While I share your disdain for unnecessarily long YouTube videos, Veritasium often (not always) gets a pass from me. I have been instant clicking pretty much every video he’s released in the past few months and always came out having learned a lot and satisfied.
The only other channel I would give the same pass is neo.
I intended no shade on Veritasium and my comment that the video is 18 minutes long wasn't an expression of disdain, merely a statement of fact. Rather, my intent was to offer an alternative for folks who prefer to read instead of or before watching a video.
This is a general problem. If you want to get a good answer to a certain class of problems (especially in the diy domain, and now even math problems), YouTube videos are the best. But you have to watch 20 minutes. This is not scalable.
For the shade tree mechanic and/or handyman, YouTube is a tremendous boon. A few years ago I needed to replace the cooking elements in my double-oven and I found repair videos on Vimeo[1]. So I built a dolly and pulled my oven out[2]. It takes all the fear and uncertainty out of a repair you've never done before.
Videos have all the tips and tricks missing from conventional repair manuals and shop guides.
For academic material,
I prefer the written word. For repairs around my home? I'll go to YouTube.
I appreciated it. Most of the time I would be interrupting my music or silence or disturbing those around me if I played videos. Friends send me links to video after video and I just can’t even review whether they are worth my time because of the above issues. At least text I can quickly scan to get a sense. I really regret how video has come to utterly dominate.
The video used modern social media length dragout techniques that make virtually all modern podcast like media so tiresome to listen to.
"You won't BELIEVE what everyone got wrong"
Here's the trumped up drama from people involved.
Here's an interview
Here's a restatement of the cliffhanger
Oops the author dropped enough info that I can read the Wikipedia article in 30 seconds. End streaming media.
The amount of "good podcasts" that are ultimately a Wikipedia page drawn out over 20-30 minutes is just ridiculous.
"Good tv" like a good john Oliver show or Frontline is chock full of information, further avenues of research if interested, and dense.
Geewhiz podcasts like these seem like the result of YouTube algorithmic game theory result rather than an improvement to the access and organization of info that Wikipedia represented.
That's not modern, that's been media since time immemorial. Geraldo spent 2 hours talking about what could be in Al Capone's vault only for them to finally open it up and it was empty. Magazines would print stories in serial format so you had to buy the next issue.
Writing and structuring to fit the length you want/need has been the norm for a century or two at least before social media came about. Hell, there's evidence that Shakespeare padded out a couple of his plays to fit the 4-pages per folio printing techniques of the time so that there weren't blank pages at the end.
> "Good tv" like a good john Oliver show or Frontline is chock full of information, further avenues of research if interested, and dense.
I have seen John Oliver state errors or misrepresent data/leave out information in favor of the comedy/supporting a particular viewpoint. A good HN thread with people knowledgeable about the subject or in the field about a John Oliver episode will usually be full of more information.
The thing that put me off veritasium was the electricity video which was immediately controversial.
Looking at just the video he left the feeling that all electricity being taught is completely wrong while actually he was talking about some edge case and failed to put it into the proper context. He did not mention at all that the proportion of what he was talking about was essentially irrelevant unless you are an electronics board designer.
EE details relevant to electronics board designers are kinda important and interesting, and I have a lot of sympathy for "technically correct". But that veritasium video was a trick question, and a misleading video. It subtly shifted between ideal model to real-world effects to smugly show how most skilled EEs are wrong about electricity, but Derek knows the truth.
In a simplified circuit model it would work like a circuit, in a as-real-world-as-possible model it would always be dominated by interference. In a carefully-segregated-semi-real model, it would be less than 1% on after 1/c seconds, would you really call that on? If it was, then 100% on would be way too much current!
So many minutes spent without explaining that the real world is very complicated and EEs apply different models to different situations as appropriate, and it's silly to say that only the field matters not the electrons because of course the electrons cause the field while the field moves the electrons, and the original question is a trick because it's an idealized thought experiment which tries to trick you into applying the wrong model but that's silly because it's an idealized thought experiment which wouldn't work in the real world so it's only purpose is to exercise a simplified model ...
Great fodder for a series of viral-y videos from multiple youtubers though. (electroboom's response was pretty good IMHO)
Yeah I really liked the AlphaPheonix video[0] where he actually built the thing in a field and explained the entire effect properly.
I'm not entirely sure if Derek didn't really understand what he was presenting in that video or deliberately based it on a really misleading bullshit gotcha to troll people and stir debate for clicks, and neither reflects very well on him.
The one that I really couldn't stand was the "How to slow aging" one, in which he interviews a man, who in my opinion clearly had some sort of cosmetic surgery done on himself to appear younger. He talks about how to reverse aging in mice, and then randomly claims he actually reversed aging _in himself_.[0]
For anyone following science in mice, this seems like an extremely huge red flag. That together with the cosmetic surgery and a clear financial incentive for the him to lie here, seeing as he is selling a book about it, was triggering just about every bullshit detecting neuron in my brain.
Veritasium however seems perfectly fine with it, and still posted the video.
I haven't ever seen anyone else bring this up, so if anyone wants to share their own hot take on this, I'd be interested to know :)
I would add I felt the wind powered car video was similar. I started watching him years ago as he had an amazing video looking at a silicon sphere being made to use as a new mass standard. In recent years though his videos seem to increasingly confuse subjects (for me) instead of clarify them.
> He did not mention at all that the proportion of what he was talking about was essentially irrelevant unless you are an electronics board designer.
If you want to get that detailed most people would freak at conventional vs electron flow. The + wire is actually where the negative electrons are emitted. But as electricity was developed people didn't know that but it all works out so it was left as is. For physics or any other scientific experiments electron flow is used.
Even the term "negative" is a can of worms it could have been called green or red or yellow not "negative". It comes from Ben Franklin and accounting terms.
In response to all the controversy he made a follow up video [0]. In the video he recreated the experiment, explaining the effect in a more technically correct manner and also apologised for not doing so on the original.
He also made it clear that the light globe in the original video did not receive enough current to light up.. it was hooked up to an alternative power source and an oscilloscope and upon receiving any signal above baseline would switch on the globe.
