Announcing bindinator.js

Having recently set up, I am “officially” announcing my side-project Bind-O-Matic.js bindinator.js. It’s a small (currently 7kB gzipped and minified) Javascript library that is designed to make developing in vanilla javascript better in every way than using one or more frameworks. It embodies my current ideas about Javascript, Web, and UI development, and programming — for whatever that’s worth.

Also, I’m having a ton of fun hacking on it.

By way of “dogfooding”, I’m simultaneously building a skunkworks version of my main work project (which is an Electron-based desktop application) with it, adapting any code I can over to it, building b8r’s own demo environment, and slowly porting various other components and code snippets to it.

Above is my old galaxy generator, updated with a bunch of SVG goodness, and implemented using b8r (it was originally cobbled together using jQuery).

Why another framework?

I’ve worked with quite a few frameworks over the years, and in the end I like working in “vanilla” js (especially now that modern browsers have made jQuery pretty much unnecessary). Bindinator is intended to provide a minimal set of tools for making vanilla js development more:

  • productive
  • reusable
  • debuggable
  • maintainable
  • scalable

Without ruining the things that make vanilla js development as pleasant as it already is:

  • Leverage debugging tools
  • Leverage browser behavior (e.g. accessibility, semantic HTML)
  • Leverage browser strengths (e.g. let it parse and render HTML)
  • Be mindful of emerging ideas (e.g. semantic DOM, import)
  • Super fast debug cycle (no transpiling etc.) — see “leverage debugging tools”
  • Don’t require the developer to have to deal with different, conflicting models

The last point is actually key: pretty much every framework tries to abstract away the behavior of the browser (which, these days, is actually pretty reasonable) with some idealized behavior that the designer(s) of the framework come up with. The downside is that, like it or not, the browser is still there, so you (a) end up having to unlearn your existing, generally useful knowledge of how the browser works, (b) learn a new — probably worse — model, and then (c) reconcile the two when the abstraction inevitably leaks.

Being Productive

Bindinator is designed to make programmers and designers more (and separately) productive, decouple their activities, and be very easy to pick up.

To make something appear in a browser you need to create markup or maybe SVG. The easiest way to create markup or SVG that looks exactly like what you want is — surprise — to create what you want directly, not write a whole bunch of code that — if it works properly — will create what you want.

Guess what? Writing Javascript to create styled DOM nodes is slower, more error-prone, less exact, probably involves writing in pseudo-languages, adds compilation/transpilation steps, doesn’t leverage something the browser is really good at (parsing and rendering markup), and probably involves adding a mountain of dependencies to your code.

Bindinator lets you take HTML and bind it or turn it into reusable components without translating it into Javascript, some pseudo-language, a templating language, or transpilation. It also follows that a designer can style your markup.

Here’s a button:

<button class="awesome">Click Me</button>

Now it’s bound — asynchronously and by name.

<button class="awesome" data-event="click:reactor.selfDestruct">
  Click Me

When someone clicks on it, an object registered as “reactor” will have its “selfDestruct” property (presumably a function) called. If the controller object hasn’t been loaded, b8r’s event handler will store the event and replay it when the controller is registered.

Here’s an input:

<inpu type="range">

And now its value is bound to the fuel_rod_position of an object registered as “reactor”:

<input type="range" data-bind="value=reactor.fuel_rod_position">

And maybe we want to allow the user to edit the setting manually as well, so something like this:

<input type="range" data-bind="value=reactor.fuel_rod_position">
<input type="number" data-bind="value=reactor.fuel_rod_position">

…just works.

Suppose later we find ourselves wanting lots of sliders like this, so we want to turn it into a reusable component. We take that markup, and modify it slightly and add some setup to make it behave nicely:

<input type="range" data-bind="value=_component_.value">
<input type="number" data-bind="value=_component_.value">
 const slider = findOne('[type="range"]');
 slider.setAttribute('min', component.getAttribute('min') || 0);
 slider.setAttribute('max', component.getAttribute('max') || 10);
 register(data || {value: 0});

This is probably the least self-explanatory step. The script tag of a component executes in a private context where there are some useful local variables:

component is the element into which the component is loaded; find and findOne are syntax sugar for component.querySelector and component.querySelectorAll (converted to a proper array) respectively, and register is syntax sugar for registering the specified object as having the component’s unique id.

And save it as “slider-numeric.component.html”. We can invoke it thus:


And load it asynchronously thus:

const {component} = require('b8r');

To understand exactly what goes on under the hood, we can look at the resulting markup in (for example) the Chrome debugger:

Chrome debugger view of a simple b8r component

Some things to note: data-component-id is human-readable and tells you what kind of component it is. The binding mechanism (change and input event handlers) is explicit and self-documented in the DOM, and the binding has become concrete (_component_ has been replaced with the id of that component’s instance). No special debugging tools required.

Code Reuse

Bindinator makes it easy to separate presentation (and presentation logic) from business logic, making each individually reusable with little effort. Components are easily constructed from pieces of markup, making “componentization” much like ordinary refactoring.

A bindinator component looks like this:

  /* style rules go here */
  <!-- markup goes here -->
  /* component logic goes here */

All the parts are optional. E.g. a component need not have any actual

When a component is loaded, the HTML is rendered into DOM nodes, the script is converted into the body of a function, and the style sheet is inserted into the document head. When a component is instanced, the DOM elements are cloned and the factory function is executed in a private context.


Bindinator is designed to have an incredibly short debug cycle, to add as little cognitive overhead as possible, and work well with debugging tools.

To put it another way, it’s designed not to slow down the debug cycle you’d have if you weren’t using it. Bindinator requires no transpilation, templating languages, parallel DOM implementations, it’s designed to leverage your existing knowledge of the browser’s behavior rather than subvert and complicate it, and if you inspect or debug code written with bindinator you’ll discover the markup and code you wrote where you expect to. You’ll be able to see what’s going on by looking at the DOM.


If you’re productive, write reusable (and hence DRY) code, and your code is easier to debug, your codebase is likely to be maintainable.


Bindinator is designed to make code scalable:

Code reuse is easy because views are cleanly separated from business logic.

Code is smaller because bindinator is small, bindinator code is small, and code reuse leads to less code being written, served, and executed.

Bindinator is designed for asynchrony, making optimization processes (like finessing when things are served, when they are loaded, and so forth) easy to employ without worrying about breaking stuff.

Core Concepts

Bindinator’s core concepts are event and data binding (built on the observation that data-binding is really just event-binding, assuming that changes to bound objects generate events) and object registration (named objects with properties accessed by path).

