Tab CompletionTab Atkins Jr.email@example.com://www.xanthir.comhttp://www.xanthir.com/2016-08-18T01:45:13+00:00All content is published in the public domain, or optionally may be licensed under the CC0 license.http://www.xanthir.com/b4iq0Fantasy World Planes2016-08-18T01:45:13+00:002016-08-17T07:00:18+00:00<p>Beyond the single world is the Ethereal Plane, where metaphysics dominates. It's filled with Ether, the raw stuff of creation, which accretes into distinct forms based on the metaphysical surroundings.<p>The makeup of the Ethereal is determined by your distance from three Poles, broad metaphysical tendencies that determine how the worlds work, and which are in complete opposition to each other. These are Stasis, Dynamism, and Entropy. (Yes, I played a lot of White Wolf as a teen.)<p>In Far Stasis, ether becomes a perfect crystal. Unchanging, without imperfections, it's an ideal form. In Far Dynamism, ether is raw potential, unable to take any specific form at all. Far Entropy is complete void, the ether there contradictorily representing its own non-existence. All three poles are inimicable to life; all the interesting stuff happens closer in.<p>As you move from Stasis to Dynamism, the etheric crystal fractures into the Elemental Pillars. These first represent pure forms of the five elemental atoms, but as you get closer to Dynamism, they become more heterogenous, gradually gaining form and shape and life.<p>The path from Stasis to Dynamism is instead the Energetic Rainbow, representing the breakdown of etheric form and energy. First is Light - pure and stable, but hard to contain. This shades into Lightning, still energetic but clearly more chaotic, but still controllable by proper application of Earth. Further on the energy loses direct physical coherence, becoming Kinetic - invisible and harder to grasp directly; doesn't travel as far but sheds its energy much more readily, making it more damaging within its useful range. A little further and we lose physical form entirely, reaching the more abstract form of Entropic energy, raw corrosion and loss of form. And finally, as we reach the pole it becomes pure Void.<p>Somewhere in the middle of the three Poles we get just the right mix to support the material world. Of course, we can't have just one - there are three, shadows of the stable fixed point cast by each of the Poles. The Static shadow is our world, the Prime Material plane, a world of physics and rules and things staying roughly the same from day to day. The Dynamic shadow is the Feywild - changing and fantastical, ruled by dreams and intuition. The Entropic shadow is the Shadowfell, a world in constant decay. The three worlds influence each other, tho our world, being the most Static, has the most stabilizing influence - things in the Feywild and Shadowfell tend to revert toward whatever they look like in the Prime. However, places of heavy magic use thin the barrier towards the Feywild and invite interesting effects, while places of death and pain draw the Shadowfell and induce monsters and ruin in the area. Insofar as the Body atoms "come from" anywhere, they originate here.<p>The Ethereal represents the "physical" half of "metaphysical", encompassing the physical worlds and the elements they're made from. Closer toward the Dynamic Pole, reality blurs and the Ethereal shades into the Astral, its meta/mental counterpart. This is where people's souls go when they dream, where reality is much more malleable. You can find pure forms of the Mental atoms here.<p>Souls travel to the Near Astral when people dream, where it's coincident with the Ethereal. In the Far Astral, out of reach of mortals in most circumstances, lie the Divine planes, where the gods make their domains. This layer is far enough out from the Ethereal that the Poles no longer hold any sway; instead, the divinities align along much more complex mandalas of metaphysics. We know that the five-fold symmetry of the Spheres holds at least some sway, due to the Divine atoms, but more is difficult to tell. Souls tend to drift this way after death, where they're collected by the gods.http://www.xanthir.com/b4iW0CSS Function Syntaxes (color and otherwise)2016-07-28T17:05:55+00:002016-07-28T17:05:55+00:00<p>Yesterday I committed a few changes to the CSS Color spec that are proving a little controversial to people without any background on the changes. Hopefully this will help!<p>Specifically, I made it so that the rgb() function (and others) can now use the syntax <code>rgb(0 255 0 / 50%)</code> for half-transparent green. Previously you'd write that as <code>rgba(0, 255, 0, 50%)</code>. Why'd I make this change?