When i watched that follow up video and he didn't apologize he only said that he wasn't clear enough. In most responses like the other above linked criticism he doesn't apologize either and just gives out a long list of reasons why he's right. In the electricity follow up video it really seemed like he was saying more along the lines of "I was always right, you just weren't smart enough to understand what i was really saying because i was unclear". So I wouldn't say that he apologized, just doubled down and accepted fault with the lack of clarity but without saying sorry in any way.
It really put me off his channel for a long time. I still watch his channel to be fair and get a lot out of it, but his videos hit different after seeing him double down on criticisms and contorting controversy instead of just saying sorry.
The Veritasium video is kind of weird. The example is good and interesting and when I watched I thought he would then introduce the concept of transmission lines (as taught in EE classes). It would make things clearer and gives an explanation and also maybe some intuition to problems like that. Instead he starts talking about the poynting vector, which makes things even more abstract and weird (and also he is slightly misleading about the poynting vector, especially for the DC case). It seems like he is trying to make things weird for the sake of weirdness and not trying to explain anything.
This guy does hour long videos on many large popular YouTubers. I tried watching one but it was so. drawn. out. Is he just creating controversy from nothing?
He's like Turkey Tom, but instead of just recapping YouTubers/YT Drama, which is already the reality TV version of YouTube content, he wants to treat it like hard hitting journalism. Which means he overinflates and exaggerates everything.
Derek Muller from Veritasium replied to the video it seems there was some behind the scenes communication which the video author (Tom Nicholas) ignored but replied to in a long comment. It seems to to create sensationalism. He got 2.1M views so I guess it worked.
Just watched the video—it has the same failings as most other debunking videos (e.g. Thunderf00t): in order to get views he must show that what he is debunking is very wrong, and so manufactures gotchas. It’s a little ironic that his video accusing Veratasium of lacking nuance is completely lacking nuance itself. Although admittedly, he’s not wrong that Veratasium is lacking nuance and is too breathless in his praise.
Which is obvious to anyone with half a brain though. So what. We have discretion to choose which of his videos to watch. I doubt he got paid by the laws of thermodynamics to make his entropy video.
Sure, but there are lots of good science content creators out there and I'd rather just watch one where I don't have to worry about it. The Waymo video is over the top credulous, even for something they were being paid to review. In general, the idea of building a channel based on "the element of truth", establishing yourself as an educator, and then shamelessly selling your credibility in that way is kind of a turn off. At least I'm not going to see you as credible in the same way anymore, and others feel the same.
That said, the channel is more popular than ever so who knows.
TV presenting pays very well in comparison to Youtube. Plus all you have to do is turn up and read a script, as opposed to filming and editing a video to high production standards, or having to pay somebody out of your ad revenue to do it for you.
Ahh, Brexit makes so much more sense now. Nothing like good old TV to really drill unskippable propaganda ads into people 20 times a day during every ad break.
That is mind boggling. In the US, I know no one under the age of ~50 that watched linear TV. Even the 50+ year olds are using their phone and watching YouTube/Whatsapp videos while “watching” linear TV.
Live sports are the only exception, but I would say that is down big time also (as Nielsen indicates). Or rather, a series of gambling ads interspersed with a sporting event.
Overall, I don’t think Nielsen is able to properly assess which screen has people’s focus.
First 10 seconds into the video I know one major reason working against him. He has a bit of lisp. Personally I don't mind, but I'd be lying if I said his videos would be better without it.
Say, how can you tell which ones should get a pass?
Is there a way the less intelligent folks (like myself) could get a notification for when you decide to watch or not watch one of Veritasium's latest creations?
Do you feel more intelligent after watching that video? If so, could you share some of the techniques you used to capitalize on passive learning?
The choice was given among these answers: (a) 3 over 2. (b) 3. (c) 6. (d) 9 over 2. (e) 9. ''The answer to this question should have been 4, not 3. Daniel B. Taylor, the College Board's executive vice president for operations, said as a result of the flawed question, he anticipated score adjustments of 10 points, up or down.
I'm wondering how they corrected the scores since the correct answer was not in the list of choices. I'm assuming that they simply excluded the question -- so if there were 154 questions in total, they recalculated as if there were only 153 questions. I'd like to imagine that the three students who reported the error got an extra boost to their scores, but probably not.
I found the notion pretty shocking how deeply the rescoring affected people. If the test writers couldn't even get it right, why fault the test takers. I get it... rules... but it still feels unfair at some angle.
Nothing unfair about it, the truth is everyone got that question wrong (because there was no right option available), so they didn't fault the test takers, instead just annulled that one and scored everyone based on the actual questions, it is as fair as it can be.
It does suck for the people who though they had that one right, it is distressing to be shown one score and then later find out that the real score is lower. That should have been avoided by having an official recourse window before publishing scores, so when problematic questions are annulled then people only see their actual final score (in my country a recourse window is standard for all public exams).
If they annulled the question, why would the score drop? Shouldn’t the scores be renormalized around the new number of questions, the easiest way being to just give everyone the points for it?
Except in this case no one got a correct answer annulled because it was impossible to give a correct answer. At most people could have avoided the guessing penalty by not answering the question. Everyone's absolute score should have gone up, though since the SATs are normalized your score can go down if other people's scores go up more.
They should have given out a normalized score like 8.1/9 in this case.
30 points is a lot. I had a perfect score (1600/1600). Getting a 1570 would have been significantly different. This is probably worse at admission cutoff thresholds.
You would still have a perfect score after the question was annulled. It's just the difference between getting (for example) 33 out of 33 questions correct, or 34 out of 34 questions correct.
Well what's interesting about it is that a perfect score would be unaffected, but anything less would be affected because wrong answers are now weighted more heavily than before.
Although I'm not sure how the SAT assigns the scores - I don't think it's as simple as a percentage correct (otherwise the score would simply be out of 100), and that there is some kind of normalization they do? Can't remember... and it might have been different then anyway.
