Weighted Error Rates
Table of Contents
People make mistakes at different rates. Some people make more mistakes than others. And one person makes more mistakes in one field (e.g. physics) than another (e.g. cooking), but that’d be reversed for someone else.
Some mistakes are worse than others. Loosely, they’re bigger mistakes. They’re harder to fix. One way a mistake can be bigger is if it results in outcomes that are really different than the goal instead of only a little different.
There is no good way to measure either the number of mistakes made nor their size. But, approximately, we can consider both things together as the weighted rate of mistakes. That includes quantity and quality both. It’s the number of mistakes weighted by how bad they are.
Mistake rates can change. A toddler makes many walking mistakes; later, as an adult, he doesn’t. One of the main points of learning is to get better at things – to lower one’s weighted rate of mistakes. Some learning is general purpose and some is field/topic specific. Most people focus on the positive side of learning – they think the goal is to get knowledge of how stuff works. But a lot of knowledge is about how to avoid or fix mistakes, too. If no mistakes ruin things, you will succeed.
People in general have weighted mistake rates that are way too high. I call that “overreaching”. They are trying to do a bunch of stuff that they aren’t good enough at. Should one learn by doing? Not that way. Learn by doing stuff that is easy enough you can do it without too much trouble and work your way up incrementally. Learn by a series of successes at gradually harder things, not by a series of failures.
Capacity to Correct Errors
You have some capacity to correct errors. You have various resources. You have time, mental energy, physical energy, mental focus, creativity, inspiration, being in a good mood, money, physical objects, friends who will give advice, computer data, internet access, and various types of knowledge. You have e.g. generic knowledge (like common sense), general knowledge about a topic, very specific knowledge about a narrow sub-topic, knowledge about generic error correction, knowledge about topical error correction, and exact error correction ideas. Put all this together and you can fix some of your mistakes.
Life goes smoothly when your weighted error rate is below your weighted error correction capacity. Don’t bite off more than you can chew. Don’t rely on doing more than you can do.
Errors are somewhat predictable and somewhat unpredictable. You often know in advance that some things will go wrong. You expect to make some errors doing those math problems. You expect your essay or novel to need editing to fix errors. You expect your software to have bugs that need fixing. But you don’t know exactly how it will go. Sometimes things go more smoothly than anticipated and you’re done early. Sometimes things are hard and take extra time. Sometimes, occasionally, things are way harder or easier than expected.
Errors have statistical fluctuations. (Sometimes Murphy strikes.) To avoid disasters, you need a buffer of spare capacity for dealing with errors. You need a margin for error. You need some safety. If your weighted error correction capacity is 100 per week, you should schedule projects and activities that create errors at a weighted rate of 67 per week. Reserving one third of your capacity for safety is a good rule of thumb. If you have time, energy and other resources left over, you can do some extra stuff on short notice or relax; that’s up to you. (The statistical fluctuations, 1/3 buffer, and calling unpredictable errors “Murphy” are from Eli Goldratt.)
If you find your life doesn’t work out how it should, aim for more than 33% safety. You could try 50% safety or even 90%. This helps because you’re underestimating your weighted error rate and/or overestimating your resources and safety. If you aim for one third safety but have systematic biases or errors that result in much lower safety, one way to help fix that is to aim for a higher amount of safety like half or three quarters – that can result in an actual safety closer to one third. Keep increasing the target safety buffer until you start succeeding instead of failing. That means you’ve increased it enough to counteract your biases, inaccurate measurements, etc.
Failure is, in short, not how you learn. Failure is bad. Yeah that requires more elaboration but as a first approximation we don’t want to fail.
What are all those errors I keep talking about? Not failures (or merely failures at optional sub-goals). Just bumps in the road. If we deal with them, we can still get to our destination. It’s OK to abort some projects, to sometimes try risky things and fail, but that shouldn’t be typical. You should actually reach a successful conclusion for many of your projects, rather than failing.
And you should know in advance which projects are risky. You can set a goal to try something out, explore it, see if you can succeed – if your goal is to do a scouting mission, and you abort the whole project, then you didn’t fail, you successfully scouted it out. That is better than starting a project, expecting to succeed, and then having to give up. Try to have a handle on what you can confidently do and what requires a scouting mission first. You should know how confident to be for which projects, and when to do some mini trial projects, some research, some getting started and seeing how it goes while keeping your options open to stop, etc.
Most people underestimate the weighted error rates of most projects. They under estimate the resource requirements (time, energy, money, knowledge, everything). And they overestimate their capacity, their resources. And they don’t take into account statistical fluctuations. They try to book their schedule 100% full with projects instead of 2/3 full. The result? Often they plan to do 500% or more of what would work. They end up in a constant state of being overly busy, stressed, rushed, etc. And then what happens? They make lots of mistakes. They screw up because they are rushing. They forget things. They aren’t at their best. They multitask (trying to jam in many projects at once) and lose time task switching. Etc. And that makes things go slower or fail entirely. When you’re overbooked, you’re less efficient, so you actually get less done.
Planning to use 67% of your capacity is better. It’s OK to finish some things early. It’s OK for some things to be pretty easy and not stressful. You’ll end up getting more done overall. And because people schedule so unrealistically, at first you may need to plan to use more like 25% of your capacity or even less. After you get used to rationally organizing your life and projects, then you can aim at the proper 67% figure.
