…first discovery that the laws of physics were not unchanged under a change of scale is interesting. It was made by Galileo. he realized that the strengths of materials were not in proportion to their sizes in exactly the right proportion, and illustrated…

…they'll stick together and stop. And this will do on this marvelous invention, which gets rid of friction, the thing which bothered Galileo all the time. He didn't do experiments by sliding things, because they don't slide. But by adding a magic touch, we…

…just get rid of friction. Then the object will slide without any difficulty forever, you see, at a constant velocity, as advertised by Galileo. No? This thing works by there being air coming out in this trough here, so this is supported on air all the…

…to compute not only the motion of that oscillating spring, but the perturbations on the planet Uranus produced by Jupiter and Saturn. Galileo got a long way in the understanding of motion when he discovered the principle of inertia, which is that if an…

…not left to itself because it's rubbing against the table. So it requires a certain imagination, and that imagination is supplied by Galileo. The next. In fact, the next thing that has to be made to complete that, that's a negative statement. If nothing…

…of many of the other sciences. Many people would like to place the beginnings of physics, the first physicist, 350 years ago with Galileo. Up until that time the study of motion had been a philosophical one based on arguments that one could pick out of…

…one's head and most of the arguments that had been presented by Aristotle in the time of the Greeks were taken as proven. Galileo was skeptical and did an experiment on motion which is essentially this one. He allowed an object to roll down an inclined…

…5, 6, 7, 8. By measuring these lengths of time, the distance the ball went in one interval, two intervals, three intervals, four intervals, Galileo was able to write that the distance in equal intervals, 1, 2, 3, 4, and so on, in time, if this was the…

…can I go to a smaller time? Well, we look around. There are other periodic phenomena. There's the human pulse, which I mentioned that Galileo had used. And if we could count the number of pulses, beats of the heart in one falling of the sand, then I…

…beats of the pulse, roughly 3,000 beats of the pulse in one falling of the sand. However, if you are a religious man, as Galileo was, and went to church, you saw lanterns and lamps hanging in the church, and it occurred to you that maybe the swinging…

…and the sticks would break even more surely. This fact that the laws of physics were unchanged under scale was first discovered by Galileo. He argued in discussing the strength of rods and bones. He argued that if you need a bone for a bigger animal,…

…And in Galileo's book called The Two New Sciences, you'll see pictures of imaginary bones of enormous dogs way out of proportion. Galileo felt that the discovery, I suppose he felt, I don't know, but the discovery of the fact that the laws of nature…

…them go around? Well, how can we understand this in more detail? Or is there anything else to say? In the meantime, Galileo was investigating the laws of motion. Incidentally, at the time of Kepler, the problem of what drove the planets around the sun…

…where wings go. But the point that the angels sit in a different direction is the one that I must now come to. Galileo, in studying the laws of motion and doing a number of experiments and seeing how balls roll down inclined planes and pendulous swung…