They should have done max(old_score, re_score) for all test takers. That's the only fair way. Although I don't know if SAT grades on a curve, which wouldn't play well with this method (I think?).
1. You can't award a bonus question to a subset of people, that is not a fair way of running a standardized test. You can't score some people as x/154 and some at x/153.
2. The old score was just plain wrong, so using it in any way is unfair.
The truth is no one got that question right because there was no right answer available. None of those available answers is "righter" than the other so it is not fair to assign a higher score to one of them like you proposed. Those people that got a higher old_score also got that question wrong, so their old_score is as wrong as any, and awarding them this unearned extra point would be unfair.
The only two fair options would be: to annul the whole test and make everyone retake; or the one taken where they annul that one question pretending it never existed and score based on the remaining questions (with each remaining question now being worth a fraction more). And this later option is in fact very fair, I don't think there is any real argument against this being fair.
It does suck that people were initially informed a wrong score and then later were disappointed with their real score. On this line I find it absurd that the SATs don't have the recourse period before they release the scores, and instead just releases the tentative scores as if they were real. This would all have been avoided if they heard the recourse and annulled the question before publishing results (as pretty much any serious exam around the world does it).
At least one of the three answered the question "correctly", so they would have gotten a worse score after rescoring, provided they answered anything else incorrectly.
The guy interviewed in the video said he answered "3", but then later when asked, said he got an 800 (perfect score). So he must have answered every other question correctly!
Thank you so very much. Reading this article was so much more valuable to me as I would have never watched an 18 min video to show a single question that needed 1 paragraph to discuss.
The video does go further - it contains some interesting content around how this concept relates to the earth's orbit around the sun, the discrepancy between the duration of an earth day and a 360 degree rotation about the earth's axis, and why astronomy days are not the same length as earth days.
Yeah, the SAT question is almost an excuse to speak about this things, and you also get to see an interview with one of the concerned candidates. Very enjoyable video.
Surely the intended meaning of the question belongs in the discussion?
You’re right, it’s contrived. But I automatically tried to compare lengths too. So it’s a good lesson in making sure that your simplification of the question still does what the question asks.
I'm not convinced that the intended meaning was to consider a rotating reference frame. I think it was simply an oversight that the straight-line answer and the around-a-circle answer aren't the same. A rotating reference frame is one way to explain that oversight, but it isn't the only one.
The rotating point of view was the "aha" for me. It's even clearer to me when you look at the 1:1 ratio with two identical coins, where when the rotating coin is upright at the bottom of the rotation, and the coin is right-side-up to the observer but is "top edge to middle coin" instead of "bottom edge to middle coin".
(Specifically, my "aha" was that one rotation of the moving coin in place was not the same as one rotation of the moving coin around the middle coin.)
I should have been more specific. I didn't mind that part as a teaching aid in general, but I thought it was contrived as a possible explanation for what the question authors expected students to visualize when they made the correct answer 3.
The video adds a lot of extra stuff beyond what is in the NY Times video: There is an interview with one of the test takers; a description of three possible correct answers (1, 3, or 4, depending on the perspective); a video demonstration of several ways to compute it; and an interesting discussion about sidereal time.
Not that you were implying otherwise, but in this case I feel the video adds quite a bit more material and a more complete story beyond the NY Times piece. In reading the NY Times piece, I would leave with the conclusion that the correct answer was not one of the options. After watching the video, I would leave with the conclusion that the question was ambiguously written leading to multiple possible answers, one of which was there, but two other valid answers were not there.
What makes sense to me is to think about something that DOESN'T roll.
Suppose I start in Greenwich, walk - without rolling - down the prime meridian to the south pole, up the international date line to the north pole, and back down the prime meridian to Greenwich.
How many rotations do I go through? One. I get a full rotation because I've followed the earth's curvature all the way around the globe once, even though I'm walking straight without rolling.
So the answer is "how many rotations due to rolling" plus "one bonus rotation for passing around the curvature of the circle."
The way I thought about it was to ask what happens if you just have a coin going around a point, which would be the natural end point of reducing the size of the second coin. That of course would give you 1, so a good first hypothesis is that the total is just however many spins the two coins go, plus 1.
The video demonstrates the 1:1 coin size case and speaks about the curvature of the line it rolls on, but your thought experiment makes it a lot clearer. As the size of the other coin goes to 0, the amount "gnawed off" of the rolling coin will also go to 0 while obviously still rotating a full revolution.
I like this; it gives me a good way to think about the "from the circle's view" - Earth center looking out at you sees your feet close and your head far away, always; you don't rotate at all.
> I get a full rotation because I've followed the earth's curvature all the way around the globe once, even though I'm walking straight without rolling.
I don't follow. You aren't walking straight without rolling. You're constantly turning to keep the angle from the center of the earth to your head, as measured through your feet, fixed. This is not a necessary part of moving around the earth; you could maintain a constant orientation to e.g. the earth's axis of rotation instead. The one rotation that you're imagining isn't due to your travel around the earth; it's due to the rolling that you're pretending you aren't doing along the way.
I tried defining a parametric equation for the position of a point on the rim of the small outer circle; if it has radius r, and it starts at coordinates (3r, 0) lying tangent to a circle of radius 3r centered at the origin, and it takes 2pi units of time to roll around the larger circle, then its position at time t is
(4r cos t, 4r sin t) - (r cos 3t, r sin 3t)
(unless I've made a mistake...?)
We then need to define what a "revolution" is. If we define it in what appears to me to be the obvious way, as having been completed whenever the vector from the center of the outer circle to the point that we're tracking on its rim is parallel to its initial value of (-r, 0), then this parameterization makes it clear that the zeroth revolution of the outer circle ends at time t = 0, the first ends at t = 2pi / 3, the second ends at t = 4pi / 3, and the third ends at t = 6pi / 3. Since the maximum value of t is 6pi / 3, it appears that there cannot be more than three revolutions.
However, I find the argument compelling that we should be able to get the number of revolutions by dividing the distance traveled by the center of the circle - 8pi - by the circumference of the circle, 2pi. This clearly tells us that there must have been four revolutions.
