3 ms·

I don't see what math's Turing-completeness has to do with models describing physical system. It means that math can describe whatever model is most accurate,

I don't see what math's Turing-completeness has to do with models describing physical system. It means that math can describe whatever model is most accurate, but it can also describe plenty of unphysical models. If you want explanations and not formulas, I'm not sure math or physics will help. They are both famously bad at explaining why, beyond "if it were different you would not be able to ask the question".

poelzi 11y ago
This is a problem of mathematical logic that is used in QM. In a classical logical system, you can't do this. You can only use formulas that have a real relation in nature and not invent something out of the blue and use it for substitution. You can describe any physical implementation with any mathematical as long as you use enough dimensions. Fact is: we are living in a 3 dimensional euclidean space, this you can experience every day. Time is some other thing. The need for 12 dimensions is just a absurd mathematical emergency exit for having something fundamentally wrong.
- monknomo 11y ago
  Time is some other thing? It isn't a dimension? How do you do Newtonian physics like that? As far as extra dimensions being a crutch, I must disagree. Take 6-axis mills for instance. To accurately describe the position of the tool you need six dimensions. That doesn't mean they are particularly strange or wrong, just that they are a little complicated. By the same token, if we invented a system of analyzing pirouetting ballerinas, it would be useful to have not only the normal 3 euclidian dimensions and time, but perhaps to have a spin dimension so we can compactly describe the ballerina's direction of spin.
  - poelzi 11y ago
    Of course you can do a integral over time for example, but you logically understand in the process that its only a virtual dimension in this case, not a real euclidean one. Your spin 'dimensions' still reside in 3 euclidean dimensions but for technical reasons you implement those vectors as an axis. Don't get me wrong, sometimes its useful to add a virtual dimension in the mathematical sense to get a shortcut in calculation, but it should be clear that those are not real ones. One the level of physical implementation, everything requiring more then 3 looks unlikely.

poelzi 11y ago

This is a problem of mathematical logic that is used in QM. In a classical logical system, you can't do this. You can only use formulas that have a real relation in nature and not invent something out of the blue and use it for substitution. You can describe any physical implementation with any mathematical as long as you use enough dimensions. Fact is: we are living in a 3 dimensional euclidean space, this you can experience every day. Time is some other thing. The need for 12 dimensions is just a absurd mathematical emergency exit for having something fundamentally wrong.

monknomo 11y ago
Time is some other thing? It isn't a dimension? How do you do Newtonian physics like that? As far as extra dimensions being a crutch, I must disagree. Take 6-axis mills for instance. To accurately describe the position of the tool you need six dimensions. That doesn't mean they are particularly strange or wrong, just that they are a little complicated. By the same token, if we invented a system of analyzing pirouetting ballerinas, it would be useful to have not only the normal 3 euclidian dimensions and time, but perhaps to have a spin dimension so we can compactly describe the ballerina's direction of spin.
- poelzi 11y ago
  Of course you can do a integral over time for example, but you logically understand in the process that its only a virtual dimension in this case, not a real euclidean one. Your spin 'dimensions' still reside in 3 euclidean dimensions but for technical reasons you implement those vectors as an axis. Don't get me wrong, sometimes its useful to add a virtual dimension in the mathematical sense to get a shortcut in calculation, but it should be clear that those are not real ones. One the level of physical implementation, everything requiring more then 3 looks unlikely.