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| The new economic growth theory uses a completely different approach than usual in classical growth theory of economics. Instead of mainly statistical analyzes combined with suggested functions from that, hear will appear fundamental analytical principles as applied on a regular basis in physics and technical engineering. Your question but will be //„why should I, after I've spent years studying very different methods, I now charge me even with this weird stuff?“//. For this in the economy not previously used mathematical methods require a lot of work to do for you. Why would you do that? May be it is just another of these goony growth-theories that since decades then only proved one thing: That the didn't work reliable. Especially they were not able to predict the financial crisis. | The new economic growth theory uses a completely different approach than usual in classical growth theory of economics. Instead of mainly statistical analyzes combined with suggested functions from that, hear will appear fundamental analytical principles as applied on a regular basis in physics and technical engineering. Your question but will be //„why should I, after I've spent years studying very different methods, I now charge me even with this weird stuff?“//. For this in the economy not previously used mathematical methods require a lot of work to do for you. Why would you do that? May be it is just another of these goony growth-theories that since decades then only proved one thing: That the didn't work reliable. Especially they were not able to predict the financial crisis. | ||
| - | Well, to understand what the method of variational calculus is //(which is described in the second part of the book)//, we should first say some words about those gadgets, which are called a //(mathematical)// model. A //“model”// is in principle any realization of the world, regardless of beeing philosophical or mathematical. Even religion is a special model of the world. Visa versa to this extreme, mathematical modeling is more closely related to measurable reality. A good model should at least reproduce measurable values of reality in, at least approximate, good quality and as an essential addition should be able to predict the behavior of the modeled system into the future reliable. Theoretical physics here is an astonishing exemption: It demands absolute equality between theoretical and measured values and exact predictions of its models as well. Even the smallest derivations between the model, which means in this case theory, and reality is not accepted. | + | ---- |
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| + | To understand what the method of variational calculus is //(which is described in the second part of the book)//, we should first say some words about those gadgets, which are called a //(mathematical)// model. A //“model”// is in principle any realization of the world, regardless of beeing philosophical or mathematical. Even religion is a special model of the world. Visa versa to this extreme, mathematical modeling is more closely related to measurable reality. A good model should at least reproduce measurable values of reality in, at least approximate, good quality and as an essential addition should be able to predict the behavior of the modeled system into the future reliable. Theoretical physics here is an astonishing exemption: It demands absolute equality between theoretical and measured values and exact predictions of its models as well. Even the smallest derivations between the model, which means in this case theory, and reality is not accepted. | ||
| In fact, the astonishing exactness of mathematical modeling in physics, today requires the most sophisticated and giant measuring equipment //**(1)**// ever build by mankind to search for any leftover inexactness. Indeed it is a philosophical very interesting question for theoretical physics too, why such mathematical theories can have such a weird exactness in reality. As much as we know today, it seems to be an absolute parity. At least for all the fundamental field theories of physical science, as for example gravity, electromagnetism and quantum dynamics. | In fact, the astonishing exactness of mathematical modeling in physics, today requires the most sophisticated and giant measuring equipment //**(1)**// ever build by mankind to search for any leftover inexactness. Indeed it is a philosophical very interesting question for theoretical physics too, why such mathematical theories can have such a weird exactness in reality. As much as we know today, it seems to be an absolute parity. At least for all the fundamental field theories of physical science, as for example gravity, electromagnetism and quantum dynamics. | ||
| - | Well, the clue is always to find the underlying field theory of a living system to get solutions of its temporal evolution //(“equation of motion”)//. The most fundamental laws to find such solutions were introduced in 1918 by Noether's theorems. They are the generalization of Euler-Lagrange algorithm of variational calculus. It could be shown that any field theory depends just on the underlying symmetries or invariants in the system under examination. So its also called the theory of invariants. The //“trick”// is just to find the main symmetries //(which is mostly synonymic for invariants)// of the system, and then you are able to find the distinct equations of motions of the system. And as a spin-off of the logics of mathematics, such solutions are distinct and unambiguous. | + | The clue is always to find the underlying field theory of a living system to get solutions of its temporal evolution //(“equation of motion”)//. The most fundamental laws to find such solutions were introduced in 1918 by Noether's theorems. They are the generalization of Euler-Lagrange algorithm of variational calculus. It could be shown that any field theory depends just on the underlying symmetries or invariants in the system under examination. So its also called the theory of invariants. The //“trick”// is just to find the main symmetries //(which is mostly synonymic for invariants)// of the system, and then you are able to find the distinct equations of motions of the system. And as a spin-off of the logics of mathematics, such solutions are distinct and unambiguous. |
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| As we will show in the second part of the book, the most fundamental symmetry of economics is the since centuries known quantity equation //MV=HP//. The further generalization of this dependency then leads to the fundamental equations of economics. Indeed the only required condition for the full theory is the validity of the generalized quantity equation //MV=HP//. Nothing else, and the solution, which is presented in its most simplified and linearized version in the first part of the book is indeed distinct //**(2)**//. | As we will show in the second part of the book, the most fundamental symmetry of economics is the since centuries known quantity equation //MV=HP//. The further generalization of this dependency then leads to the fundamental equations of economics. Indeed the only required condition for the full theory is the validity of the generalized quantity equation //MV=HP//. Nothing else, and the solution, which is presented in its most simplified and linearized version in the first part of the book is indeed distinct //**(2)**//. | ||