What was wrong with the parameterization approach?
Yes, but that intuition doesn't seem to work for the case where small disk is rolling around the inside of large one, not outside. What's the intuition for why we then subtract one rotation rather than adding one ?!
Very basically, to go the same direction, a small disk on the inside and the outside of a large disk need to spin opposite directions. When you're on the outside, your spinning direction agrees with the direction you go around the circle (i.e. the rotations add). When you're on the inside your spinning direction is the opposite of the direction you go around the circle (the rotation subtracts).
You're intuitively rolling the other way. Going on the surface means that you're falling forwards while going inside means that you're falling backwards.
I think you can always arrive at the correct answer by tracking the distance traveled by the center of the rolling object.
In the original SAT question, the center of the rolling circle is 4r from the center. That means it travels an arc of 8pi. Then assuming no-slip, that works out to 4 rotation.
In your case, rolling on the inside, the center of the rolling circle will only be 2r from the center. Using the same logic, this yields 2 rotations.
Yes - the relationship between distance traveled by center and number of rotations (= distance/diameter) is a nice generalization, although the guy in the video went so fast that I didn't understand his derivation of this relationship (related to speed, etc).
This is definitely the easier way to understand it. Imagine a point in the centre of the circle that is traveling. Draw the line that point takes, and then calculate using the new circle.
That intuition makes a lot of sense to me, especially if I picture the person's frame of reference.
Kind of reminds me (a layman) of winding numbers. I suppose there are topologically inspired variations of this problem that might be even more "paradoxical" (or perhaps just silly). If you moonwalk the second half, you undo your rotation? Or if you follow specially designed subterranean tunnels, you can end up doing 0 or negative rotations!
No, GP does mean spinning there. As they walk around the earth, their head points away from the north pole, then away from the equator, then away from the south pole, then away from the equator, then away from the north pole again.
It happens that they also went around the earth, but the "rotations" in the part you quoted refers to the spinning.
The guy who figured this out (who Veritasium interviewed) is crazy smart.
Also, a lot of kids math problems (middle school and below) are super vague. I get that they're designed to teach a concept, but they could do it in a more exact/precise (idk what the word is) way.
The vagueness is seen as a feature, not a bug. The kid is supposed to read between the lines and find out what the problems are really about.
That's straight how my teachers would explain it to us, and you see that line of thinking in the "problem solving" bits where the text is intentionally made harder to decrypt.
Reading skills and shared background assessments are baked into most math tests, even if that's not the focus of it.
> The vagueness is seen as a feature, not a bug. The kid is supposed to read between the lines and find out what the problems are really about.
Pity the poor child who is capable of thinking both inductively and reductively. Such lax testing standards reminds me of the story of the WWII cryptographer in Cryptonomicon who is asked to work out how long a ship would take to travel down the river, comes up with a new theory of fluid dynamics, and flunks the test.
Practically I think that just means that the kids end up getting taught vast quantities of "exam technique" rather than content.
I taught myself the essence of calculus when I was 14 or 15 - there were holes in my knowledge but it took I'd estimate 5 years for regular education to catch up to the intuition I built then (on a houseboat on the Thames even, sounds romantic except for the fumes)
I was homeschooled through 6th grade, entering regular school, it was striking just how "slow" everything seemed.
Conversely, I struggled immensely for a year and a half, once my 3 year lead on material ran out.
The difference in quality and speed in something you're self-motivated to do and are doing at your own pace, versus something you're being told to do at someone else's pace, even with the same person in both cases, is quite astounding.
Or maybe that's the viewpoint of someone with ADD, and most people can keep steady progress _and_ lead balanced lives. I'll never really know.
Yes. Kids moving countries hit that wall at full speed, and have to learn the exam system and quirks on top of the actual content.
The interesting aspect to me was how they need to take a step back and look at it as a set of made up conventions, when they might have just absorbed it as universal truth otherwise.
Depends on the kid. Don't you think?
For some the repetition is the only chance they get to find a pattern.
I think where "traditional" education truly sucks tho (unless you are blessed with a gifted teacher), is giving you an overwiew of how the pieces fit together and what is behind each of them.
I think vagueness is kindof ok in math/physics questions - if you think about it there's usually and interpretation that makes more sense, but I doubt most of them are made that way on purpose.
Where I really hate to see it is humanities e.g. psychology tests/surveys - if after reading a question I immediately think of 3 different interpretations I just think it's a bad test. And if I spend any more time thinking about it I get almost nowhere.
> there's usually an interpretation that makes more sense
Yes, I see it as "background" part, or "common sense" perhaps.
I's funny when for instance you have grocery questions about little Jimmy having 3 bags with 4 buns in each, so how many sausages does he need to make hotdogs with all the buns ?
That's cute and straightforward as long as you know what a hotdog is, which is common sense for the question writer.
I don't think that's something that needs to be (or can be) changed, as long as school and exams are seen as a formative step, and not a single chance you'll have to make a decent living. Kids in the later group will have a hard time either way.
> That's cute and straightforward as long as you know what a hotdog is, which is common sense for the question writer.
Even if you don’t know what a hotdog is, it’s indicated you use sausages and buns to make them. The most straightforward method of doing that would lead to the correct answer.
There may be kids that figure that’s too simple and assume they need two or three sausages per bun, but those will be the minority.
Most sandwiches are made with two pieces of bread. Buns happen to be two-pieces-in-one, which isn't disclosed in the question. Somebody who has passing familiarity with sandwiches but not hotdogs or buns specifically might think it takes two buns to make one hot dog.
Thankfully I think most questions usually aren't like this. Cultural loading in questions is a popular excuse for discrepancies in testing outcomes but those discrepancies have a nasty tendency to persist even when tests are redesigned. Usually there's something else going on which causes the outcome discrepancies, particularly bad parenting.
This has been a huge contention point of Common Core and why so many kids had such huge problems with the overall test. Hard questions that seem/potentially-are vague, but are hard questions first.
