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Infinitesimals complex analysis5/30/2023 ![]() Each extension has some very nice properties to it, and a reason for its existence. So the problem is not that we can't find its value, the problem is that there are 3 extensions of h(x) beyond the interval. We can find h(0) (if we define it from the Lambert W function). The problem is not that we can't find an answer for this. But it can help us with ours, when we make it more observable.I thought we already answered this question here. We can work at exercising them more explicitly.Īnd then there’s software! We’ve made modern programming languages and APIs more amenable to analysis: more declarative, more readable, more testable. Working in production software, we also need sense-making skills. We work on those, and that’s good, because they don’t occur naturally in humans. Once I’m in the code, my analysis skills come out.Īnalysis skills are essential for software development. Now I know where to go: the GET /price code in the pricing service, and its recent release history. Now I ask, “Is that normal?” and aggregate all the GET /price spans, and I find a jump in latency a few hours ago. The trace tells me which part takes the most time: a span called GET /price. ![]() Then I can ask, “Why is it slow sometimes?" I can click on a slow dot to get a trace. I can ask whether that happens with a heatmap, and find out: sometimes. Here’s one: I expect my services to respond to a /cart request reliably and in a reasonable time. Add arbitrary queries, and we get the sense-making circle of forming new questions. It explains itself in traces, and lets us see what happens at scale in production. Observable software is amenable to sense-making. These days, I am careful to write observable code, leading to observable software. That understanding keeps our programs malleable. You can look at it carefully and predict what it will do, then verify that understanding with a unit test. What does it mean to do sense-making in software? Every incident response offers an example.Įarly in my career, I learned to write readable, testable code. They respond, “Wow, good point, let’s meet with the whole team about these.” Soon we have a better product and a team that’s invested in the work. Now I have detailed questions for the product and design people. For one: it takes one access level to add an item, but a higher one to change it-what if a user makes a typo? New question: what feels arbitrary? Everyone chimes in with an example. Hmm, maybe the team doesn’t feel good about what they’re implementing. It makes everything harder for the user, and it feels so arbitrary. Xiaoping agrees: adding access controls isn’t fun. Marina says not really she was just more excited by the last feature than this one they’re implementing. Maybe as a manager, I notice that people’s voices in standup sound duller than they used to. What does it mean to do sense-making in teams? This is a qualitative, evidence-based method for theory formation and investigation. I like Brene Brown’s research into what deeply happy people have in common. Some scientists do sense-making very explicitly. We can move it in the direction we hope for. Narrow in on what matters to you and get a good-enough understanding of that.Ī good-enough understanding lets us influence our complex system to our liking. The sense-making circle gives you better questions. Sense-making involves coming up with a theory, asking questions to investigate it, and getting something better than answers. Now we’re in the realm of complex systems. This feels good.īut once I hook my program up to software written by a bunch of other people, or put it in front of users who do who-knows-what with browser plugins, most bets are off. Then I can change that program to do what I want. It’s appropriate for parts of our system: I can totally analyze a program. We do sense-making naturally in order to exist as part of the world.Īnalysis, by contrast, is a skill we learned on purpose. And we don’t do this by knowing everything about them, but by noticing things and discussing it with each other. We form ideas of what all that means for us. We form ideas of how our communities work, how each other works, how our social and political systems work. They’re always changing, so even if you omnisciently knew how it worked at one moment, you’d be wrong the next.Ĭomplex systems include families, teams, and distributed software systems under development.įortunately, we all have the skill of sense-making. They respond to and influence their environment. We have to add another skill: sense-making.Ĭomplex systems have parts that learn and change, with relations that vary with state and history. Given enough time and teammates, we can analyze a very complicated system and fix it when it breaks.īut complex systems don’t yield to analysis. We can break down a simple system, look at its parts and their relations, and master it. When we work at it, professionals are pretty good at analysis.
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