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PROFESSOR: OK. Let's turn then to the Dirac equation and motivated, basically. Through the Dirac equation is the simplest way to do perturbation theory for the hydrogen atom. It helps us derive what we should think of perturbation. So I'll discuss that quickly. And there may be some of that done in recitation. So we're going to discuss now the Dirac equation. So the Dirac equation begins with the observation that we have E squared minus p squared c squared for a free particle is m squared c to the fourth. This dispersion relation that rates E and p for any particle. So if you wanted to describe the dynamics of a relativistic particle, you could say, look, the energy is the square root of p squared c squared plus m squared c to the fourth. Therefore, I should take the Hamiltonian to be that thing. I should take H' to be that. And work with a Schrodinger equation that has this H with the square root. Nobody does that, of course. But you can do a little bit w...

[MUSIC PLAYING] CHILD: Alexa, turn off the lights. AMAZON ALEXA: OK. CHILD: [GIGGLING] Alexa, turn on the lights. AMAZON ALEXA: OK. SARAH HANSEN: Today on Chalk Radio, robots and humans become collaborative partners. CYNTHIA BREAZEAL: It's not about, let's build machines that look like people and act like people. It's, let's build machines that dovetail with us in a way that we can bring forth all of ourselves to help us achieve the goals that are really important to us. SARAH HANSEN: I'm your host, Sarah Hansen. This week, we're talking with a researcher and educator who's working to bridge the gap between human well-being and artificial intelligence. From kindergarten to college classrooms, she's preparing the next generation of informed technology users and empathetic designers. CYNTHIA BREAZEAL: I'm Cynthia Breazeal. I am a professor at MIT at the Media Lab. I am also director of a new MIT-wide initiative called Responsible AI for S...

Let's turn our attention to how the operating system (OS) deals with input/output devices. There are actually two parts to the discussion. First, we'll talk about how the OS interacts with the devices themselves. This will involve a combination of interrupt handlers and kernel buffers. Then we'll discuss how supervisor calls access the kernel buffers in response to requests from user-mode processes. As we'll see, this can get a bit tricky when the OS cannot complete the request at the time the SVC was executed. Here's the plan! When the user types a key on the keyboard, the keyboard triggers an interrupt request to the CPU. The interrupt suspends execution of the currently-running process and executes the handler whose job it is to deal with this particular I/O event. In this case, the keyboard handler reads the character from the keyboard and saves it in a kernel buffer associated with the process that has been chosen to receive incoming keystrokes. I...