<p>This is part of a general overhaul to how CSS defines functions that fantasai and I are pushing. <a href="https://wiki.csswg.org/ideas/functional-notation" title="">The overall strategy is written up on our wiki</a>, but the general idea is that CSS has some informal rules about how to organize things and use certain punctuation characters. In particular, in CSS properties we normally just separate values with spaces, relying on distinguishable syntax (like <code><string></code> vs <code><number></code> vs <code><length></code>) or just careful ordering to keep things unambiguously parseable. We use punctuation separators only for very specific purposes: commas are used to separate repetitions of a base value (like layers in the <code>background</code> property, or font names in the <code>font-family</code> property), and occasionally, when we can't do anything better, a slash is used to separate two otherwise-ambiguous values (like font-size vs line-height in the <code>font</code> shorthand, transition-delay vs transition-duration in the <code>transition</code> shorthand, or the multiple pieces of syntax in a <code>border-image</code> layer).<p>However, functions violated those rules. They used commas extensively and somewhat inconsistently, just to separate values from each other. On the one hand, this makes CSS functions look slightly more like functions in a traditional programming language; on the other hand, it meant you had to learn a different mental model of how CSS's syntax works, and type a bunch of comma characters that weren't actually necessary. fantasai and I have gradually come to the position that it's worthwhile to unify CSS's syntaxes, making functions more property-like. (Our position can be summed up aptly as "functions are just named chunks of CSS syntax".)<h2>Color</h2><p>So that brings us to the Color spec. Color 3 was already a function-full spec, and Color 4 more than doubles that number, adding hwb(), gray(), lab() and lch(), and color(). The first four of those look similar to the existing rgb()/etc functions, just taking a couple of numbers, so they were originally designed with the same syntax, separating every number with commas.<p>But color() was a bit more complex, more like a CSS property. It had to take a colorspace name, an arbitrary number of arguments to the colorspace, an alpha, then finally a fallback value in case the colorspace wasn't loaded or was invalid. Putting commas between every value there just got ridiculous, not to mention made it difficult to read; in particular, it was hard to tell where the colorspace arguments ended and the alpha began.<p>So, I opened <a href="https://github.com/w3c/csswg-drafts/issues/266" title="">Issue 266</a> about it, and discussion eventually led us to making it use CSS property syntax pretty much exactly: color() takes a comma-separated list of colors (each one serving as fallback for the previous), and within each color, everything is space-separated. Because colorspaces can take an arbitrary number of numeric parameters, the alpha value was ambiguous (hard to even tell whether or not there <i>was</i> an alpha at a casual glance), and so we employed the slash to separate it visually from the parameters.<p>At this point, tho, it was slightly weird to have this one color function use this particular syntax form, while none of the others used anything like it. Welp, all the color functions were on our wiki page's list of things to overhaul anyway, so bombs away! We went ahead and changed all the new functions to use the same syntax (all values space-separated, with an optional slash-separated alpha), and then added a <i>new</i> syntax variant to the old functions with the same form.<p>(I stress, this is a <i>new variant</i> syntax, not a replacement. All your old <code>rgb(0, 255, 0)</code> code is fine and will never be incorrect. We're just classifying it as a legacy syntax; we've got a handful of those cluttering up CSS specs.)<p>So, now all the color functions use the same syntax form, and they all agree with our general push to make functions resemble properties more closely. It may feel a little weird at first, but I think you'll appreciate it as you get used to it (a few characters less typing, at the very least). And we've been edging this way for quite a while - as far back as linear-gradient() we were trying to use commas reasonably, with the complex sizing/positioning part up front completely space-separated and commas used only to separate the color-stop repetitions.http://www.xanthir.com/b4hf0Cleanly Handling a Fork on GitHub2016-06-08T18:22:21+00:002016-06-08T18:17:58+00:00<p>One of the greatest things about GitHub is the ease with which you can fork a project and make your own changes. <br><p>One of the worst things about GitHub is the ease with which you can fork a project and then lose track of the changes upstream is making.<p>This is extra-true when you want to make occasional PRs for a project with regular commits; it's easy for your fork to get way behind in a way that makes it really annoying to write patches that'll merge cleanly later. This guide collects my personal experience in handling this situation with minimal pain.