Personally, I'm a big fan of what Gates was attempting to do, but I have teachers in my family who couldn't get rid of Common Core from their schools fast enough. Debates with them were never good and me, not being an operator, wouldn't dare tell them how to do their jobs.
But, I understand difficult, standardized testing isn't a good answer, but really how do you get a whole nation to up-skill?
De-centralize and de-nationalize schooling. It's clear the feds have no idea how to make the education system work. Let the states have ~50 different curricula, or individual schools to have ~hundreds or ~thousands of different curricula. Even if they're bad on average, some of them will probably figure out how to make an actually good US school by sheer luck. Once we have that, the others have a model to copy.
> Once we have that, the others have a model to copy.
That is a bold expectation. Some schools will have an incentive to just have as much pupils pass the exam by lowering the bar, other will be incentivized to just teach the bare minimum, others won't have enough money if the model of excellence is expensive (and it probably will be).
And the model that applies to, say, a child who grew up with college-educated parents won't necessarily apply to the child from a blue collar family.
That is just to say that this is a hard problem. My intuition is that the only way to achieve the best education (excluding the case of hypergifted people) seems to be by throwing money at it through personalized education and tutoring and solving the child's other life problems, i.e. the wealthy kid model, but obviously that's not realistic when it comes to mass education. But maybe mass education (at the level we seem to expect from it) isn't realistic.
Or maybe we should reduce the number of subjects taught in school to math, language and physical education.
The problem with trying to make a good school is that strong students pretty much teach themselves and their performance far exceeds any effects from good teaching methods. If any school starts to show decent results then word gets around and it becomes a magnet school. Magnet schools attract wealthy and high-performing students, which totally swamp the effects of the teaching method you're trying to study.
Good teachers unfettered by standardized course plans, when dealing with brilliant students, keep pace with and support those students. If this attracts even more brilliant students, all the better! Then the brilliant students will also support and motivate each other leading to even better outcomes. This is an ideal situation unless you're one of those Harrison Bergeron people who wants to cap high achievers so they don't leave the dummies in the dust.
We really should be prioritizing the brightest students, because their brilliance has the best payoff for all of society. Better to have 100 students who are genuine math wizards and are prepared to continue building on what they know than to have 10000 students who sort of learn basic calculus then forget all of it, with those previous 100 lost in the noise and never given the resources to reach their potential.
On the contrary, standardized course plans are actually the most effective way to provide truly reliable instruction at all levels in a mass lecture/group education format. One key reason why those 100 math wizards don't all become PhD's is that math instruction at both school and university level leads to the proliferation of random gaps in learning where some content just wasn't reinforced effectively. Since math instruction generally builds on previously-learned math, once you accumulate enough of these gaps you hit a wall, and will need remedial instruction (often sought via autonomous self-teaching, of course) to make any progress. The dynamic is structurally the same between the "dummies" and the "math whizs", all that changes is the level at which the problem arises.
Focusing on a standardized course plan that the student is able to learn, memorize and ultimately repeat effortlessly makes it easy to ensure that absolutely everything was reinforced properly.
Congrats: what you’re asking for is exactly how things work now! The feds do not set currricula, each state does independently. Common Core is an opt-in, state-led initiative, which was based on the idea of examining the latest research and practices in education across the country, and adjusting curricula to match.
I haven’t been in public school in 15 years but there was 2 public school districts, a public-private magnet school associated with the State University and a Private Catholic school with radically different curriculum in my hometown. Even between the two high schools in the same district there was different courses and funding because of the property taxes funding specific schools and one school was on the nice side of town.
As far as I understand, most public schools are decentralized, at least the State level, if not further. Are you claiming that is not the case currently?
Except that as soon as someone says 'hey X works, here's the data to prove it's all the rent seekers who have gotten happy with the alternatives will fight against its adoption. When I was younger I used to buy into the 'laboratories of democracy' concept, now I think it's more like 'meth labs of bureaucracy.'
Schools and teachers have ways to make sure improvements don't happen. These include - same pay regardless of performance, not hiring or firing based on performance, and teachers don't want to learn or do anything differently, especially if it's even slightly harder than what they already do. They're not really professionals that improve or have any career growth besides management and accumulating number of years experience. Schools don't care either, nor do governments bother to incentivize them to care.
Except in, say, China, where none of that applies and education works great.
> Schools and teachers have ways to make sure improvements don't happen. These include - same pay regardless of performance, not hiring or firing based on performance, and teachers don't want to learn or do anything differently, especially if it's even slightly harder than what they already do
You can just say unions, no need to beat around the bush. Anyway, I don't really agree. Of course some teachers are stuck in the mud, but other teachers are eager to try new things and improve outcomes. If unfettered by standardization they would be eagerly experimenting with new approaches to teaching their subjects. And if school funding weren't reliant on teachers "teaching the test", then schools would find ways to reward these teachers because it makes the administration look good to have passionate and proactive teachers.
There are problems of course, but they end up with higher levels of education despite that. If a country was serious about education, they could just make it work. I guess having to balance too many competing interests weakens it. We don't want extreme lifetime poverty for school dropouts either, which might be part of what's needed to motivate success.
> Even if they're bad on average, some of them will probably figure out how to make an actually good US school by sheer luck. Once we have that, the others have a model to copy.
How could anyone know that, if each school has its own curriculum and exams? If you got 4 gold stars out of 5 on your reading comprehension and I got three palm leaves out of 4 at literature interpretation, which one of us is getting a better education?
> De-centralize and de-nationalize schooling. It's clear the feds have no idea how to make the education system work. Let the states have ~50 different curricula, or individual schools to have ~hundreds or ~thousands of different curricula. Even if they're bad on average, some of them will probably figure out how to make an actually good US school by sheer luck. Once we have that, the others have a model to copy.
Sadly, we already know what works, individualized/custom attention that exposes the kid to a lot of fields. A worse way to put it, more money == better education. And this is largely true even if specifically wrong.
But once you try to scale that up, everything falls apart.
Which is a big problem I have with these sort of tests. A problem that exists in most I.Q.-like assessments. Rather than evaluating how well the student is able to use their brain it's instead filtering those who were coached to think the same way as the test writers. That creates homogenity which is why I believe there are cultural divides in test results.
