Appears to be analogous to the dot product, but also defined for infinite dimensions.
Good selection: Acústico MTV - Gilberto Gil (1994).
- 1967 Louvação (1967) album
Video 1. Lunik 9 Gilberto Gil (1967)Source. Ciro Santilli prefers Elis Regina's interpretation however. - 1972 Expresso 2222 album.
Video 2. Expresso 2222 by Gilberto Gil (1972)Source. youtu.be/aSFahdu5ga8?t=4584 In the 2002 documentary Tempo Rei he explains the origin of the song as being based on seeing trains come by in Bahia, when they still existed before the automobile decimation. - 1975 Refazenda (1975) album. This album is just too Legendary. The cover is also legendary.
Video 4. Refazenda by Gilberto Gil (1975)Source.Video 6. Tenho sede by Gilberto Gil (1975)Source. Video 7. Sítio Do Picapau Amarelo by Gilberto Gil (1977)Source.This song is the opening theme of the 1977 children's television series based on the renowned children books of the same name by Brazilian author Monteiro Lobato.- Date unclear
Video 8. A Paz by Gilberto Gil (1967)Source. Performed 2009. The earliest recording we can find is from 1994: www.discogs.com/master/190615-Gilberto-Gil-Unplugged
Runner ups:
Video 9. Beira-Mar by Gilberto Gil. Source.
The opposite of elementary particle.
A computer is a highly layered system, and so you have to decide which layers you are the most interested in studying.
Although the layer are somewhat independent, they also sometimes interact, and when that happens it usually hurts your brain. E.g., if compilers were perfect, no one optimizing software would have to know anything about microarchitecture. But if you want to go hardcore enough, you might have to learn some lower layer.
It must also be said that like in any industry, certain layers are hidden in commercial secrecy mysteries making it harder to actually learn them. In computing, the lower level you go, the more closed source things tend to become.
But as you climb down into the abyss of low level hardcoreness, don't forget that making usefulness is more important than being hardcore: Figure 1. "xkcd 378: Real Programmers".
First, the most important thing you should know about this subject: cirosantilli.com/linux-kernel-module-cheat/should-you-waste-your-life-with-systems-programming
Here's a summary from low-level to high-level:
- semiconductor physical implementation this level is of course the most closed, but it is fun to try and peek into it from any openings given by commercials and academia:
- photolithography, and notably photomask design
- register transfer level
- interactive Verilator fun: Is it possible to do interactive user input and output simulation in VHDL or Verilog?
- more importantly, and much harder/maybe impossible with open source, would be to try and set up a open source standard cell library and supporting software to obtain power, performance and area estimates
- Are there good open source standard cell libraries to learn IC synthesis with EDA tools? on Quora
- the most open source ones are some initiatives targeting FPGAs, e.g. symbiflow.github.io/, www.clifford.at/icestorm/
- qflow is an initiative targeting actual integrated circuits
- microarchitecture: a good way to play with this is to try and run some minimal userland examples on gem5 userland simulation with logging, e.g. see on the Linux Kernel Module Cheat:This should be done at the same time as books/website/courses that explain the microarchitecture basics.
- instruction set architecture: a good approach to learn this is to manually write some userland assembly with assertions as done in the Linux Kernel Module Cheat e.g. at:
- github.com/cirosantilli/linux-kernel-module-cheat/blob/9b6552ab6c66cb14d531eff903c4e78f3561e9ca/userland/arch/x86_64/add.S
- cirosantilli.com/linux-kernel-module-cheat/x86-userland-assembly
- learn a bit about calling conventions, e.g. by calling C standard library functions from assembly:
- you can also try and understand what some simple C programs compile to. Things can get a bit hard though when
-O3is used. Some cute examples:
- executable file format, notably executable and Linkable Format. Particularly important is to understand the basics of:
- address relocation: How do linkers and address relocation work?
- position independent code: What is the -fPIE option for position-independent executables in GCC and ld?
- how to observe which symbols are present in object files, e.g.:
- how C++ uses name mangling What is the effect of extern "C" in C++?
- how C++ template instantiation can help reduce link time and size: Explicit template instantiation - when is it used?
- operating system. There are two ways to approach this:
- learn about the Linux kernel Linux kernel. A good starting point is to learn about its main interfaces. This is well shown at Linux Kernel Module Cheat:
- system calls
- write some system calls in
- pure assembly:
- C GCC inline assembly:
- write some system calls in
- learn about kernel modules and their interfaces. Notably, learn about to demystify special files such
/dev/randomand so on: - learn how to do a minimal Linux kernel disk image/boot to userland hello world: What is the smallest possible Linux implementation?
- learn how to GDB Step debug the Linux kernel itself. Once you know this, you will feel that "given enough patience, I could understand anything that I wanted about the kernel", and you can then proceed to not learn almost anything about it and carry on with your life
- system calls
- write your own (mini-) OS, or study a minimal educational OS, e.g. as in:
- learn about the Linux kernel Linux kernel. A good starting point is to learn about its main interfaces. This is well shown at Linux Kernel Module Cheat:
- programming language
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