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Comment by afarrell | Hacker News Reader

> This quality of “not stopping at an unsatisfactory answer” deserves some examination.

> This requires a lot of intrinsic motivation, because it’s so hard; so most people simply don’t do it.

It also requires self-confidence, persuasiveness, and social power.

Without these traits, your attempts to really understand something will be dismissed as "overthinking things" or "trying to understand the universe". Those around you will urge you to "stop thinking just do the task" or "do the obvious thing" as they lose patience with you. If you don't resist them you'll end up moving forward despite feeling confused, sometimes completely. You'll then end up pissing people off when you execute too slowly or fail (in their eyes, intentionally).

> This is a habit. It’s easy to pick up.

Not if the people around you are exhausted by you.

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I want to add - habits like that are great to pick up, and fine tune, when you're in college.

More so if you're a college student that can focus 100% on your academic life/studies, unburdened by things like work.

EVEN more so if you have great mentors, professors, etc. that can guide you to the right place.

I'm not saying that one CAN NOT do the things above, if you're a busy student with work on the side, and very limited resources as far as mentors or professors go...but I do think that those lucky enough to find themselves in the right positions, are more likely to mature - and quicker.

(And it was no surprise to see that the author is a PPE grad from Oxford)

Your points about social context are great ones and 100% valid, but I want to make a case for "stop thinking just do the task":

---

Often, trying (and potentially failing) to do a task is the best way to learn about it. The key is to be very explicit about what parts of that task you actually understand and which ones you're pulling out of your ass.

This is especially true when creating software. It's super rare to have requirements that are concrete and detailed enough to form a comprehensive understanding of the final design before you start developing it. Instead there are usually parts that have clarity and others that are fuzzy. If you can enumerate those and keep them separate you can often leverage the parts you understand to make progress on those you do not. Writing placeholder/obviously-terrible code to stand in for the unknown parts just so that you can spin up a running system is a great way to do that. Along the way you'll see what patterns emerge, where you hit walls, etc, which is not always easy to imagine with raw abstract thought. And having "working" software that you can play with is a great way to find edge cases and otherwise make progress on those unknowns. Once you've gained a more complete understanding you can replace the placeholder junk with well-designed/actually-thought-out modules.

(Another obvious reason to do this is if your company will literally go out of business if you wait until you have a perfect understanding to launch a product/service, but I think most people here get that.)

I'm not sure how much this generalizes, but it also works well for me when writing. I usually start with a vague understanding of an idea I hope to communicate, then jot down disjointed sentences to capture parts of it. As I do so it gradually becomes clear how things are connected, where my reasoning is muddy, what I thought I knew but can't express so probably don't, etc, and I can use this gained understanding to iteratively rewrite and reshape my message until it becomes something coherent. Sometimes, anyway; other times I don't end up sending/publishing it at all because along the way I learned that the thing I was hoping to communicate was based on a faulty assumption or is not as straightforward as I thought it was. Which is great, because either way I've learned something.

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I guess I'd say it differently: "keep thinking and do the task".

Agree with this. I think of education as a "series of increasingly smaller lies". If you try to explain everything right away with complete fine-grained truthfulness, you quickly get to molecular dynamics, and don't have to stop there.

A common unspoken theme in the post is, the art of learning is knowing "what" to care about and "when".

It’s worth mentioning that this desire to think through things deeply often runs contrary to a bias for action, and it’s very difficult to measure progress in thought. There is a long phase of thinking very hard, and a short phase where things suddenly become clear. So, thinking through and understanding things deeply is often discouraged as a consequence.

The key is to decouple the two.

When you are required to act, act and act decisively. If you are clear that the understanding could be deeper (and it usually can), you trigger a work effort to understand more. So the next time you need to make a decision you’re more informed.

There are both extremes, and best not to be at either one of them.

Example: I forget the name of the principle, but in mathematics the statement "P implies Q" is considered true if P can never be true. As an example, let P be "George Washington was a woman" and Q be "Queen Elizabeth is a man". Then the statement "If GW was a woman, then QE is a man" is considered to be a true statement.

I have a friend who refuses to accept that such a statement should be considered "true". And he has put off studying real analysis until he can learn enough logic theory to convince himself on the validity of accepting such statements as true. I do not think he'll ever get to study real analysis, because he is full of "No! I need to understand this really really well before proceeding!" statements.

It's a fine approach if you have an infinite amount of time.

The other issue, as another commenter pointed out: It's very difficult to measure progress in thought. The mind is great at fooling itself, and not until you try to solve real problems (or discuss them with others) will you expose most of the gaps in your mind. The same person in the above anecdote does suffer from this. He definitely puts in effort to learn a lot (and has succeeded), but there are always more things to learn, and he moves on to the next topic before really applying what he has learned. As someone who talks to him often, it's really hard to tell if he understands. He is the classic case of "I'm sure I can solve problems when I need to, with a bit of review".

