36:I[383949,["/_next/static/immutable/chunks/1398ofyqrhx4a.js","/_next/static/immutable/chunks/0t40umg6hy8qx.js","/_next/static/immutable/chunks/2uspw589s4ova.js","/_next/static/immutable/chunks/0lup-wm95fye4.js","/_next/static/immutable/chunks/2xvdcd8pkkmev.js","/_next/static/immutable/chunks/3ac0x9so7a-m6.js","/_next/static/immutable/chunks/3vvcl33bfnpfb.js","/_next/static/immutable/chunks/1rjt8b3m8c5kq.js","/_next/static/immutable/chunks/2fhyv3228wuuz.js","/_next/static/immutable/chunks/2fwcnlg92491e.js","/_next/static/immutable/chunks/1ro_riwwfy4z1.js","/_next/static/immutable/chunks/222ll6utk9ao_.js","/_next/static/immutable/chunks/3_hjfmmp-iede.js","/_next/static/immutable/chunks/2a4tc_3oyxmst.js","/_next/static/immutable/chunks/0oz12lkjxk60o.js","/_next/static/immutable/chunks/3r_-527bd7kov.js","/_next/static/immutable/chunks/0t9rgvr0ksja_.js","/_next/static/immutable/chunks/3adoyl4bf3qlp.js"],"ProfileSubscriptionsContent",1] 37:T618,something else I've been working on, an app that holds your did:plc rotationKey https://plc.directory/did:plc:bf57wcfbkne5sjsk6w62pkcq/log/audit it pairs with a "relay" (wip name) that serves as the PDS and also holds one of three Shamir shares used to recover the key. very far from prod ready it's all open, you can find it on tangled: https://tangled.org/malpercio.dev/ezpds I'd welcome any and all possible contributors who may be interested! I think there's several interesting directions to go from here. There's the direction I'm headed, which is for the app to hold the root rotation key, but otherwise a PDS is hosted "elsewhere", right now, it would be the PDS I'm building in tandem with it. Afterwards, I want to explore a desktop app, using Iroh to establish a tunnel between the desktop app and the hosted "relay"/PDS, where the desktop app serves to hold the repo/blobs, and the relay provides network access and perhaps a mirror that can be served when the desktop is unavailable. A possible pivot from that plan would be to double-down on the wallet or "atprotocol-companion", it's an app that stores your entire identity on the protocol and provides tools for managing it, such as managing rotation keys, browsing one's own PDS, etc. PDS-on-a-phone does seem very interesting as well, and is where I started, however it was seeming intractable, at least on iOS, due to stringent rules on apps for running in the background. However that may be possible on Android, or through some clever other tricks! If you have ideas, reach out anytime. :)38:T428,let initialState = [ { mass: 42, position: [3, 1, 2], momentum: [-3.2, 4.1, 1.8] }, // .. all the other objects we care about ... ] function update(state, dt) { return state.map(obj => { // how much do other things affect this object? const forces = calculateGravity(obj, state) // newton's second law: const nextMomentum = obj.momentum.map((p, i) => p + forces[i] * dt) const nextPosition = obj.position.map((x, i) => x + (nextMomentum[i] / obj.mass) * dt) return { mass: obj.mass, momentum: nextMomentum, position: nextPosition } }) } const G = 6.674e-11 function calculateGravity(obj, state) { const force = [0, 0, 0] for (const other of state) { if (other === obj) continue const d = [ other.position[0] - obj.position[0], other.position[1] - obj.position[1], other.position[2] - obj.position[2] ] const r = Math.hypot(...d) // distance const f = (G * obj.mass * other.mass) / (r * r * r) force[0] += f * d[0] force[1] += f * d[1] force[2] += f * d[2] } return force }39:T400,type Point = [number, number, number] type PointState = { value: number, velocity: number } let initialState: Map = Map.fill( { value: 0, velocity: 0 } ) function update(state, dt) { return state.map((pointState, point, ds) => { const { value, velocity } = pointState const nextVelocity = velocity + tension(state, point, ds) * dt const nextValue = value + nextVelocity * dt return { value: nextValue, velocity: nextVelocity } }) } const C = 1 function tension(field, [x, y, z], ds) { const neighbors = [ field.get([x + ds, y, z]), // right field.get([x - ds, y, z]), // left field.get([x, y + ds, z]), // above field.get([x, y - ds, z]), // below field.get([x, y, z + ds]), // in front of field.get([x, y, z - ds]) // behind ].map(ps => ps.value) const neighborSum = neighbors.reduce((a, b) => a + b, 0) const ownValue = field.get([x, y, z]).value const result = neighborSum - neighbors.length * ownValue return result * (C * C) / (ds * ds) }3a:T450,type Point = [number, number, number] type Arrow = [number, number, number] type Field = Map let initialState = { electric: Field.fill([0, 0, 0]), magnetic: Field.fill([0, 0, 0]), } const C = 1 function update({ electric, magnetic }, dt) { const nextElectric = electric.map((e, point, ds) => e + curl(magnetic, point, ds) * (C * C * dt) ) const nextMagnetic = magnetic.map((b, point, ds) => b - curl(nextElectric, point, ds) * dt ) return { electric: nextElectric, magnetic: nextMagnetic } } function curl(field, [x, y, z], ds) { // which way the arrow points as you step along each axis const dx = (field.get([x + ds, y, z]) - field.get([x - ds, y, z])) / (2 * ds) const dy = (field.get([x, y + ds, z]) - field.get([x, y - ds, z])) / (2 * ds) const dz = (field.get([x, y, z + ds]) - field.get([x, y, z - ds])) / (2 * ds) // do the surrounding arrows turn as you loop around this point? return [ dy.z - dz.y, // looping around the x-axis dz.x - dx.z, // looping around the y-axis dx.y - dy.x // looping around the z-axis ] }1a:[["$","div",null,{"className":"spacer h-4 w-full"}],["$","$L36",null,{"did":"did:plc:xhwhcrlq75w45zmm6ea7jgjn","subscriptions":[{"uri":"at://did:web:malpercio.dev/site.standard.publication/3mf5rwgcak2fk","name":"Mal’s Musings","record":{"url":"https://mal-s-musings.pckt.blog","name":"Mal’s Musings","$type":"site.standard.publication","theme":{"dark":{"link":"#34d399","text":"#e3f2ed","accent":"#064e3b","background":"#0f1f18","surfaceHover":"#0b2a21"},"font":"legible","$type":"pub.leaflet.publication#theme","light":{"link":"#059669","text":"#052e23","accent":"#064e3b","background":"#f0fdf4","surfaceHover":"#dcfce7"},"transparency":100},"basicTheme":{"$type":"site.standard.theme.basic","accent":{"b":59,"g":78,"r":6,"$type":"site.standard.theme.color#rgb"},"background":{"b":244,"g":253,"r":240,"$type":"site.standard.theme.color#rgb"},"foreground":{"b":35,"g":46,"r":5,"$type":"site.standard.theme.color#rgb"},"accentForeground":{"b":231,"g":252,"r":220,"$type":"site.standard.theme.color#rgb"}},"description":"","preferences":{"showComments":true,"showMentions":true,"showPrevNext":false,"showInDiscover":true,"showRecommends":true}},"indexed_at":"2026-02-25T01:12:20.186633+00:00","identity_did":"did:web:malpercio.dev","draft_leaflet":null,"documents_in_publications":[{"document":"at://did:web:malpercio.dev/site.standard.document/3mhludu47ojvm","documents":{"uri":"at://did:web:malpercio.dev/site.standard.document/3mhludu47ojvm","data":{"path":"/ezpds-working-name-21m8bg2","site":"at://did:web:malpercio.dev/site.standard.publication/3mf5rwgcak2fk","tags":[],"$type":"site.standard.document","title":"'ezpds' - working name","content":{"$type":"blog.pckt.content","items":[{"$type":"blog.pckt.block.text","facets":[{"index":{"byteEnd":144,"byteStart":80},"features":[{"uri":"https://plc.directory/did:plc:bf57wcfbkne5sjsk6w62pkcq/log/audit","$type":"blog.pckt.richtext.facet#link"}]}],"plaintext":"something else I've been working on, an app that holds your did:plc rotationKey https://plc.directory/did:plc:bf57wcfbkne5sjsk6w62pkcq/log/audit"},{"$type":"blog.pckt.block.text","plaintext":"it pairs with a \"relay\" (wip name) that serves as the PDS and also holds one of three Shamir shares used to recover the key."},{"$type":"blog.pckt.block.text","plaintext":"very far from prod ready"},{"$type":"blog.pckt.block.image","attrs":{"alt":"output.gif","src":"https://pckt-blog-media.s3.us-east-2.amazonaws.com/images/5bc6405e-c046-4526-85a0-d15095a47c14/output.gif","align":"center","width":"500"}},{"$type":"blog.pckt.block.text","facets":[{"index":{"byteEnd":82,"byteStart":43},"features":[{"uri":"https://tangled.org/malpercio.dev/ezpds","$type":"blog.pckt.richtext.facet#link"}]}],"plaintext":"it's all open, you can find it on tangled: https://tangled.org/malpercio.dev/ezpds"},{"$type":"blog.pckt.block.text","plaintext":"I'd welcome any and all possible contributors who may be interested!"},{"$type":"blog.pckt.block.text","plaintext":"I think there's several interesting directions to go from here."},{"$type":"blog.pckt.block.text","plaintext":"There's the direction I'm headed, which is for the app to hold the root rotation key, but otherwise a PDS is hosted \"elsewhere\", right now, it would be the PDS I'm building in tandem with it."},{"$type":"blog.pckt.block.text","plaintext":"Afterwards, I want to explore a desktop app, using Iroh to establish a tunnel between the desktop app and the hosted \"relay\"/PDS, where the desktop app serves to hold the repo/blobs, and the relay provides network access and perhaps a mirror that can be served when the desktop is unavailable."},{"$type":"blog.pckt.block.text","plaintext":"A possible pivot from that plan would be to double-down on the wallet or \"atprotocol-companion\", it's an app that stores your entire identity on the protocol and provides tools for managing it, such as managing rotation keys, browsing one's own PDS, etc."},{"$type":"blog.pckt.block.text","plaintext":"PDS-on-a-phone does seem very interesting as well, and is where I started, however it was seeming intractable, at least on iOS, due to stringent rules on apps for running in the background. However that may be possible on Android, or through some clever other tricks! If you have ideas, reach out anytime. :) "},{"$type":"blog.pckt.block.text","plaintext":""}]},"updatedAt":"2026-03-21T20:37:50+00:00","description":"something else I've been working on, an app that holds your did:plc rotationKey https://plc.directory/did:plc:bf57wcfbkne5sjsk6w62pkcq/log/audit it pairs with a \"relay\" (wip name) that serves as the PDS and also holds one of three Shamir shares used to recover the key. very far from prod 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pizza thoughts","record":{"url":"https://bnewbold.leaflet.pub","icon":{"ref":{"$link":"bafkreibdxk5dz67z5st2r2yynpxgrec4w7ztifsydwq7jphpqdnsucl7tm"},"size":64316,"$type":"blob","mimeType":"image/png"},"name":"at:// pizza thoughts","$type":"site.standard.publication","theme":{"$type":"pub.leaflet.publication#theme","primary":{"b":39,"g":39,"r":39,"$type":"pub.leaflet.theme.color#rgb"},"accentText":{"b":255,"g":255,"r":255,"$type":"pub.leaflet.theme.color#rgb"},"pageBackground":{"a":100,"b":250,"g":252,"r":253,"$type":"pub.leaflet.theme.color#rgba"},"backgroundColor":{"b":213,"g":230,"r":237,"$type":"pub.leaflet.theme.color#rgb"},"accentBackground":{"b":15,"g":15,"r":148,"$type":"pub.leaflet.theme.color#rgb"},"showPageBackground":false},"basicTheme":{"$type":"site.standard.theme.basic","accent":{"b":15,"g":15,"r":148,"$type":"site.standard.theme.color#rgb"},"background":{"b":213,"g":230,"r":237,"$type":"site.standard.theme.color#rgb"},"foreground":{"b":0,"g":0,"r":0,"$type":"site.standard.theme.color#rgb"},"accentForeground":{"b":255,"g":255,"r":255,"$type":"site.standard.theme.color#rgb"}},"description":"mini-proposals, guides, ruminations, and other AT stuff","preferences":{"showComments":true,"showInDiscover":true}},"indexed_at":"2026-01-23T22:06:44.146228+00:00","identity_did":"did:plc:44ybard66vv44zksje25o7dz","draft_leaflet":null,"documents_in_publications":[{"document":"at://did:plc:44ybard66vv44zksje25o7dz/site.standard.document/3mph4hzvbdc2v","documents":{"uri":"at://did:plc:44ybard66vv44zksje25o7dz/site.standard.document/3mph4hzvbdc2v","data":{"path":"/3mph4hzvbdc2v","site":"at://did:plc:44ybard66vv44zksje25o7dz/site.standard.publication/3m2x76zrtrs23","tags":["atproto"],"$type":"site.standard.document","title":"The AT-URI Syntax Mess","content":{"$type":"pub.leaflet.content","pages":[{"id":"019f1020-97a9-7bb6-9327-e78262ab254e","$type":"pub.leaflet.pages.linearDocument","blocks":[{"$type":"pub.leaflet.pages.linearDocument#block","block":{"alt":"pizza baking in a home oven","$type":"pub.leaflet.blocks.image","image":{"ref":{"$link":"bafkreigh5rleonndmd23hpegv4kx7oza5n5aekafsjigpsrux3oxyhuc64"},"size":391730,"$type":"blob","mimeType":"image/webp"},"aspectRatio":{"width":2048,"height":1536}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":222,"byteStart":217},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":316,"byteStart":308},"features":[{"uri":"https://www.rfc-editor.org/info/rfc3986/#section-3.2","$type":"pub.leaflet.richtext.facet#link"}]}],"plaintext":"It's time to tackle one of the most unfortunate warts in the atproto specifications: that the AT URI syntax, as currently specified, is not a valid URI or URL. We put DIDs in the URI \"authority\" place (just after the at://), and they conflict with the host/port hierarchal URI syntax components specified in RFC 3986."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":65,"byteStart":48},"features":[{"uri":"https://github.com/bluesky-social/atproto-website/issues/417","$type":"pub.leaflet.richtext.facet#link"}]},{"index":{"byteEnd":227,"byteStart":221},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":279,"byteStart":250},"features":[{"uri":"https://datatracker.ietf.org/doc/charter-ietf-atp/","$type":"pub.leaflet.richtext.facet#link"}]}],"plaintext":"The core issue was surfaced in 2025 (by @mcc in this github issue), and is coming to a head now for two reasons. First, more folks are trying to use AT URIs in places expecting a well-formed URI (or URL), such as in HTML tags. And second, the ATP Working Group at the IETF has a deliverable of standardizing the AT URI scheme with a permanent registration."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"The purpose of this post is give some background on the situation, then talk through some ways we could try and fix it. Unfortunately, I don't think there are any great options on the table: any path the ecosystem takes is going to involve some developer pain and disruption."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"I care a lot about this because I think AT URIs are quietly one of the best and most important features of the protocol! Putting an individual account identifier in the authority section, instead of a provider hostname, is both concretely and symbolically one of the Big Ideas of atproto: accounts are the ultimate authority for their content, and can seamlessly move between hosting providers. Accounts are in the driver seat, and resolve to a current network location. That aspect isn't going to change, and if we can resolve this syntax mess then folks can go nuts and start using AT URIs all over the place."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"What Went Wrong?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"To ground things a bit, here is an example AT URI pointing at a specific record, with a DID in the authority place:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"plaintext","plaintext":"at://did:plc:vwzwgnygau7ed7b7wt5ux7y2/app.bsky.feed.post/3k5nobkf2w72g"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"And the generic syntax:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"plaintext","plaintext":"at:// / / "}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":7,"byteStart":4},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":84,"byteStart":60},"features":[{"uri":"https://www.iana.org/assignments/uri-schemes/uri-schemes.xhtml","$type":"pub.leaflet.richtext.facet#link"}]}],"plaintext":"The at: URI schema was originally designed in 2022, and was provisionally registered in 2023. We knew that putting a DID in the authority part could cause compatibility issues, and would mean the syntax wasn't a valid web URL under the WHATWG specification. But we (incorrectly) thought that it still complied with the URI syntax, as standardized in RFC-3986."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"Designing AT Protocol has always been a group effort, both inside and outside Bluesky, but I feel a personal responsibility for this particular syntax mess. I spent a fair amount of time in spring 2023 reviewing and \"hardening\" the written specifications to catch issues exactly like this."