Finite Element Method Quotes

Twenty minutes later, Three Body’s Von Neumann architecture human-formation computer had begun full operations under the Qin 1.0 operating system. “Run solar orbit computation software ‘Three Body 1.0’!” Newton screamed at the top of his lungs. “Start the master computing module! Load the differential calculus module! Load the finite element analysis module! Load the spectral method module! Enter initial condition parameters … and begin calculation!” The motherboard sparkled as the display formation flashed with indicators in every color. The human-formation computer began the long computation.

SALV. I will now say something which may perhaps astonish you; it refers to the possibility of dividing a line into its infinitely small elements by following the same order which one employs in dividing the same line into forty, sixty, or a hundred parts, that is, by dividing it into two, four, etc. He who thinks that, by following this method, he can reach an infinite number of points is greatly mistaken; for if this process were followed to (37) eternity there would still remain finite parts which were undivided. Indeed by such a method one is very far from reaching the goal of indivisibility; on the contrary he recedes from it and while he thinks that, by continuing this division and by multiplying the multitude of parts, he will approach infinity, he is, in my opinion, getting farther and farther away from it. My reason is this. In the preceding discussion we concluded that, in an infinite number, it is necessary that the squares and cubes should be as numerous as the totality of the natural numbers [tutti i numeri], because both of these are as numerous as their roots which constitute the totality of the natural numbers. Next we saw that the larger the numbers taken the more sparsely distributed were the squares, and still more sparsely the cubes; therefore it is clear that the larger the numbers to which we pass the farther we recede from the infinite number; hence it follows [83] that, since this process carries us farther and farther from the end sought, if on turning back we shall find that any number can be said to be infinite, it must be unity. Here indeed are satisfied all those conditions which are requisite for an infinite number; I mean that unity contains in itself as many squares as there are cubes and natural numbers [tutti i numeri].

Run solar orbit computation software ‘Three Body 1.0’!” Newton screamed at the top of his lungs. “Start the master computing module! Load the differential calculus module! Load the finite element analysis module! Load the spectral method module! Enter initial condition parameters … and begin calculation!” The motherboard sparkled as the display formation flashed with indicators in every color. The human-formation computer began the long computation. “This is really interesting,” Qin Shi Huang said, pointing to the spectacular sight. “Each individual’s behavior is so simple, yet together, they can produce such a complex, great whole! Europeans criticize me for my tyrannical rule, claiming that I suppress creativity. But in reality, a large number of men yoked by severe discipline can also produce great wisdom when bound together as one.” “Great First Emperor, this is just the mechanical operation of a machine, not wisdom. Each of these lowly individuals is just a zero. Only when someone like you is added to the front as a one can the whole have any meaning.” Newton’s smile was ingratiating. “Disgusting philosophy!” Von Neumann said as he glanced at Newton. “If, in the end, the results computed in accordance with your theory and mathematical model don’t match reality, then you and I aren’t even zeroes.” “Indeed. If that turns out to be the case, you will be nothing!” Qin Shi Huang turned and left the scene.