A seemingly complex system is often explained based on a simple theory. A physicist often prefers a simpler theory to a more complex one, when both explain and predict the same phenomena. Such examples are abundant in classical physics. If you recall a physics class, the teacher drew a lot of diagrams using points and lines to explain a mechanical theory. A point represents material or mass and a line represents a force and its direction. In explaining a theory of momentum of force or how the equilibrium of a balance is achieved, he draws the picture shown in Fig. 1 below.

Figure 1 IMAGES

He goes on to explain that momentum is mass times the length of a lever from an arbitrary point to the point where the mass exerts force on the lever as a result of the gravitational acceleration. In other words, M1 x L1 = M2 x L2 means the balance is at equilibrium. However, if a person stops and thinks of a balance which exists in the real world, he can't achieve balance with points and lines. Every material he uses has volume and density or shape of some kind. He wonders why the teacher pretends the world is so simple while in reality it is complex. He would argue that even a real world balance in a simple form would look like the one below in Figure 2.

Figure 2 IMAGES

Then he would be able to argue the physics principle that governs real systems. He is right, because that is what engineering is about in most cases; taking into consideration such things as the density, strength or elasticity of a material when designing a real thing. However, a theory that can be derived from points and lines can explain more of the universal truth, and this fact can be seen when one looks at the complex real system described below.

Let's cut the beam into two blocks connected to a line or rigid beam with no mass as shown in Fig. 3. So long as the two blocks are connected firmly to the rigid beam, nothing changes. Correct. Now let's put a string at the center of gravity of each block and hang each block from the rigid beam; do it to both blocks. Again, we see that so long as the line represents a rigid body, it should work; that is, the balance is still in its equilibrium state. Let's make the strings a bit longer to make the system look clearer as shown in Fig. 4.

Figure 3 IMAGES

Figure 4 IMAGES

The system still works, right? Now let's rotate both blocks 90 degrees as shown in Fig. 5. How does the system look? To the rigid beam or the line the force from the block is being applied at one point. Then why not represent it by a point of material, and draw the picture by points and lines as shown in Fig. 6.

Figure 5 IMAGES

Figure 6 IMAGES

I hope you have seen the beauty of physics. Points and lines, which don't exist in the real world, can explain very effectively the equilibrium state of a balance beam. This is why a physicist continues to try to explain physical phenomena in simple terms.

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