Bindinator provides a bunch of convenient toTargets — DOM properties to which you might want to write a value, in particular value, text, attr, style, class, and so forth. In most cases bindings are self-explanatory, e.g.


There are fewer fromTargets (value, text, and checked) which update bound properties based on user changes — for more complex cases you can always bind to methods by name and path.

Components are simply snippets of web content that get inserted the way you’d want and expect them to, with some syntax sugar for allowing each snippet to be bound to a uniquely named instance object.

And, finally, b8r provides a small number of convenience methods (which it needs to do what it does) to make it easier to work with ajax (json, jsonp), the DOM, and events.

The Future

I’m still working on implementing literate programming (allowing the programmer to mix documentation, examples, and tests into source code), providing b8r-specific lint tools, building out the standard control library (although mostly vanilla HTML elements work just fine), and adding more tests in general. I’m tracking progress publicly using Trello.

Usability on the Underside

A minimalist cocoa app
A minimalist cocoa app

I’ve always thought it ironic that Apple makes the most usable computers and the least usable APIs. I’m referring, of course, to AppleScript — just kidding. At first I thought it was a huge failing (and belies Steve Jobs’s claimed obsession with making even the stuff the user never sees beautiful; but then he likely never looked at APIs); then I excused it as Apple wanting to make dealing with its APIs a pons asinorum that less capable programmers wouldn’t be able to cross.

(Note: I’m not kidding that AppleScript is horrible. Just that it’s twenty years old and that horse has been beaten to death.)

I think I was right the first time.

But, it has gotten a lot better.

Perhaps the single most impressive piece of software Apple ever shipped was HyperCard. There was, basically, nothing wrong with HyperCard that couldn’t have been easily fixed by version 3. The chief problems with HyperCard were that:

  • Images were not a first class entity (in VB3, for example, you could load an image into an image variable much like you could load a text file into a string variable in almost any language with decent string manipulation (i.e. not C/C++ or Pascal, but every other popular language).
  • Binary blobs were not a first class entity (something that you’d probably implement for free while implementing the above).
  • The UI gadgets weren’t native UI gadgets.
  • There was no bridge to the native Toolbox short of writing a plugin in C/C++ or using the crazy-but-genius third party HyperTalk compiler.

That may seem like a lot of key flaws, but there’s nothing there that can’t be solved with a bunch of rudimentary programming. Consider what HyperCard got right:

  • First of all, it was shockingly stable — you could often work on HyperTalk projects for days with no serious crashes (let alone System reboots). This was in an era when computers (both Mac and PC) crashed like crazy.
  • You could quickly build user interfaces with drag-and-drop, including bitmap drawing tools
  • State persistent by default
  • Every application was its own database
  • By default you ran inside the development environment — you lived in the development environment
  • Shockingly fast — once HyperTalk 2 came out with its JIT compiler, performance was amazingly good (see note below).
  • Its language was amazingly accessible — both readable and writable — more readable than AppleTalk and far, far more writeable. Most people, including non-coders, could figure out how to do simple stuff within a few hours.
  • Awesome levels of introspection (which allowed metaprogramming)
  • First class debugging tools
  • Always-available REPL

Many of these virtues have yet to be matched by any programming language. VB3 essentially took a few of these virtues, replaced the incredibly easy to work with but hard-to-implement HyperTalk with the very easy to use and already-implemented BASIC, fixed all the obvious faults, and became the foundation of Microsoft’s entire approach to software development. And, say what you will about Microsoft, they do make good development tools.

Note on performance: we had an ambitious multimedia project written in VB3 that barely ran on maximally configured Windows PCs (we were using then-bleeding-edge 486 DX2/66 desktops for development, and our target platform was the then just-shipped IBM Thinkpad 750 (which cost $11,000 in Australia and had a 486DX4/75 CPU by my recollection; it was also the first name-brand MS-DOS compatible laptop with both color graphics and sound). I cloned the project on my aging Quadra 700 (68040 25MHz) using HyperCard and it ran circles around the PCs.

Usable Languages

It’s not easy to create a really approachable programming language.


It’s been done a few times — notably with BASIC. Javascript is a major achievement, but compared to HyperTalk it’s still very difficult to learn. Javascript essentially thrived by being ubiquitous, indispensable, and based on a simplified subset of the widely understood C-ish syntax:

if (x == y && z != q){ p = foo ? bar : baz; }

could be in any one of a dozen C-ish languages, including Javascript. HyperCard was based on a simplified subset of the even more widely understood English syntax:

get the width of button ok
get it * 2
set the width of button ok to it

Javascript was chiefly indispensable because browsers lacked obvious functionality and simply wouldn’t address it — so instead of simple ways to center stuff or make image-buttons change when the user clicked on them, we got a weird new programming language. (E.g. it took the addition of CSS for us to make it possible for something to change its appearance based on mouse events without programming, and having to code CSS is hardly an improvement over having to code in Javascript.) I’m not sure if this was a conspiracy by Netscape to make Javascript popular — never ascribe to any other cause that which is adequately explained by incompetence — but it really took a huge amount of community effort for programming in Javascript to become even vaguely tolerable.

When I finally was forced to get good at programming Javascript (around 2005), just figuring out how to get some kind of debugger working was a major pain in the neck that many developers never bothered to figure out, and writing browser-portable code was a so difficult most developers threw up their hands and just targeted IE6.

My point is that Javascript isn’t a usable language, it’s just more usable than C or Java (not saying much) and supported by a ubiquitous and indispensable environment (the browser) which has grown to have many of the virtues of HyperCard over time (e.g. browsers are pretty stable now, you get a REPL and a decent debugger) while retaining many of the faults (native UI elements are conspicuously missing, and would be amazingly useful given how much effort goes into making half-assed faux elements).

(It’s worth noting that the web was at least partially inspired by HyperCard. The syntax for comments:

<!-- comment -->

looks to me like a little ode to HyperCard, whose comment syntax was

-- comment

although I’m told they both got it from some precursor; still the influence of HyperCard on the web is pervasive.)

I’m not saying that we should have to write

set the borderLeft of the style of button "OK" to "2px solid black" 

instead of the far more economical (but hardly intuitive):

$("#ok").css({borderLeft: "2px solid black"})

but the fact all web developers find the latter programming style tolerable is something of a miracle, and relies on the rise of jQuery — the currently preferred library for papering over the manifold stupidities of web browsers.

I think it’s safe to say that something like

find("button.ok").style.borderLeft = "2px solid black"

would be reasonably intuitive, C-ish, and decently economical, but despite 25 years of progress and a huge amount of effort by some of the best programmers working at some of the richest companies in the world, the best we can come up with right now out-of-the-box is something like:

document.querySelector("button.ok").style.borderLeft = "2px solid black"

which is both far less readable and less intuitive than the HyperTalk version and yet less concise.

