Following Misner, Wheeler and Thorne. Foundations of General Relativity Basic Definitions Events: Things that happen at a particular point in spacetime Coordinates: How you label events in spacetime. There is no unique way of assigning coordinates Written as $x_{\mu}$, where $\mu$ ranges from 0 to 3 A coordinate transformation is a set of 4 equations. Each one determines how the new coordinate depends on the old 4 coordinates Coordinate singularities can occur (think of the north pole of the earth on latitude and longitude) These can be dealt with via multiple patches of coordinates Vectors: The seperation between two events in spacetime....

This was a slow month. I was overly ambitious in how quickly I could read Baumann’s Cosmology. Luckily, there is no rush; I’ll try and finish it before the semester ends. I’ll also try and finish Preskill’s notes, but this is less urgent. I tried bumping up the resolution of the camera experiment by storing the raw pixel data in some off-chip DRAM via a gearbox FIFO system. I need to write a testbench, since it’s buggy on the fabric....

I’m writing this 10 minutes before midnight since it slipped my mind during the day. Such is life. I finally finished “Understanding Digital Signal Processing”. Overall, good textbook. The author spent a lot of time working through numerical examples of some of the more complicated algorithms, which might not be everyone’s cup of tea, but it was ocassionally helpful to me. The book dragged on at the end, since a lot of the DSP tricks are very similar in nature (re: exploit some symmetry in the FIR coefficients to do the same computation with fewer/ more efficient operations)....

I’m sweating bullets as I write this, and I sprained my fingers during sparring, but I’m still going to bloody write this thing. I’m almost done with “Understanding Digital Signal Processing”. I just have the last chapter to trudge through (the last chapter happens to be 200 pages of very niche DSP techniques, but I should be done by mid-July). I got through IIR filters, which involved brushing off my complex analysis knowledge to understand stability conditions....

Following John Preskill’s 1998 Quantum Information and Computation notes. Introduction Landauer’s principle: It takes energy to erase information (since erasure always compresses phase space, such processes are irreversible) You can store a bit of information as one molecule in a box. If it’s on the left, it’s on, else it’s off. If you slowly compress the volume in half, you’re gaurenteed to be in the LHS. The change in entropy is k ln 2, which has some associated work that needs to be performed Logic gates used to perform computation are typically irreversible For instance, NAND is irreversible, since one bit of information is lost for each gate NOT is an example of a reversible gate Charles Bennett observed that any computation can in principle be done reversibly You can construct a Toffoli gate: Input is (a,b,c) Output is $(a,b, c \otimes (ab))$ So a and b get mirrored, and the third bit gets flipped if the first two bits are both 1 (otherwise, it mirrors the input) a Toffoli gate is universal (provided you throw away the ancilla bits when interpreting You can in principle do any computation up to the end, print out a copy of the answer (logically reversible process), then step back the computation back to the beginning Maxwell’s Demon The aforementioned ideas allows a resolution of the Maxwell’s demon paradox The original formulation is as follows: You have a partitioned box (split into A and B parts) and some demon which observes the molecules in the box If a fast particle is moving from A to B and it will cross the partition, then the demon allows it through If a fast particle is moving from B to A across the partition, the demon blocks it Over time, you will get faster particles on the right and slower ones on the left with minimal work....

Referencing “Modern Compiler Implementation in ML” by Andrew W. Appel. Lexical Analysis This refers to breaking up the input source code into individual words/tokens A “token” is a sequence of characters that can be treated as a unit in the grammer of a programming language Some common tokens which are typical in programming languages: ID: think names of any kind (variable, function classes etc.) NUM: Think integers REAL: Think floating point RESERVED: Words which are reserved in the programming language....

Following Baumann’s Cosmology. Conventions We are assuming a (- + + + ) signature for the metric. Greek letters for spacetime indices, and Latin letters for spatial indices overdots for physical time derivatives and primes for conformal time derivatives Qualitative Overview Meters are a cumbersome unit to work with at universe scales. We use lightyears and parsecs instead 1 ly is roughly 9.5E15 m 1 parsec (pc) is defined as the distance at which the radius of the Earth’s orbit around the Sun subtends an angle of one arcsecond (re: $\frac{1}{3600}$ of a degree) In light years, 1 parsec is around 3....

The semester has finally ended, and I didn’t fail any of my classes. I consider that a success! Immediately after finals, I once again picked up “Understanding Digital Signal Processing” by Richard Lyons; I plan on slowly working through all of the chapters in the book. I’ve just finished the discrete Fourier Transform section and learned a lot about leakage, the Nyquist criterion, windowing and a whole bunch of other weird digitization effects....

Following the book “Understanding Digital Signal Processing” by Richard G. Lyons. Discrete Sequences and Systems Definitions and Notation Signal Processing: the science of analyzing time-varying physical processes Analog refers to waveforms that are continuous in time and can take on a continuous range o amplitude values Comes from analog computers, where physical electronic differentiators and integrators were used to model differential equations Discrete: the time variable is quantized This means that the signal at intermediate values is unknown....

Almost done with the semester. Since finals are approaching, here’s a quick update: I’ve kept punting the camera module debugging. I tried ordering another module to see if it was a hardware issue, but it seems to have gotten lost in the mail? With regards to the GameTank verilog port, I’ve started porting over a 6502 CPU core into system verilog. The reasoning behind this is twofold: to get a better understanding of the 6502, and also to add a global enable to the module....