It good to think about how Euclid's postulates look like in the real projective plane:
- two parallel lines on the plane meet at a point on the sphere!Since there is one point of infinity for each direction, there is one such point for every direction the two parallel lines might be at. The parallel postulate does not hold, and is replaced with a simpler more elegant version: every two lines meet at exactly one point.One thing to note however is that ther real projective plane does not have angles defined on it by definition. Those can be defined, forming elliptic geometry through the projective model of elliptic geometry, but we can interpret the "parallel lines" as "two lines that meet at a point at infinity"
- points in the real projective plane are lines in
- For every two projective points there is a single projective line that passes through them.Note however that not all lines in the real plane correspond to a projective line: only lines tangent to a circle at zero do.
Unlike the real projective line which is homotopic to the circle, the real projective plane is not homotopic to the sphere.
The topological difference bewteen the sphere and the real projective space is that for the sphere all those points in the x-y circle are identified to a single point.
One more generalized argument of this is the classification of closed surfaces, in which the real projective plane is a sphere with a hole cut and one Möbius strip glued in.
Appears to be the best classic open source roguelike of the 2020's.
This website is really cool! crawl.akrasiac.org:8080/#lobby You can spectate players live and chat! Also has statistics.
Devs of this game are smart, they have one good in-tree tileset, unlike some other text-based games that didn't have an in-tree option...
Build on Ubuntu 21.10:
sudo apt install build-essential libncursesw5-dev bison flex liblua5.1-0-dev \
libsqlite3-dev libz-dev pkg-config python3-yaml binutils-gold python-is-python3 \
libsdl2-image-dev libsdl2-mixer-dev libsdl2-dev libfreetype6-dev libpng-dev \
fonts-dejavu-core advancecomp pngcrush
git clone --depth 1 --branch 0.28.0 https://github.com/crawl/crawl
cd crawl/crawl-ref/source
echo 0.28-a > util/release_ver
make -j`nproc` TILES=y
./crawlThis launches the UI version already for you.
Example where this level is sufficient: nodejs/sequelize/raw/parallel_update_async.js.
Messaging software that force you to have a mobile phone Updated 2025-01-10 +Created 1970-01-01
Chat programs that don't have a proper web-only operation and force you to have a mobile phone, e.g. WhatsApp.
Heck, even Signal, which is supposed to be super secure and good for your privacy, forces you to disclose your freaking cell phone to all contacts! lifehacker.com/how-to-use-signal-without-revealing-your-private-phone-1818996580
What is my phone breaks? What if I don't want to have a fucking phone? What if I move countries and have to change the fucking number? Also evil but less because done by all: chat programs that can't send you an email if you don't see the message in X minutes.
The solution to "how to prevent spam" is simple: your ID is a public key that you own the private key for. If you start getting spammed, generate a new public key, and send it to all contacts, and dump the previous ID.
Just use MuseScore instead.
Weight: light.
Can import from: MIDI.
Ubuntu 20.04:
sudo apt install tuxguitar tuxguitar-alsa tuxguitar-jsa tuxguitar-osstuxguitar-jsa was needed, otherwise no sound: askubuntu.com/questions/457321/tuxguitar-no-sound-in-14-04Has OK step sequencer non-realtime up/down/left/right guitar based composition interface.
Has chord insertion.
Has bend editor.
Could be more amazing, but it is OK.
A bit limited by being very "guitar oriented". Shows you guitar strings, and you enter offset to each string. So to enter two adjacent notes you need to use two seprate strings and thing about the offsets. If only it had a more piano based interface.
Drum notation is also atrocious, you have to go to the top chord, and use high numbers starting at 36.
Taboola is a clickbait trained neural network. Which happens to have been written by Adolf Hitler.
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