At the other extreme, of course, are people who are not really that motivated to understand. They are satisfied if they get the answer at the back of the book. You won't get far with just that.

> If you don't resist them you'll end up moving forward despite feeling confused, sometimes completely. You'll then end up pissing people off when you execute too slowly or fail (in their eyes, intentionally).

This sounds more like an issue at work, and your experience is fairly universal - most jobs I've worked at have it. In my experience, understanding things well is sadly not valued on the job. They want you to "execute", and want you to minimize the time you spend learning. And of course, they would rather hire someone else instead of ensuring your proper learning/training.

A real logician can correct me if I'm wrong, but I think those statements are considered "vacuously true" for the same reason we say the empty set is a member of every set and x^0 is 1: it makes the rules of calculation simpler if we define it that way than other ways. But you can't use these convenient definitions to learn anything new.

You can keep multiplying your equation by x^0 and union-ing your set with the empty set and or-ing your proposition with "If eggs are diamonds then fish can talk" all the livelong day, but you never gain any more information.

I pretty much told him the same: That we declared such statements to be true merely for convenience - it makes the proofs shorter. And that none of the theorems he would normally deal with would have a different "outcome" if we don't accept such statements - they'd still be valid theorems.

But he won't be convinced until he formally studies logic. No idea when that will happen.

Well I have "formally" studied formal logic and he's in for a disappointment. Formal logic is a game, especially boolean logic, which has no grounding in truth, the world, or anything. Sometimes it's a useful game, but there's no inherent meaning behind it.

Tell your friend that implication works that way because that's what we've assumed, nothing more, nothing less.

> Formal logic is a game, especially boolean logic, which has no grounding in truth, the world, or anything.

Thing is: He knows this. He's not a "beginner" who wants to learn a bit more. He just hasn't spent enough time pondering vacuously true statements, and is assuming there is more to it than there is, and hopes studying logic will shed some light. So he refuses to study analysis until he has time to study logic.

No doubt, if he ever gets to logic, he'll end up with more questions and branching off further and further. He'll never get around to analysis. But like the top level comment - he doesn't like it when people tell him not to bother.

Though not implication, there is some reasoning to some other vacuously true statements. Take for example:

All purple cows are smart.

This statement is true, because the set of purple cows is empty. It might seem, odd, but it's because we can rephrase it as:

There does not exist a purple cow that is not smart.

When you phrase it like that, I think most people would intuitively agree that it should evaluate to true. In other words, to preserve symmetry between the universal and existential qualifiers, you need the first statement to also be true. Without the ability to transform "exists" into "foralls" would make first order predicate logic pretty much useless. In addition, if the emptiness of a set actually changed how the quantifiers worked, it would be a big problem: breaking referential transparency, if you will.

I don't recall there being a similar justification for implication in boolean logic, but I think the reasoning is similar. Hope that helps!

> I don't recall there being a similar justification for implication in boolean logic, but I think the reasoning is similar.

You can apply a similar equivalence, the contrapositive. Using the same example I gave sidethread:

0. (Premise - I wish to snottily imply that "that guy" did not graduate from high school.)

1. "If that guy graduated from high school, I'm the King of England."

(1) is exactly equivalent to (2):

2. "If I'm not the King of England, that guy didn't graduate from high school."

A positive proposition in (1) is negative in (2), and vice versa. But they are the same thing; if one is defined, the other is also defined.

> the statement "P implies Q" is considered true if P can never be true. As an example, let P be "George Washington was a woman" and Q be "Queen Elizabeth is a man". Then the statement "If GW was a woman, then QE is a man" is considered to be a true statement.

> I have a friend who refuses to accept that such a statement should be considered "true".

This is a weird thing to refuse to accept, since it is an ordinary part of vernacular English, a common way of dismissing an assertion as false.

"If that guy graduated high school, I'm the King of England."

Actually there were women who dressed like men, pretended to be men -- and if it, surprisingly, turns out this was the case with GW, then that won't make QE a man.

I have to agree with your friend :-)

Yeah, there's a bunch of caveats here. You also need to be reasonably quick to understand things, otherwise you'll be spending a lifetime trying to understand some pretty basic concepts and never get to anything interesting.

In general, there are a bunch of starting conditions necessary for this kind of approach to glean value.

I don’t agree because I still do this all the time. Sure some people get annoyed, assholes will try to make you feel bad for asking dumb questions, or even mock you publicly. The fact is, your understanding grows so quickly when you ask questions that this doesn’t matter.

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