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One of the neat things about the PCG random number generator by Melissa O’Neill is its use of instruction-level parallelism: the PCG state update can run in parallel with its output permutation. However, PCG only has a limited amount of ILP, about 3 instructions. Its overall speed is limited by the rate at which a CPU can run a sequence where the output of one multiply-add feeds into the next multiply-add. … Or is it? With some linear algebra and some AVX512, I can generate random numbers from a single instance of pcg32 at 200 Gbit/s on a single core. This is the same sequence of random numbers generated in the same order as normal pcg32, but more than 4x faster. You can look at the benchmark in my pcg-dxsm repository. skip ahead the insight multipliers trying it out results skip ahead One of the slightly weird features that PCG gets from its underlying linear congruential generator is “seekability”: you can skip ahead k steps in the stream of random numbers in log(k) time. The PCG paper (in section 4.3.1) cites Forrest Brown’s paper, random numbers with arbitrary strides, which explains that the skip-ahead feature is useful for reproducibility of monte carlo simulations. But what caught my eye is the skip-ahead formula. Rephrased in programmer style, state[n+k] = state[n] * pow(MUL, k) + inc * (pow(MUL, k) - 1) / (MUL - 1) the insight The skip-ahead formula says that we can calculate a future state using a couple of multiplications. The skip-ahead multipliers depend only on the LCG multiplier, not on the variable state, nor on the configurable increment. That means that for a fixed skip ahead, we can precalculate the multipliers before compile time. The skip-ahead formula allows us to unroll the PCG data dependency chain. Normally, four iterations of the PCG state update look like, state0 = rng->state state1 = state0 * MUL + rng->inc state2 = state1 * MUL + rng->inc state3 = state2 * MUL + rng->inc state4 = state3 * MUL + rng->inc rng->state = state4 With the skip-ahead multipliers it looks like, state0 = rng->state state1 = state0 * MULs1 + rng->inc * MULi1 state2 = state0 * MULs2 + rng->inc * MULi2 state3 = state0 * MULs3 + rng->inc * MULi3 state4 = state0 * MULs4 + rng->inc * MULi4 rng->state = state4 These state calculations can be done in parallel using NEON or AVX vector instructions. The disadvantage is that calculating future states in parallel requires more multiplications than doing so in series, but that’s OK because modern CPUs have lots of ALUs. multipliers The skip-ahead formula is useful for jumping ahead long distances, because (as Forrest Brown explained) you can do the exponentiation in log(k) time using repeated squaring. (The same technique is used in for modexp in RSA.) But I’m only interested in the first few skip-ahead multipliers. I’ll define the linear congruential generator as: lcg(s, inc) = s * MUL + inc Which is used in PCG’s normal state update like: rng->state = lcg(rng->state, rng->inc) To precalculate the first few skip-ahead multipliers, we iterate the LCG starting from zero and one, like this: MULs0 = 1 MULs1 = lcg(MULs0, 0) MULs2 = lcg(MULs1, 0) MULi0 = 0 MULi1 = lcg(MULi0, 1) MULi2 = lcg(MULi1, 1) My benchmark code’s commentary includes a proof by induction, which I wrote to convince myself that these multipliers are correct. trying it out To explore how well this skip-ahead idea works, I have written a couple of variants of my pcg32_bytes() function, which simply iterates pcg32 and writes the results to a byte array. The variants have an adjustable amount of parallelism. One variant is written as scalar code in a loop that has been unrolled by hand a few times. I wanted to see if standard C gets a decent speedup, perhaps from autovectorization. The other variant uses the GNU C portable vector extensions to calculate pcg32 in an explicitly parallel manner. The benchmark also ensures the output from every variant matches the baseline pcg32_bytes(). results The output from the benchmark harness lists: the function variant either the baseline version or uN for a scalar loop unrolled N times or xN for vector code with N lanes its speed in bytes per nanosecond (aka gigabytes per second) its performance relative to the baseline There are small differences in style between the baseline and u1 functions, but their performance ought to be basically the same. Apple clang 16, Macbook Pro M1 Pro. This compiler is eager and fairly effective at autovectorizing. ARM NEON isn’t big enough to get a speedup from 8 lanes of parallelism. __ 3.66 bytes/ns x 1.00 u1 3.90 bytes/ns x 1.07 u2 6.40 bytes/ns x 1.75 u3 7.66 bytes/ns x 