Tiers of answers to half-baked questions(blog.plover.com)
blog.plover.com
Tiers of answers to half-baked questions
https://blog.plover.com/misc/half-baked.html
50 comments
This is interesting because I work with professional mathematicians and they are the exact opposite. They always start off with a semi-formalized idea and play with it a lot before trying to hone in on something formal. And conversely they have absolutely no problem listening to / thinking about non-rigorous ideas. They also do excellent work, so I would say this is a positive trait wrt productivity.
Any tips for people who are quick to be dismissive? Asking for a friend, he often is not generous with his interpretation of peoples’ questions.
I don't think there's much better advice than what the OP has already said: train yourself to wonder if there's a deeper question that the asker might be asking. Ultimately it's a question of humility. I think dismissiveness is often motivated by an assumption that the asker has made a simple rookie thinking error, and that an involved answer isn't worth your time.
I too fill in the blanks and expect the same courtesy to be given me. As such I have began to bluntly refuse to participate in discussion with an uncooperative party like what you describe. I can find more constructive things to do with my time and they have no reason to expect otherwise.
Like you say, it's very curious why some people do expect their attitude to be accepted. If it is something they have learned to do, then what can be done to make them unlearn it? My attempts at this have so far clearly been too blunt, probably since I'm no saint and seldom suppress my irritation at their intellectual dishonesty faster than thinking of a scathing way to confront them...
Like you say, it's very curious why some people do expect their attitude to be accepted. If it is something they have learned to do, then what can be done to make them unlearn it? My attempts at this have so far clearly been too blunt, probably since I'm no saint and seldom suppress my irritation at their intellectual dishonesty faster than thinking of a scathing way to confront them...
I expect there's a fine line here between being generous and being seen as patronizing, but I try to cultivate a similar mindset (with varying degrees of success). I've always found it a sign of someone trustworthy, generally possessed by much more experienced colleagues.
Whenever I have to ask a semi-complicated question my brain does a mad scramble to assemble what I already know, what I think I know, what the other person knows, what I've already tried, my assumptions, why I want to know it...
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I think this is related to X-Y problems where someone wants to do x, thinks that y is the way to accomplish it, but can’t do Y either, and so goes online to ask about Y.
Everyone else knows that Y is a weird or unusual thing to be doing, but either helpfully tries to explain how to do it, which won’t solve their real problem anyway, or tells them that Y is dumb and they’re dumb for asking about it.
A really helpful answer would try and think about what could motivate someone to ask about Y, and if unable to think of one, will ask why on earth they want to do Y and what are they are really trying to do.
Similar to this situation is that they’re asking a question _because they want to know something about the world_ and trying to meet them halfway or ask clarifying questions is much more helpful than literally answering their question as asked.
Everyone else knows that Y is a weird or unusual thing to be doing, but either helpfully tries to explain how to do it, which won’t solve their real problem anyway, or tells them that Y is dumb and they’re dumb for asking about it.
A really helpful answer would try and think about what could motivate someone to ask about Y, and if unable to think of one, will ask why on earth they want to do Y and what are they are really trying to do.
Similar to this situation is that they’re asking a question _because they want to know something about the world_ and trying to meet them halfway or ask clarifying questions is much more helpful than literally answering their question as asked.
To their credit, the economics SE recently answered the question "why is the price of oil negative?" with an explanation of futures, and not with "it isn't"
The closest thing I've experienced is the value of a CRT computer monitor in my locale, which is a negative 15 dollars because you have to buy a sticker from the city in order to dispose of it.
Note that while this can be helpful in general, it's often unhelpful on Stack Exchange.
It results in people who do want to know about Y ending up with a high-scoring search result which doesn't contain information about Y.
And even for the original questioner, the discussions about why they want to do Y may well take up more time than it would have taken for them to read an accurate response, decide to rule out doing Y, and go on to ask X separately.
It results in people who do want to know about Y ending up with a high-scoring search result which doesn't contain information about Y.
And even for the original questioner, the discussions about why they want to do Y may well take up more time than it would have taken for them to read an accurate response, decide to rule out doing Y, and go on to ask X separately.
On nearly every question in the Q&A groups at work, I have to ask "What are your high level goals with this?"
I think this is not the case in all three examples given in the posted article.
I have ask this half baked question many time in many places and I have received the lower tier answers all the time.
Driving on a multi-lane highways with no traffic (yes it can happen, eg upstate NY Adirondacks overnight ) you can straighten the road shifting lanes to always be on the inside of the curve. Calculate the shortest path.