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":94,"byteStart":81},"features":[{"uri":"https://www.rfc-editor.org/info/rfc3986/#section-1.2.3","$type":"pub.leaflet.richtext.facet#link"}]}],"plaintext":"The root of the issue came from motivated reading of RFC-3986, and in particular Section 1.2.3:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.blockquote","plaintext":"For some URI schemes, the visible hierarchy is limited to the scheme itself: everything after the scheme component delimiter (\":\") is considered opaque to URI processing."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":352,"byteStart":325},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":401,"byteStart":363},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"At the time I interpreted this to mean that the underlying principle was that a URI was the scheme name and then colon character. Everything after that, as described in section 3.2, 3.3, and on, seemed like optional \"hierarchal\" syntax, which could be ignored. There are plenty of valid URI schemes that do this, like email (mailto:John.Doe@example.com), usenet (news:comp.infosystems.www.servers.unix)."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":152,"byteStart":132},"features":[{"uri":"https://www.rfc-editor.org/info/rfc7595/#section-3.2","$type":"pub.leaflet.richtext.facet#link"}]}],"plaintext":"Further guidance for URIs which are intended for permanent IANA registration (which we want for the AT URI scheme) are described in RFC-7595 Section 3.2, which says:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.blockquote","plaintext":"Schemes SHOULD avoid improper use of \"//\". The use of double slashes in the first part of a URI is not a stylistic indicator that what follows is a URI: double slashes are intended for use ONLY when the syntax of the contains a hierarchical structure. In URIs from such schemes, the use of double slashes indicates that what follows is the top hierarchical element for a naming authority (Section 3.2 of RFC 3986 has more details). Schemes that do not contain a conformant hierarchical structure in their SHOULD NOT use double slashes following the \":\" string."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"That makes it clear what the best practice is, though i'll note that these are \"SHOULD\" not \"MUST\"."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":107,"byteStart":105},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":163,"byteStart":144},"features":[{"uri":"https://www.rfc-editor.org/info/rfc3986/#appendix-A","$type":"pub.leaflet.richtext.facet#link"}]},{"index":{"byteEnd":198,"byteStart":181},"features":[{"uri":"https://url.spec.whatwg.org/","$type":"pub.leaflet.richtext.facet#link"}]}],"plaintext":"Overall, it seems clear that the generic/hierarchal syntax restrictions are intended to be required when // is used. The formal ABNF grammar in RFC-3986 Appendix A requires it. The WHATWG URL syntax leaves no ambiguity about this. And on a pragmatic level, the actual strings fail to parse with most real-world URL and URI libraries."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"Why this motivated reasoning in the first place? Because we love the current simple syntax. It's clean and idiomatic. It looks familiar to developers, doesn't involve any encoding/decoding or string mangling, and riffs on accepted semantics. Because DIDs always have at least two colons, confusion with hostnames (or IP addresses) is not actually ambiguous. If the URI syntax was valid, it felt like there might be a path to getting support elsewhere over time, like in browsers and generic URI parsing libraries."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"What Can We Do About It?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"There are billions of AT URIs in the wild today. Many of these are in content-addressed data records which can not be update without changing the record version (hash). Or in millions of cryptographically signed label objects from hundreds of providers. This means that the current syntax is going to be encountered and needs to be at least partially supported by atproto implementations indefinitely."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"With that in mind, I think there are a few broad approaches the ecosystem could take:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":54,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"Keep the existing syntax, and stop calling it a \"URI\": for example, call them \"AT reference identifiers\" or something like that. This would mean abandoning the IETF working group charter goal of standardizing the URI scheme. It would also cause endless confusion and ambiguity when trying to use the strings on the web, in other protocols, etc. I think this is a bad outcome and we should not take this path."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":68,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"Keep the existing syntax, and get the IETF URI syntax rules changed: this would be a huge lift, sort of a \"move the mountain\" play. It would require a huge amount of standards body diplomacy and social capital, and would probably take years. I do think the outcome might be the best for both the atproto ecosystem and the internet protocol space generally. I think the URI/URL specification would be cleaner, and implementations clearer, if the authority part were more flexible in the generic case. This would make it easier for future protocols and URI schemes to use alternative semantics, without encoding or string mangling hacks. But it would be a big swing, and i'm not sure it would be wise to attempt it."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":45,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"Change the AT URI syntax to be IETF compliant: there are a few different approaches we could take, which I discuss in a separate section below. None of them are as clean as the current syntax, and atproto implementations would need to support both versions, and handle normalization and equality checks carefully. Rolling out the change would take a long time, soak up developer time and attention, and some degree of user-impacting breakage feels inevitable along the way (because not all deployed software will support the new syntax). On the other hand, folks could start doing integrations with other software and protocols sooner, and the IETF working group would have an easier time getting through the initial charter."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"My current feeling is that we should explore the second and third options in parallel. Figure out how much work and disruption these would actually be, come up with firmer proposals, and talk to folks. The venue for making a final decision should be the IETF working group (aka, on the mailing list), though we should take input from the broader atmosphere developer ecosystem in to account."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"Alternative Syntax"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"How could we change the AT URI syntax to be valid under the existing IETF URI rules?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"Personally, i'm broadly against approaches that involve different URI schemes; string encoding/decoding; alternative identifiers; or identifier mangling. I'll run through a few examples of those first."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":132,"byteStart":109},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":165,"byteStart":138},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"One of the more direct approaches would be to percent-encode the DID in the authority section. So instead of at://did:plc:abc123/..., use at://did%3Aplc%3Aabc123/.... One advantage of this is that future DID methods with reserved characters could be used, or even other non-DID identifiers. But we know from their use in web URLs that percent encoding can be a total pain. They are ugly and unclear to look at, so folks will frequently display them in original form. Putting entire AT URIs in query parameters would involve double-encoding. There is no clear an reliable way to know if an input string has been sufficiently encoded/decoded. It is very easy to forget to encode when constructing a string. Decoding requires an extra string pass/copy and often an allocation. Blech. But I would guess this is the direction that standards folks will nudge us in."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":158,"byteStart":135},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":209,"byteStart":186},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"A similar category of approaches would be to map DID syntax to allowed URI \"host\" syntax. For example, replace the colons with dashes (at://did-plc-abc123/...), or invent new hostnames (at://abc123.plc.did/...). These are cleaner-looking and avoid some of the encoding problems, but they do add a level of translation and indirection which is likely to cause confusion."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":156,"byteStart":88},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"Some folks have proposed skipping the AT URI schema entirely and using \"DID URLs\", like did:plc:vwzwgnygau7ed7b7wt5ux7y2/at/app.bsky.feed.post/3k5nobkf2w72g. I don't like this because it is ambiguous how a DID URL string in the wild is supposed to be interpreted. You'd need to guess that it is \"for atproto\". It makes the URI strings less identifiable (\"what is this for\"). It would also lock the protocol in to use of DIDs long-run, and we might want to support non-DID persistent account identifiers in the future."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":102,"byteStart":75},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"Other folks have proposed always using handles instead of DIDs in AT URIs (at://handle.example.com/...). This is already allowed under the AT URI specification, and follows the IETF URI rules. But this goes against the \"persistent identifier\" strength of DIDs in atproto. Handles can change, but DIDs stay the same for the entire lifetime of an account."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":22,"byteStart":20},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":91,"byteStart":69},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":123,"byteStart":102},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":206,"byteStart":201},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"We could stop using // in the URI, either going with a single slash (at:/did:plc:abc123/...) or none (at:did:plc:abc123/...). I think folks would frequently type or correct the single slash version to at://. And the no-slash version looks more like a URN and could be confusing to new developers or end users. But I think these is moving in the right direction."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":132,"byteStart":108},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":238,"byteStart":211},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":514,"byteStart":508},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"My current pick for an alternative syntax would be to go with an empty authority section and three slashes: at:///did:plc:abc123/.... This is allowed under the URI rules, and frequently shows up with file URIs (file:///home/root/notes.txt) where the authority part is optional. The DID ends up under the first path segment, and does not need to be encoded or mangled. Regular URI/URL libraries should work fine. It would be simple to disambiguate these from current AT URIs (just check if the strings starts at:///). It's just a single character change. On the other hand, this feels like it is bending the spirit of the URI syntax: we would be shifting the \"authority\" part to a \"path\" part just to resolve syntax restrictions. I'm not sure what IETF folks and the IANA URI registry reviewers would think about this. It looks a bit off visually, and folks are likely to \"correct\" these to double-slash manually."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"What Else?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"This post has focused on the primary use-case of AT URIs: globally referencing public records in the network. But there are a couple other things going on with atproto URIs which are worth noting."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":169,"byteStart":144},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"A short form of AT URIs is used in DID documents to confirm DID/handle mapping. These show up in the \"alsoKnownAs\" array of URIs, and look like at://username.example.com. Handles are always valid hostnames, which means these are already valid URIs (and URLs). Changing all of these would require broad DID document updates, which would be a pain. I think we can simply keep this syntax for this use-case without too much confusion or disruption."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":242,"byteStart":236},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":334,"byteStart":329},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"Design work is under way on \"permissioned data\" for atproto. This isn't under the current IETF working group charter, but we expect it to end up there under a future re-charter. Part of the current \"spaces\" proposal would include a new ats:// URI scheme (\"Authenticated Transfer Space\"). This scheme would have similar syntax to at://, including a \"space authority DID\" in the URI authority place. Whatever solution we come up with for AT URIs would presumably transfer over to ATS URIs."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"Part of the IETF working group charter is coming up with criteria and a registry for \"account identifier systems\". The current atproto specifications require the use of DIDs, and specifically two DID methods are supported (DID PLC and DID Web). It is possible that non-DID identifier systems might end up being allowed by the working group. In general, the generic syntax of future account identifiers will be relevant to the AT URI syntax, and should be included as part of the final criteria."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":81,"byteStart":66},"features":[{"uri":"https://leaflet.pub/3a68c557-f767-494b-81f9-b38c1a878a69","$type":"pub.leaflet.richtext.facet#link"}]},{"index":{"byteEnd":102,"byteStart":85},"features":[{"uri":"https://leaflet.pub/4c5def15-d1f5-4476-a008-51176e615bc6","$type":"pub.leaflet.richtext.facet#link"}]}],"plaintext":"There are some other small changes we could make to AT URIs, like blob references or record versioning. Those are relatively simple changes to the path structure, and don't touch on the core question here of authority part syntax."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.horizontalRule"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"That's the big picture! I expect this will be discussed over the next few months, both on the IETF ATP mailing list and elsewhere in the atproto developer ecosystem. It would be great if we could come to a rough consensus by the end of the year, perhaps at the IETF 127 meeting in November."}}]}]},"coverImage":{"ref":{"$link":"bafkreigh5rleonndmd23hpegv4kx7oza5n5aekafsjigpsrux3oxyhuc64"},"size":391730,"$type":"blob","mimeType":"image/webp"},"bskyPostRef":{"cid":"bafyreicyhovoioy3rdsbnbovvdbjh4ifgjnatrjqs7mkcekupobm73kje4","uri":"at://did:plc:44ybard66vv44zksje25o7dz/app.bsky.feed.post/3mph4i3kfjk2v","commit":{"cid":"bafyreicc3jh3mezs7bjz7sgxb6clev5snh2w2lj3iopcxp4b4bxjty2o6i","rev":"3mph4i3ukps2y"},"validationStatus":"valid"},"description":"Why AT URIs are not valid under IETF RFC-3986, what the impact is, and some possible ways 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i haven't written yet","preferences":{"showComments":true,"showInDiscover":true}},"indexed_at":"2026-01-23T22:04:44.066465+00:00","identity_did":"did:plc:fpruhuo22xkm5o7ttr2ktxdo","draft_leaflet":null,"documents_in_publications":[{"document":"at://did:plc:fpruhuo22xkm5o7ttr2ktxdo/site.standard.document/3mncmabgnmc2x","documents":{"uri":"at://did:plc:fpruhuo22xkm5o7ttr2ktxdo/site.standard.document/3mncmabgnmc2x","data":{"path":"/3mncmabgnmc2x","site":"at://did:plc:fpruhuo22xkm5o7ttr2ktxdo/site.standard.publication/3m23dstduds2v","tags":["physics"],"$type":"site.standard.document","title":"physics as a game loop. part 1: objects and waves","content":{"$type":"pub.leaflet.content","pages":[{"id":"019e7e39-6ef3-700a-981b-482250e78248","$type":"pub.leaflet.pages.linearDocument","blocks":[{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"suppose you're developing a theory of how the world works."