2.09 u4 8.52 bytes/ns x 2.33 x2 7.59 bytes/ns x 2.08 x4 10.49 bytes/ns x 2.87 x8 10.40 bytes/ns x 2.84 The following results were from my AMD Ryzen 9 7950X running Debian 12 “bookworm”, comparing gcc vs clang, and AVX2 vs AVX512. gcc is less keen to autovectorize so it doesn’t do very well with the unrolled loops. (Dunno why u1 is so much slower than the baseline.) gcc 12.2 -march=x86-64-v3 __ 5.57 bytes/ns x 1.00 u1 5.13 bytes/ns x 0.92 u2 5.03 bytes/ns x 0.90 u3 7.01 bytes/ns x 1.26 u4 6.83 bytes/ns x 1.23 x2 3.96 bytes/ns x 0.71 x4 8.00 bytes/ns x 1.44 x8 12.35 bytes/ns x 2.22 clang 16.0 -march=x86-64-v3 __ 4.89 bytes/ns x 1.00 u1 4.08 bytes/ns x 0.83 u2 8.76 bytes/ns x 1.79 u3 10.43 bytes/ns x 2.13 u4 10.81 bytes/ns x 2.21 x2 6.67 bytes/ns x 1.36 x4 12.67 bytes/ns x 2.59 x8 15.27 bytes/ns x 3.12 gcc 12.2 -march=x86-64-v4 __ 5.53 bytes/ns x 1.00 u1 5.53 bytes/ns x 1.00 u2 5.55 bytes/ns x 1.00 u3 6.99 bytes/ns x 1.26 u4 6.79 bytes/ns x 1.23 x2 4.75 bytes/ns x 0.86 x4 17.14 bytes/ns x 3.10 x8 20.90 bytes/ns x 3.78 clang 16.0 -march=x86-64-v4 __ 5.53 bytes/ns x 1.00 u1 4.25 bytes/ns x 0.77 u2 7.94 bytes/ns x 1.44 u3 9.31 bytes/ns x 1.68 u4 15.33 bytes/ns x 2.77 x2 9.07 bytes/ns x 1.64 x4 21.74 bytes/ns x 3.93 x8 26.34 bytes/ns x 4.76 That last result is pcg32 generating random numbers at 200 Gbit/s.
The International Obfuscated C Code Contest has a newly revamped web site, and the Judges have announced the 28th contest, to coincide with its 40th anniversary. (Or 41st?) The Judges have also updated the archive of past winners so that as many of them as possible work on modern systems. Accordingly, I took a look at my 1998 winner to see how much damage time hath wrought. When it is built, my program needs to go through the C preprocessor twice. There are a few reasons: It’s part of coercing the C compiler into compiling OFL, an obfuscated functional language. OFL has keywords l and b, short for let and be, so for example the function for constructing a pair is defined as l pair b (BB (B (B K)) C CI) In a less awful language that might be written let pair = λx λy λf λg (f x y) Anyway, the first pass of the C preprocessor turns a l (let) declaration into a macro #define pair b (BB (B (B K)) C CI) And the second pass expands the macros. (There’s a joke in the README that the OFL compiler has one optimization, function inlining (which is actually implemented by cpp macro expansion) but in fact inlining harms the performance of OFL.) The smaller the OFL interpreter, the more space there is for the program written in OFL. In the 1998 IOCCC rules, #define cost 7 characters, whereas l cost only one. I think the modern rules don’t count C or cpp keywords so there’s less reason to use this stupid trick to save space. Running the program through cpp twice is a horrible abuse of C and therefore just the kind of joke that the IOCCC encourages. (In fact the Makefile sends the program through cpp three times, twice explicitly and once as part of compiling to machine code. This is deliberately gratuitous, INABIAF.) There were a couple of ways this silliness caused problems. Modern headers are sensitive to which version of the C standard is in effect, wrt things like restrict keywords in standard library function declarations. The extra preprocessor invocations needed to be fixed to use consistent -std= options so that the final compilation doesn’t encounter language features from the future. Newer gcc emits #line directives around macro expansions. This caused problems for the declaration l ef E(EOF) which defines ef as a primitive value equal to EOF. After preprocessing this became #define ef E( #line 1213 "stdio.h" (-1) #line 69 "fanf.c" ) so the macro definition got truncated. The fix was to process the #include directives in the second preprocessor pass rather than the first. I vaguely remember some indecision when writing the program about whether to #include in the first or second pass, in particular whether preprocessing the headers twice would lead to trouble. First pass #include seemed to work and was shorter so that was what the original submission did. There’s one further change. The IOCCC Judges are trying to avoid compiler warnings about nonstandard arguments to main. To save a few characters, my entry had int main(int c) { ... } but the argument c isn’t used so I just removed it. The build commands still print “This may take some time to complete”, because in the 1990s if you tried to compile with optimization you would have been waiting a long time, if it completed at all. The revamped Makefile uses -O3, which takes gcc over 30 seconds and half a gigabyte of RAM. Quite a lot for less than 2.5 KiB of C!