Like the Cold War era stories where spies use seemingly innocuous or nonsensical code phrases to identify each other. "The sparrow flies at midnight. Calculate the velocity it would need to reach Berlin in 7 days."
I always found that "feature" annoying because students who knew the material well could fail questions testing its mastery due to imprecise instructions. (My personal pet peeve is not making it clear whether "or" is inclusive or exclusive.)
I can't think of a situation in which "or" would ever be used in an exclusive sense unless it was explicitly called out as an XOR or included "but not both".
Yes. When I taught my son who is on the spectrum, I realized how much we “normal” adults took for granted. Very often, when I read a math problem, I have to stop and explain to him which implicit assumptions are here to expect. And more often than not, the solution will change significantly when the presumptions are not met.
I don’t know if the vagueness is intentional. It can open interesting perspectives but it can also be a burden for children, who has difficulties understanding the context.
I’m no genius, but I used to score well on such tests as a youngster. I was handed an IQ test circa ~1996 and got about two thirds through it before I found a question where none of the responses were correct. I brought it to the teacher’s attention. “There is no way you could possibly be right, this test was reviewed first!”
Anyway, blame it on photocopy errors or whatever, but the answers were wrong. Still mad about it.
I took another one ~2007 when I was looking to be a marketing person for a construction equipment rental company. This one was about 30 questions over 60 minutes. I got to question 26, which was some extraordinarily complicated question about how many cuts would it take to chop down a large board into the pieces you needed. After I wasted several minutes methodically writing this out, I realized the true test was realizing it was a time waster question one should skip. 27-30 were far simpler and then the buzzer ran out on me.
I approach tests by going to the next question if the answer isn't immediately solvable. Then, when reaching the end, I go back and spend more time on the ones I hadn't solved. That maximizes the score.
I apply that technique everywhere. For example, when working the bug list, I'll solve the easy problems first, and the toughest last. That also maximizes the score, as the bug submitter's only care is if the bug is fixed, not how hard it is to fix.
I applied this to school tests but not in my work, well sometimes, if I'm procrastinating and need a few quick wins. But for timed tests, it's essential to skip something you're struggling with and get some points on the other questions.
In (software) engineering you want to take on enough of the hard stuff early on, to make sure you're not painting yourself into a corner with naive solutions...
the true test was realizing it was a time waster question one should skip
I remember something similar on the LSAT. Odious practice; if you get a wicked problem in a professional context, you don't have the option of just blowing it off. Of course, you could say it's about learning to prioritize with limited resources, but that's meta-gaming the applicants and selecting for corner-cutters. There's a place for corner cutting; in emergency situations it's sometimes the right thing to do. The problem is that selecting for corner cutters also incentivizes exploiting the system for less noble motives.
I don't see the problem with a corner cutter question located around the end of a test.
It filters people into:
- those who don't manage time efficiently by investing too much energy on a problem.
- those who did cut the corner and as a result got an edge with a few more questions solved
- the genius ones, who solved everything, in whatever order
If the objective of a test is classifying candidates and time management is one of the metric considered, then this kind of testing pattern absolutely makes sense.
I was one of those who never cut corners and just focused on the problem at hand until failure, and now that I am working and need to get things done I wished my teachers trained me that skill.
Worst one I ever saw was a question to prove something that was vacuously true if you got the preceding question correct.
People spent ages trying to find their mistake. I was one of the first to finish because I quickly concluded I wasn't going to find the mistake (after checking a mere 3 times).
Not at all. The authority figure simply could not live in a world where the question was wrong. A better response, in his role as a school teacher, would have been to tackle the question in depth as a class or otherwise show me how I was mistaken. But given as I was immediately dismissed I’ll never know for sure.
Why should we take the meaning of revolution in this problem not as the contacting point to meet the circle again, but just as the pointing the same direction? I think this is the source of confusion here.
I'm not the native speaker of English and I might take the meaning of "revolution" very absurdly here. Just curious and I have to ask this. :-)
None of the explanations gave me an intuition for it except the circle rolling down a straight line with the same length as its circumference.
A roll down the line will rotate the circle once. Coming back the same. But rolling around one corner will add half a circumference, and another half for rolling around the other. So you get 2 * 0.5 extra circumferences, and so + 1 C. Somehow that helps with the other polynomials for me too. Super cool.
Triangle is probably easier to see (120 deg rotation when you turn the corner). Then you can see that the key is the sum of exterior angles, and this holds as you increase num sides. In the limit, you get a circle.
The best intuition for me was the YouTube comment that said to imagine the rolling coin/circle is picked up on its edge, in 3D, rolling like a unicycle wheel. It turns forwards to roll and measure distance, and it turns sideways to travel around the circular path. i.e. "N" rotations for circumference distance on one axis (the straight line distance) plus one full rotation on a different axis around the circle. When the coin is lying flat, both have to happen on the same axis.
To me the intuitive explanation is that if they were gears, with shafts fixed in a block, the small wheel would turn 3 times per turn of the big wheel, but in the given scenario the small gear also has to go around the big one, hence the R/r+1 solution.
Yeah. I think that’s the intuition I have about this too. It rotates once by virtue of going around, and three times by virtue of the size of the big circle.
If you imagine a very tiny circle it’d still rotate a full time.
For my inner eye, I can see that the circle will rotate half a circumsphere to get around the corner.
But I can’t really explain why. It’s the same distance.
I get that when a road turns left, it’s longer on the right side, but these are lines that have no width and so there’s no stretch and by definition we’ve kept the length the same.
People are going to have one of two interpretations. If a coin rolls around another coin, is the distance traveled equal to the edge along the the static coin? Or is it the distance traveled by the center of the rotating coin?
If it’s defined by the former, the answer is 3 because the circumference is 3x as long as that of the traveling coin. If it’s defined by the latter then it’s 4 because the circumference of the base coin buffered out by the radius of the traveling coin is 4x as long that of the traveling coin.