I once vaguely phrased this what shortest line that can be drawn between two parallel curved line a constant distance apart. I think this is mathematically half baked and could be restates.
Driving on a multi-lane highways with no traffic (yes it can happen, eg upstate NY Adirondacks overnight ) you can straighten the road shifting lanes to always be on the inside of the curve. Calculate the shortest path.
I once vaguely phrased this what shortest line that can be drawn between two parallel curved line a constant distance apart. I think this is mathematically half baked and could be restates.
Perhaps a good starting point would be to look at a "chord"[1], which is a line segment between two points on a circle. Then you'd look at a chord that is tangent to the inner circle of a set of two concentric circles. You can find the length of the chord from the radii of the circles.
But what you're asking about is more general. You are looking for some sort of shortest path between two parallel curves [2]. Which seems like it would be a tricky problem to solve. Are you considering physics here? If you are, you are basically looking at a "racing line" [3]. And that's a complicated problem since it involves a lot of physics and engineering. You can't look at a single turn in a track and determine the best racing line. That's because the best racing line for a specific turn depends on the best racing lines of the nearby turns. You'd have to look at the track as a whole. There are entire theses written on this topic [4].
But a highway road is not the same as a racing track. In highway engineering they often use the Euler Spiral [5] to construct the turns, because of its nice properties. Funny enough, Euler Spirals play a role in optimizing your entry into turns on a track [6]!
I think those might be some good jump-off points for further inquiry.
[1]: https://en.wikipedia.org/wiki/Chord_(geometry)
[2]: https://en.wikipedia.org/wiki/Parallel_curve
[3]: https://en.wikipedia.org/wiki/Racing_line
[4]: https://dspace.mit.edu/bitstream/handle/1721.1/64669/7068253...
[5]: https://en.wikipedia.org/wiki/Euler_spiral
[6]: https://en.wikipedia.org/wiki/Euler_spiral#Auto_racing
But what you're asking about is more general. You are looking for some sort of shortest path between two parallel curves [2]. Which seems like it would be a tricky problem to solve. Are you considering physics here? If you are, you are basically looking at a "racing line" [3]. And that's a complicated problem since it involves a lot of physics and engineering. You can't look at a single turn in a track and determine the best racing line. That's because the best racing line for a specific turn depends on the best racing lines of the nearby turns. You'd have to look at the track as a whole. There are entire theses written on this topic [4].
But a highway road is not the same as a racing track. In highway engineering they often use the Euler Spiral [5] to construct the turns, because of its nice properties. Funny enough, Euler Spirals play a role in optimizing your entry into turns on a track [6]!
I think those might be some good jump-off points for further inquiry.
[1]: https://en.wikipedia.org/wiki/Chord_(geometry)
[2]: https://en.wikipedia.org/wiki/Parallel_curve
[3]: https://en.wikipedia.org/wiki/Racing_line
[4]: https://dspace.mit.edu/bitstream/handle/1721.1/64669/7068253...
[5]: https://en.wikipedia.org/wiki/Euler_spiral
[6]: https://en.wikipedia.org/wiki/Euler_spiral#Auto_racing
One thing to note is that this shortest path won’t typically be much shorter. Consider a circular ring road. The circumference on the inside is pi * d and on the outside is pi * (d + w), where w is the width of the road, so the amount you save by driving on the inside is pi * w which is probably less than 100m.
In a more general simplified case where you always stick to the inside of every curve and jump from left to right for free, the amount you save compared to sticking to the middle lane is the line integral:
Because roads are not very curvy, the integral of k will be small and so the distance saved is very low. And note this is an overestimate because it doesn’t cost in changing from side to side
In a more general simplified case where you always stick to the inside of every curve and jump from left to right for free, the amount you save compared to sticking to the middle lane is the line integral:
\frac14 w \int k \mathrm ds
Because roads are not very curvy, the integral of k will be small and so the distance saved is very low. And note this is an overestimate because it doesn’t cost in changing from side to side
In motorsports it’s known as the racing line.
You’re right, the gains are small for the average road user :)
Wikipedia article https://en.wikipedia.org/wiki/Racing_line
You’re right, the gains are small for the average road user :)
Wikipedia article https://en.wikipedia.org/wiki/Racing_line
The real gains come not from decreasing the distance travelled (sometimes the racing line does the opposite), they come from limiting the radius of the turn so you can carry more speed through. At least thats what I've learned from playing Grid 2 for far to many hours.