I have made a new release of nsnotifyd, a tiny DNS server that just listens for NOTIFY messages and runs a script when one of your zones changes. This nsnotifyd-2.2 release includes a new feature: nsnotify can now send NOTIFY messages from a specific source address Thanks to Adam Augustine for the suggestion. I like receiving messages that say things like, Thanks for making this useful tool available for free.
Recently the Spritely Institute published an introduction to Petnames, A humane approach to secure, decentralized naming. I have long been a fan of petnames, and graph naming systems in general. I first learned about them in the context of Mark Miller’s E programming language which was a distributed object capability system on the JVM. I gather Spritely are working on something similar, but with a more webby lisp/scheme flavour – and in fact Mark Miller is the second author on this article. An interesting thing that the article sort of hints at is that these kinds of systems have a fairly smooth range of operating points from decentralized petnames all the way to centralized globally unique names. Zooko’s triangle is actually more like a fan when the “human friendly” point is fixed: there’s an arc describing the tradeoffs, from personal through local to global. As a first step away from petnames, I like to use the term “nickname” for nearby instances of what they call “edge names” in the article: a nickname is not as personal as a petname, it’s a name you share with others. A bit further along the arc is the article’s example of the “bizdir” local business directory. It’s a trusted (and hopefully trustworthy) naming authority, but in a more local / federated fashion rather than centralized. How can a petname system function at the global+centralized point, so it could replace the DNS? It needs to pass the “billboard test”: I type in a name I see on a billboard and I get to the right place. (It might be a multipart name like a postal address or DNS name, with an extra “edge name” or two to provide enough disambiguating context.) I imagine that an operating system supplier might provide a few preconfigured petnames (it probably includes its own petname so the software can update itself securely), a lot like its preconfigured PKIX CA certificates. These petnames would refer to orgs like the “bizdir”, or Verisign, or Nominet, that act as nickname registries. Your collection of petnames is in effect your personal root zone, and the preconfigured petnames are in effect the default TLDs. When I was thinking about how a decentralized graph naming system could be made user-friendly and able to pass the billboard test I realised that there are organizational structures that are hard to avoid. I expect there would inevitably be something like the CA/Browser forum to mediate between OS suppliers and nickname registries: a petname ICANN. I wrote an older iteration of these ideas over a decade ago. Those notes suffer from too many DNS brainworms, but looking back, there’s some curious anti-DNS discussion. How might it be useful to be able to reach a name by multiple paths? Could you use that for attestation? What might it look like to have a shared context for names that is not global but is national or regional or local?