The point is that the question is vague and is open to multiple different "correct" answers. SAT questions should only have one correct answer, with no possibility of any others.
It's not just that it was poorly worded, but rather poorly conceived/analyzed. Apparently they had wanted the right answer to be "3", and therefore basically asked the wrong question (which would been a bit awkward to word!).
I felt the same way, the question is pretty ambiguous, there are two readings, one corresponds with a somewhat "unintuitive" answer provided, and another doesn't, but is maybe more intuitive to some people, and yet "everyone got it wrong". I think its a bad question because the terms aren't defined clearly, but the "everyone got it wrong besides these people" framing is also not really true imo. I also didn't see why the original answer isn't considered defensible because from the view inside the circle, each of the 4 "rotations" doesn't look like a rotation because you don't start and end them from the same view.
It depends on the viewer’s perspective. From the coin’s point of view it rotates three times, but to an outside viewer it rotates four times. I think the outside viewer’s perspective is far more intuitive, so four is really the “most” correct answer to me.
Yea, I think the difference between “how many rotations” and “how far is the center of the small disk traveling” is pretty big. I was completely lost as to how you “add one” until I watched what the video called a “rotation”. It would have never occurred to me to call the coin being upright a rotation… the Art of Problem solving question in another comment thread was more clearly worded for that scenario
The question wording was about "revolutions" of the small disk. The distance traveled by the small disk center (= 4x it's own diameter) was only used as a way to calculate the number of revolutions, but I'm still not getting the intuition for how each diameter of distance traveled by the disk center equals one rotation regardless of the shape of path followed (it's obvious for a flat line of course).
If a coin rolls such that its complete perimeter touches the other surface exactly once it will move the distance of its perimeter. In this case the total distance is 3x the perimeter so the edge answer is 3. Shape doesn’t matter.
If you’re wondering how many times the traveling coin 360s you have to account for the fact that it is rotating both because it’s rolling and because it’s going around the the other thing. You can simplify this by just imagining it’s the edge again, but the edge is going along the radius of the inner and traveling coin (3+1).
Dumb it down. How far does a point travel? X units. X units / coin perimeter = coin rotations required to travel X. Ergo the only question is whether the distance traveled is along the perimeter of the 3r coin or if it’s based on the center of the traveling coin (3+1).
(as I commented elsewhere) I found it useful to picture a unicycle; a straight line track means the wheel rolls forwards the same distance as the length of the track. Curve the track around to the right into a circle and when the unicycle rolls forward in a straight line it's getting away from the track (at a tangent) - it would have to slide sideways to get to where the track is. That is some extra movement for the curved track compared to the straight track which has to be accounted for somewhere, somehow, and of course the unicycle turns right while rolling forwards to follow the curve in the track. When it gets back to the start, it must have done 1 complete turn to the right as well as all the rolling forwards. As long as the track is simple (no loops, bridges, crossings), e.g. a square with rounded corners, going around and back to the start needs the left and right turns to balance out to get to 1 complete turn - too much turning right spirals in, too much turning left spirals out, only a balanced amount of left and right turning that ends up as 1 complete turn can meet up back at the beginning.
Seeing the turns in two axes made it clear to me that the forwards rolling is always the length of the track because changing the shape doesn't change the length, and the sideways turn is always one for any simple loop or it wouldn't be a circuit. That fixes your question "how each diameter of distance traveled by the disk center equals one rotation regardless of the shape of path followed" - you say it's obvious for a straight line, and curving the line can't change the length of the line, the extra rotation to go round a circuit must be one, so there's nothing which can vary.
(If you lie the unicycle down on its side, the 1 complete turn to the right needed to follow the curve around to the start doesn't go away, it has to happen, and now it has to happen in the same axis as the rolling forwards happens so it's much less clear (to me). If the only thing the wheel can do is roll forwards, this extra movement from earlier to avoid getting away from the track can only be extra rolling - the extra one turn for the loop, spread over the N turns for the distance).
The text of the question did not ask about distance, it asked about revolutions.
“In the figure above, the radius of circle A is one-third the radius of circle B. Starting from position shown in figure, circle A rolls around circle B. At the end of how many revolutions of circle A will the center of circle A first reach its starting point?”
I hope they don't. The argument for removing it is basically that if you understand geometry, then the conclusion is obvious; but since this is an area where most people's understanding of geometry is incorrect (myself included, before today), the article is valuable. I don't see how it's different from articles on other mathematical paradoxes (Simpson's paradox, for example).
I love the Wikipedia animations -- they are usually extremely helpful -- but when I'm trying to read the article, I find them distracting. I usually move another window on top to obscure the animations so I can concentrate on the article. But there must be a better way. Is there a hotkey to stop animations? For Firefox in particular?
EDIT: I don't want to stop animations permanently with about:config; I just want to pause and un-pause.
One interesting thing that's not in the video: there is a real application beyond the astronomy one, a scenario where you would want to roll one object around another object, and care about how many rotations it makes.
I like this perspective as well. If the coin is rotating around a point (radius 0), the point on the coin edge touching the point will not move at all, yet the coin will make one rotation before returning to its original position.
The application to sidereal time is where this really gets interesting. It’s far from a trivial question of semantics or a mathematical trick. It’s something astronomers have known about for ages, since the amount of time it takes for the Earth to make one rotation is different from the perspective of distant stars than from the perspective of the sun.
Indeed. This was my favorite part of the video. The discussion of the problem and SAT part are interesting, but when it delves into the sidereal time aspect, it just flies off into a direction where never saw coming and presented some fascinating aspects I’d never had need to consider.
what is perplexing to me is that I've been thinking about the sidereal problem for the last or so
...(because I heard on a podcast that the earliest sunset occurs more than a week before the solstice and the latest sunrise occurs after the solstice, but still the solstice is the shortest day, and they said something about the tilt of the earth and I was thinking that was not explanatory, so I've been idly noodling about it)...
and I just got this problem wrong! didn't even occur to me :) in my defense, the thumbnail for this video does not state the question so I wasn't sure what I was supposed to do, but guided by the multiple choice I selected 3
but talk about having my brain primed for the question... doh!