What if you want to get more done? Get more powerful. Learn more. Get more resources. Work your way up. Stuff gets easier with practice and skill. You can improve to the point that something used to take a lot of resources but now takes low resources. But just adding more stuff to your schedule is not a way to get more done; it’s actually a way to get less done.
Some examples of getting more powerful: I can now read using less time than I used to. I can write a lot of stuff, much better, much more easily than I used to be able to. Other people get good at carpentry, putting on makeup, sketching or whatever else, so the amount they can get done with the same resources goes up over time. It’s like typing: at first it’s slow and hard and takes a lot of attention, but after you get good at it then it barely takes any resources to type. Reading too: it’s really slow and hard for a 5 year old to read, but most adults can read naturally and intuitively – it becomes easy, automatic, cheap. Walking is the same way too: hard for a toddler, but easy for you because you’re better at it. Even holding an object in your hand is something that you used to make errors at when you were one year old, and you couldn’t even do it the day you were born, but now it’s easy. Eating with a fork is also hard if you don’t have the skill (maybe, today, you suck at eating with chopsticks, but you know perfectly well that people who grew up with chopsticks can do it with no problem).
Note that resources aren't just about having e.g. a dictionary or YouTube (which are both great resources). You also need to know how, when and why to use it. Otherwise you don't get problem solving and error correcting value out of it. For lots of people, their dictionary might as well be alien technology.
Want to get more done in life? Increase your skills by study and by doing successful projects. Learn stuff and practice stuff and learn by doing successfully on projects where you aren’t stressed out or very rushed or other things that make learning hard. Life can be a bit relaxed and nice and pleasant and suitable for being a thoughtful person and, if you always do stuff that way, you’ll end up really smart and productive and get way more done than people who are always trying to cope with their latest disaster (always busy putting out fires as Goldratt calls it).
Expediting projects and firefighting are inefficient. They should be uncommon. Not zero though. Expediting 2% is fine. As Goldratt explained, expediting 0% of the time is actually inefficient (it means you have unnecessarily high safety buffers).
You can increase your weighted error correction capacity by increasing various resources, especially your skill. And you can manage your project schedule efficiently. It’s not efficient to be stressed or overly rushed or doing a project with way too little budget (so that causes a bunch of problems), etc. It’s not efficient to be a few steps away from disaster all the time.
What’s efficient is to do things that are easy. Easy means efficient. Finding something easy means you are doing it efficiently. Easy means your error correction capacity isn’t being taxed; it’s not near the limit. Easy means you aren’t at risk of failure. Easy means you aren’t near running out of any resources. All that stuff means you actually get the project done using fewer resources, so you can get more done overall.
What if you want to do a hard project? Two answers. One, get more resources (often that means, particularly, knowledge – learn more stuff that is related, e.g. get better at various prerequisites, until it’s less hard). Two, break it into smaller pieces – sub-projects. A big, complex project is tough. A series of small, easy projects is better.
In general learning and doing can be viewed with four parts: management/organization, breaking complex/hard stuff into smaller parts (called “analysis” when it comes to thinking), doing small/simple/easy stuff, and combining stuff to get bigger things (called “synthesis” when it comes to thinking). In other words, the parts are splitting stuff up, combining stuff, doing small/easy/efficient stuff, and overall organization to manage the splitting, combining and doing (something has to coordinate those pieces so they work together well).
So you want to increase your capacity to handle stuff. That means increasing the size of what is “small” for you. As you improve, stuff which used to be hard/big can become simple, easy, low risk of failure, easy to fit in your resource and error correction capacity budget.
You want to organize what you do by figuring out how to separate complexity/difficulty into independent parts so that each part is easy enough. What if those parts are still hard? Split again. You can split many times. You can do sub-sub-sub-sub-projects – it’s just limited by your capacity to organize and keep track of what you’re doing and combine parts later. (For combining, don’t do it all at the end. If your first sub-project has 3 sub-sub-projects, do all 3 and then, as the next step, combine then to finish the sub-project. Don’t move on to the second sub-project until the first sub-project is done, which means its parts have been combined to actually form the sub-project. Don’t build up a huge backlog of little parts that need tons of combining later.)
There’s also learning better ways of doing things that use less resources. That is, itself, a resource (a type of knowledge). But it’s notable. You don’t just learn skills to get more done. You get better at identifying what doesn’t need to be done. You find alternative ways to do things that are easier. Work smart, not hard.
Sub-projects have the benefit of having success many times instead of just at the end when the main project is done. For some big goals, you might die before you even finish the main project. That’s OK. You can work on quantum gravity, life extension or AGI anyway, or some other big project, and be happy with success on sub-projects. You can contribute to something bigger than yourself. Or not. It’s also fine to e.g. design or build buildings that actually get finished in a few years each. It’s OK either way.
A future topic is how you correct errors. Broadly, you use resources. You have some capacity to correct some weighted amount of errors, which is often looked at for a time period like a day. But there are also specific mechanisms for correcting error beyond “use resources to improve things”. Some mechanisms are field specific and some are generic. I’ll discuss them in future articles.