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I’m sitting in a small coffee shop in Brooklyn. I have a warm drink, and it’s just started to snow outside. I’m visiting New York to see Operation Mincemeat on Broadway – I was at the dress rehearsal yesterday, and I’ll be at the opening preview tonight. I’ve seen this show more times than I care to count, and I hope US theater-goers love it as much as Brits. The people who make the show will tell you that it’s about a bunch of misfits who thought they could do something ridiculous, who had the audacity to believe in something unlikely. That’s certainly one way to see it. The musical tells the true story of a group of British spies who tried to fool Hitler with a dead body, fake papers, and an outrageous plan that could easily have failed. Decades later, the show’s creators would mirror that same spirit of unlikely ambition. Four friends, armed with their creativity, determination, and a wardrobe full of hats, created a new musical in a small London theatre. And after a series of transfers, they’re about to open the show under the bright lights of Broadway. But when I watch the show, I see a story about friendship. It’s about how we need our friends to help us, to inspire us, to push us to be the best versions of ourselves. I see the swaggering leader who needs a team to help him truly achieve. The nervous scientist who stands up for himself with the support of his friends. The enthusiastic secretary who learns wisdom and resilience from her elder. And so, I suppose, it’s fitting that I’m not in New York on my own. I’m here with friends – dozens of wonderful people who I met through this ridiculous show. At first, I was just an audience member. I sat in my seat, I watched the show, and I laughed and cried with equal measure. After the show, I waited at stage door to thank the cast. Then I came to see the show a second time. And a third. And a fourth. After a few trips, I started to see familiar faces waiting with me at stage door. So before the cast came out, we started chatting. Those conversations became a Twitter community, then a Discord, then a WhatsApp. We swapped fan art, merch, and stories of our favourite moments. We went to other shows together, and we hung out outside the theatre. I spent New Year’s Eve with a few of these friends, sitting on somebody’s floor and laughing about a bowl of limes like it was the funniest thing in the world. And now we’re together in New York. Meeting this kind, funny, and creative group of people might seem as unlikely as the premise of Mincemeat itself. But I believed it was possible, and here we are. I feel so lucky to have met these people, to take this ridiculous trip, to share these precious days with them. I know what a privilege this is – the time, the money, the ability to say let’s do this and make it happen. How many people can gather a dozen friends for even a single evening, let alone a trip halfway round the world? You might think it’s silly to travel this far for a theatre show, especially one we’ve seen plenty of times in London. Some people would never see the same show twice, and most of us are comfortably into double or triple-figures. Whenever somebody asks why, I don’t have a good answer. Because it’s fun? Because it’s moving? Because I enjoy it? I feel the need to justify it, as if there’s some logical reason that will make all of this okay. But maybe I don’t have to. Maybe joy doesn’t need justification. A theatre show doesn’t happen without people who care. Neither does a friendship. So much of our culture tells us that it’s not cool to care. It’s better to be detached, dismissive, disinterested. Enthusiasm is cringe. Sincerity is weakness. I’ve certainly felt that pressure – the urge to play it cool, to pretend I’m above it all. To act as if I only enjoy something a “normal” amount. Well, fuck that. I don’t know where the drive to be detached comes from. Maybe it’s to protect ourselves, a way to guard against disappointment. Maybe it’s to seem sophisticated, as if having passions makes us childish or less mature. Or perhaps it’s about control – if we stay detached, we never have to depend on others, we never have to trust in something bigger than ourselves. Being detached means you can’t get hurt – but you’ll also miss out on so much joy. I’m a big fan of being a big fan of things. So many of the best things in my life have come from caring, from letting myself be involved, from finding people who are a big fan of the same things as me. If I pretended not to care, I wouldn’t have any of that. Caring – deeply, foolishly, vulnerably – is how I connect with people. My friends and I care about this show, we care about each other, and we care about our joy. That care and love for each other is what brought us together, and without it we wouldn’t be here in this city. I know this is a once-in-a-lifetime trip. So many stars had to align – for us to meet, for the show we love to be successful, for us to be able to travel together. But if we didn’t care, none of those stars would have aligned. I know so many other friends who would have loved to be here but can’t be, for all kinds of reasons. Their absence isn’t for lack of caring, and they want the show to do well whether or not they’re here. I know they care, and that’s the important thing. To butcher Tennyson: I think it’s better to care about something you cannot affect, than to care about nothing at all. In a world that’s full of cynicism and spite and hatred, I feel that now more than ever. I’d recommend you go to the show if you haven’t already, but that’s not really the point of this post. Maybe you’ve already seen Operation Mincemeat, and it wasn’t for you. Maybe you’re not a theatre kid. Maybe you aren’t into musicals, or history, or war stories. That’s okay. I don’t mind if you care about different things to me. (Imagine how boring the world would be if we all cared about the same things!) But I want you to care about something. I want you to find it, find people who care about it too, and hold on to them. Because right now, in this city, with these people, at this show? I’m so glad I did. And I hope you find that sort of happiness too. Some of the people who made this trip special. Photo by Chloe, and taken from her Twitter. Timing note: I wrote this on February 15th, but I delayed posting it because I didn’t want to highlight the fact I was away from home. [If the formatting of this post looks odd in your feed reader, visit the original article]
One of the biggest mistakes that new startup founders make is trying to get away from the customer-facing roles too early. Whether it's customer support or it's sales, it's an incredible advantage to have the founders doing that work directly, and for much longer than they find comfortable. The absolute worst thing you can do is hire a sales person or a customer service agent too early. You'll miss all the golden nuggets that customers throw at you for free when they're rejecting your pitch or complaining about the product. Seeing these reasons paraphrased or summarized destroy all the nutrients in their insights. You want that whole-grain feedback straight from the customers' mouth! When we launched Basecamp in 2004, Jason was doing all the customer service himself. And he kept doing it like that for three years!! By the time we hired our first customer service agent, Jason was doing 150 emails/day. The business was doing millions of dollars in ARR. And Basecamp got infinitely, better both as a market proposition and as a product, because Jason could funnel all that feedback into decisions and positioning. For a long time after that, we did "Everyone on Support". Frequently rotating programmers, designers, and founders through a day of answering emails directly to customers. The dividends of doing this were almost as high as having Jason run it all in the early years. We fixed an incredible number of minor niggles and annoying bugs because programmers found it easier to solve the problem than to apologize for why it was there. It's not easy doing this! Customers often offer their valuable insights wrapped in rude language, unreasonable demands, and bad suggestions. That's why many founders quit the business of dealing with them at the first opportunity. That's why few companies ever do "Everyone On Support". That's why there's such eagerness to reduce support to an AI-only interaction. But quitting dealing with customers early, not just in support but also in sales, is an incredible handicap for any startup. You don't have to do everything that every customer demands of you, but you should certainly listen to them. And you can't listen well if the sound is being muffled by early layers of indirection.
