Since I have had great luck in being able to have my questions answered re my rifle problem I would like to throw this out.

This is my second time through, A MANY-COLORED GLASS, by Freeman Dyson, this week, so I know a thorough understanding of this concept is crucial to understanding this part of the book and I don't seem to be able to grasp it. The problem is one of pyysics and has to do with symetry breaking, going from a disordered state to an ordered state.

He writes: "Another name for the process of phase transition from disorder to order is symmetry breaking. From a mathematical point of view, a disordered phase has a higher degree of symmetry than an ordered phase. For example, the enviorment of a molecule of water dissolved in humid air is the same in all directions, while the envoronment of the same molecule after it is precipitated into a snowflake is a regular crystal with a crystalline axis oriented along particular directions. The molecule sees its environment change from the greater symmetry of a sphere to the lesser symmetry of the hexagonal prism. The change in the environment from disorder to order is associated with the sudden loss of symmetry. Sudden loss of symmetry is characteristic of many of the most important phase transitions in the history of the universe."

What I don't get is what does he mean when he says, "...from a mathematical point of view..."?

Also puzzling to me is, it seems like a hexagonal prism is more ordered than a water molecule. Water molecules aren't in a distinct shape, they change shape constantly. The hexagonal prism, the result of freezing the water molecule, on the other hand, is ridgid. So it seems to me that the hexagonal prism is more ordered than the water molecule.

At first I wondered if there was a misprint but writing subsequent to the above paragraph

follows the same logic. I don't get it.

I have been stumped before with things like this, that I don't understand, and attempts to help myself learn by following Google threads only serve to confuse me more. In order to understand these problems I generally need a basic explaination or an analogy to which I can relate.

Any help either in a direction of something to read or a basic explaination would be most certainly appreciated.

Thanks,

Tom

This is my second time through, A MANY-COLORED GLASS, by Freeman Dyson, this week, so I know a thorough understanding of this concept is crucial to understanding this part of the book and I don't seem to be able to grasp it. The problem is one of pyysics and has to do with symetry breaking, going from a disordered state to an ordered state.

He writes: "Another name for the process of phase transition from disorder to order is symmetry breaking. From a mathematical point of view, a disordered phase has a higher degree of symmetry than an ordered phase. For example, the enviorment of a molecule of water dissolved in humid air is the same in all directions, while the envoronment of the same molecule after it is precipitated into a snowflake is a regular crystal with a crystalline axis oriented along particular directions. The molecule sees its environment change from the greater symmetry of a sphere to the lesser symmetry of the hexagonal prism. The change in the environment from disorder to order is associated with the sudden loss of symmetry. Sudden loss of symmetry is characteristic of many of the most important phase transitions in the history of the universe."

What I don't get is what does he mean when he says, "...from a mathematical point of view..."?

Also puzzling to me is, it seems like a hexagonal prism is more ordered than a water molecule. Water molecules aren't in a distinct shape, they change shape constantly. The hexagonal prism, the result of freezing the water molecule, on the other hand, is ridgid. So it seems to me that the hexagonal prism is more ordered than the water molecule.

At first I wondered if there was a misprint but writing subsequent to the above paragraph

follows the same logic. I don't get it.

I have been stumped before with things like this, that I don't understand, and attempts to help myself learn by following Google threads only serve to confuse me more. In order to understand these problems I generally need a basic explaination or an analogy to which I can relate.

Any help either in a direction of something to read or a basic explaination would be most certainly appreciated.

Thanks,

Tom

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