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":83,"byteStart":74},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"if you're a software developer, you might be familiar with a concept of a game loop. you have some state and update function. you call the update function in a loop, and so the state changes over time."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":43,"byteStart":38},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"in a sense, a game loop describes the world of your game. most games are pretty complex but here's a very simple one — a counter:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"let initialState = 0\n\nfunction update(state) {\n return state + 1;\n}\n\nfunction loop() {\n let state = initialState;\n while (true) {\n state = update(state);\n }\n}"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"this \"world\" just has a single number that grows with each tick: first it's 0, then it's 1, then it's 2, and so on till the end of time."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"now, what is physics?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":70,"byteStart":67},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":287,"byteStart":229},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"the basic idea of physics is to describe the behavior of things in our world in a way that lets us make predictions (and verify whether they were correct). so, putting on the software developer hat, you could think of physics as \"reverse-engineering\" the game loop of the universe itself — finding its \"state\" and \"update function\". we just need to find all the \"things\" and describe how those \"things\" evolve:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"let initialState = [\n /* ... particles? positions? forces? ... */\n]\n\nfunction update(state) {\n const nextState = /* ??? physical laws ??? */\n return nextState;\n}\n\n// game loop stays the same\nfunction loop() {\n let state = initialState;\n while (true) {\n state = update(state);\n }\n}"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"if we fill these two gaps, we can predict everything that happens."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"or so we might hope!"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.horizontalRule"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":379,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"when i started writing this, i only meant to write about quantum mechanics as a game loop. however, i wanted to show a few game loops from classical physics first — and learning those has been so interesting that it snowballed into a post of its own. if you struggled with physics but can read pseudocode, i hope this post will convey the joy i had learning about these things."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.horizontalRule"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"let's add continuous time"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":182,"byteStart":176},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":213,"byteStart":208},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"of course, this presupposes that it's possible to describe our universe this way at all. in the real world, time seems to be continuous — it seems to \"pass\". we somehow need update to describe what happens after a time — not at some \"next frame\"."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":49,"byteStart":47},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"to make our game loop continuous, let us add a dt parameter:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"function update(state, dt /* a bit of time */) {\n const nextState = /* ??? physical laws ??? */\n return nextState;\n}"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"now our physical laws can refer to a concept of time rather than \"nth frame\". the \"counter\" from before would now be a \"clock\":"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"function update(state, dt) {\n return state + dt; // instead of state + 1 before\n}"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":41,"byteStart":39},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"but here is a trick question about the dt parameter."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"suppose you wanted to calculate \"the state of the world in five seconds\". which of these do you think would produce better results?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.unorderedList","children":[{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":31,"byteStart":15},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"a) calculating update(state, 5) once"}},{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":34,"byteStart":15},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":68,"byteStart":63},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":89,"byteStart":83},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":114,"byteStart":111},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"b) calculating update(state, 0.01), then passing the result as state into the next update call, and so on, for 500 times"}},{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":37,"byteStart":15},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":71,"byteStart":66},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":92,"byteStart":86},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":120,"byteStart":114},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"c) calculating update(state, 0.00001), then passing the result as state into the next update call, and so on, for 500000 times"}},{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","plaintext":"d) these would all produce the same result"}}]}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"(scroll down for answer)"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":""}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":""}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":""}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":""}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":""}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":""}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":""}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":""}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":""}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":""}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":142,"byteStart":135},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":181,"byteStart":175},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":193,"byteStart":185},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":243,"byteStart":227},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":246,"byteStart":244},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"the answer is — for the \"clock\" example above the answer is (d), but generally for most physics the answer is (c). in fact, to get a perfect answer, we'll want to apply the update an infinite number of times — each with an infinitely small dt. (math can help with this.)"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"we can think of the nature's game loop as being something like this:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"function loop() {\n let state = initialState;\n for (let dt of time() /* for every bit of time */) {\n state = update(state, dt);\n }\n}"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":10,"byteStart":8},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":22,"byteStart":14},"features":[{"$type":"pub.leaflet.richtext.facet#bold"},{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":39,"byteStart":22},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"imagine dt is actually infinitely small here, and there are infinitely many of them. nature doesn't mind it, so we won't mind it either."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"(computers mind it, but luckily this code isn't for computers.)"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"this is actually rather profound. if you just tried to guess how the world works, you might have looked for laws that say \"what happens in three seconds\", \"what happens in five seconds\", and so on. but it's often not possible directly! in practice, physical laws seem to want to be described as \"what happens at every instant\"."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":39,"byteStart":36},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":170,"byteStart":164},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":228,"byteStart":226},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":309,"byteStart":290},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":311,"byteStart":309},"features":[{"$type":"pub.leaflet.richtext.facet#code"},{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":329,"byteStart":311},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"in either case, this actually makes our job easier. we only need to figure out what happens \"now\" at each moment, not what happens \"over time\". in other words, our update function doesn't even need to be correct for arbitrary dt — five seconds, three seconds, etc. we only need it to get ever correct-er as dt gets ever smaller."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":34,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]},{"index":{"byteEnd":40,"byteStart":34},"features":[{"$type":"pub.leaflet.richtext.facet#code"},{"$type":"pub.leaflet.richtext.facet#bold"}]},{"index":{"byteEnd":67,"byteStart":40},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"to sum up, our job is to find the update function for the universe:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"let initialState = [\n /* ... particles? positions? forces? ... */\n]\n\nfunction update(state, dt) {\n const nextState = /* ??? physical laws ??? */\n return nextState;\n}"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":25,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]},{"index":{"byteEnd":30,"byteStart":25},"features":[{"$type":"pub.leaflet.richtext.facet#bold"},{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":39,"byteStart":30},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]},{"index":{"byteEnd":54,"byteStart":39},"features":[{"$type":"pub.leaflet.richtext.facet#bold"},{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":130,"byteStart":54},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"if we could describe the state and its update function over time, we'd have \"solved\" the universe and be able to predict anything."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":27,"byteStart":25},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"(and who knows, maybe it is written in this pseudocode javascript)"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.horizontalRule"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"newton's world: a game loop for objects"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"take newtonian gravity — which has been a successful model for centuries and seemed to work decently for both planets and apples."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"when we describe movement of objects (in newtonian gravity), the \"state\" would be things like masses, positions and momentums:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"let initialState = [\n { mass: 42, position: [3, 1, 2], momentum: [-3.2, 4.1, 1.8] },\n // .. all the other objects we care about ...\n]"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"the \"update function\" would then update those every instant of time:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"function update(state, dt) {\n return state.map(obj => {\n // how much do other things affect this object?\n const forces = calculateGravity(obj, state)\n // newton's second law:\n const nextMomentum = obj.momentum.map((p, i) => p + forces[i] * dt)\n const nextPosition = obj.position.map((x, i) => x + (nextMomentum[i] / obj.mass) * dt)\n return { mass: obj.mass, momentum: nextMomentum, position: nextPosition }\n })\n}"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":22,"byteStart":6},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"here, calculateGravity is a pure function that accumulates how each object is affected by every other object at a given instant:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"const G = 6.674e-11\nfunction calculateGravity(obj, state) {\n const force = [0, 0, 0]\n for (const other of state) {\n if (other === obj) continue\n const d = [\n other.position[0] - obj.position[0],\n other.position[1] - obj.position[1],\n other.position[2] - obj.position[2]\n ]\n const r = Math.hypot(...d) // distance\n const f = (G * obj.mass * other.mass) / (r * r * r)\n force[0] += f * d[0]\n force[1] += f * d[1]\n force[2] += f * d[2]\n }\n return force\n}"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"if you wanted to make it feel more real, you could then introduce additional concepts on top of this framework to implement collisions, bouncing, friction, and so on. many game engines do just that!"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":2,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]},{"index":{"byteEnd":260,"byteStart":3},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"in newtonian gravity, the state includes positions, masses and momentums (or, equivalently, velocities) of each relevant object. the update function figures out how objects \"act\" on each other at each instant in time, and adjusts their momentums and positions."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"this model describes the world of \"big things\" approximately well, and lets us make rough predictions about how it evolves over time."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":155,"byteStart":141},"features":[{"uri":"https://en.wikipedia.org/wiki/Three-body_problem","$type":"pub.leaflet.richtext.facet#link"}]},{"index":{"byteEnd":284,"byteStart":281},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"for some cases, we can easily take an infinite sum of this \"instant by instant\" calculation to answer \"what will happen in ten seconds\", but in other cases we can't do it as neatly — so the best we can do are special cases or approximations. still, this is a win because we know how the world \"evolves\" over time; the rest is computing."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":28,"byteStart":22},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"but then, some things really don't fit this model."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":12,"byteStart":6},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"like, at all."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"light is one of those things."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.horizontalRule"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"a rippling wobble"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"if you try to throw a stone, it rises and falls tracing a parabola. this actually follows from the newtonian model quite nicely: the stone's momentum changes on each instant, eventually pointing down."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":53,"byteStart":44},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":60,"byteStart":58},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"most importantly, a stone always lands at a specific place. it may not be the place you were aiming for but at least it is quite specific."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":28,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"light doesn't work this way."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"get yourself a dark room and drill a tiny circular hole in one of its walls. then shine some light from that hole into the room. now go into the room and close the door behind you. what will you see?