<h2>One: Set an "upstream" remote</h2><p>If you run <code>git remote -v</code> in your repo, you'll see the remote repositories that your local copy knows about. These are things that are easy to push to. By default, it'll only contain the GitHub URL for your fork, labeled "origin". You're gonna be interacting with the original repo you forked from a lot, so you want to give it an easy name, too:<pre class='code'>git remote add upstream https://github.com/ORIGINAL_OWNER/ORIGINAL_REPOSITORY.git</pre><p>Now you can easily refer to the original repo as <code>upstream</code>.<h2>Two: Regularly re-sync with upstream</h2><p>Whenever you're about to start some new work in your fork, re-sync it with the upstream first, so you have all the new commits and are less likely to conflict badly:<pre class='code'>git fetch upstream
git checkout master
git merge upstream/master
git push</pre><p>This should cleanly merge and just do a "fast-forward" on your repo, rather than actually making a merge commit, as long as you faithfully do what I suggest in the next step.<h2>Three: NEVER COMMIT TO YOUR MASTER BRANCH</h2><p>If you want a clean, easy workflow, you want to NEVER, <b>EVER</b> commit to your local master branch. The master branch's <b>sole</b> purpose is to track upstream exactly, so you can always cleanly work against the current version and write easy-to-merge PRs.<p>Instead, <i>always</i> make your changes in branches. When you push the branch to your remote, you can do a PR; when the PR is accepted, you can pull the newly-updated upstream and then delete your branch. <code>master</code> always remains a source of upstream truth, unpolluted by your personal code unless blessed by the upstream maintainers.<p>(This is good advice in general; always make changes in branches and only commit to master when you're done, but I'm usually lazy and just always commit to master for personal projects. But it's super-important to get this right for forks, or else you're in for a lot of pain.)<h2>Four: Rebase your branches regularly</h2><p>Say you're in the middle of writing a new proposed feature (in a branch, of course) and you notice that upstream has some new commits that touch code you're going to be modifying soon. You'd like to get that code into your branch now, before you start modifying things, so you don't have merge conflicts later. But how?<p>First, resync your master as stated in step 2. Then, rebase your topic branch on top of the new upstream code:<pre class='code'>git checkout MY_COOL_BRANCH
git rebase master</pre><p>This'll undo your commits, pull in the new stuff from upstream, then replay your commits on top of it, so when you eventually make a PR, the upstream maintainers will have a perfect clean merge, with your commits sitting on top of their latest code.<h2>Five: Force-push commits that just fix PR nitpicks</h2><p>When you eventually do submit your PR, the review will probably catch some small mistakes you need to fix. You <i>can</i> just make those fixes and push them to the PR branch, but then when it's eventually merged there will be a lot of silly little "fix typo" commits scattered around.<p>Instead, just fix the commit itself, using the <code>git commit --amend</code> option, then force-push that to your remote with <code>git push --force</code>. Force-pushing is normally a <i>very bad idea</i>, because git is usually rightfully trying to stop you from making a mistake when it rejects a push, but in this case changing the history of a short-lived PR branch is unimportant and makes things look cleaner overall.http://www.xanthir.com/b4hH1Magical Metaphysics2016-06-07T18:06:29+00:002016-05-16T06:23:12+00:00<p>I've been working on a homebrew fantasy world in my spare time for years. It'll probably never go anywhere, but it's fun to think about! One of the things I've wanted to nail down for a long time was the <i>magic physics</i> of the world, what elements made up reality in this extremely magical world.<p>I had a few requirements to keep in mind when developing this.<p>First and foremost, it had to be "complex". By this I mean--well, it's easiest to explain by contrast. In the real world, physics is "simple". The fundamental units of reality (quarks, photons, etc) have basically nothing to them. They're just a few numbers that combine together in trivial ways. The complexity of our world comes not from any fundamental complexity, but rather from enormous numbers of these super-simple things combining together. Even tho each individual thing has no complexity at all, and neither does the way they interact, the aggregate is capable of displaying tons of complexity.