This is the third of seven chapters in Richard Feynman's, The Character of Physical Law, a series of lectures he gave at Cornell in 1965. The previous two were:
As a sign of his genius, he did not have a prepared manuscript for these lectures, only some notes. They were delivered extempore and then written up from the recordings. For example, in the course of this lecture he constructed a chart on a chalkboard. He is truly unusual among such geniuses to be able to communicate so clearly. Truly amazing.
1. Feynman spent the bulk of the lecture presenting examples of conservation in nature, especially the conservation of energy. But near the end he does begin to reflect on the possible significance of it all.
The main conclusion he reaches is that science is uncertain. It is in its very nature to reach beyond the known to the unknown, and this requires guesswork and the expectation that the laws that already seem to work in one area will also work in another. But he makes it clear that scientists can't assume they will continue to work.
For example, when it was found that a neutron could deteriorate into a proton and an electron, Niels Bohr famously suggested that they had finally found a situation where energy was not conserved. By that time he was so used to time-held notions going out the window that he had a penchant for wanting to overturn time honored scientific notions.
But it turned out he was wrong. There was another tiny particle, an anti-neutrino, that was involved, and energy was conserved.
For Feynman, though, it was important for scientists to be willing to throw out the conservation of energy principle if the evidence seemed to warrant it. And so it is for all true truth-seekers in every area except for the axiomatic.
2. The conservation of energy takes up the most space in the lecture. As usual, Feynman puts it in incredibly clear terms. He uses the analogy of a mother who leaves her child alone in a room with 28 blocks. One way or another, she will always be able to account for 28 blocks when she comes back to the room.
Perhaps the child will throw one block out the window. Perhaps the child has put one in a box--she can weigh the box to find out if she knows how much it weighed before and how much each block weighs. If there is a sink full of water, she can measure how high the water level has risen to account for submerged blocks.
And so he gives the analogy to the conservation of energy. Sometimes the energy hides, but science so far has always been able to account for all the "blocks" before and after some process.
3. Electric charge is always conserved. Feynman gets into a little relativity in his discussion here. Charge is always conserved locally, meaning in a particular frame of motion. Someone in a different frame of motion may not seem to observe conservation of charge.
He notes also that many things that are conserved come in units. Charges come in units. Another thing that comes in units and is conserved are "baryons," a heavier type of atomic particle like a proton or a neutron. The standard model of physics wasn't quite assembled completely when Feynman gave these lectures, but it was well on its way.
Two other conservations he mentions are the conservation of momentum (mass times velocity) and the conservation of angular momentum (the area created by motion over time from a certain reference point, such as the area between the moving planets per given time and the sun).
In all these things, Feynman sees deep yet seemingly inexplicable connections.