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"if light behaved like a stone — a thing you \"throw\" that \"lands\" somewhere — you might expect that all light would concentrate on the opposite wall of the room — in a circle the size of your hole."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":127,"byteStart":118},"features":[{"uri":"https://en.wikipedia.org/wiki/Airy_disk","$type":"pub.leaflet.richtext.facet#link"}]}],"plaintext":"but that's not what happens! with a small enough circular hole and clean enough light, you'll see something called an Airy disk:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.image","image":{"ref":{"$link":"bafkreifrlavtsokj26dv37c6ehyc24y5c5k7tcigbct6t7orr5oegq65wa"},"size":10690,"$type":"blob","mimeType":"image/webp"},"aspectRatio":{"width":400,"height":400}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"if you're not convinced that this is different from \"an equal circle on the other side of the room\", here's a clearer picture with a laser:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.image","image":{"ref":{"$link":"bafkreib7g3xiiig2bwmurynd4qzn23ovomegmniiiggug6lgkgxt6aoybm"},"size":428784,"$type":"blob","mimeType":"image/webp"},"aspectRatio":{"width":3840,"height":2880}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"this definitely doesn't look like \"a single circle in front of me\"."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":147,"byteStart":144},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":164,"byteStart":152},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":182,"byteStart":168},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"this means that light doesn't seem to behave like stones (which only ever \"fly forward\") — light seems to radiate and spread out. but radiate how and by how much and in what manner and so on?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"to answer this, let's simplify the situation to an idealized case."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"suppose it was possible to \"narrow down\" our hole down to a single point. in that case, there would be no zebra pattern yet. however, light still wouldn't \"fly forward\" like a stone. in the idealized case of a single point, the light would spread equally in every direction."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"in a sense, this makes light behave almost opposite from a stone!"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"when we talk about things like stones or planets or apples in the newtonian paradigm, we see them as points moving forwards in space. you'd expect them to \"keep flying\" in a single direction."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":67,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]},{"index":{"byteEnd":76,"byteStart":67},"features":[{"$type":"pub.leaflet.richtext.facet#bold"},{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":341,"byteStart":76},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"but when we talk about light, it seems to behave a lot more like a vibration — it's as if there's \"wobbling\" in the space, and that \"wobbling\" itself propagates through it. since every tiny point of the space \"touches\" all of its neighbor points at once, and no neighbor is special, the \"wobbling\" will naturally spread in every direction."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"okay, but why do we get this zebra pattern then?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":145,"byteStart":130},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"to get the zebra pattern, we need to add the hole dimensions back, which we lost with the idealized single point. a hole contains infinitely many points, each point contributing its own \"wobble\"."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"now let's see what happens when these \"wobbles\" overlap."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"imagine two people shaking a tree to obtain some fruit. if their shakes are synchronized, they're shaking the tree twice as hard. but if their shakes come at precisely the opposite times, each shake will cancel the other's shake out, and the tree won't move at all. if they shake at different speeds, the tree may start moving in peculiar patterns. we might say their shakes \"interfere\" with each other."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":212,"byteStart":208},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"the same thing happens here. when you drill an actual hole in an actual room, no matter how small it ends up, it will actually be composed of infinitely many \"single points\". the equal wobbles spreading from each of those points will overlap with each other. some will mutually amplify, while others will cancel each other out."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":131,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"and that's how you get this \"in and out\" zebra pattern — which, if you think about it, is a similar pattern to ripples in a pond:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.unorderedList","children":[{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","plaintext":"the space seems to \"wobble\""}},{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","plaintext":"each single point spreads \"wobbling\" equally in all directions"}},{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","plaintext":"those travelling \"wobbles\" overlap, creating peaks and valleys"}},{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","plaintext":"those moving peaks and valleys look like travelling \"ripples\""}},{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","plaintext":"so the \"wobbling-over-time\" seems to \"ripple-over-space\""}}]}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"that's what physicists call waves."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"note that if you've read about this before, you might have seen a different pattern like this (known as \"single slit diffraction\"):"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.image","image":{"ref":{"$link":"bafkreiem33g3hut7voe4hrkwtwgzj6oab5pnzoi4wbs4v2b5rs776zbksm"},"size":2428,"$type":"blob","mimeType":"image/webp"},"aspectRatio":{"width":480,"height":360}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":34,"byteStart":23},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"this experiment uses a rectangular hole that's thinner on one side, which is why it loses the circular simplicity of the pond. i think the circular hole looks much more illustrative so i used it instead."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"let's now bring it back to the update function."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.horizontalRule"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"a game loop for waves"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"the newtonian update function evolves objects with positions."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":187,"byteStart":182},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":229,"byteStart":207},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"but to describe light, we'd need different state than \"objects with positions, masses, and momentums\". we'd need to describe a thing that can \"wobble\" — perhaps a pond, or maybe a field — something like Map. our update function would then need to describe how a \"wobble\" at a point propagates through that field at each instant of time — from a point to its neighbors, and so on."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"turns out, there's a very concise and elegant way to do this."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"first, let's imagine our field filled up with some data at every point:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"type Point = [number, number, number]\ntype PointState = { value: number, velocity: number }\n\nlet initialState: Map = Map.fill(\n // set up our infinite map with these at every point\n { value: 0, velocity: 0 }\n)"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":59,"byteStart":54},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":117,"byteStart":109},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":137,"byteStart":132},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"we only need to store two things for each point — a value (how \"far\" it has \"wobbled\" at this point) and a velocity (how much the value is changing this instant, and whether it's going up or down)."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":19,"byteStart":14},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":61,"byteStart":56},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":140,"byteStart":135},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":246,"byteStart":241},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":251,"byteStart":248},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"don't confuse value with coordinates of the points. the value is solely a measure of the \"wobbling\" itself (our field). in a pond, the value means \"how tall is the water right here\". if you imagine a field as a grid of numbers in space, the values are those numbers."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":40,"byteStart":34},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"now, how do we actually write the update function?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":202,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"the big idea is that whenever there's a \"rip\" in our field at some point (e.g. one point dipping below or above the surrounding water level), we want it to pull back — the pond wants to \"mend itself\"."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"we can quantify this by counting how \"far\" it is from its neighbors:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"function tension(field, [x, y, z]) {\n const neighbors = [\n field.get([x + 1, y, z]), // right\n field.get([x - 1, y, z]), // left\n field.get([x, y + 1, z]), // above\n field.get([x, y - 1, z]), // below\n field.get([x, y, z + 1]), // in front of\n field.get([x, y, z - 1]) // behind\n ].map(ps => ps.value)\n const neighborSum = neighbors.reduce((a, b) => a + b, 0)\n const ownValue = field.get([x, y, z]).value\n return neighborSum - neighbors.length * ownValue\n}"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":14,"byteStart":7},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":19,"byteStart":18},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":269,"byteStart":235},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"if the tension is 0, our point is happy to stay where it is. if it's positive, the value is too low and \"wants\" to go up to match the neighbor values. if the tension is negative, it means our value is too high, and \"wants\" to go down. it wants to be like its neighbors!"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":26,"byteStart":20},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"now let's write the update function to make it do that."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":3,"plaintext":"first attempt"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"our first attempt might look like this:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"function update(state, dt) {\n return state.map((pointState, point) => {\n const { value } = pointState\n const nextValue = value + tension(state, point) * dt\n return { value: nextValue }\n })\n}"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":32,"byteStart":27},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"this says: if some point's value disagrees with its neighbors, we pull it closer to them. do this for all points forever, end of story."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":206,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"curiously, this actually works, but it gives us something other than light. the behavior we've just discovered is how temperature works: every disturbance is eventually settled by every point averaging out."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"this is cool (sometimes literally) but it's not how light works!"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"somehow, light doesn't average out."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"it keeps on moving."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":3,"plaintext":"second attempt"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":53,"byteStart":45},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":74,"byteStart":69},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":102,"byteStart":97},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":162,"byteStart":154},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":176,"byteStart":164},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":200,"byteStart":195},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"this is actually why we're storing per-point velocity in addition to value. instead of adjusting value (current value at a point), we'll be adjusting the velocity, and put that in control of the value:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"function update(state, dt) {\n return state.map((pointState, point) => {\n const { value, velocity } = pointState\n const nextVelocity = velocity + tension(state, point) * dt\n const nextValue = value + nextVelocity * dt\n return { value: nextValue, velocity: nextVelocity }\n })\n}"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":57,"byteStart":53},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"this is enough to create a rippling wobble — aka a wave!"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"but why?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":33,"byteStart":19},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":54,"byteStart":40},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"we'll first answer why it wobbles, then why it ripples."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":3,"plaintext":"why it wobbles"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"why doesn't it just die out, like temperature?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":34,"byteStart":29},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":99,"byteStart":92},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"suppose some point has a low value — a dip among its neighbors. this will give that point tension: it will \"want\" to align with them. think of a person trying to fit in with the rest of the society."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":45,"byteStart":37},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":100,"byteStart":65},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":108,"byteStart":100},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":127,"byteStart":108},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":236,"byteStart":231},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"at each instant, we put tension into velocity. look what happens: until we've reached the goal, the velocity keeps accumulating — first, by a lot (high tension), then by less (lower tension), and finally it stops increasing when value reaches the neighbor average."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"okay, we've reached the goal, so we can relax now?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":39,"byteStart":27},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"no! we've only stopped the accumulation — it's like we've been pressing gas less hard and we just took the foot off the pedal. but we're still moving — in fact, we're moving faster than ever before!"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":12,"byteStart":4},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":63,"byteStart":58},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"the velocity is still positive, so we keep increasing the value."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"oops!"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":86,"byteStart":81},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":192,"byteStart":182},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":197,"byteStart":193},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"we blow past the target we were aiming for (the average of our neighbors) so now we'll become the high point among the neighbors, the tension turns negative, and the neighbors start pulling us down. we've deviated again, so we're feeling the pressure to conform."