<p>Magic, on the other hand, is always "complex" at its root. It generally assumes the existence of minds as a fundamental unit of reality (whereas in the real world minds are just one of the patterns that vast quantities of unthinking particles can arrange themselves into). Sometimes it has "morality" baked in as a physical force; often it has complex things like "fire" or "earth" as core concepts. This makes magic easier to comprehend at a surface level, because it's made out of "big" things we can wrap our minds around, which combine in ways that are complex and ideosyncratic, but don't involve the dizzying amounts of <i>data</i> that the real world's fundamentals do. The elements of magic thus have to reflect this.<p>Secondly, it has to involve fives. Five is a good number of things, mentally and spiritually significant. So early on, long before I knew what anything would be, I knew I'd have five spheres of five atoms each.<p>So let's dive in!<h2>The Sphere of Elements</h2><p><b>Fire, Water, Earth, Wind, Wood</b><p>This was the simplest of all. I knew I needed to involve the classical "elements" of fire/water/earth/air, and I had a few common choices for what to make the fifth. I chose to go for "wood" for a few reasons. One, it's very physical, and helps tie together "elemental" magic with a druid-ish theme. Two, I already knew from my <a href="http://www.xanthir.com/b4fM1" title="">fantasy races</a> that I wanted elves to have wooden skeletons, and for this to be properly mystically significant, I'd need wood to be a fundamental force. Three, wood is usually mystically significant in stories, which means its likely to be pretty core to the magic system, so I had to include it <i>somewhere</i>. Some other common choices I rejected are "metal" (already served by "earth"), "void" (too abstract/encompassing for what's supposed to be only one sphere of the world, also this feels a little sci-fi-y and I ended up letting Energies have that), and "heart" (very non-physical, so it doesn't fit well, and it's more over in the mental sphere that I knew I wanted to do).<p>A wrinkle: atoms can be "hard" or "soft"; the "hard" ones are suitable for making magical staffs with that aid in channeling related atoms. The hard/soft dichotomy is pretty literal, so Wood and Earth are both hard. This explains why staffs are commonly wood or metal, and/or contain gems (which are Earth) - they help channel elemental magic!<h2>The Sphere of Energies</h2><p><b>Heat/Light, Electricity/Magnetism, Kinetic, Entropy, Void</b><p>Lacking any hard atoms to make staves from, the energies are somewhat difficult to channel directly, particularly in the heat of combat. Instead they're usually admixed with an appropriate element, to aid in using an elemental staff to channel them. This produces the so-called "Wizard's Elements": <b>Fire</b> (Heat+Fire, or something Heat+Earth or Heat+Air), <b>Lightning</b> (Electricity+Air/Earth), <b>Thunder</b> (Kinetic+Air), <b>Acid</b> (Entropy+Water, or sometimes Entropy+Earth for Corrosion), and <b>Cold</b> (Void+Water/Air).<p>This one started out easy. I knew I wanted the D&D damage types, because I intended this world to be D&D-based, and what do you know, there are five common damage types. I also wanted to somehow include some slightly science-y things, but it seemed too on-the-nose to make them a sphere of their own, and I couldn't come up with a decent pentad for them anyway. I was pretty happy when I realized I could combine those two and get a more flexible sphere out of the deal.<h2>The Sphere of Biology</h2><p><b>Flesh, Blood, Bone, Elan, Soul</b><p>Flesh, Blood, and Bone are fairly self-explanatory. They cover all the things bodies are made of: cartilage and bone are both Bone; skin, muscle, and organs are mostly Flesh; mucus, blood, tears, and other liquids are variations on Blood.<p>Soul is the thinking substance, that our identities and selves are made of. Brains are a Flesh/Soul melange, for example.<p>Elan is "life energy", the animating force that distinguishes living things from dead. Without Elan infusing it, flesh is inert, and decomposes. With Elan, it's vital, active, and growing. Many simple healing spells are nothing more than increasing Elan in the body and letting natural healing take place, albeit at an accelerated pace. <p>Biology has more complex atomic interactions than the previous spheres. Bone is another "hard" atom, and thus suitable for making staffs with that aid in channeling, particularly other Biology atoms. But curiously, Bone is almost impervious to Elan; healing bone breaks is very difficult unless you have skill in Bone, and a Bone staff is absolutely worthless for channeling Elan. This has curious consequences! For one, healers are stuck using elemental staffs, at lower efficiency, which partially explains why it's always easier to harm than to heal. For two, it means that Biology specialists carrying Bone wands are definitely <i>not</i> healers, and the second most common use of Biology is... necromancy. (Note: Bone instruments <i>are</i> useful to actual surgeons, who have real training in Flesh/Blood/Bone beyond just "throw Elan at it until it's better".)