A tangential rant on idiotic naming and the misuse of namespaces

How is it that despite everything being namespaced to hell and back these days, “querySelector” isn’t called — I don’t know — “find”? Why not have a global function named “find” for fuck’s sake, or a global find object that supported find.byURL(), find.byCSSSelector(). What’s the point of sticking everything in its own private name space if you can’t give things people use constantly a short, meaningful, intuitive name?

End rant.

Which gets us back to Apple

The first thing in the original Inside Macintosh (after introductory stuff) was a minimalist Macintosh application (I can’t remember whether it was in Pascal or C) that launched, opened up a Window with a text editor inside it, and had a menu and a main event loop. It was something like four pages of code. Note that this application did not handle undo, did not save or load files (maybe it did), and didn’t support multiple documents, and it didn’t behave nicely with other applications (e.g. redraw its Window after being sent to the background) because MacOS was single-tasking at the time. It was barely more than “hello world” in a Window.

This was because, in the original toolbox, when you created a window you had to do things like track mouse behavior in the window’s close box yourself. The fact you didn’t need to handle every keystroke inside the text editor was actually one of the miraculously cool things about the Mac toolbox in 1984 (but the Inside Mac documentation and natively-hosted compilers were still a couple of years away in 1984).

Thanks to over thirty years of progress, and the efforts of some of the greatest programmers and the most design-and-usability-focused (and now richest) company the world has ever known we can now do the equivalent of the above in — I have no idea how much code, so let’s find out. I tried googling for an example somewhere and the best I could come up with was this pure-code Obj-C “Hello World” for iOS.

This approach isn’t necessarily the first thing you should learn when learning to develop applications for a platform, but it should probably be the second or third. You should have a pretty good idea how absolutely everything works at some level.

#import <Foundation/Foundation.h>
#import <UIKit/UIKit.h>

@interface MyDelegate : UIResponder< UIApplicationDelegate >

@implementation MyDelegate
- ( BOOL ) application: ( UIApplication * ) application
           didFinishLaunchingWithOptions: ( NSDictionary * ) launchOptions {
  UIWindow *window = [ [ [ UIWindow alloc ] initWithFrame: 
    [ [ UIScreen mainScreen ] bounds ] ] autorelease ];
  window.backgroundColor = [ UIColor whiteColor ];
  UILabel *label = [ [ UILabel alloc ] init ];
  label.text = @"Hello, World!"; = CGPointMake( 100, 100 );
  [ label sizeToFit ];
  [ window addSubview: label ];
  [ window makeKeyAndVisible ];
  [ label release ];

  return YES;

int main( int argc, char *argv[ ] )
  UIApplicationMain( argc, argv, nil, NSStringFromClass( [ MyDelegate class ] ) );

That’s actually a lot better than I would have guessed, and a gigantic improvement over writing a minimal Mac application in 1986 (but about on par with writing a MacApp 2.x application in 1993). I can’t find a similar example for Swift, and I’d prefer to implement a desktop application (as its minimal functionality is less minimal than an iPhone app which (for example) is killed by the OS rather than being quit. So I used this longer but similarly minimal Obj-C desktop example as a starting point. Note that this example doesn’t even display “Hello World”, so I added that.

One thing I really like about this second example is that it doesn’t require defining a new class or subclass — like the original Inside Mac example it’s a function, so it doesn’t seem as much like magic — create an instance of the Application class, and send it the .run() method and you’re done, but now WTF does that class do? Sure it’s dealing with objects but it’s really clear what’s going on and where you need to drill down to understand a particular thing better. Similarly, it gives you a very good idea of (for example) what loading a XIB (or NIB) does for you and where it fits into the application’s life cycle.

import Cocoa

func main() -> Int {
    // give me an application instance
    let app = NSApplication.sharedApplication()
    app.setActivationPolicy(.Regular) // no clue if this is necessary or default
                                      // behavior would be fine
    // build out our menu (iOS apps do not need to do any of this
    let menubar = NSMenu()
    let appMenuItem = NSMenuItem()
    app.mainMenu = menubar
    let appMenu = NSMenu()
    let appName = NSProcessInfo.processInfo().processName
    let quitTitle = "Quit " + appName
    // the only thing we're making that actually DOES something is implementing 
    // the Quit menu item
    let quitMenuItem = NSMenuItem(title: quitTitle, action: "stop:", keyEquivalent: "q") = app
    appMenuItem.submenu = appMenu
    // this is where we create our window and completely define how it looks -- it 
    //could be entirely replaced by loading a XIB
    let window = NSWindow(
        contentRect: NSRect(x: 0, y: 0, width: 400, height: 400),
        styleMask: NSTitledWindowMask,
        backing: .Buffered,
        `defer`: false // I assume defer is a keyword
    window.cascadeTopLeftFromPoint(NSPoint(x: 20, y: 20)) // playing nice with 
                                 // other apps -- iOS apps don't do this either
    window.title = appName // iOS apps don't have a title, and we don't really 
                           //need to set this
    // now we're putting "Hello, world" in nice big letters in the Window
    let label = NSText(frame: NSRect(x: 0, y: 250, width: 400, height: 40))
    label.editable = false
    label.selectable = false
    label.string = "Hello, world"
    label.font = NSFont(name: "Helvetica Neue", size: 30.0)
    label.alignment = .Center
    label.backgroundColor = NSColor.windowBackgroundColor()
    // Having defined the window we're good to go
    app.activateIgnoringOtherApps(true) // Magic happens here!
    return 0;

I think this is really neat. You can copy and paste this code into an XCode Swift Playground and invoke main() and voila!

This is longer than the iPhone example, but a lot of the lines could be skipped if I went for brevity. If I didn’t prettify the text or define lots of constants (per the example I copied) then it would be just as short as the iOS example while, I think, using less magic and being clearer in what it does. I’m particularly proud of figuring out that I could get the Quit item to send a message (“stop:”) to NSApp without creating a selector referring to the local context (which would have forced me down the “define a subclass and yada yada magic happens” route… I think — I tried just defining a local function and passing its name as a selector but that did not work). That said, the keyboard shortcut for the quit menu item doesn’t work (as I note in the comments).