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"like a car losing speed and then accelerating backwards, it will take time before our velocity points downwards and we finally reverse course. what's next? we reach the goal, but do we stop there?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":117,"byteStart":112},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"no! again, we're going to overshoot for the same reason. we've been accumulating negative velocity, and now our value dips below the neighbor average again. and the peer pressure now points up..."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"so this is where the \"wobbling\" comes from! we keep pressing \"gas\" until we reach the target so naturally we always overshoot it. then we keep pressing \"gas\" in the opposite direction and the same thing happens. it's like we are destined to forever miss the target."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":9,"byteStart":4},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"the value at a point is wobbling back and forth."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":3,"plaintext":"why it ripples"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"so why doesn't the \"wobbling\" go on forever in a single point? why does it seem to quiet down in one place while rippling on elsewhere?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":91,"byteStart":87},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":160,"byteStart":158},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":234,"byteStart":232},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":266,"byteStart":264},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":293,"byteStart":290},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":348,"byteStart":337},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":438,"byteStart":431},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"well, it's because we're always trying to move towards the neighbors' averages — but they have already changed because they've also tried to move closer to us! so actually, on the second pass they got closer, so although we still do overshoot, their pull wasn't as strong. however, since our neighbors have moved in our direction, our neighbors' neighbors will now start feeling the pull towards the new averages around them, so they'll move too, etc."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":169,"byteStart":163},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":241,"byteStart":236},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"it's like if someone is trying very hard to be like everyone else but they try too hard and overdo it. however, now that they're starting to backpedal, the people around them have already started to adjust to them, so the people around those people start moving, and so on."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":57,"byteStart":52},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":114,"byteStart":109},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"this is why, if you \"poke\" any point and change its value, it will try to \"align\" with neighbors, disturbing them in the process, and so the disturbance will keep getting spread out in all directions forever."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"that's what physicists call a wave!"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.horizontalRule"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"let's add continuous space"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"one problem with our formulation above is that we assume each point has a fixed set of six neighbors from each side of an infinite grid:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":" const neighbors = [\n field.get([x + 1, y, z]), // right\n field.get([x - 1, y, z]), // left\n field.get([x, y + 1, z]), // above\n field.get([x, y - 1, z]), // below\n field.get([x, y, z + 1]), // in front of\n field.get([x, y, z - 1]) // behind\n ].map(ps => ps.value)"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":100,"byteStart":93},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":165,"byteStart":155},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"alas, that's not very useful for our universe because it seems like you can find a new point between any two points. in other words, our space seems to be continuous, so we need to somehow fix this."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":80,"byteStart":77},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":90,"byteStart":86},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":113,"byteStart":111},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"earlier, we had the same problem with time, and we fixed it by replacing the + 1 with + dt \"instant\" and using dt everywhere."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":55,"byteStart":52},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":64,"byteStart":60},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"we can actually apply the same fix here. let's swap + 1 for + ds:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"function tension(field, [x, y, z], ds /* a bit of space */) {\n // ...\n const neighbors = [\n field.get([x + ds, y, z]), // right\n field.get([x - ds, y, z]), // left\n field.get([x, y + ds, z]), // above\n field.get([x, y - ds, z]), // below\n field.get([x, y, z + ds]), // in front of\n field.get([x, y, z - ds]) // behind\n ].map(ps => ps.value)\n // ..."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":153,"byteStart":151},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"instead of navigating space by going \"up one cell\" or \"left one cell\", we'll navigate it as \"up a step\" and \"down a step\", and we'll write \"a step\" as ds — an abstract \"arbitrarily small distance\" number."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":21,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]},{"index":{"byteEnd":23,"byteStart":21},"features":[{"$type":"pub.leaflet.richtext.facet#code"},{"$type":"pub.leaflet.richtext.facet#bold"}]},{"index":{"byteEnd":36,"byteStart":23},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]},{"index":{"byteEnd":38,"byteStart":36},"features":[{"$type":"pub.leaflet.richtext.facet#code"},{"$type":"pub.leaflet.richtext.facet#bold"}]},{"index":{"byteEnd":51,"byteStart":38},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"in other words, what dt is to time, ds is to space."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":18,"byteStart":16},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"of course, this ds has to come from somewhere. in math it comes from differentiation — literally \"zooming in forever\" around a point."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":24,"byteStart":22},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"we could imagine that ds supplied by the structure of the field:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"function update(state, dt) {\n return state.map((pointState, point, ds /* a bit of space */) => {\n // ...\n const nextVelocity = velocity + tension(state, point, ds) * dt\n // ...\n })\n}"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":12,"byteStart":10},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":105,"byteStart":103},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":142,"byteStart":136},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":181,"byteStart":179},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"like with dt, we should keep in mind that our calculations don't need to be correct for any particular ds. rather, it's enough that our update formula gets ever correct-er as the ds gets ever-smaller."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":3,"plaintext":"fixing up the units"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":27,"byteStart":25},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"to complete the shift to ds, we need to fix up the units."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":43,"byteStart":38},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":98,"byteStart":86},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":132,"byteStart":124},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"conceptually, tension means \"how fast value should accelerate\", so its unit should be value/time^2. but we used to return a distance."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":133,"byteStart":112},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"this worked accidentally but now that we're using an arbitrary step size, we need to fix up the units by adding * (C * C) / (ds * ds):"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"const C = 1\nfunction tension(field, [x, y, z], ds) {\n // ...\n const result = neighborSum - neighbors.length * ownValue\n return result * (C * C) / (ds * ds)\n}"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"we're doing two things:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.unorderedList","children":[{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":15,"byteStart":4},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":52,"byteStart":50},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"the / (ds * ds) rescales it so that the choice of ds \"zoom level\" doesn't make the tension seem larger or smaller."}},{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":13,"byteStart":4},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":26,"byteStart":25},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"the * (C * C) introduces C as a speed of our waves (set to one), connecting time with space so we can fix up the units. "}}]}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":30,"byteStart":23},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":90,"byteStart":34},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":114,"byteStart":102},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"now the return type of tension is value*(distance/time)(distance/time)/(distance*distance), or simply value/time^2, which is exactly what we would want from an acceleration of the value."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":36,"byteStart":30},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"with this set of changes, our update function describes a wave in a continuous space — for example, how a sound wave spreads."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"now the big question: does it describe light?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.horizontalRule"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"first stumble: polarization"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"let's recap our previous hypothesis for the nature of light:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"type Point = [number, number, number]\ntype PointState = { value: number, velocity: number }\n\nlet initialState: Map = Map.fill(\n { value: 0, velocity: 0 }\n)\n\nfunction update(state, dt) {\n return state.map((pointState, point, ds) => {\n const { value, velocity } = pointState\n const nextVelocity = velocity + tension(state, point, ds) * dt\n const nextValue = value + nextVelocity * dt\n return { value: nextValue, velocity: nextVelocity }\n })\n}\n\nfunction tension(field, [x, y, z], ds) {\n // ...\n}"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":164,"byteStart":142},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"this works for sound, and for a while, physicists thought that it also can describe light. however, experiments were showing that light waves carry more information than \"a number moving up and down\"."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"check out the next ten seconds on this video:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"url":"https://www.youtube.com/embed/JMvRgvml84A?rel=0&start=329","$type":"pub.leaflet.blocks.iframe","height":600,"aspectRatio":{"width":16,"height":9}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"there are two pieces of fancy glass (\"filters\") placed after each other. when you turn either sideways, they both block out the light."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":64,"byteStart":54},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":97,"byteStart":83},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":105,"byteStart":98},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"in particular, notice that when he rotates the filter underneath, the intersection somehow shines through the dimmed filter above it:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.image","image":{"ref":{"$link":"bafkreieaufuy4fr3d5gamzoj5uwrkmxvwojlazeibkvywzxwm34cp67a5e"},"size":57618,"$type":"blob","mimeType":"image/webp"},"aspectRatio":{"width":2206,"height":1336}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"this is weird on multiple levels:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.unorderedList","children":[{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":39,"byteStart":30},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":107,"byteStart":98},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"we know light has a color (or frequency — how fast the wave's peaks arrive) and brightness (or amplitude — how large each wobble is), but neither of those things \"cares\" about rotation. so why does rotating a filter do anything to the waves at all?"}},{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":197,"byteStart":151},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"if the filter on top was filtering by color or by brightness, we'd expect it to \"not to know\" about the filter beneath it. but somehow it lets through only rays that passed through the filter below, blocking out everything else. how could it possibly \"know\" which waves have passed through the filter below? there's just not enough information in our model of the wave."}}]}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":149,"byteStart":141},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":426,"byteStart":423},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"the fact that rotation plays a role is a giveaway hint — not only do waves have frequency and amplitude, but they also come at us carrying an angle. this angle is not about \"where the wave is coming from\" — it's more like internal information about the wave itself. a wave coming from a point could be a \"2 o-clock wave\". another wave coming from the same point could be a \"9 o-clock wave\". that angle is really about \"how is it wobbling while moving towards us\". it's like if you classified dogs by the direction they wag their tails."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":301,"byteStart":297},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"then this explains filters: maybe the outer filter only passes \"2 o-clock waves\" through while turned. normally, everything goes dark because the screen sends waves at the wrong angle for it. but the filter beneath projects those waves onto another angle, so the light coming out of it wobbles at just the right angle for the outer filter."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"this effect is called polarization."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.horizontalRule"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"a field of arrows"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"to account for angles, we need to change the state data structure:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"type Point = [number, number, number]\ntype Arrow = [number, number, number]\ntype PointState = { value: Arrow, velocity: Arrow }\n"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":47,"byteStart":40},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"in particular, we don't have a field of numbers anymore. since waves are carrying a direction of wobble (e.g. \"2 o-clock wave\"), our field needs to be capable enough to store information at each point that lets such wobbles propagate. instead of an infinite space of raw numbers (as we had with sound), we'll have an infinite space of 3D arrows. the next ten seconds here give an intuition:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"url":"https://www.youtube.com/embed/aXRTczANuIs?rel=0&start=623","$type":"pub.leaflet.blocks.iframe","height":600,"aspectRatio":{"width":16,"height":9}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"our wobbles now aren't just pushing numbers up and down, but they squeeze and rotate arrows on their path. however, just like before, those displacements spread from neighbors to neighbors outwards."