<p>Necromancy uses all the non-Elan parts of Biology to do its work, warping bodies and souls in unnatural ways. (They <i>can't</i> use Elan, actually - it encourages natural growth and forms, which would unravel the work they're doing.) Bone is great for necromancers, then, as it enhances all of their spells.<p>This split in Biology carries over to its interactions with the Energies. Bone has a strong affinity to Void and Entropy; necromancers are well-known for an Entropy/Flesh blend known as "Necrotic energy", and some specialize in a powerful Void/Entropy blend known as "Uttercold". Flesh and Electricity have a unique affinity as well, such that some necromancers use it as an alternative animating energy. On the other hand, Elan has a strong affinity with Light, blending to produce the popular "Radiant energy" that is particularly damaging to undead. Soul has a unique affinity with Kinetic Energy, such that most Soul practitioners pick up some Kinetic skill as a matter of course, and is readily channeled by Earth wands, particularly crystalline ones.<h2>The Sphere of Psychology</h2><p><b>Joy, Sadness, Disgust, Anger, Fear</b><p>These are the five atoms of minds. Note that we do our actual <i>thinking</i> with our souls; these atoms constitute the emotional core of our being that our minds are built around.<p>Like the other spheres, many simple spells are just raw application of these atoms. The classic fear spell is just pumping the target with excess Fear; simple heroism spells are just elevating Anger. Many warding and shielding spells involve use of Disgust. And of course, the representative skill of the mentalist discipline, charming, is in its simplest form just overloading the target with Joy - an ecstatic person is literally happy to do whatever you say.<p>Of course, these are not without downsides. A simple charm is immediately recognized by the target (tho they don't <i>care</i> about it until it wears off), as sudden euphoria is not a normal feeling, and is easy to spot in others. And the mind is not unfeeling Earth, able to be crudely shoveled around without damage; flooding a mind with an excess of psychological atoms can do permanent damage to a person's psyche.<p>Skilled users instead <i>carefully</i> manipulate the psychological atoms, weaving them together in complex interactions that use little actual force, and are much more difficult to detect. <br><p>The common "psionic" discipline is often considered to be psychological by laypeople, but this is mistaken. While psionics traditionally includes <i>some</i> psychology, its flashier effects (telepathy, telekinesis, etc) are actually usually based in the Soul/Kinetic affinity pair.<h2>The Sphere of the Divine</h2><p><b>White, Blue, Black, Red, Green</b><p>Divine magic flows directly from the gods, and comes bundled with each god's own idiosyncratic preferences and restrictions. Within that chaos, tho, arcanists have discovered five consistent aspects. Not only do gods themselves tend to organize around these aspects, but entire pantheons tend to stabilize around filling the five aspects equally. As such, most arcanists consider the five divine aspects to be the fifth atomic sphere, thus completing the pentad.<p>[snip explanation, they're the Magic: the Gathering color-wheel philosophies]<p>These can manifest in dramatically different ways. For example, one of the more popular pantheons is the Unconquered Sun, a triune deity preaching Right Thoughts (Blue), Right Body (Green), and Right Heart (White), opposed by the twin evils of the quick death (murder, Red) and the slow death (decay, Black). On a very different spectrum, the Garlandite pantheon is led by Garland, god of blood and pain (cast as the <i>good</i> god of this pantheon, believe it or not), opposed by the Four Distractions, each associated with one of the other four aspects. <p>"Arc" pantheons that center in one aspect but embrace the two neighboring ones are common. Druidic religions, for example, are almost always centered in Green with a reverence for nature, but embrace both organization (White) and savagery (Red), while typically fighting against death/corruption (Black) and technology/artifice (Blue). The Unconquered Sun's White-centered arc structure is common in many folk pantheons.<p>Destiny scholars suggest that the Divine sphere, more than any other, is strongly self-balancing. If a particular aspect becomes strong in an area, it automatically draws strong opposition from its enemy aspects to counter it. There is no known instance of a stable, long-lived religion that did not incorporate the five aspects in major positions, whether good or evil, balanced in some significant way.