I think that's the whole point of Grid 2, just to tech people about racing lines.
Yep, that Wikipedia article talks about that, and one it suggests are further too https://en.m.wikipedia.org/wiki/Trail_braking
Simple. Put up walls all the way along the road, then pull a string tight from one end of where you're driving to the other. Then you just measure the string!
This looks a lot like the xyproblem[1] which I have fallen prey to many times. You start out by thinking about something - highways in your case - then you formulate a model, which might turn out to work or might not. But then you make the mistake of asking about your own formulation of the problem rather than the original problem. From my own experience, even if your formulation turns out to be right, asking about the original context will usually result in higher quality answers.
[1]: http://xyproblem.info/
[1]: http://xyproblem.info/
Ugh I loathe this concept, although it's real. But 9 times out of 10 when you ask about a complicated problem online, which you've reduced to its simplest components because it's impossible to explain the entire context to an outsider in a text field, you'll get some internet smartass screaming 'xy problem!' to dismiss your question (this is not directed at the parent comment, just a general observation)
Fun edge case: I first thought you should always drive either leftmost or rightmost lane in curves. But if a "curve" only turns a couple of degrees you might be better of ignoring its existence and just go straight through.
What's the question? Given a specific example you can do the calculation. Generally the ideal route is going to consist of hugging the insides of curves + straight lines that are tangent between two opposite-direction curves. But for arbitrary curves I don't think you can say much more that's interesting or useful.
This is a good approach and good advice for better communication in general: you have to listen to both the exact words and the intent behind them. Coming from technical fields, many of us are rather biased to dismiss what others say for technical reasons only, when if we cared a bit more to look into what they are really trying to say or figure out, we could help them, understand them, and start much more interesting debates. This is too often seen in political debate too, though the bias here might come from a different side (if you can nitpick on the form of an argument, you don't have to care about anything else).
I really loved this breakdown.
Two useful related thoughts:
1. https://www.perspectiveapi.com via Google that rates comments based on their utility and toxicity
2. Generally adding emotional intelligence and psychology into the picture instead of focusing solely on answering the top-level question directly. Being able to emphasize with the person asking the question is invaluable in figuring out the best way to frame your answer.
Sooooo many developers could use a healthy dose of improvement in #2.
Two useful related thoughts:
1. https://www.perspectiveapi.com via Google that rates comments based on their utility and toxicity
2. Generally adding emotional intelligence and psychology into the picture instead of focusing solely on answering the top-level question directly. Being able to emphasize with the person asking the question is invaluable in figuring out the best way to frame your answer.
Sooooo many developers could use a healthy dose of improvement in #2.
This illustrates more than anything the Dunning–Kruger effect. Dilettantes and dabblers with a little knowledge often tend to be the more nasty on online forums, while actual experts have the humility of not just knowing the limits of their knowledge but more importantly have enough information to contextualize even those questions which might appear dumb to an untrained mind.
and often people answer not to help the questioner (and future readers) but to show off the little knowledge they have
On the Physics SE a similar cluster of questions are asked about the finiteness of the speed of light e.g https://physics.stackexchange.com/questions/230703/do-we-kno..., why the Principle of Least Action exists, and the “paradox” of size of the universe being larger than it’s age x c
The linked question on "why is C finite" is a good example. Each answer is basically just "the speed of light is finite because the field I know most about (cosmology, relativity, etc.) breaks in this specific way when it's infinite".
Having said that, I do believe the correct answer is some form of "we don't know". But that would be considered a half baked answer according to the author. It's also deeply unsatisfying on an emotional level.
So all the answers are basically modifying the intent of the asker in order to answer related questions which _are_ satisfying. This is compounded by the StackExchange community upvoting highly knowledgeable answers. Fortunately you can see the disputes on these answers also get upvotes in the answer's comments.
Having said that, I do believe the correct answer is some form of "we don't know". But that would be considered a half baked answer according to the author. It's also deeply unsatisfying on an emotional level.
So all the answers are basically modifying the intent of the asker in order to answer related questions which _are_ satisfying. This is compounded by the StackExchange community upvoting highly knowledgeable answers. Fortunately you can see the disputes on these answers also get upvotes in the answer's comments.
In theoretical physics, "why X" stands for absolutely nothing more than "please derive X from some other principle". Some people will use Y to derive X. Others will say that's not a real explanation, you really should use Z to derive X. And yet others will flip the derivation around and say that X really is the fundamental principle, and use it to derive Y and Z! (The route one takes depends on what one views as "more fundamental", a metaphysical notion that nobody agrees on.)