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"this is confusing so let's take stock of how arrows work:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.unorderedList","children":[{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":112,"byteStart":103},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"imagine a sound wave aimed directly at your face. it wobbles by contracting air but the wobbles happen alongside the travel direction. it doesn't wobble \"left to right\" or \"up and down\" as it moves towards you — it wobbles \"apart from / towards you\". since this exactly matches the direction of travel, we didn't need to reflect that in the formulas — it's superfluous."}},{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":68,"byteStart":60},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":136,"byteStart":131},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"on the other hand, a light wave aimed directly at your face does not wobble along the travel direction at all. on the contrary, it never wobbles \"apart from / towards you\", and instead it wobbles \"left to right\" or \"up and down\" or any other axis."}},{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","plaintext":"the \"rotation\" carried by light waves is an axis (e.g. \"2 o-clock wave\") but the waves themselves may come from any direction. this is why, to avoid losing information, the field itself needs to be a field of 3D arrows — a 3D arrow per each point. a field tracks the state of all waves together so it needs to be able to sum up how differently rotated waves from different sides are rotating and stretching each point (i.e. 3D arrow) in the field."}}]}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.horizontalRule"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"second stumble: tension"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"now what should the update function do with the arrows?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"recall that previously our update function was using tension, pushing each point to \"get closer\" in value to its neighbors' average:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"function update(state, dt) {\n return state.map((pointState, point, ds) => {\n const { value, velocity } = pointState\n const nextVelocity = velocity + tension(state, point, ds) * dt\n const nextValue = value + nextVelocity * dt\n return { value: nextValue, velocity: nextVelocity }\n })\n}"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"we could try to apply tension to arrows (have each arrow rotate and stretch towards its neighbors), but this misses a needed constraint."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":95,"byteStart":92},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"suppose a light wave is moving towards your face. if the update function of the light field was using tension, nothing would stop the light wave from wiggling \"towards / from you\" just like sound does."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"however, we know experimentally that this doesn't happen. light coming at you can wiggle up-down or left-right (i.e. \"sideways\") but it just doesn't wiggle back-and-forth — not even a little bit."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"so the formula has to do something different."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.horizontalRule"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"wires and magnets"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"now let's take a slight detour from the nature of light."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":20,"byteStart":0},"features":[{"uri":"https://www.youtube.com/watch?v=9Tm2c6NJH4Y","$type":"pub.leaflet.richtext.facet#link"}]}],"plaintext":"this wonderful video about Maxwell's laws has two illustrations."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"in the 1820s, it was discovered that an electric current (i.e. a wire with electricity flowing) pulls a compass needle perpendicular to the flow, i.e. a change in electricity creates a magnetic field around it:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.image","image":{"ref":{"$link":"bafkreigweylruwii66hkuxmn266fvmrujzyx7ch2otyr2qnkblzcepp4au"},"size":373802,"$type":"blob","mimeType":"image/webp"},"aspectRatio":{"width":2448,"height":1362}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"a decade later, it was discovered that a change in the magnetic field (e.g. by moving a magnet) will induce current in the wire around it:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.image","image":{"ref":{"$link":"bafkreifgqpymb7vf7zeciv2q65t6cdajdljzvzyvxlqz6socczj3zzyive"},"size":188390,"$type":"blob","mimeType":"image/webp"},"aspectRatio":{"width":2380,"height":1350}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":192,"byteStart":115},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"so there's these two fields: magnetic field and electric field, and there's this weird symmetry between them where one's speed of change relates to how much the other one is curling around it."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":131,"byteStart":128},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"in other words, there is a geometric transformation happening: as one of the fields is changing, the other one springs up around it, sort of \"curling\" around it, proportionally to how fast the change is."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"now forget about electricity and magnetism. suppose you just have a field of arrows and want to find \"whirlpools\". this function does just that — for each point, it can answer whether it's \"curly\" around it:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"function curl(field, [x, y, z], ds) {\n // which way the arrow points as you step along each axis\n const dx = (field.get([x + ds, y, z]) - field.get([x - ds, y, z])) / (2 * ds)\n const dy = (field.get([x, y + ds, z]) - field.get([x, y - ds, z])) / (2 * ds)\n const dz = (field.get([x, y, z + ds]) - field.get([x, y, z - ds])) / (2 * ds)\n // do the surrounding arrows turn as you loop around this point?\n return [\n dy.z - dz.y, // looping around the x-axis\n dz.x - dx.z, // looping around the y-axis\n dx.y - dy.x, // looping around the z-axis\n ]\n}"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":135,"byteStart":123},"features":[{"uri":"https://www.youtube.com/watch?v=erMopRd-MXg","$type":"pub.leaflet.richtext.facet#link"}]}],"plaintext":"intuitively, you can think of curling as a measure of \"how much does it look like a whirlpool around this point\". here's a 2D intuition:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.image","image":{"ref":{"$link":"bafkreic3ymu3fyvqpk2mpb2xb4zk7thiqoppatu2swmikzzx4j3luoypbe"},"size":96374,"$type":"blob","mimeType":"image/webp"},"aspectRatio":{"width":1152,"height":1134}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"here, the yellow arrows are the original field whose curl we're measuring, while the blue arrows are the curl at each point."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":99,"byteStart":97},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":170,"byteStart":166},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"note how blue arrows work as \"whirlpool detectors\" of the yellow arrows' flow. blue arrows stick up where the yellow gets curly (in one direction), blue arrows stick down when the yellow gets curly in the other direction, and they're zero-ish where yellow is not curly."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"it's like stalactites and stalagmites that grow only inside tornadoes."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":113,"byteStart":92},"features":[{"uri":"https://www.youtube.com/watch?v=4yzV8m8X3Kk","$type":"pub.leaflet.richtext.facet#link"}]}],"plaintext":"the above picture has a 2D input vector field; in 3D, it is even more difficult to imagine. this 3D visualization may help somewhat:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.image","image":{"ref":{"$link":"bafkreibn3wlvzy3mqbs5pxk32ansvveff3l4fbvwcuvbgigaxeyvxjvdkq"},"size":141528,"$type":"blob","mimeType":"image/webp"},"aspectRatio":{"width":1712,"height":1384}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":104,"byteStart":89},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":183,"byteStart":136},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"think of the arrows as water flow, and then think of the ball as an unmoving sphere that can only rotate in the water. the question is: is the water at this point making the ball spin? if yes, imagine the axis it spins around. the arrow of the curl around that point will stick out of that axis exactly like the electric field sticks out here:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.image","image":{"ref":{"$link":"bafkreigweylruwii66hkuxmn266fvmrujzyx7ch2otyr2qnkblzcepp4au"},"size":373802,"$type":"blob","mimeType":"image/webp"},"aspectRatio":{"width":2448,"height":1362}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.image","image":{"ref":{"$link":"bafkreifgqpymb7vf7zeciv2q65t6cdajdljzvzyvxlqz6socczj3zzyive"},"size":188390,"$type":"blob","mimeType":"image/webp"},"aspectRatio":{"width":2380,"height":1350}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"that's the curl at that point. every time the field gets \"curly\" around that point, the curl \"sticks out\" perpendicularly."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"in other words, curl converts \"whirlpools\" into \"thumbs up\"."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"now we see the relationship between the two fields:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.unorderedList","children":[{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","plaintext":"electric curl changes the magnetic field"}},{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","plaintext":"magnetic curl changes the electric field"}}]}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":38,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]},{"index":{"byteEnd":53,"byteStart":38},"features":[{"$type":"pub.leaflet.richtext.facet#bold"},{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":54,"byteStart":53},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]},{"index":{"byteEnd":91,"byteStart":85},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"as one field changes, the other field curls around it. the curlier one field is, the faster the other field changes. this works in both directions, at every point, all the time — like in a game loop."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.horizontalRule"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"maxwell's world: a game loop for light"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"let's describe electric and magnetic fields as an update function:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"type Point = [number, number, number]\ntype Arrow = [number, number, number]\ntype Field = Map\n\nlet initialState = {\n electric: Field.fill([0, 0, 0]),\n magnetic: Field.fill([0, 0, 0]),\n}\n\nconst C = 1\n\nfunction update({ electric, magnetic }, dt) {\n const nextElectric = electric.map((e, point, ds) =>\n e + curl(magnetic, point, ds) * (C * C * dt)\n )\n const nextMagnetic = magnetic.map((b, point, ds) =>\n b - curl(nextElectric, point, ds) * dt\n )\n return {\n electric: nextElectric,\n magnetic: nextMagnetic\n }\n}\n\nfunction curl(field, [x, y, z], ds) {\n // ... same as before ...\n}"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":22,"byteStart":21},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":25,"byteStart":24},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]},{"index":{"byteEnd":31,"byteStart":30},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"this is it! (suppose +, - and * are defined for vectors.)"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"notice that there is no velocity here."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":123,"byteStart":119},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":205,"byteStart":201},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"temperature had no velocity too, but that caused the field to immediately average out and killed waves. here, we don't need velocity because the two fields continually set each other off: each field's curl tells the other field how to change at every moment. in a sense, the two fields take turns being each other's velocities."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"also, both of the issues we flagged earlier are fixed now. the electric and magnetic fields both deal with arrows, which gives us polarization. and, together with other maxwell equations, this guarantees the waves will only wobble \"sideways\" (unlike sound)."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":131,"byteStart":128},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":159,"byteStart":154},"features":[{"$type":"pub.leaflet.richtext.facet#code"}]}],"plaintext":"it turned out that these two fields, locked in a perpetual mutual transformation, explain both electric and magnetic phenomena, and the light itself. the C * C coefficient in the formula is the speed of light squared. in earlier formulas, it was composed of two known coefficients related specifically to magnets and charges. it was a \"big moment\" for physics that those coefficients, already known and measured experimentally in labs, ended up related to speed of light."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":25,"byteStart":11},"features":[{"uri":"https://www.falstad.com/emwave1/","$type":"pub.leaflet.richtext.facet#link"}]}],"plaintext":"there is a wonderful demo that lets you see how the field \"actually\" looks like when stuff is changing — the arrows represent the electric field, and the colors (red/green) represent the magnetic field. here's a recording in case it doesn't work in your browser:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"url":"https://www.youtube.com/embed/1NToO13PTgo?rel=0","$type":"pub.leaflet.blocks.iframe","height":600,"aspectRatio":{"width":16,"height":9}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"finally, you might have noticed that we haven't introduced any way to actually get something \"into\" the field unless you hardcode it."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":220,"byteStart":195},"features":[{"uri":"https://en.wikipedia.org/wiki/Larmor_formula","$type":"pub.leaflet.richtext.facet#link"}]}],"plaintext":"we could try to add a list of charges to the state and write an update function for them, but classical physics genuinely has some holes there (for example, if you follow it strictly, every atom must immediately collapse — oh no) that don't have nice classical fixes."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"so this sounds like a good place to stop — for now."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.horizontalRule"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"epilogue"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"we've traced a long road and ended up with a few update loops."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"the first is newtonian gravity which keeps a list of \"objects\" and moves them at each instant according to the law of gravity:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"$38"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"the second update loop we've looked at is a field wave update loop driven by tension — pulling each point closer to its neighbors:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"$39"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"(if we manipulate value instead of velocity, we get heat instead.)"