Veritasium: The SAT Question Everyone Got Wrong [video]
youtube.com
youtube.com
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...
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.
(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.)
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.
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).
The effect of noise on your score is supposed to be around 30 points. A 10-point effect is too small to measure. How can that be "shockingly deep"?
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).
One of the ones you got 'correct' is annulled - now, you got 8/9 correct. You scored 88%.
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.
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.
Everyone who gave the answer 3 was initially scored as correct but then had it annulled and saw their overall scores drop.
The only other channel I would give the same pass is neo.
Nice, thanks for the mention, I'll check this out. At first sight, typically looks like stuff I would enjoy.
Fortunately we have youtube.
According to last years research, over 50% of people are still watching linear TV via broadcast or cable:
https://arstechnica.com/gadgets/2022/08/for-the-first-time-e...
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.
That said, the channel is more popular than ever so who knows.
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.
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)
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.
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 :)
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.
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.
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.
I did not want to watch a video and preferred reading about this irrespective of the length of the video.
"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.
I'm cranky this morning, sorry
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.
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.
After reading the NYT article, I would say there was no need for me to spend an additional 15min watching the video.
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.
[1] https://vimeopro.com/fisherpaykeltechnical/training-videos/v...
Thank you for clarifying what "often" means.
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?
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.
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."
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!
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.
0. Walking in a circle is different from spinning. They are 2 separate things that should be counted separately.
Adding them together should be a type error.
It happens that they also went around the earth, but the "rotations" in the part you quoted refers to the spinning.
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)
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?
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.
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.
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.
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.
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.
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.
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 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)
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.
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.
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.
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?
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?
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.
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.
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.
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.
There are several states in which that would be absolutely disastrous.
Also: Many highly advanced nations have a national-level curriculum. What is different and why does it work?
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?
Except in, say, China, where none of that applies and education works great.
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.
Yup the school system plagued by epidemic cheating where cheating is even accepted to some level (you are an idiot if you don't cheat).
"Do you want the burger or the ribs?"
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.
Eh. I knew about it before I took the SAT. It was in various brain teasers books.
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.
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.
Why?
Because he self-identifies with some definition of iq.
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.
(If the reports come in faster than they can be fixed, of course one can never catch up regardless of the algorithm.)
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.
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.
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).
https://artofproblemsolving.com/wiki/index.php/2015_AMC_10A_...
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. :-)
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.
If you imagine a very tiny circle it’d still rotate a full time.
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.
I vote 3 personally
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).
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).
“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?”
Are revolutions the coin rotating 360 degrees or are they the complete perimeter rotating across the other coin and touch the other one exactly once.
The problem is intended to be mapped onto a distance perspective and figured out that way. So it’s very much distance.
[0]: https://youtu.be/oEN0o9ZGmOM?t=523s
[1]: https://www.scientificamerican.com/article/the-sat-problem-t...
EDIT: I don't want to stop animations permanently with about:config; I just want to pause and un-pause.
https://addons.mozilla.org/en-US/firefox/addon/toggleanigif/
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).
https://en.wikipedia.org/wiki/Epicyclic_gearing
These are used for car differentials, bicycle gear hubs, pencil sharpeners, and many other applications.
...(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!
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.
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!
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.
Not sure if it is mathematically accurate but it seemed to make sense to me.
Which tire wears down more:
A tire that rolls around a circle of circumference D.
A tire that rolls down a flat surface, total distance D?
Maybe tires are more resistant to rolling on curvatures?
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.
So, why not hundreds of reports?
The SAT has math questions ranging from easy to hard-ish. Plenty of the questions have very obvious answers.
Unlike the AP Physics 2 exam, for example.
(1480 combined, did a prep class but didn't pay much attention to the language bits)
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.
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!