It's completely fair if you don't think any of the answers were satisfying, but it's not like there's another option on the table.
A lot of laypeople think that a truly satisfying answer must be mechanistic -- something like "there's an invisible jelly everywhere and it wobbles at a finite speed, and that is the speed of light" -- but the 20th century taught us that this completely natural desire is actually counterproductive, because you have to add piles of epicycles to hide the jelly's other effects.
It's completely fair if you don't think any of the answers were satisfying, but it's not like there's another option on the table.
A lot of laypeople think that a truly satisfying answer must be mechanistic -- something like "there's an invisible jelly everywhere and it wobbles at a finite speed, and that is the speed of light" -- but the 20th century taught us that this completely natural desire is actually counterproductive, because you have to add piles of epicycles to hide the jelly's other effects.
Yeah. I think answers which aren't technically correct but are highly knowledgeable and deeply related are still very useful.
>"there's an invisible jelly everywhere and it wobbles at a finite speed, and that is the speed of light"
As a layperson, is this analogous to "the electromagnetic field is everywhere and wobbles at a finite speed"?
>"there's an invisible jelly everywhere and it wobbles at a finite speed, and that is the speed of light"
As a layperson, is this analogous to "the electromagnetic field is everywhere and wobbles at a finite speed"?
"Field" is the abstraction we use in physics to say "there is a value associated with each point, and we're just not going to say whether it's representing the displacement of some invisible jelly, or the rotational velocity of some invisible tiny gears, or if it doesn't even make sense to ask the question". When we say the electromagnetic field wobbles, we just mean some abstract value is going from positive to negative and back.
I know that sounds unsatisfying, but there's good historical reason for doing this. Maxwell, for example, had a rich intuitive understanding of the electromagnetic field as a set of many invisible jellies and gears pushing on each other. His original equations were also 5x longer than the modern form and impossible for anybody else to understand, plus all the extra ingredients made tons of predictions that played poorly with relativity. The sheer butchery one needs to make intuitive pictures like this compatible with relativity is so high that we've basically collectively decided to give up. We now say fields make up real jellies and gears, they're not made of jellies and gears. They're just fields.
I know that sounds unsatisfying, but there's good historical reason for doing this. Maxwell, for example, had a rich intuitive understanding of the electromagnetic field as a set of many invisible jellies and gears pushing on each other. His original equations were also 5x longer than the modern form and impossible for anybody else to understand, plus all the extra ingredients made tons of predictions that played poorly with relativity. The sheer butchery one needs to make intuitive pictures like this compatible with relativity is so high that we've basically collectively decided to give up. We now say fields make up real jellies and gears, they're not made of jellies and gears. They're just fields.
I gotcha. Not the right way to think about it. To be clear, you're saying fields are essentially virtual mathematical notions from which emerges actual stuff?
Given the premise that fields are explicitly not consisted of an "invisible jelly", I'll ask what is definitely a "half-assed question" -
How and where _do_ fields "exist"? Where are they in the standard model? Intuition says maybe they reside in spacetime near particles. I have a hunch from QFT that the fields are technically "everywhere" and are merely highly excited into particles when energy transforms the field in certain spots.
I doubt either of my guesses is the right answer but I'm mostly just curious how literally you mean to take the viewpoint that fields are "virtual" in nature.
Since this is a half-assed question, feel free to give a half-assed answer.
Given the premise that fields are explicitly not consisted of an "invisible jelly", I'll ask what is definitely a "half-assed question" -
How and where _do_ fields "exist"? Where are they in the standard model? Intuition says maybe they reside in spacetime near particles. I have a hunch from QFT that the fields are technically "everywhere" and are merely highly excited into particles when energy transforms the field in certain spots.
I doubt either of my guesses is the right answer but I'm mostly just curious how literally you mean to take the viewpoint that fields are "virtual" in nature.
Since this is a half-assed question, feel free to give a half-assed answer.
> To be clear, you're saying fields are essentially virtual mathematical notions from which emerges actual stuff?
Perhaps, but I think that's a bit unfair. There's no dividing line between "mathematical notions" and "actual stuff". For example, when you poke a bowl of jello, it springs back, so it feels like "actual stuff". But in terms of the mathematics, it's because the configuration of fields that corresponds to compressed jello has a higher energy value than when uncompressed. In other words, while we don't assign intuitive properties like "solidity" and "elasticity" to fields, the relation between the fields and those properties in macroscopic objects is quite direct!