As well as changing the way I organise my writing, last year I made some cosmetic improvements to this site. I design everything on this site myself, and I write the CSS by hand – I don’t use any third-party styles or frameworks. I don’t have any design training, and I don’t do design professionally, so I use this site as a place to learn and practice my design skills. It’s a continual work-in-progress, but I’d like to think it’s getting better over time. I design this site for readers. I write long, text-heavy posts with the occasional illustration or diagram, so I want something that will be comfortable to read and look good on a wide variety of browsers and devices. I get a lot of that “for free” by using semantic HTML and the default styles – most of my CSS is just cosmetic. Let’s go through some of the changes. Cleaning up the link styles This is what links used to look like: Every page has a tint colour, and then I was deriving different shades to style different links – a darker shade for visited links, a lighter shade for visited links in dark mode, and a background that appears on hover. I’m generating these new colours programatically, and I was so proud of getting that code working that I didn’t stop to think whether it was a good idea. In hindsight, I see several issues. The tint colour is meant to give the page a consistent visual appearance, but the different shades diluted that effect. I don’t think their meaning was especially obvious. How many readers ever worked it out? And the hover styles are actively unhelpful – just as you hover over a link you’re interested in, I’m making it harder to read! (At least in light mode – in dark mode, the hover style is barely legible.) One thing I noticed is that for certain tint colours, the “visited” colour I generated was barely distinguishable from the text colour. So I decided to lean into that in the new link styles: visited links are now the same colour as regular text. This new set of styles feels more coherent. I’m only using one shade of the tint colour, and I think the meaning is a bit clearer – only new-to-you links will get the pop of colour to stand out from the rest of the text. I’m happy to rely on underlines for the links you’ve already visited. And when you hover, the thick underline means you can see where you are, but the link text remains readable. Swapping out the font I swapped out the font, replacing Georgia with Charter. The difference is subtle, so I’d be surprised if anyone noticed: I’ve always used web safe fonts for this site – the fonts that are built into web browsers, and don’t need to be downloaded first. I’ve played with custom fonts from time to time, but there’s no font I like more enough to justify the hassle of loading a custom font. I still like Georgia, but I felt it was showing its age – it was designed in 1993 to look good on low-resolution screens, but looks a little chunky on modern displays. I think Charter looks nicer on high-resolution screens, but if you don’t have it installed then I fall back to Georgia. Making all the roundrects consistent I use a lot of rounded rectangles for components on this site, including article cards, blockquotes, and code blocks. For a long time they had similar but not identical styles, because I designed them all at different times. There were weird inconsistencies. For example, why does one roundrect have a 2px border, but another one is 3px? These are small details that nobody will ever notice directly, but undermine the sense of visual together-ness. I’ve done a complete overhaul of these styles, to make everything look more consistent. I’m leaning heavily on CSS variables, a relatively new CSS feature that I’ve really come to like. Variables make it much easier to use consistent values in different rules. I also tweaked the appearance: I’ve removed another two shades of the tint colour. (Yes, those shades were different from the ones used in links.) Colour draws your attention, so I’m trying to use it more carefully. A link says “click here”. A heading says “start here”. What does a blockquote or code snippet say? It’s just part of the text, so it shouldn’t be grabbing your attention. I think the neutral background also makes the syntax highlighting easier to read, because the tint colour isn’t clashing with the code colours. I could probably consolidate the shades of grey I’m using, but that’s a task for another day. I also removed the left indent on blockquotes and code blocks – I think it looks nicer to have a flush left edge for everything, and it means you can read more text on mobile screens. (That’s where I really felt the issues with the old design.) What’s next? By tidying up the design and reducing the number of unique elements, I’ve got a bit of room to add something new. For a while now I’ve wanted a place at the bottom of posts for common actions, or