physics

While it is correct, this oversimplifies the point. The finding was that certain wheather patterns can be modelled better than before by using a quantum physics equation. To further the point: The model of this quantum physics equation is also useful for quantum computers built with superconducting materials. Underlying is the question though, why does this equation apply to the earths wheather? There seem to be parallels in the quantum and "macro" model, like windings of electron and wheather currents. Maybe the right view to modeling the earth is about dynamics as much as it is about topoligical phenomenons. After all, topology is used for solving gravitational problems, too. Then why can the earth can be treated as a topoligical insulator and what implications does this have? Can we learn something from it that can be applied to other wheather phenomenons? Or maybe even to the earths core?

MikePlacid 3y ago
> why can the earth can be treated as a topoligical insulator I am missing something here. Topology is a field of mathematics that studies the properties of objects that do not change under continuous deformations. So before asking why can Earth be treated as a topological something - one should specify what topology he is looking at, that is what continuous deformations of Earth he is talking about. So - what continuous deformations of Earth are you talking about?
- deleted 3y ago
  [deleted]
- zornthewise 3y ago
  [dead]
- kergonath 3y ago
  That’s a culture difference issue. A topological insulator is a kind of material with specific properties (heavily simplified, that its inside is an electric insulator and its surface is an electric conductor). That’s where the topological aspect comes from. It has nothing to do with topology in mathematics except the name.
  - staunton 3y ago
    > It has nothing to do with topology in mathematics except the name. Well, the description of a topological insulator does use a tiny bit of topology.
  - gmadsen 3y ago
    that is simply not true. They are classified by their topological invariants, which affects their properties.
  - civilitty 3y ago
    The topological aspect, very much in the mathematical sense, is that the insulator maintains those properties even when deformed. So when you cut a topological insulator in half to expose the non-conducting inside, that exposed surface becomes conducting again.
    - MikePlacid 3y ago
      That makes me confused even more. Isn’t cutting a non - continuous deformation, that breaks topology?
- gmadsen 3y ago
  based on the article, they are representing weather patterns on earths surface as a topological insulator. I don't know which class of insulator, but the catagorization of all topological insulators have equivalent classifying spaces of Hamiltonians. Which give you the invariants that you are asking about for deformations of H1 to H2.
  - MikePlacid 3y ago
    That makes sense to me, but - neither H1 nor H2 is Earth, they are Hamiltonian spaces. And the statement that puzzles me is: “the Earth can be treated as a topological insulator”. So… I remain puzzled ((
kergonath 3y ago
That’s a whole lot of fancy words. The core is that they used a fancy wave equation. In that context, the topological insulator is an inspiration rather than an exact and accurate model. It’s similar to the layman view of an atom as a miniature solar system. There are some similarities, but also very significant differences and not all knowledge is transferable from one to the other. It is not particularly surprising that we would find new solutions to Navier-Stokes equation applied at the level of a whole planet, these things are very complex and far from completely understood. > Then why can the earth can be treated as a topoligical insulator and what implications does this have? That’s jumping to conclusions a bit. Again, they have found similarities in atmospheric flows and magnetic currents in topological insulators. It does not mean that the Earth is one, or that all properties of topological insulators also applies to the Earth. > Or maybe even to the earths core? There is bound to be some similarities, as with any fluid flow (assuming we’re not talking about the solid inner core). There are also significant differences in things like viscosity, compressibility, etc. So yeah, that’s a possibility, but as in the atmosphere, that would not make the outer core a particularly quantum object.
danbruc 3y ago
The finding was that certain wheather patterns can be modelled better than before by using a quantum physics equation. I think this is the wrong way of looking at this, quantum physics does not really have anything to do with this. Both systems, the oceans and topological insulators, share some of their structure and dynamics which means that the same mathematical models can be used to describe some aspects of both systems. Large groups of people or animals can, to a certain extend, be described with fluid dynamics equations as they have some common structure, i.e. being composed of many particles interacting with each other locally. But the link is not from fluids to groups of people or the other way around, the link is a similar structure underlying both systems which makes mathematical models transferable between the two.

MikePlacid 3y ago

> why can the earth can be treated as a topoligical insulator I am missing something here. Topology is a field of mathematics that studies the properties of objects that do not change under continuous deformations. So before asking why can Earth be treated as a topological something - one should specify what topology he is looking at, that is what continuous deformations of Earth he is talking about. So - what continuous deformations of Earth are you talking about?

deleted 3y ago
[deleted]
zornthewise 3y ago
[dead]
kergonath 3y ago
That’s a culture difference issue. A topological insulator is a kind of material with specific properties (heavily simplified, that its inside is an electric insulator and its surface is an electric conductor). That’s where the topological aspect comes from. It has nothing to do with topology in mathematics except the name.
- staunton 3y ago
  > It has nothing to do with topology in mathematics except the name. Well, the description of a topological insulator does use a tiny bit of topology.
- gmadsen 3y ago
  that is simply not true. They are classified by their topological invariants, which affects their properties.
- civilitty 3y ago
  The topological aspect, very much in the mathematical sense, is that the insulator maintains those properties even when deformed. So when you cut a topological insulator in half to expose the non-conducting inside, that exposed surface becomes conducting again.
  - MikePlacid 3y ago
    That makes me confused even more. Isn’t cutting a non - continuous deformation, that breaks topology?
gmadsen 3y ago
based on the article, they are representing weather patterns on earths surface as a topological insulator. I don't know which class of insulator, but the catagorization of all topological insulators have equivalent classifying spaces of Hamiltonians. Which give you the invariants that you are asking about for deformations of H1 to H2.
- MikePlacid 3y ago
  That makes sense to me, but - neither H1 nor H2 is Earth, they are Hamiltonian spaces. And the statement that puzzles me is: “the Earth can be treated as a topological insulator”. So… I remain puzzled ((

kergonath 3y ago

That’s a whole lot of fancy words. The core is that they used a fancy wave equation. In that context, the topological insulator is an inspiration rather than an exact and accurate model. It’s similar to the layman view of an atom as a miniature solar system. There are some similarities, but also very significant differences and not all knowledge is transferable from one to the other. It is not particularly surprising that we would find new solutions to Navier-Stokes equation applied at the level of a whole planet, these things are very complex and far from completely understood. > Then why can the earth can be treated as a topoligical insulator and what implications does this have? That’s jumping to conclusions a bit. Again, they have found similarities in atmospheric flows and magnetic currents in topological insulators. It does not mean that the Earth is one, or that all properties of topological insulators also applies to the Earth. > Or maybe even to the earths core? There is bound to be some similarities, as with any fluid flow (assuming we’re not talking about the solid inner core). There are also significant differences in things like viscosity, compressibility, etc. So yeah, that’s a possibility, but as in the atmosphere, that would not make the outer core a particularly quantum object.

danbruc 3y ago

The finding was that certain wheather patterns can be modelled better than before by using a quantum physics equation. I think this is the wrong way of looking at this, quantum physics does not really have anything to do with this. Both systems, the oceans and topological insulators, share some of their structure and dynamics which means that the same mathematical models can be used to describe some aspects of both systems. Large groups of people or animals can, to a certain extend, be described with fluid dynamics equations as they have some common structure, i.e. being composed of many particles interacting with each other locally. But the link is not from fluids to groups of people or the other way around, the link is a similar structure underlying both systems which makes mathematical models transferable between the two.