My answer to this after reading the question was 1, because by definition it is one revolution. So I thought that was trick, and the answer essentially is none of the above. But there is a lot more nuance here than just that with multiple definitions of revolution versus rotations, and sidereal time is where this answer can get weird.
The only ambiguity there would be revolution/rotation about what center - the small disk's own center or the center of the large one. It seems pretty obvious they are expecting you to calculate something, so assuming this is a trick question and the answer is 1 would seem a risky interpretation, and anyways wasn't one of the answer options.
But isn’t that precisely the distinction between rotation and revolution already provides? When I first read it I thought, well they used the word revolution so clearly the answer is 1. If they had stated “rotations” then the answer is obviously 4.
It’s pretty ridiculous they couldn’t use the right word when the distinction was taught back it elementary school during the discussion of the motion of the earth.
But why is it obviously 4 ? Is it equally obvious that if the small disk was rolling around the inside of the large disk then the answer would be 2 ?
If you already know the relationship between distance traveled by the center of the small circle and number of rotations, then of course both answers (for outside of circle, or inside) are obvious, but the inside case doesn't seem intuitive.
btw, it seems they were intending "3" to be the right answer, but the wording isn't even close to what it'd have to be for that to be the right answer!
The way I think of it, is if the outer circle is just sliding with friction such that the same point of the little circle is in contact with the big circle, it would undergo a single full rotation. Or is you slid a box along the surface of the drum, it would naturally undergo a single rotation. So then when add in the "rolling", you get the 3.
Well, it depends on which definition you use. If you consider the circles planets, then it's one revolution by the astronomical definition. If you consider them gears, then it's 4 revolutions by the mechanical definition.
There is an intuitive way to see why this is true.
Picture a circle rolling around the outside of another. Easy to picture, right? Even if it’s not clear how many times it rotates, you can still visualize it.
Now imagine the outer circle has to spin around the inside of the first circle.
Stack two quarters, and try to spin the top quarter around the inside of the bottom quarter.
You can’t do it. There’s no room. If they’re identical size, the top quarter can’t spin "around" the inner edge of the bottom quarter.
Now put a penny on top of a quarter. Spin that around. Not along the outside, but along the inside of the quarter. You’ll see the penny is tracing a very tight circle. There’s not much room.
Now put the penny next to the quarter and spin it around the outer edge of the quarter. It goes easily. Plenty of room.
If you do the naive calculation, you’d get the same answer for both cases. But clearly there’s a difference.
The difference is more apparent if you imagine the coins had little teeth, like gears. If you go around the outside, it’ll go just fine. But if you hollow out the quarter and put teeth along the inside, and try to spin the penny around in that, you’ll find that it doesn’t make anywhere close to a full rotation each time you go around.
This becomes even more apparent when you turn the circumference of the fixed circle into a straight line. (As the video suggested but didn't show in the same way.) The center of the rolling circle will trace a line parallel and equal length to the fixed line, whether above or below it. If you reform the circle the outer line will be too short to form a complete circle, and the inner line will overlap itself.
The way I think of this is: If instead of having a small circle rolling around a larger one, think of a circle with ANY non-zero radius rolling around one with a zero (or really really small) radius. You’ll always end up with at least one rotation, regardless of how small the other circle is. So +1 makes sense.
The way I thought about it, you have to roll around the larger one and you have to roll around yourself (+1). So if they are two same size circles, it's 1 for the other and 1 for yourself. If the other one has 3 times bigger radius, it is 3 for the bigger one and 1 for yourself. Etc.
Not sure if it is mathematically accurate but it seemed to make sense to me.
I'd say they are less resistant to going on positive curvatures. It's like a bum that goes deeper into the tire, deforming tire more which should result in more wear than driving on even surface.
I'm surprised that only 3 people reported the error.
While problem is not trivial, my initial reaction was "it can't be 3, it's too obvious". And it seems that a lot of people in the comments here do get to the right answer on their own.
Second part of the video is way more interesting, where he discusses how this toy problem actually relates to how we define what a year is depending on whether we look at the stars or at what's on Earth.
Interesting: I took the SAT in 1982 and don’t remember this problem. They don’t give you your % right, just percentile and a mysterious score between 200 and 800 for some reason. Does 800 mean 100%?
When I took the SAT a couple decades later, there were multiple sittings per year. Is it possible you took it at a different time? You should be able to check the news coverage and see which sitting it refers to.
Back in 1982 our school’s entire SAT prep was: “bring only #2 pencils. Sharpen them before you come. Fill the bubble completely and don’t leave any other marks. If you can eliminate one answer, it’s worth picking one randomly, else skip the question.” I don’t remember that there was any SAT prep culture like there is these days. Nobody had heard of ACT — perhaps it didn’t exist yet.
There were apparently about 50 of us in my year at MIT who had 800/800, and apparently that was pretty standard. I don’t think I was the only one in my HS class of 39.
The scaled scores are intended to be directly comparable, so the mapping from raw score to scaled score depends on the difficulty of the questions on the particular test that you took. On a sufficiently hard section, you can miss a question and still get an 800.
I guess if you're smart enough to realize that 4 is the right answer, but isn't one of the choices, then the next question is "what were they thinking?", which is why 3 would be the smart guess to get your answer marked as correct.
the video starts out with the question and then says you can pause if you want to work on it. Then it the next thing it says is something about the answer.
Tldr it was a four choice multi choice question but the all the options were wrong because the people setting the test got it wrong.
So I'm not sure everyone got it wrong, just that they weren't confident enough in a rushed test to cross out A,B,C and D and write in the correct answer!
https://www.nytimes.com/1982/05/25/us/error-found-in-sat-que...
(Gift link.)
And a recent Scientific American article:
https://www.scientificamerican.com/article/the-sat-problem-t...
(Both of these are linked from the video description itself.)
I'll bet Marilyn vos Savant wouldn't have got this one wrong[1]. :-)
[1]: https://web.archive.org/web/20130121183432/http://marilynvos...