links to related and follow-up posts. As I do more and more long-form, reflective writing, I want to be able to say “if you liked this, you should read this too”. I want something that catches your eye, but doesn’t distract from the article you’re already reading. Louie Mantia has a version of this that I quite like: I’ve held off designing this because the existing pages felt too busy, but now I feel like I have space to add this – there aren’t as many clashing colours and components to compete for your attention. I’m still sketching out designs – my current idea is my rounded rectangle blocks, but with a coloured border instead of a subtle grey, but when I did a prototype, I feel like it’s missing something. I need to try a few more ideas. Watch this space! [If the formatting of this post looks odd in your feed reader, visit the original article]
Humanity's Last Exam by Center for AI Safety (CAIS) and Scale AI
Most of our cultural virtues, celebrated heroes, and catchy slogans align with the idea of "never give up". That's a good default! Most people are inclined to give up too easily, as soon as the going gets hard. But it's also worth remembering that sometimes you really should fold, admit defeat, and accept that your plan didn't work out. But how to distinguish between a bad plan and insufficient effort? It's not easy. Plenty of plans look foolish at first glance, especially to people without skin in the game. That's the essence of a disruptive startup: The idea ought to look a bit daft at first glance or it probably doesn't carry the counter-intuitive kernel needed to really pop. Yet it's also obviously true that not every daft idea holds the potential to be a disruptive startup. That's why even the best venture capital investors in the world are wrong far more than they're right. Not because they aren't smart, but because nobody is smart enough to predict (the disruption of) the future consistently. The best they can do is make long bets, and then hope enough of them pay off to fund the ones that don't. So far, so logical, so conventional. A million words have been written by a million VCs about how their shrewd eyes let them see those hidden disruptive kernels before anyone else could. Good for them. What I'm more interested in knowing more about is how and when you pivot from a promising bet to folding your hand. When do you accept that no amount of additional effort is going to get that turkey to soar? I'm asking because I don't have any great heuristics here, and I'd really like to know! Because the ability to fold your hand, and live to play your remaining chips another day, isn't just about startups. It's also about individual projects. It's about work methods. Hell, it's even about politics and societies at large. I'll give you just one small example. In 2017, Rails 5.1 shipped with new tooling for doing end-to-end system tests, using a headless browser to validate the functionality, as a user would in their own browser. Since then, we've spent an enormous amount of time and effort trying to make this approach work. Far too much time, if you ask me now. This year, we finished our decision to fold, and to give up on using these types of system tests on the scale we had previously thought made sense. In fact, just last week, we deleted 5,000 lines of code from the Basecamp code base by dropping literally all the system tests that we had carried so diligently for all these years. I really like this example, because it draws parallels to investing and entrepreneurship so well. The problem with our approach to system tests wasn't that it didn't work at all. If that had been the case, bailing on the approach would have been a no brainer long ago. The trouble was that it sorta-kinda did work! Some of the time. With great effort. But ultimately wasn't worth the squeeze. I've seen this trap snap on startups time and again. The idea finds some traction. Enough for the founders to muddle through for years and years. Stuck with an idea that sorta-kinda does work, but not well enough to be worth a decade of their life. That's a tragic trap. The only antidote I've found to this on the development side is time boxing. Programmers are just as liable as anyone to believe a flawed design can work if given just a bit more time. And then a bit more. And then just double of what we've already spent. The time box provides a hard stop. In Shape Up, it's six weeks. Do or die. Ship or don't. That works. But what's the right amount of time to give a startup or a methodology or a societal policy? There's obviously no universal answer, but I'd argue that whatever the answer, it's "less than you think, less than you want". Having the grit to stick with the effort when the going gets hard is a key trait of successful people. But having the humility to give up on good bets turned bad might be just as important.