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"finally, we've looked at the update loop for electricity, magnetism, and light — which turned out to be aspects of the same thing:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.code","language":"javascript","plaintext":"$3a"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"note how newton's gravity was \"global\" — it had to read global state to update every object — while fields were \"local\" and only dealt with neighbors. instant changes at distance seem suspicious, and modern theories (including relativity theory) avoid that."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"the common thing is that we're describing the behavior of a big thing (the universe) by specifying what we think happens at every point, at every moment, what to remember, and how it transforms."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":52,"byteStart":46},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"another common thing is that all of these are models — they have conditions in which they break down. a broken model sometimes reveals a \"more correct\" model underneath, although even today there is no single model that would answer all of our questions."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":58,"byteStart":49},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"finally, all of the update loops so far are from classical physics."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":146,"byteStart":141},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"i originally wanted to write about quantum physics but i had too much fun writing about these loops, as i mostly learned about how they work while researching this article. these classical loops break down in pretty big ways, which is a topic for a future article."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"but here's a sneak peek."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.horizontalRule"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"sneak peek: where is the wave"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"let's come back to our room, shoot some electrons into the hole, and detect them on the opposite wall. you've tried this with one, and it appears to fly like a stone and land on a particular spot:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.image","image":{"ref":{"$link":"bafkreiatm5o5gyhgs25vkf2vqnbuuiibrmdplvsh2hhdargtlrmuwuoofi"},"size":1366,"$type":"blob","mimeType":"image/webp"},"aspectRatio":{"width":764,"height":496}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"great, so an electron is like a stone."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"you turn on your electron gun and you leave it shooting a whole lot of electrons into the wall. then you look at the result:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.image","image":{"ref":{"$link":"bafkreihh3vhjt2dezx3mis4y7de2w6agho3jmwfbujtiavavfllvlms4l4"},"size":3282,"$type":"blob","mimeType":"image/webp"},"aspectRatio":{"width":408,"height":106}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"why are they all over the place?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":117,"byteStart":112},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"if an electron flies like a stone, it should fly straight and land right opposite. okay, you might say, we know light is a wave, and we know why this happens for light. waves \"interfere\" with each other."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":9,"byteStart":3},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":54,"byteStart":50},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"so maybe, if you fire lots of electrons, they can also move like waves, radiating, overlapping, and canceling each other out."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"maybe electrons are waves too. weird but okay."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"so you try the experiment again, watching the buildup more closely. you don't want the presumed \"waves\" related to different electrons to mess each other up so you shoot one electron at a time."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"still — shooting one of them at a time — they're kind of smearing around. maybe something is literally knocking them off course?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.image","image":{"ref":{"$link":"bafkreic46jw7kmz4eq7pjicvaonxth4msny6y6mfof4ueuw7xa7opqwncm"},"size":2294,"$type":"blob","mimeType":"image/webp"},"aspectRatio":{"width":944,"height":428}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":90,"byteStart":87},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"to check whether the problem is with waves or something knocking off course, you leave two holes open behind the electron gun."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"your idea goes like this:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.unorderedList","children":[{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","plaintext":"if something's just knocking them off course, you'll see two clusters of electrons, or at least the same picture shifted twice"}},{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","plaintext":"if something wavy is going on, you'll see a \"double slit diffraction\" pattern from waves, similar to what light does:"}}]}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"url":"https://www.youtube.com/embed/4pYWIj7xDqs?rel=0","$type":"pub.leaflet.blocks.iframe","height":600,"aspectRatio":{"width":16,"height":9}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"you leave the electron shotgun firing and go for a coffee."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"you come back and you see it built up — it's wavy!"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.image","image":{"ref":{"$link":"bafkreidp2ysli4zaj3coilmxwhfq6pqqlp7uthxrrvigihph6yssgivrgi"},"size":10244,"$type":"blob","mimeType":"image/webp"},"aspectRatio":{"width":840,"height":228}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"oh well, so electrons are waves then."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"but then..."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":33,"byteStart":23},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"what if you shoot them one by one from behind the two holes? then, even if they're wavy, they should never interfere with each other."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"you see the pattern building up:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.image","image":{"ref":{"$link":"bafkreicwinsytemm2wmguqn3nuexdij6265idv7upil5qktdgumy3goppq"},"size":222070,"$type":"blob","mimeType":"image/webp"},"aspectRatio":{"width":1442,"height":1908}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"this is the same pattern as light from two holes interfering."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":36,"byteStart":33},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":69,"byteStart":65},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":105,"byteStart":102},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":165,"byteStart":155},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"except here you're only shooting one electron at a time. you see each of them land. and each lands in one definite spot. the wavy pattern only shows up in statistics — a distribution over time."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"you look at the wall one last time."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":8,"byteStart":3},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"it looks as if two waves were interfering."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":17,"byteStart":13},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"but waves of what?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":8,"byteStart":4},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"and when did they interfere?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":22,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"where are the waves???"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":""}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":""}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":""}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":""}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":""}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":""}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.horizontalRule"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":3,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":131,"byteStart":4},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"i'm pretty new to learning (and teaching) physics. i'm a novice but i tried to keep things accurate, with a bit of editorial flair."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":50,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":62,"byteStart":50},"features":[{"did":"did:plc:fpruhuo22xkm5o7ttr2ktxdo","$type":"pub.leaflet.richtext.facet#didMention"}]},{"index":{"byteEnd":192,"byteStart":64},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"any material corrections are appreciated — ping @danabra.mov. individual experiment descriptions are slightly editorialized but i expect them to be consistent with the current understanding."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":46,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":138,"byteStart":47},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":153,"byteStart":138},"features":[{"$type":"pub.leaflet.richtext.facet#italic"},{"uri":"https://en.wikipedia.org/wiki/Airy_disk#/media/File:Rubinar-1000_plus_2x_K-1_telekonv_Airy_disk_1.jpg","$type":"pub.leaflet.richtext.facet#link"}]},{"index":{"byteEnd":186,"byteStart":153},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"some illustrations were taken and cropped from Roger Bach et al 2013 New J. Phys. 15 033018 DOI 10.1088/1367-2630/15/3/033018, CC BY 3.0. Airy disk photo by Roman Napreyev, CC BY-SA 4.0."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":93,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"the few screenshots of youtube videos are taken from the videos embedded earlier on the 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data","circles"],"$type":"site.standard.document","title":"Reintroducing Spaces","content":{"$type":"pub.leaflet.content","pages":[{"id":"01a044d9-83cd-7ff9-af1e-f1bcbf552b5a","$type":"pub.leaflet.pages.linearDocument","blocks":[{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":95,"byteStart":87},"features":[{"$type":"pub.leaflet.richtext.facet#underline"},{"uri":"https://atproto.com/blog/atproto-spaces-alpha","$type":"pub.leaflet.richtext.facet#link"}]}],"plaintext":"Atproto Spaces are a new primitive in the atproto stack. We just launched the protocol in alpha. Check it out, give the blogpost a read, and sign up on the alpha PDS!"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":155,"byteStart":132},"features":[{"$type":"pub.leaflet.richtext.facet#underline"},{"uri":"https://dholms.leaflet.pub/3meluqcwky22a","$type":"pub.leaflet.richtext.facet#link"}]}],"plaintext":"My own intuition around this protocol has been consistently evolving as I’ve worked on it. You can trace much of that through the Permissioned Data Diary series I wrote during the design process. Now with some time and perspective, I wanted to zoom back out, look at the design of Spaces and take a shot at succinctly motivating them as a new primitive. "}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"Design Goals"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":125,"byteStart":102},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"Our initial goal was to extend atproto to work for non-public data. Specifically though, we wanted to enable social use cases. Which is to say that the protocol isn’t intended for just bookmarks or even “gated posts”, but needs to work for large multi-user social contexts such as a 100k user forum."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":55,"byteStart":20},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"Our next goal is to maintain existing atproto intuition. Users publish records, those records are canonically stored in the user’s PDS, authority rests in the author’s DID, and applications crawl PDSes and sync data to build their own views. Succeeding in this means that many difficult questions around things like moderation and credible exit are already answered!"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":56,"byteStart":37},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"An extension of that goal is that it must be atmospheric. I use “atmospheric” to refer to the same underlying data getting remixed across apps in different lights. Think: Bluesky posts showing up as comments under a standard.site blog or rpg.actor characters walking across the bottom of your streamplace stream. Atmospheric features are the features that make this network feel like one deeply integrated experience rather than a bunch of isolated apps that just happen to have the same login."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":65,"byteStart":38},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"And finally, the protocol needs to be secure and legible to users. This protocol enables many-to-many sharing in a multi-app, multi-pds, multi-modality network. That’s a lot of variables! This all comes to a head in the OAuth consent screen. And being able to communicate what an app is allowed to do in a concrete way in just a couple sentences is absolutely critical to the Atmosphere being broadly approachable and usable."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"✨ Spaces ✨"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"Spaces are our new primitive. Each space represents a shared social context. They’re a simple and concrete mechanism for organizing and permissioning data. Built around an abstraction of locality, each record is “in” a space and only one space. Each space is explicitly tied to a particular modality and owned by a single entity."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"alt":"a diagram abstractly showing a space with three records in it","$type":"pub.leaflet.blocks.image","image":{"ref":{"$link":"bafkreicqz45nqgtbmmdfdt3eohalynxcfcyr4wyuvol43s6j22m3iu2rc4"},"size":49258,"$type":"blob","mimeType":"image/webp"},"width":380,"aspectRatio":{"width":1072,"height":1008}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"As we explored this new primitive, we realized that it seems uniquely able to thread the needle on all of our design goals."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":36,"byteStart":13},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]},{"index":{"byteEnd":103,"byteStart":97},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":235,"byteStart":199},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]},{"index":{"byteEnd":251,"byteStart":249},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":402,"byteStart":397},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"Spaces are a deeply social primitive (fitting for a social networking protocol!). Spaces are not really about “who do I, as an individual, share this piece of content with”. Spaces are meant for establishing a shared social context. Records are in that context, and everyone with access to that context has the exact same view over it. It’s a shared common reality, and this shared sense of space allows for truly social applications."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"We’ve started describing spaces as “mini atprotos” (btw if that sounds heavy duty, don’t worry spaces are actually very lightweight & low overhead). That analogy turns out to hold startlingly well. Not only does it help communicate the new primitive, but it also has the huge benefit that almost all of the really difficult questions of using the protocol for real-world social networks can be answered pretty simply: they’re the same as existing atproto! From moderation to account migration to the role of applications, intuition from public atproto maps very closely to spaces."