I actually don’t think the current Apple APIs are all that bad. They’re about on par with MacApp. There is a pretty big impedance mismatch between what the base initializers for the different UI elements do and what you would want them to do if you wanted to write applications this way, which I suspect is because almost no-one does, but while defaults may not look good, they’re not dysfunctional. I could just create the label and set its string property and it would work fine — but why is the default background color not the window background color or — better — transparent? why is the default font not the standard font and size for a label or a text field but something else entirely (the default text settings for a 1989 NeXT machine perhaps)?

I think the problem is that this isn’t where learning app development starts (after perhaps a simpler, more engaging introduction — look how I can create a “Hello, world” app in one minute using XCode. OK, fine, but how the hell would I make an application from scratch if I needed to? How is all this being hooked together? How does the Window hook up to its view controller? How can I use the same view controller for different views? (By the way, this is not addressed by my little example.) Understanding how the basic wiring works also makes XCode’s ridiculously complicated UI more comprehensible — since you now know certain things exist, you know to look for them, and you also know how to simply make stuff work without guessing where it’s buried in the XCode UI.

That said, this is far better than I expected. It would be great if there were initializers that allowed a typical task to be completed in one line (e.g. create a label, position it, and set its content) and if there were better defaults (and the label’s default font settings corresponded to reasonable expectations). If you omit the call to NSWindow.cascadeTopLeftFromPoint then the window appears in a really stupid place. Similarly, why isn’t there a NSMenuItem initializer that lets you stick the new item in a menu? I’m clearly missing something with respect to event handling, and that’s because the relevant initializers aren’t making it easy to do the common, correct thing. I don’t think you can argue that the badness of Apple’s Cocoa APIs is acting as a pons asinorum. In fact it’s more like it’s creating extra work for mediocre programmers.

(Correction: ignore the stuff I say about the menu item not working and the correct event wiring not being implemented by default — by putting a capital “Q” as the parameter for the keyboard equivalent I inadvertently made the shortcut command+shift+q which was why it appeared not to work when I didn’t bother to look at my menu. So my estimation of the APIs improves by a small notch — better default behavior but more magic going on: how does the window know it belongs to app?)

Learning to write Unity Shaders

Dynamically generated infinite scrolling terrain with a custom shader
Dynamically generated infinite scrolling terrain with a custom shader (inside the Unity editor)

Unity has replaced Photoshop in terms of adding features faster than I can assimilate them. It’s been possible to write custom shaders for years, but every time I tried to do something non-trivial I would give up in frustration. Recently, however, I finally wrote some pretty nice dynamic terrain and dynamic planet code and was very frustrated with shading options.

What I wanted to do, in essence, was embed multiple tiling textures inside a single texture, and then have a shader continuously interpolate between a pair of those shaders based on altitude, biome, or whatever. This doesn’t appear to be something other people are doing, so I was not going to be able to take an existing shader and tweak a couple of things to make it work. I’d actually need to understand what I was doing.

If you look at the picture, you’ll see seamless transitions (based on altitude) between a sand dune texture (at sea level) and a forest texture (at middle levels) and further up the beginning of a transition to bare rock. I’ve got a darker blue-tinged rock below the sand, so the material I’m using looks like this:

A single texture that contains multiple tiling textures.
A single texture that contains multiple tiling textures. Most of the texture is blank, but you get the idea.

Obviously there’s room for expansion. I could do some really interesting things with this technique (even moreso if I can interpolate between three or four samples without choking the GPU). I haven’t figured out how to benchmark this stuff — I’m not seeing any hit on the GPU using Unity’s profile, but I haven’t tried running this on a mobile device — so far, this shader seems to run just as fast as (say) a standard diffuse shader.

How to Start

Writing shaders is actually pretty simple. The big problems are finding useful documentation (I couldn’t find any useful documentation on ShaderLab, but it turns out that nVidia’s cg documentation appears to do the trick) and tutorials (I couldn’t find any). It doesn’t help that Unity has made radical changes to its Shader language over time (not really their fault, the underlying GPU architectures have been in flux) which makes a lot of the tutorials you do find worse than useless.

For the record, I’m still using Unity 4.6.x so this may all be obsolete in Unity 5.x. That said, I was working off the latest Unity 5.x online documentation.

The closest thing to useful tutorials I could find is in the Unity documentation — specifically Surface Shaders Examples. Sadly, you’re going to need to infer a great deal from these examples, because I couldn’t find explanations of the simplest things (e.g. how data gets from the shader’s UI to the actual pixel shader code — there’s a lot of automagical linking going on).

Shader "Custom/DynamicTerrainShader" {
	Properties {
		_MainTex ("Base (RGB)", 2D) = "white" {}
		_Color ("Main Color", Color) = (0,0,0,1)
		_WorldScale("World Scale", Float) = 0.25
		_AltitudeScale("Altitude Scale", float) = 0.25
		_TerrainBands("Terrain Bands", Int) = 4
	SubShader {
		Tags { "RenderType"="Opaque" }
		LOD 200
		#pragma surface surf Lambert

		sampler2D _MainTex;
		float _WorldScale;
		float _AltitudeScale;
		float4 _Color;
		int _TerrainBands;

		struct Input {
			float3 worldPos;
			float2 uv_MainTex;
            float2 uv_BumpMap;

		void surf (Input IN, inout SurfaceOutput o) {
			float y = IN.worldPos.y / _AltitudeScale + 0.5;
			float bandWidth = 1.0 / _TerrainBands;
			float s = clamp(y * (_TerrainBands + 2) - 2, 0, _TerrainBands);
			float t = frac(s);
			t = t < 0.25 ? t * 0.5 : ( t > 0.75 ? (t - 0.75) * 0.5 + 0.875 : t * 1.5 - 0.25);
			float band = floor(s)  * bandWidth;
			float2 uv = frac(IN.uv_MainTex * _WorldScale) * (bandWidth - 0.006, bandWidth - 0.006) + (0.003, 0.003);
			uv.y = uv.y + band;
			float2 uv2 = uv;
			uv2.y = uv2.y + bandWidth;
			half4 c = tex2D(_MainTex, uv) * (1 - t) + tex2D(_MainTex, uv2) * t;
			o.Albedo = c.rgb * 0.5;
			o.Alpha = c.a;
	FallBack "Diffuse"

So here’s my explanation for what it’s worth.

To refer to properties in your code, you need to declare them (again) inside the shader body. Look at occurrences of _MainTex as an instructional example. As far as I can tell you have to figure out which parameters are available where, and which type declarations in the shader body correspond with the (different) types in the properties declaration by osmosis.

The Input block is where you declare which bits of “ambient” information your shader uses from the rendering engine. Again, what you can declare in here and what it is you simply need to figure out from examples. I figured out how worldPos worked from the example which turns the soldier into strips.

