Kepler's Third Law: The ratio of the square of an object's orbital period with the cube of the semi-major axis of its orbit is the same for all objects orbiting the same primary. Data used by Kepler (1618): Planet R = Mean distance to sun (AU) T = Period(days) R^3/T^2 = constant Mercury R= 0.389 T= 87.77 R^3/T^2 = 7.64 Venus R= 0.724 T = 224.70 R^3/T^2 = 7.52 Earth R= 1 T = 365.25 R^3/T^2 = 7.50 Mars R = 1.524 T = 686.95 R^3/T^2 = 7.50 Jupiter R = 5.20 T = 4332.62 R^3/T^2 = 7.49 Saturn R = 9.510 T = 10759.2 R^3/T^2 = 7.43 Upon finding this pattern Kepler wrote: I first believed I was dreaming... But it is absolutely certain and exact that the ratio which exists between the period times of any two planets is precisely the ratio of the 3/2th power of the mean distance. - translated from Harmonies of the World by Kepler (1619) Essentially, Kepler discovered if you take the Circumference of an squished circle and put it in a ratio with the radius of a squished circle you get a constant (which is a value ~2.38 × π) Kepler didn't need gravity or mass, just a telescope and time.
18:56 come on! This is just the negation of the negation from dialectical materialism! Rand didn't invent this! She knew it because they taught it in the Soviet Union! Rand ripping off Marx!? What!? 🙄🙄🙄
I am really struggling to follow your introductory logic here. I see no "paradox" anywhere in any of the examples. It seems to me that your argument assumes observed proportionality, e.g., that pressure is proportional to temperature, required a completed proven model in order to state such an observation, which obviously is not needed. If I squeeze my hands together, I feel the temperature rising between my pressurized hands. P is proportional to T. P relates to T. P is also related to volume, volume and temperature are also related, the number of moving objects in a room increases the temperature of the room. I didn't need to know what gas is was to discover 99% of the ideal gas law. This are just facts, and if we tabulate those relationships, a constant falls out. That connecting of facts is what creates a theory (a story/explanation which connects facts). So you don't need the theory before the facts, that's impossible. There is no paradoxes here.
Right, there really isn't a contradiction for exactly the reason you state. But some people do think there is a contradiction here. 8:38 you are one of the people who already notice the faulty premise. You don't suffer from the mistake many in math and physics suffer from. If you keep following the video you can build off of your current understanding to learn more about the integrative aspect of induction.