> How and where _do_ fields "exist"? Where are they in the standard model? Intuition says maybe they reside in spacetime near particles. I have a hunch from QFT that the fields are technically "everywhere" and are merely highly excited into particles when energy transforms the field in certain spots.
Indeed, they're technically "everywhere". You commonly hear that for the Higgs field, but it's true for all others as well, such as the electron field, whose excitations are electrons.
Perhaps, but I think that's a bit unfair. There's no dividing line between "mathematical notions" and "actual stuff". For example, when you poke a bowl of jello, it springs back, so it feels like "actual stuff". But in terms of the mathematics, it's because the configuration of fields that corresponds to compressed jello has a higher energy value than when uncompressed. In other words, while we don't assign intuitive properties like "solidity" and "elasticity" to fields, the relation between the fields and those properties in macroscopic objects is quite direct!
> How and where _do_ fields "exist"? Where are they in the standard model? Intuition says maybe they reside in spacetime near particles. I have a hunch from QFT that the fields are technically "everywhere" and are merely highly excited into particles when energy transforms the field in certain spots.
Indeed, they're technically "everywhere". You commonly hear that for the Higgs field, but it's true for all others as well, such as the electron field, whose excitations are electrons.
Isn’t the ultimate answer always “we don’t know”, “because”, or “42”? It has to be deeply unsatisfying because we don’t know what the ultimate question is, do we? We can’t stop asking.
Earlier today, on the subject of why I made a particular design choice, I went straight for tier 6. I absolutely could have promoted my response to tier 5, or even 4, but I was too focused on prevailing as correct to see that one can affirm the reasons why someone is asking a question without necessarily seizing on the more absurd aspects of the question. I think I'll be more mindful of this in the future.
Terrific article.
Terrific article.
I don’t know. My main gripe with StackOverflow is question getting closed for being opinion based or not worth debating. When constant debate is actually fun and interesting. (And you don’t have to watch the threads if you don’t care.)
Questions for the sole purpose of debate are discouraged and off the rule. if you want to have a chat, find a chat room.
That does not mean that such questions never come through to reach not just an answer, but two or more trying to compete--which the voting system should be able to handel--or they are trying to mediate pretty much in unisono--which should be a comment to improve the question, or answer with a differentiated view on what the questionair got wrong and right.
That also depends on the kind of stack. The more scientific, the more rigid the rules. The more liberally academic, the more people looking to practice their rhethorics.
That does not mean that such questions never come through to reach not just an answer, but two or more trying to compete--which the voting system should be able to handel--or they are trying to mediate pretty much in unisono--which should be a comment to improve the question, or answer with a differentiated view on what the questionair got wrong and right.
That also depends on the kind of stack. The more scientific, the more rigid the rules. The more liberally academic, the more people looking to practice their rhethorics.
If you like constant debates and open ended questions, why not use Quora, or maybe even reddit.
Has Quora gotten any better for content? Maybe I just don't use it right. It is on my list with Technet for sites that are entirely garbage. Every time I was led to Quora the answers were always 3 top comments of different companies advertising something.
It has begun resembling the real world, just like any platform that gets too many users. But I doubt if you ask things like open ended debate questions you are not willing to see 1-2 ad answers, as long as there are other high quality answers. Many people are on quora posting high quality answers. Some examples:
1. Cliff Click
2. John Romero
Well. Some very precise question is very open to debate. Like what’s package manager to use on Linux. They will be competing answers, votes, and answers that will be super interesting. At least to me.
But stack overflow explicitly discourages such open ended questions, like what package manager to use. Any such discussion will be full of arguments and counter arguments, which is better suited for reddit anyways.
I think people may give half hearted questions to get better answers. Maybe half hearted questions get more interaction by people trying to clarify things, or perhaps the answers are written with more common language than jargon?
Could there be other reasons (apart from "Questioner Is Stupid" or Troll) to ask vaguely formatted questions?
Could there be other reasons (apart from "Questioner Is Stupid" or Troll) to ask vaguely formatted questions?
6. I can't do it, so nobody can.
I am much too emotionally invested in intellectual honesty...
I am much too emotionally invested in intellectual honesty...
I have started proselytizing this approach to my colleagues, because some of them are simply too formally minded to "pull themselves out" enough to interpret such statements generously. I do think some subset do use this sort of denigrating approach to cement their authority, which I find silly.