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"Spaces are quite legible. Of course this isn’t a gimme, the Atmosphere is pretty novel, and we’re all familiar with the new challenges of communicating this novel network to users. However, as I mentioned, this question of legibility comes to a head in the OAuth screen. In a context like that, describing “spaces” is much more grounded than trying to communicate ACLs or circles (as we’ll discuss in the next section)."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":124,"byteStart":118},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":329,"byteStart":321},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":551,"byteStart":540},"features":[{"$type":"pub.leaflet.richtext.facet#underline"},{"uri":"https://bulletin.my/","$type":"pub.leaflet.richtext.facet#link"}]},{"index":{"byteEnd":653,"byteStart":646},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"One thing I didn’t expect when we started out designing spaces is how excited I would be for their applicability in public contexts as well. This realization partially underlies our shift in naming from “permissioned data protocol” to “atproto spaces”. This name shifts the focus from “who can see what” to locality. This new notion of locality is super handy and opens up all sorts of new options for data modeling. As a result of this locality, sync is also very lightweight and friendly. It felt so good to build my spaces example app and not have to comb through the entire global network. Locality in the sync protocol gave me exactly the data I needed."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":175,"byteStart":164},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"To be upfront, the effect of designing spaces to be usable in multi-user social contexts is that they are less tailored towards permissioned publishing. Spaces are least tuned to the use case of publishing a bunch of individual pieces of content where each record has a different audience. If you realize that this seems like a weird approach to “I have a bunch of recipes and I want to share each with a totally different audience”, you’re not wrong! That use case was just not the primary design goal of atproto spaces."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"That being said, I think spaces still work in that case. This deserves a blogpost & an example app of its own. However, a simple “out” for cases like this is to just put all your recipes in a space that you share with one or more applications and then let those applications manage the access logic. "}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"Spaces vs Circles"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"In an effort to further bolster intuition around spaces, I also wanted to compare them to the most commonly-suggested alternate approach. I broadly refer to this approach as “Circles” (after Google+ Circles). "}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.unorderedList","children":[{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":7,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"Circles: the content is the object, audience is an attribute you attach to it. You write a post, then tag it with who can see it. "}},{"$type":"pub.leaflet.blocks.unorderedList#listItem","content":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":6,"byteStart":0},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"Spaces: space is the object, content is published into it. A post goes \"into\" a space and is viewable by anyone with access to the space."}}]}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"Circles come in many forms. The simplest is just “putting ACLs on records”. Once you start enabling large multi-user social use cases like forums, you realize you need to share the same ACL across many records owned by many users. Now you have a circle!"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"alt":"a diagram showing a circle attached to three different records","$type":"pub.leaflet.blocks.image","image":{"ref":{"$link":"bafkreihn5h7bjrnk2cw73b6al7plj4sf3cfff36szh6lrxa6mvfesp4k3a"},"size":45406,"$type":"blob","mimeType":"image/webp"},"width":592,"aspectRatio":{"width":1178,"height":1076}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"In their fullest forum, circles can be created by anyone, re-used by anyone, and apply to any data. For example, my friend can create the circle “Besties” and I can share recipes, blogposts, and videos with that circle."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"However, softer versions of circles include arguments that records should be able to be in more than one space. Once you change this invariant, a record is no longer “in” a space. The record “exists” (outside of any given space), and then each space is attached as metadata, giving the record visibility in that space. We’re back to circles!"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"Circles seem simple at first pass, and they’re are many folks’ first instinct for social permissioning (including mine!). However they hide a lot of complexity. For one, there’s a lot of cognitive overhead, juggling who’s in which circle and which content is shared with whom. And thinking through the repercussions of sharing a post with multiple circles is difficult to understand. For instance, if I share with my “Family” and my “Besties” circles, are they able to see each other’s comments and likes? "}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"All of this complexity gets dramatically exacerbated in the multi-app, multi-pds, multi-modality network that I described earlier."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":74,"byteStart":45},"features":[{"$type":"pub.leaflet.richtext.facet#bold"}]}],"plaintext":"I have a claim, which I’ll (cheekily) call Daniel’s Circles Postulate:"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.blockquote","plaintext":"It is only possible to safely and legibly share a record with two different circles if those circles were created by the same entity and are for the same modality."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":248,"byteStart":245},"features":[{"$type":"pub.leaflet.richtext.facet#bold"},{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":249,"byteStart":248},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":259,"byteStart":249},"features":[{"$type":"pub.leaflet.richtext.facet#bold"},{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":294,"byteStart":259},"features":[{"$type":"pub.leaflet.richtext.facet#italic"}]},{"index":{"byteEnd":302,"byteStart":294},"features":[{"$type":"pub.leaflet.richtext.facet#bold"},{"$type":"pub.leaflet.richtext.facet#italic"}]}],"plaintext":"To quickly get the intuition behind this claim, consider that “Besties” circle from before (different account & different modality). If I upload a video with my video app and share it with Besties, my friend (who created the circle) can use his recipe app to change the access perimeter on my video. Not only does this violate all rules and intuition about resource ownership, but even if it is actually what you intend to do, I have no earthly idea how you would make those side-effects legible to either of the users involved or go about communicating that capability in the recipe app’s OAuth screen."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"In short, the Atmosphere is a very dynamic network, there are a lot of variables at play. In this flux, I believe we benefit by having a deeply social, grounded, and concrete primitive that orders our interaction model. I don’t believe that any variation on circles (ACLs, the full fluid expression, or just allowing records to surface in multiple spaces) gives that to us."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"But I think we found it in spaces."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.header","level":2,"plaintext":"Conclusion"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":53,"byteStart":45},"features":[{"$type":"pub.leaflet.richtext.facet#underline"},{"uri":"https://atproto.com/blog/atproto-spaces-alpha","$type":"pub.leaflet.richtext.facet#link"}]},{"index":{"byteEnd":144,"byteStart":132},"features":[{"$type":"pub.leaflet.richtext.facet#underline"},{"uri":"https://bsky.network/account","$type":"pub.leaflet.richtext.facet#link"}]}],"plaintext":"So please give it a go! Check out the recent blogpost for directions on how to get started with the alpha, or just head over to the new BPS site to get your invite code for the alpha PDS."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"Please let me know your thoughts! Share what you build. Let me know what works, and let me know what doesn’t. What’s confusing, what’s a pain to do, what breaks. "}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"I can’t express enough how much I appreciate all the feedback along the way, so please keep it coming. I really believe this protocol is going to be critical for the Atmosphere, so we need to make sure it’s something we’re all excited about building on. 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Encyclopedia Galactica with various guides and writings to help you understand the atmosphere(atproto ecosystem).","preferences":{"showComments":true,"showMentions":true,"showPrevNext":true,"showInDiscover":true}},"indexed_at":"2026-01-23T22:04:14.470576+00:00","identity_did":"did:plc:rnpkyqnmsw4ipey6eotbdnnf","draft_leaflet":null,"documents_in_publications":[{"document":"at://did:plc:rnpkyqnmsw4ipey6eotbdnnf/site.standard.document/3mstvdbgoqc2p","documents":{"uri":"at://did:plc:rnpkyqnmsw4ipey6eotbdnnf/site.standard.document/3mstvdbgoqc2p","data":{"path":"/3mstvdbgoqc2p","site":"at://did:plc:rnpkyqnmsw4ipey6eotbdnnf/site.standard.publication/3lxn3sgnjpc2a","tags":["atproto","capitalism","thoughts"],"$type":"site.standard.document","title":"Social Capital ","content":{"$type":"pub.leaflet.content","pages":[{"id":"019f8a96-cabd-7446-9669-f3dfb1d603df","$type":"pub.leaflet.pages.linearDocument","blocks":[{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":148,"byteStart":139},"features":[{"did":"did:plc:wllajaihnqrivbhxouer4jqz","$type":"pub.leaflet.richtext.facet#didMention"}]}],"plaintext":"I accidentally found a 19 year old article from The Guardian today titled \"Will MySpace ever lose its monopoly?\" by Victor Keegan. (thanks @kagi.com for showing it when I searched \"myspace\" earlier today)"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"src":"https://www.theguardian.com/technology/2007/feb/08/business.comment","$type":"pub.leaflet.blocks.website","title":"Victor Keegan: Will MySpace ever lose its monopoly?","description":"Rupert Murdoch's influence could eventually extend in ways that would make his grip on satellite television seem parochial, says Victor Keegan.","previewImage":{"ref":{"$link":"bafkreidfdlsm2hcafrjz54vkniztevdqyahikbcpwdwwovgkzw7ghd3q54"},"size":51045,"$type":"blob","mimeType":"image/png"}}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":""}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"In retrospect, MySpace did lose its monopoly a few years after this was written, February 2007. MySpace was my first social media, and 07 was also roughly the first year I had access to the internet as a 13 year old living in a rural area. So for me it was a bit fun to read the thoughts of the time as an adult, and see some echoes of current problems still in being social on the internet. Things like \"users don't get paid\" for \"User-generated content\", and what caught my eye."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.blockquote","facets":[{"index":{"byteEnd":42,"byteStart":28},"features":[{"$type":"pub.leaflet.richtext.facet#highlight","color":{"b":128,"g":210,"r":237,"$type":"pub.leaflet.theme.color#rgb"}}]}],"plaintext":"Users have invested so much social capital in putting up data about themselves it is not worth their changing sites, especially since every new user that MySpace attracts adds to its value as a network of interacting people."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"Social capital. That stuck with me; I haven't stopped thinking about that. I think that's the perfect way to explain what you are building on social media. But what is your social capital? It's capital that both you and I have produced. It's our likes, it's our posts, it's the friends we made, the jokes we laughed at online, it's our social life on the internet. We shouldn't have to leave behind the fruits of our social interactions because it is time to move onto a new platform."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"Moving your social capital is one of the major things the atprotocol is solving. You should be able to pack your suitcase and move to a new site. It even describes the next problem. Where do you go once you've packed?"}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.blockquote","plaintext":"It is common knowledge that a fax machine is worthless until others have one too. That is what is happening in social networking except that, unlike a fax machine, it can't be instantly swapped for another. It is easy to change search engines, even if it is Google. But if you change social networks you not only have to move all your videos, audios, messages, photos elsewhere but you also lose your network of friends unless they migrate with you."}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":35,"byteStart":23},"features":[{"uri":"https://en.wikipedia.org/wiki/Fax","$type":"pub.leaflet.richtext.facet#link"}]},{"index":{"byteEnd":216,"byteStart":208},"features":[{"uri":"https://blacksky.community/","$type":"pub.leaflet.richtext.facet#link"}]},{"index":{"byteEnd":420,"byteStart":397},"features":[{"uri":"https://move.blacksky.community/","$type":"pub.leaflet.richtext.facet#link"}]},{"index":{"byteEnd":457,"byteStart":439},"features":[{"uri":"https://blacksky.community","$type":"pub.leaflet.richtext.facet#link"}]}],"plaintext":"Well, there are other \"fax machines\" now that you can swap out. Atprotocol lets you pack and take those connections with you. It's still early in the grand scheme of things, but you can already see this with Blacksky. Blacksky has been the atproto community's vanguard and leader in manufacturing an alternative fax machine for their community. You can move your social capital to their server at move.blacksky.community. You can login on blacksky.community and view posts that are served from their server, even those posted with Bluesky. You can even make private posts now to the connections you made on Bluesky if you are a part of the Blacksky community. This really takes the dream of packing up your social capital and going to a new home, and sprinkles in new functionality that builds on top of what you've already built. "}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","facets":[{"index":{"byteEnd":103,"byteStart":89},"features":[{"uri":"https://Eurosky.social","$type":"pub.leaflet.richtext.facet#link"}]},{"index":{"byteEnd":120,"byteStart":105},"features":[{"uri":"https://northskysocial.com/","$type":"pub.leaflet.richtext.facet#link"}]},{"index":{"byteEnd":306,"byteStart":297},"features":[{"uri":"https://mu.social","$type":"pub.leaflet.richtext.facet#link"}]}],"plaintext":"There are other manufacturers tooling up to produce fax machines or with test units out, Eurosky.social, northsky.social, and others are some great examples. They are hosting places where you can transfer your social capital. Creating alternative ways to view your social capital with things like mu.social, and both with goals to give their communities brand new fax machines they run so you can talk to other people on the atmosphere from an alternative view of it that is not ran by Bluesky PBC. "}},{"$type":"pub.leaflet.pages.linearDocument#block","block":{"$type":"pub.leaflet.blocks.text","plaintext":"Almost 2 decades from when this article was written, not everyone will probably know what a Fax Machine is. But they still have social capital, and the dream of being able to move between platforms is here. With the atprotocol you can take what you built with you when you go, and the ones you made it with. 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Jacob Zweifel

Jake's Jots

Jacob Zweifel

Jake's Jots

Mal’s Musings

at:// pizza thoughts

underreacted

Daniel's Leaflets

Hitchhiker's Guide to the Atmosphere