<p>This requirement for balance can manifest in fairly simple dualities, like the Unconquered Sun's pantheon, or in vastly more intricate pantheons, like the ten carefully intertwined cults of Ravnican society, each embracing a different pair of aspects and all serving a vital role in the maintenance of the Infinite City, or the five unbalanced "wedges" (two neighboring aspects and their mutual enemy) exemplified by the Dragonlords.<h2>Other Symmetries and Patterns</h2><p>Many traditions organize the spheres into two overlapping pair structures: Elements and Energies are of the world, while Biology and Psychology are of the body; Elements and Biology are physical, Energies and Psychology are ephemeral. Divinity is usually seen as above and transcending each of these divisions; the "pyramid metaphor" is common, with the four "base" spheres holding up the Divine peak.<p>Some theorists insist that the pure "greater pentad" structure laid out here is too pat, and the actual structure is much messier and harder to categorize. It's not uncommon to view Elements and Energies as two lobes of a conjoined structure, sharing a single Fire/Light atom. Similarly, Biology and Psychology are sometimes merged into a greater structure, with the five mental atoms emerging from Soul.http://www.xanthir.com/b4hG0More Efficient Encoding of Primes2016-05-28T02:17:22+00:002016-05-15T05:01:24+00:00<p><a href="http://www.xanthir.com/b4g01" title="">Earlier</a> I talked about efficiently encoding lists of primes via encoding the gaps between them, in a UTF-8 inspired encoding. That's great, but there's a much simpler, even more efficient way to encode a list of all primes - use bitfields!<p>In its simplest, least efficient form, you just associate each successive bit with each successive integer - the first bit is for 1, the second is for 2, etc. The bit is 1 if the associated number is prime, and 0 if it's composite.<p>This trivial, stupid encoding has an efficiency of 8 numbers per byte, which means it's equivalent to the previous gap-encoding as long as the average gap is less than 8 (which covers quite a lot of numbers!). But we can, of course, make it much better.<p>The first and most obvious improvement is to throw out all the even numbers. Past 2, every prime is odd, so all the even bits are guaranteed to be 0 in the naive scheme. That's wasted space; we can just assume they're composite and spend our actual data budget on the odd numbers. So now the Nth bit corresponds to the (2<i>N + 1)th number. This *doubles</i> our efficiency, encoding 16 numbers per byte, and roughly doubling the number of digits for which this is more efficient than the gap-encoding (covering the primes up to e^16, or ~9 million).<p>At this point we should pause and recognize the additional benefits we get from this encoding. Not only is it more efficient for quite a lot of primes (the primes up to 9M fill about 500kB of memory, and allow efficient prime testing/factorizing of numbers up to nearly 100 trillion), but it also gives us <i>constant-time random access</i> to the primality information. If you want to find out whether a random N is prime or not, you just look up the (N/16)th byte, and then check the (N/2 + 1)%8th bit. For some algorithms this is really important!<p>Okay, back to efficiency. Excluding all the even numbers is great, but it's of course also true that, once you get past 3, all the numbers divisible by 3 are composite. Combining that with the previous "no evens" insight, we can chop down the relevant set to just two out of every six numbers - only the values that are equal to 1mod6 or 5mod6. With this, we can encode 50% more numbers in a given number of bits! To be specific, it gives us 24 numbers per byte, exceeding the efficiency of gap-encoding up to e^24, or about 20 billion.<p>And we can go further! We can additionally exclude the numbers divisible by 5, leaving us with only 8 possibilities out of every 30 numbers (1, 7, 11, 13, 17, 19, 23, 29; mod 30), for an extra 25% density, winning the efficiency race up to ~10 trillion. This has some additional benefits, too - each "set" of possibles is 8 large, same as the number of bits in a byte, which simplifies the math considerably - you look in the N/30th byte, then grab the corresponding bit from the group. This limit also exceeds what we can reasonably use - storing the numbers up to 10 trillion would take about a third of a terabyte, greatly exceeding the RAM of desktop machines. So even in extreme cases, you'll get to store/use <i>more</i> primes with this method than the gap-encoding, and you get the random-access benefit to boot.<p>We could go further and exclude the multiples of 7, but the benefits are fairly small (encode about 16% more in a given space) and the math becomes a lot more annoying (49 possible primes spread across 210 numbers) and loses the nice symmetries of the previous values, so it's best to probably just stop there.