Tiers of answers to half-baked questions
blog.plover.com
blog.plover.com
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.
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...
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.
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.
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.
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...
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
where k is the curvature (strictly speaking k should be an adjusted curvature of 1/((1/K) - (w/2)) where K is the actual curvature).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
You’re right, the gains are small for the average road user :)
Wikipedia article https://en.wikipedia.org/wiki/Racing_line
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.
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.
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.
>"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"?
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.
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.
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.
Terrific article.
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.
Could there be other reasons (apart from "Questioner Is Stupid" or Troll) to ask vaguely formatted questions?
I am much too emotionally invested in intellectual honesty...