Note that the Input block declaration determines what is passed as Input (referred to as IN in the body). The way the declaration works (you declare the type rather than the variable) is a bit puzzling but it kind of makes sense. The SurfaceOutput object is essentially a set of parameters for the pixel that is about to be rendered. So the simplest shader body would simply be something like o.Albedo = (1,0,0,1) which would be the constant color red (depending on the basic shader type, lighting would or wouldn’t be applied, etc.).

Variables and calculations are all about vectors. Basically everything is a vector. A 3D point is a float3, a 2D point is a float2. You can add and multiply vectors (component by component) so (1,0.5) + (-0.5, 0.25) -> (0.5,0.75). You can mix scalars and vectors in some obvious and not-so-obvious ways (hint: it usually pays to be explicit about components).

The naming conventions are interesting. For vectors, you can use x, y, and z as shorthand for accessing specific components. I’m not sure if the fourth coordinate is w or a or something else. I’m also pretty sure that spatial coordinates are not in the order I think they are (so I do ok with foo.x, but get into trouble if I try to handle specific components via (,,) expressions. Hence lines like uv.y = uv.y + band instead of uv = uv + (0,band,0) (which doesn’t work).

You may have noticed some handy functions such as floor and frac being used and wonder what else there is. I couldn’t find any list or references on the Unity website, but eventually found this cg standard library documentation on nVidia’s website (for its shader language). Everything I tried from this list seemed to work (on my nVidia-powered Macbook Pro).

If you’re looking for control structures and the like, I haven’t found any aside from the ternary operator — condition ? value-if-condition-true : value-if-condition-false — which is fully supported, can be nested, etc.. This alone would probably have driven me away just five years ago before I learned to stop worrying and love the ternary operator.

Why no switch statements, loops and such? I’m writing a pixel shader here and I suspect it relies on every program executing the same instruction at the same time, so conditional loops are out. (Actually I may be wrong about this — see the cg language documentation. I don’t know how closely ShaderLab corresponds to cg though.)

Once you see that list of functions you’ll understand why I am using piecewise linear interpolation between the materials (it looks just fine to me).

Some final points — the shader had terrible problems with the edges of the sub-textures until I changed the bitmap sampling to point (versus linear or trilinear interpolation). I suspect this may be a wrapping issue, but (as you may find) debugging these suckers is not easy.

One final comment — even though you’re essentially writing assembler for your GPU, shader programming is pretty forgiving — I haven’t crashed my laptop once (although Unity itself seems to periodically die during compiles).

What does a good API look like?

I’m temporarily unemployed — my longest period of not having to work every day since I was laid off by Valuclick in 2010 — so I’m catching up on my rants. This rant is shaped by recent experiences I had during my recent job interview process (I was interviewed by two Famous Silicon Valley Companies, one of which hired me and the other of which “didn’t think I was a good fit”). Oddly enough, the company that hired me interviewed me in an API-agnostic (indeed almost language-agnostic) way while the company that didn’t interviewed me in terms of my familiarity with an API created by the other company (which they apparently are using religiously; although maybe not so much following recent layoffs).

Anyway, the API in question is very much in vogue in the Javascript / Web Front End world, in much the same way as CoffeeScript and Angular were a couple of years ago. (Indeed, the same bunch of people who were switching over to Angular a few years back have recently been switching over to this API, which is funny to watch). And this API and the API it has replaced in terms of mindshare is in large part concerned with a very common problem in UI programming.

A Very Common Problem in UI Programming

Probably the single most common problem in UI programming is synchronizing data with the user interface, or “binding”. There are three fundamental things almost any user-facing program has to do:

  • Populate the UI with data you have when (or, better, before) the UI first appears on screen
  • Keep the UI updated with data changed elsewhere (e.g. data that changes over time)
  • Update the data with changes made by the user

This stuff needs to be done, it’s boring to do, it often gets churned a lot (there are constant changes made to a UI and the data it needs to sync with in the course of any real project). So it’s nice if this stuff isn’t a total pain to do. Even better if it’s pretty much automatic for simple cases.

The Javascript API in question addresses a conspicuous failing of Javascript given its role as “the language of the web”. In fact almost everything good and bad about it stems from its addressing this issue. What’s this issue? It’s the difficulty of dealing with HTML text. If you look at Perl, PHP, and JSP, the three big old server-side web-programming languages, each handles this particular issue very well. The way I used to look at it was:

  • A perl script tends to look like a bunch of code with snippets of HTML embedded in it.
  • A PHP script tends to look like a web page with snippets of code embedded in it.
  • A JSP script tends to look like a web page with horrible custom tags and/or snippets of code embedded in it.

If you’re trying to solve a simple problem like get data from your database and stick it in your dynamic web page, you end up writing that web page the way you normally would (as bog standard HTML) and just putting a little something where you want your data to be and maybe some supporting code elsewhere. E.g. in PHP you might write “<p>{$myDate}</p>” while in  JSP you’d write something like “<p><%= myDate %></p>”. These all look similar, do similar things, and make sense.

It’s perfectly possible to defy these natural tendencies, e.g. write a page that has little or no HTML in it and just looks like a code file, but this is pretty much how many projects start out.

Javascript, in comparison, is horrible at dealing with HTML. You either end up building strings manually “<p>” + myDate + “</p>” which gets old fast for anything non-trivial, or you manipulate the DOM directly, either through the browser’s APIs, having first added metadata to your existing HTML, e.g. you’d change “<p></p>” to “<p id=”myDate”></p>” and then write “document.getElementById(‘myDate’).text = myDate;” in a script tag somewhere else.

The common solution to this issue is to use a template language implemented in Javascript (there are approximately 1.7 bazillion of them, as there is of anything involving Javascript) which allow you to write something like “<p>{{myDate}}</p>” and then do something like “Populate(slabOfHtml, {myDate: myDate});” in the simplest case (cue discussion about code injection). The net effect is you’re writing non-standard HTML and using a possibly obscure and flawed library to manipulate markup written in this non-standard HTML (…code injection). You may also be paying a huge performance penalty because depending on how things work, updating the page may involve regenerating its HTML and getting the browser to parse it again, which can suck — especially with huge tables (or, worse, huge slabs of highly styled DIVs pretending to be tables). OTOH you can use lots of jQuery to populate your DOM-with-metadata fairly efficiently, but this tends to be even worse for large updates.

The API in question solves this problem by uniting non-standard HTML and non-standard Javascript in a single new language that’s essentially a mashup of XML and Javascript that compiles into pure Javascript and [re]builds the DOM from HTML efficiently and in a fine-grained manner. So now you kind of need to learn a new language and an unfamiliar API.

