The First Sample Gives the Most Information

This is a really powerful concept; I can immediately think of at least two fields this applies to:

• When you're not sure how to build a software user interface, you might think "let's run an A/B test on 1000 people and see which performs better". But you'll get 90 percent of the value just by showing it to one or two users and watching them use it, live.

• When you're learning to cook, one of the first things they teach you is to sample your food throughout. The first sip or bite will immediately tell you how to adjust the recipe (eg add more salt, add something spicy, or a dash of vinegar)

I like this post and am not intending to argue against its point by the following:

I read the paragraph about orders of magnitude and immediately started thinking about whether there are good counterexamples. Here are two: wires are used in lengths from nanometers to kilometers, and computer programs as a category run for times from milliseconds to weeks (even considering only those which are intended to have a finite task and not to continue running until cancelled).

Common characteristics of these two examples are that they are one-dimensional (no “square-cube law” limits scaling) and that they are arguably in some sense the most extensible solutions to their problem domains (a wire is the form that arbitrary length electrical conductors take, and most computer programs are written in Turing-complete languages).

Perhaps the caveat is merely that “some things scale freely such that the order of magnitude is no new information and you need to look at different properties of the thing”.

Nice neat little post.

Maybe a caveat I would add is that when your friend gives you a sample, they probably give one from the center of their own concept space for the subject. Theirs is probably quite similar to most others, but there might be differences. Note that this isn't a problem when giving examples to clarify some of your points, because there the whole point is to transmit your concept space.

Game idea: give one player a category, and see how many (misleadingly non-central) examples they can provide, without giving away what the category is to the guesses of the rest of the group.

Well now I have a post to link to for this point. Thanks! :)

I've noticed that misinformative articles are usually wrong from the get-go: fact checking the very first claim in an article is highly predictive of how the rest of the piece will turn out (which is really interesting; I suppose it indicates that most such articles are preaching to a choir, so they don't worry about roping people in carefully and trying not to trip BS detectors). Good-faith articles often contain errors, but rarely at the very start.

More precisely, the first sample gives the most information about the mean. Learning one person's income tells you a lot about incomes in general, even though incomes are heavy-tailed.

Imagine you had no prior knowledge of how wealthy people are on Earth, or even how to think about the concept of "wealth." For you, the meaning of the term is as inscrutable as the term "flargibargh." You might sample a very poor person, and think everybody's living in poverty. You might sample a middle-class person, and miss the existence of the very rich and poor. You might (unlikely) sample a billionaire and think everybody's incredibly wealthy.

However, those samples help you avoid the mistakes of thinking that wealth is commonly extremely negative, or of a gigantic magnitude (i.e. on the order of Avogadro's number). It gets you vastly closer to the mean than you might land at if you had absolutely zero knowledge of what the concept of "wealth" refers to, and didn't even know that it's a word to measure something relevant to humans (in which domain manageable numbers are common).

However, the first sample gives you no information about the distribution of the sample. As the problem above illustrates, sampling one person tells you nothing about whether wealth is distributed on a bell curve, a heavy-tailed distribution, is exactly even, has a linear distribution, or some other form.

It's very important to gain the skill of "get a sample or example" when dealing with new territory. At the same time, you need to understand what that sample does or does not tell you. Mistakenly thinking that a sample gives you information about X can lead you to make decisions based on that illusory "information," when if you'd known your ignorance better you might not have acted.

And then, of course, it's important to make sure that your sample is actually a sample of what you think it is...

Mark mentions that he got this point from Ben Pace. A few months ago I heard the extended version from Ben, and what I really want is for Ben to write a post (or maybe a whole sequence) on it. But in the meantime, it's an important idea, and this short post is the best source to link to on it.

Agree. Not only is asking “what’s an example” generally highly productive, it’s about 80% as productive as asking “what are two examples”.

Related:  I got two masters degrees, at midlife, after doing other stuff.  I also moved back to the USA during that time and found it useful to learn a lot of little things I never needed to think about in Taiwan, like how to fix a car.  So, having learned a handful of new skills in the past eight years or so, from car repairs to calculus, as a general heuristic I find doing something independently from beginning to end and fixing the problems along the way the first time teaches about 50% of the knowledge.  2-3 times gets to 75%.  3-5 times gets to 90%.  Past the 90% mark, you spend the rest of your life making small improvements in the last 10% of the knowledge.

Basically, you don't need to do that many Taylor series to see the pattern and grok what's going on (and have improved your understanding of polynomial representations of calculus, and start getting intuitions when other approaches are used).  You don't need to switch the motor mounts on that many cars to basically get it (and to have learned frankly a lot about similar types of car work).  Etc.

That first time, maybe the second in some cases, is the biggest lift and the biggest learning.

Also worth minding that information ≠ knowledge/understanding, and that understanding behaves differently. You might not understand the first five examples, and then the sixth example lets you triangulate some crucial aspect, which allows you to go back and re-understand more deeply the previous examples.