One of the goals of physics, and science in general, is to make predictions. The behavior of a simple pendulum, for example, is relatively easy to predict. However, predicting the motion of all of these bricks is much more complicated. We may need to know the precise moment when each brick will fall. Few things in life are as simple as a pendulum. And even predicting the motion of a pendulum can be complicated, if we lack an ideal set of initial conditions. Consider, for example, all the different ways this pendulum can interact with itself. This behavior can be very convoluted. And most things in life and in physics are far messier than a pendulum. Yet predictions still need to be made. If we have no way of making predictions, then we have no way to test if our theories are true. Also, making predictions has considerable practical importance. For example, we may need to know if a structure is stable. If the structure is unstable, we may need to know how far away from it to stand to be safe. But calculating an equation for the motion of each of these objects can be very difficult, if not impossible. High school and college classes on physics teach students how to deal with relatively simple situations. In these cases, it is possible to calculate elegant equations for the motions of the objects. However, for an even slightly less ideal situation, calculating an equation for the motion becomes hopelessly complex. Even with a seemingly simple set of starting conditions, the results can be far different from what we would expect. Yet these are the types of problems we are often faced with in real life. We therefore need a breakthrough for how to calculate situations such as these. And not just the simple situations, but the complex ones too. For example, suppose we want to know how the behavior of this cloth will look in slow motion. And suppose we need to know all the details of the cloth’s folds and creases. Or suppose we have this situation. Or, suppose we want to know which of the objects will stay on this platform. Finding answers to questions such as these is possible, but it is not by solving equations in the way that is taught in classrooms. The key to solving these problems is to perform what we call a “simulation.” These simulations can be performed very quickly if they are running on a powerful computer. But, any simulation can in principle also be done by hand with pencil and paper. In both cases, the principles are the same. Running a simulation would, for example, tell us whether or not this building will fall over. And if it will fall over, the simulation will tell us the details of how. Simulations can be performed for electric circuits, for General Relativity, for Quantum Mechanics, and for any other system. To understand how a physics simulation can be performed for any situation, no matter how complex, let us first consider a very simply situation in Newtonian physics. Suppose we have two particles that exert an attractive force on each other, and that are also affected by gravity. Suppose that we know the positions and velocities of the two particles at a given moment in time. If we want to find the positions of the particles at a very small increment of time later, we can approximate this by assuming that the particles continue moving at constant velocities during this very small increment of time. Based on the positions of the particles, we can calculate the attractive force they exert on one another. We also know that they are affected by gravity. If we think of gravity as a force, then all the forces can be represented with arrows as shown. By adding the arrows together, we can calculate the net force on each object at this moment in time. The acceleration of each object can then be calculated as the force divided by the mass. The acceleration is how quickly the velocity is changing. If we want to find the velocity of each particle a very small increment of time later, we can approximate this by assuming that the acceleration of each particle is constant during this very small increment of time. We can now use this new velocity to approximate the positions of the particles another small increment of time later, as we did before. We can then use the new positions to calculate the forces on the particles at this new moment in time, and the process repeats itself. In this way, we can perform a simulation that approximates the motions of the particles. This is not an exact answer due to the fact that the velocity and acceleration of each particle do not stay constant during each increment of time, but are constantly changing. We can make our approximations better by choosing smaller increments of time for each step of our simulation. The smaller the increment of time, the less the velocity and acceleration will change during this time period, and the closer our simulation will be to reality. We can therefore make our approximations as accurate as we want by choosing a sufficiently small increment of time for each time step, and there are also many other techniques for increasing the accuracy. Even if a physical system is not described by Newton’s Laws of motion, but by a completely different set of equations, the principles discussed here of performing simulations through many small time step increments can still be applied. In the case of quantum mechanics, the simulation will only give us probabilities, but these probabilities will accurately reflect the probabilities of the actual physical system. But, what if the physical system being simulated is an entire human brain? If we believe that a brain is composed of atoms and molecules behaving according to the laws of physics, simulating a human brain should theoretically be no different than simulating any other physical system, provided we had sufficient computing power. If this is truly an accurate simulation, then we should be able to simulate a conversation with the person, and to know the probabilities of all their responses. If we choose to simulate a conversation about the nature of consciousness, then just as a real person would insist that they are conscious and self-aware, the simulated brain would also make the exact same statements. Would this mean that the computer is just as conscious and self-aware as the brain of an actual person? What if this exact same simulation of the brain is not done on a computer, but all the calculations are instead done by hand with paper and pencil? Although doing such a simulation by hand with paper and pencil would be extremely time consuming, it could theoretically be done in principle. This would mean that we could also have a meaningful conversation with the brain simulated by equations on a piece of paper, and it would claim that it is self-aware. Would this mean that the paper on which the equations are being written possesses consciousness? If we believe that a piece of paper can’t possibly possess consciousness, would this imply that the brain and consciousness can inherently never be simulated? But, since everything governed by the laws of physics can in principle be simulated, would this imply that our brains are not fully governed by the laws of physics? Further discussion is available in the video titled “Philosophy of Physics.” Much more information about physics and mathematics is available in the other videos on this channel, and please subscribe for notifications when new videos are ready.