My final interview with the company that did not hire me involved doing a “take home exam” where I was asked to solve a fairly open-ended problem using this API, for which I had to actually learn this API. The problem essentially involved: getting data from a server, displaying a table of data, allowing the user to see detail on a row item, and allowing the user to page through the table.

Having written a solution using this unfamiliar API, it seemed very verbose and clumsy, so I tried to figure out what I’d done wrong. I tried to figure out what the idiomatic way to do things using this API was and refine them. Having spent a lot of spare time on this exercise (and I was more-than-fully-employed at the time) it struck me that the effort I was spending to learn the API, and to hone my implementation, were far greater than the effort required to implement the same solution using an API I had written myself. So, for fun, I did that too.

Obviously, I had much less trouble using my API. Obviously, I had fewer bugs. Obviously I had no issues writing idiomatic code.

But, here’s the thing. Writing idiomatic code wasn’t actually making my original code shorter or more obvious. It was just more idiomatic.

To bind an arbitary data object to the DOM with my API, the code you write looks like this:


The complex case looks like this:

$(<some-selector>).bindomatic(<data-object>, <options-object>);

Assuming you’re familiar with the idioms of jQuery, there’s nothing new to learn here. The HTML you bind to needs to be marked up with metadata in a totally standard way (intended to make immediate sense even to people who’ve never seen my code before), e.g. to bind myDate to a particular paragraph you might write: “<p data-source=”.myDate”></p>”. If you wanted to make the date editable by the user and synced to the original data object, you would write: “<input data-bind=”.myDate”>”. The only complaints I’ve had about my API are about the “.” part (and I somewhat regret it). Actually the syntax is data-source=”myData.myDate” where “myData” is simply an arbitrary word used to refer to the original bound object. I had some thoughts of actually directly binding to the object by name, somehow, when I wrote the API, but Javascript doesn’t make that easy.

In case you’re wondering, the metadata for binding tabular data looks like this: “<tr data-repeat=”.someTable”><td data-source=”.someField”></td></tr>”.

My code was leaner, far simpler, to my mind far more “obvious”, and ran faster than the code using this other, famous and voguish, API. There’s also no question my API is far simpler. Oh, and also, my library solves all three of the stated problems — you do have to tell it if you have changes in your object that need to be synced to the UI — (without polluting the source object with new fields, methods, etc.) while this other library — not-so-much.

So — having concluded that a programming job that entailed working every day with the second API would be very annoying — I submitted both my “correct” solution and the simpler, faster, leaner solution to the second company and there you go. I could have been laid off by now!

Here’s my idea of what a good API looks like

  • It should be focused on doing one thing and one thing well.
  • It should only require that the programmer tell it something it can’t figure out for itself and hasn’t been told before.
  • It should be obvious (or as obvious as possible) how it works.
  • It should have sensible defaults
  • It should make simple things ridiculously easy, and complex things possible (in other words, its simplicity shouldn’t handcuff a programmer who wants to fine-tune performance, UX, and so on.

XCode and Swift

I don’t know if the binding mechanisms in Interface Builder seemed awesome back in 1989, but today — with all the improvements in both Interface Builder and the replacement of Objective-C with the (potentially) far cleaner Swift — they seem positively medieval to me, combining the worst aspects of automatic-code-generation “magic” and telling the left hand what the left hand is doing.

Let’s go back to the example of sticking myDate into a the UI somewhere. IB doesn’t really have “paragraphs” (unless you embed HTML) so let’s stick it in a label. Supposing you have a layout created in IB, the way you’re taught — as a newb — to do it this is:

  1. In XCode, drag from your label in IB to the view controller source code (oh, step 0 is to make sure both relevant things are visible)
  2. You’ll be asked to name the “outlet”, and then XCode will automagically write this code: @IBOutlet weak var myDate: UILabel!
  3. Now, in — say — the already-written-for-you viewDidLoad method of the controller you can write something like: myDate.text = _myDate (it can’t be myDate because you’re used myDate to hold the outlet reference).

Congratulations, you have now solved one of the three problems. That’s two lines of code, one generated by magic, the other containing no useful information, that you’ve written to get one piece of data from your controller to your view.

Incidentally, let’s suppose I wanted to change the outlet name from “myDate” to “dateLabel”. How do I do that? Well, you can delete the outlet and create a new outlet from scratch using the above process, and then change the code referencing the outlet. Is there another way? Not that I know of.

And how to we solve the other two problems?

Let’s suppose we’d in fact bound to an input field. So now my outlet looks like this: @IBOutlet weak var myDate: UITextField! (the “!” is semantically significant, not me getting excited).

  1. In XCode, drag from the field in IB to the view controller source code.
  2. Now, instead of creating an outlet, you select Action, and you make sure the type is UITextField, and change the event to ValueChanged.
  3. In the automatically-just-written-for-you Action code add the code _myDate = sender.text!

You’re now solved the last of the three problems. You’ve had a function written for you automagically, and you’ve written one line of retarded code. That’s three more lines of code (and one new function) to support your single field. And that’s two different things that require messing with the UI during a refactor or if a property name gets changed.

OK, what about the middle problem? That’s essentially a case of refactoring the original code so that you can call it whenever you like. So, for example, you write a showData method, call it from viewDidLoad, and then call it when you have new data.

Now, this is all pretty ugly in basic Javascript too. (And it was even uglier until browsers added documentQuerySelector.) The point is that it’s possible to make it very clean. How to do this in Swift / XCode?

Javascript may not have invented the hash as a fundamental data type, but it certainly popularized it. Swift, like most recent languages, provides dictionaries as a basic type. Dictionaries are God’s gift to people writing binding libraries. That said, Swift’s dictionaries are strongly typed which leads to a lot of teeth gnashing.

Our goal is to be able to write something like:


It would be even cooler to be able to round-trip JSON (the way my Javascript binding library can). So if this works we can probably integrate a decent JSON library.

So the things we need are:

  • Key-value-pair data storage, i.e. dictionaries — check!
  • The ability to add some kind of metadata to the UI
  • The ability to find stuff in the UI using this metadata

This doesn’t seem too intimidating until you consider some of the difficulty involved in binding data to IB.


The way tables are implemented in Cocoa is actually pretty awesome. In essence, Cocoa tables (think lists, for now) are generated minimally and managed efficiently by the following mechanism:

The minimum number of rows is generated to fill the available space.

