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Physics has strict laws. But, hockey, also, has strict rules, yet many different games can be developed within those rules. Same thing in Physics. You are free to choose, arbitrary, by your feeling, by your human experience, the initial conditions for your Physics problem. Or, invention. That's completely arbitrary, can be called art, skills, talent, intuition, genius. Like, how high you want to put ball before you leave it to the gravitational forces. That initial height IS NOT dictated by laws of Physics. It is determined by you. But, once you leave the ball, the Physics law takes over, and their strictness has to be followed and be aware of. Hence, the creativity in Engineering is in determining the initial conditions. They are up to you. Then, and only then you use laws of Physics to obtain the next result. For instance, Physics Laws, or even Laws of Electromagnetics, will not tell you, nor will prevent you, to determine the shape, amplitude of voltages for your generators. If sinusoidal voltages suit you, chose them. If other voltage shape suits you, chose that shape. And only then, you use the laws of electrical circuits to find the system states, voltages, currents, energy within the circuit. Creativity in Engineering is in choosing correct, useful, desired initial conditions.
Similar thing is in hockey. The rules of hockey will not tell you how to win. The same way language grammar will not and can not tell you how to write a winning novel or screenplay. The rules of hockey are hockey axioms, and you use them to create instances of the game, within the rules framework. Each game is a set of theorem obtained from the initial hockey axioms, and proved by the way of arbitrary not interfering with the game.
In Physics, differential equations can not tell you how to construct a new machine or make an invention. Why? Because differential and integral equations are waiting for YOU to tell them their initial and boundary conditions, i.e. STARTING CONDITIONS, they are waiting for you to tell them what and when to calculate, in the form of integrand, integral limits, initial and boundary conditions.
Physics has strict laws. But, hockey, also, has strict rules, yet many different games can be developed within those rules. Same thing in Physics. You are free to choose, arbitrary, by your feeling, by your human experience, the initial conditions for your Physics problem. Or, invention. That's completely arbitrary, can be called art, skills, talent, intuition, genius. Like, how high you want to put ball before you leave it to the gravitational forces. That initial height IS NOT dictated by laws of Physics. It is determined by you. But, once you leave the ball, the Physics law takes over, and their strictness has to be followed and be aware of. Hence, the creativity in Engineering is in determining the initial conditions. They are up to you. Then, and only then you use laws of Physics to obtain the next result. For instance, Physics Laws, or even Laws of Electromagnetics, will not tell you, nor will prevent you, to determine the shape, amplitude of voltages for your generators. If sinusoidal voltages suit you, chose them. If other voltage shape suits you, chose that shape. And only then, you use the laws of electrical circuits to find the system states, voltages, currents, energy within the circuit. Creativity in Engineering is in choosing correct, useful, desired initial conditions.
Similar thing is in hockey. The rules of hockey will not tell you how to win. The same way language grammar will not and can not tell you how to write a winning novel or screenplay. The rules of hockey are hockey axioms, and you use them to create instances of the game, within the rules framework. Each game is a set of theorem obtained from the initial hockey axioms, and proved by the way of arbitrary not interfering with the game.
In Physics, differential equations can not tell you how to construct a new machine or make an invention. Why? Because differential and integral equations are waiting for YOU to tell them their initial and boundary conditions, i.e. STARTING CONDITIONS, they are waiting for you to tell them what and when to calculate, in the form of integrand, integral limits, initial and boundary conditions.
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