When the user scrolls the table, new rows are created as necessary, and old rows disposed of. But, to make it even more efficient rather than disposing of unused rows, they are kept in a pool and reallocated as needed — so the row that scrolls off the top as you scroll down is reused to draw the row that just scrolled into view. (It’s more complex and clever than this — e.g. rows can be of different types, and each type is pooled separately — but that’s the gist.) This may seem like overkill when you’re trying to stick ten things in a list, but it’s ridiculously awesome when you’re trying to display a list of 30,000 songs on your first generation iPhone.

In order for this to work, there’s a tableDelegate protocol. The minimal implementation of this is that you need to tell the table how many rows of data you have and populate a row when you’re asked to.

So, for each table you’re dealing with you need to provide a delegate that knows what’s supposed to go in that specific table. Ideally, I just want to do something like self.bind(data) in the viewDidLoad method, how do I create and hook up the necessary delegates? It’s even worse if I want to use something like RootViewController (e.g. for a paged display) which is fiddly to set up even manually. But, given how horrible all this stuff is to deal with in vanilla Swift/Cocoa, that’s just how awesome it will be not to have to do any of it ever again if I can do this. Not only that, but to implement this I’m going to need to understand the ugly stuff really well.


Adding Metadata to IB Objects

The first problem is figuring out some convenient way of attaching metadata to IB elements (e.g. buttons, text fields, and so on). After a lot of spelunking, I concluded that my first thought (to use the accessibilityIdentifier field) turns out to be the most practical (even though, as we shall see, it has issues).

There are oodles of different, promising-looking fields associated with elements in IB, e.g. you can set a label (which appears in the view hierarchy, making the control easy to find). This would be perfect, but as far as I could tell it isn’t actually accessible at runtime. There’s also User Defined Runtime Attributes which are a bit fiddly to add and edit, but worse, as far as I’ve been able to tell, safely accessing them is a pain in the ass (i.e. if you simply ask for a property by name and it’s not there — crash!). So, unless I get a clue, no cigar for now.

The nice thing about the accessibilityIdentifier is that it looks like it’s OK for it to be non-unique (so you can bind the same value to more than one place) and it can be directly edited (you don’t need to create a property, and then set its name, set its type as you do for User Defined Runtime Attributes). The downside is that some things — UITableViews in particular — don’t have them. (Also, presumably, they have an impact on accessibility, but it seems to me like that shouldn’t be a problem if you use sensible names.)

So my first cut of automatic binding for Swift/Cocoa took a couple of hours and handled UITextField and UILabel.

class Bindery: NSObject {
    var view: UIView!
    var data: [String: AnyObject?]!
    init(view v:UIView, data dict:[String: AnyObject?]){
        view = v
        data = dict
    func subviews(name: String) -> [UIView] {
        var found: [UIView] = []
        for v in view!.subviews {
            if v.accessibilityIdentifier == name {
        return found
    @IBAction func valueChanged(sender: AnyObject?){
        var key: String? = nil
        if sender is UIView {
            key = sender!.accessibilityIdentifier
            if !data.keys.contains(key!) {
        if sender is UITextField {
            let field = sender as? UITextField
            data[key!] = field!.text
    func updateKey(key: String){
        let views = subviews(key)
        let value = data[key]
        for v in views {
            if v is UILabel {
                let label = v as? UILabel
                label!.text = value! is String ? value as! String : ""
            else if v is UITextField {
                let field = v as? UITextField
                field!.text = value! is String ? value as! String : ""
                field!.addTarget(self, action: "valueChanged:", forControlEvents: .EditingDidEnd)
    func update() -> Bindery {
        for key in (data?.keys)! {
        return self

Usage is pretty close to my ideal with one complication (this code is inside the view controller):

    var binder: Bindery
    var data:[String: AnyObject?] = [
        "name": "Anne Example",
        "sex": "female"

    override func viewDidLoad() {
        // Do any additional setup after loading the view, typically from a nib.
        binder = Bindery(view:self.view, data: data).update()

If you look closely, I have to call update() from the new Bindery instance to make things work. This is because Swift doesn’t let me refer to self inside an initializer (I assume this is designed to avoid possible issues with computed properties, or to encourage programmers to not put heavy lifting in the main thread… or something). Anyway it’s not exactly terrible (and I could paper over the issue by adding a class convenience method).

OK, so what about tables?

Well I figure tables will need their own special binding class (which I shockingly call TableBindery) and implement it so that you need to use an outlet (or some other hard reference to the table) and then I use Bindery to populate each cell (this lets you create a cell prototype visually and then bind to it with almost no work). This is how that ends up looking like this (I won’t bore you with the implementation which is pretty straightforward once I worked out that a table cell has a child view that contains all of its contents, and how to convert a [String: String] into a [String: AnyObject?]):

    var data:[String: AnyObject?] = [
        "name": "Anne Example",
        "sex": "female"
    override func viewDidLoad() {
        tableBinder = TableBindery(table:table, array: tableData).update()

In the course of getting this working, I discover that the prototype cells do have an accessibilityIdentifier, so it might well be possible to spelunk the table at runtime and identify bindings by using the attributes of the table’s children. The fact is, though, that tables — especially the sophisticated multi-section tables that Cocoa allows — probably need to be handled a little more manually than HTML tables usually do, and having to write a line or two of code to populate a table is not too bad.

Now imagine if Bindery supported all the common controls, provided a protocol for allowing custom controls to be bound, and then imagine an analog of TableBindery for handling Root view controllers. This doesn’t actually look like a particularly huge undertaking, and I already feel much more confident dealing with Cocoa’s nasty underbelly than I was this morning.

And, finally, if I really wanted to provide a self.bindData convenience function — Swift and Cocoa make this very easy. I’d simply extend UIView.

The Graph with a Trillion Edges

After looking at this thread on Hacker News about this paper from a bunch of Facebook researchers, and this excellent article by Frank McSherry, I tried to understand McSherry’s approach (since I found the paper kind of impenetrable) and this is my take on it.

The Basic Problem

Let’s suppose you’re Facebook and you have about 1B members who have an arbitrary number of links to each other. How do you scale and parallelize queries (especially iterated queries) on the data?

McSherry basically implements a single thread algorithm on his laptop using brute force. (He uses a publicly available database of 128B edges.) As I understand it, his approach is pretty simple:

  • Encode each connection as a 64 bit number (think connection from A (32 bits) to B (32 bits).
  • Store the numbers in RAM as a sequence of variable-length integer encoded differences. E.g. a set of numbers beginning with 4, 100, 2003, 2005,… would be encoded as 4, 96, 1903, 2,… Since the average distance between 128B values scattered among 1T is 8, the expected distance between connections (64-bit values) will be around 9, which we can encode as ~4 bits of data (using variable-length encoding) instead of 64 bits, and storage needed is proportional to number of values stored [1]).
  • Look for a connection from A to anyone by running through the list and looking for values starting with A’s 32 bits. (You can make this search arbitrarily efficient — trading memory requirements for performance — by partitioning the list into a lookup table.)
  • Store the numbers on disk as deltas between the numbers encoded as a Hilbert Curve [2] using variable-length integer encoding for efficiency. (The naive encoding has an average of ~5bits between values; the optimized encoding was 2.

[1] Each entry will be log(n) bits in size, there’ll be c of them, and the average difference (to be encoded) will be log(c/n) bits. If we assume c scales as n^2 (highly dubious — it means if the world’s population increased by a factor of 2, I’d have twice as many friends) then we get n^2 * log(n) for storage. If we assume c scales as n log(n) (probably still generous) then we get n log(n) * log(log(n)). At any given scale that function looks pretty linear, although it is actually faster than linear — the gradient hangs around 5 for n between 1B and 100B — I don’t think it’s a cause for concern.

[2] A simple way of looking at Hilbert Curve encoding is that it treats a binary number as a series of 2-bit numbers, with each pair of bits selecting a sector of a 2×2 square (in a somewhat non-obvious way). So all numbers starting with a given pair of bits are found in the same sector. Then, look at the next two bits and subdivide that sector in a similarly non-obvious way until you run out of bits. (In an earlier post, McSherry explains Hilbert Curve implementation a graphically.) Incidentally, simply interleaving the bits of the two numbers has much the same effect.

That’s it in a nutshell. Obviously there are plenty of simple ways to optimize the lookups.

He points out that the database he used comes in 700 files. These could each be processed by 700 different computers (stored slightly less efficiently, because the average distance between deltas goes up slightly) and any request could easily be split among them.

The interesting thing is that running in one thread on a laptop, this approach runs faster and scales better than the 128 core systems he benchmarks against.


So let’s suppose I wanted to emulate Facebook and have access to 256 virtual machines. (I could easily afford to do this, as a startup, using AWS or similar.) How would I do this in practice? Remember that Facebook also has to deal with users creating new connections all the time.

First of all (kind of obviously) every connection gets stored twice (i.e. connections are two-way). We need this for worst-case scenarios.

Let’s suppose I number each of my virtual machines with an 8-bit value. When I store a connection between A and B I encode the connection twice (As AB and BA) and take the last 8 bits of one value and record them as a connection on machines with the corresponding number. Each machine stores the value in its representation of its link database.

How would this work in practice?

Well, each value being stored is effectively 56-bits (8 bits are pulled off the 64-bit value to pick the machine are and thus the same). Let’s divide that into 32-bits and 24-bits and store (in some efficient manner) 2^24 lists of 32-bit numbers, again stored in some efficient manner (we can break down and use McSherry’s approach at this point — effectively we’re progressively using McSherry’s approach on different portions of the numbers anyway).

So any lookup will entail grabbing 24-bits of the remaining 56-bits leaving us with 1/2^32 of the original data to search. Our efficient encoding algorithm would be to split the remaining data using the same approach among the cores, but I’m sure you get the idea by now.

So in a nutshell:

To record the existence of the edge AB:

  1. Encode as 2 64-bit values.
  2. Reduce to two 56-bit values and 2 8-bit values.
  3. Ask the 2 (or occasionally 1) machines designated for the 2 8-bit values.
  4. Each machine reduces the 56-bit value to a 32-bit value with a 24-bit lookup.
  5. Then inserts the remaining 32-bit value in a list of ~E/2^32 values (where E is the total number of edges, so 232 values for a 1T vertex DB)

Inserting a value in a list of n values is a solved O(log(n)) problem. Note that all connections Ax will be stored on one machine, but connections xA will be scattered (or vice versa) because we’re storing two-way connections. (Important for the worst case, see below.)

To find all edges from A:

  1. Grab 8-bits using the same algorithm used for storing AB.
  2. Ask the designated machine for the list of ~E/2^32 connections from A.

So to sum up — storing a connection AB involves bothering two machines. Determining if A’s connections involves bothering 1 machine in most cases, and (see below) all the machines in rare cases. However, the rare cases should never actually exist.

Worst Case Response

One problem here is that the worst case response could be huge. If A has 10M outgoing edges then one machine is going to have to cough up one giant database. (If one node has more connections than can easily be stored on one machine then we can deal with that by getting our machine names from the entropic bits of both user ids, but let’s ignore that for now.)

In sufficiently bad cases we reverse the lookup. And reverse lookups will never be bad! If we hit the machine containing all of Ax for all connections of the form Ax — there are too many to deal with, so the machine tells us to reverse the lookup, and we ask all our machines for connections xA, and we can reasonably expect those to be evenly distributed (if 256 bots sign up for and follow A simultaneously, there will be 256 new entries of the form Ax on one machine, but only one connection of the form xA on each machine).

So, the worst case performance of this design comes down to the cost of transmitting the results (which we can evenly distribute across our machines) — you can’t really do better than that, and the key step is treating each machine at having responsibility for one square in a grid picked using Hilbert Curves.

Note that the worst case isn’t terribly bad if we just want to count connections, so interrogating the database to find out how many outgoing links A has is practical.

Anyway, that never happens…

One can assume in the case of most social networks that while there will often be worst cases of the form A follows B (i.e. B has 10M followers) there will never be cases where A follows 10M users (indeed anyone like that could be banned for abuse long, long before that point is reached).

It follows that when someone posts something (on Twitter say) it only gets pulled by followers (it doesn’t get pushed to them). A posts something — solved problem, just update one list. B asks for update — we need to check B’s followers — solved problem. So we don’t even need to store two-way connections or worry about reverse lookups.


This is apparently very similar to PageRank (Google’s algorithm for evaluating websites), which I’ve never bothered to try to understand.

Consider that each edge represents A links to B, and we rank a page by how many incoming links it has and we throw out pages with too many outgoing links (i.e. link farms, sitemaps). Then we iterate, weighting the value by the previously calculated values of each page. Google (et al) add to that by looking at the text in and around the link (e.g. “publicly available database of 128B edges”, above, links to a page about exactly that, so Google might infer that the linked page is “about” things in those words (or in the case of “click here” type links, look at words around the link).

So if from incoming links we infer that a page is about “scalable algorithms”, and from the quality of the pages with incoming links the quality of the page itself — and we maintain a database of connections between topics and pages — then when someone searches for “scalable algorithms”, we take the id of “scalable” and algorithms”, find pages about both, sort them by “quality”, create a web page, and festoon it with sponsored links and ads. By golly we’ve got a search engine!