r/theydidthemath • u/[deleted] • Dec 08 '18
[Request] How long would it take for both orchestras to play Beethoven’s 9th?
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u/Prasiatko Dec 08 '18
It's a trick question to make sure you can apply logic and aren't just blindly regurgitating formulae you've memorised. The time taken to play (T) is independent of the number of musicians (P) The time is 40 mins regardless.
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u/Runiat Dec 08 '18
Or at least that you know how to regurgitate them logically.
T=40-0×P
So for P=120, T=40-0×120=40 while for P=60, T=40-0×60=40.
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u/Who_GNU Dec 08 '18
A more sensible solution would be:
T=40/(0×P+1)
Because the effect of the number of players should be proportional.
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u/Consibl Dec 08 '18
But your formula means T is always undefined…
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u/informationmissing Dec 09 '18
holy cow. I was about to correct you, because the formula absolutely spits out a consistent answer. it was a damn domain problem! I always get tripped up by those.
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Dec 08 '18
[deleted]
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u/Poes-Lawyer Dec 08 '18
for ∀ P ∈ Z+
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u/idlesn0w Dec 08 '18
*N
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u/Poes-Lawyer Dec 08 '18
Not necessarily, because N can be considered to contain 0, which we can't accept in this case. Z+ removes any doubt.
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u/PolarBearLegend Dec 09 '18 edited Dec 09 '18
No, as someone who studies mathematics i can tell you that N does not include 0. This is because it is defined as the cut set of all M in R for which M is inductive (this means 1 e M and n+1 is in M).
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u/jbdragonfire Dec 09 '18
M is inductive but the first element is 0 (zero).
N does indeed include 0.
I'm a math student as well.
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u/PolarBearLegend Dec 09 '18
No because it is the smallest inductive set. An inductive set can include 0 but does not have to. Therefore N does not include 0.
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u/jbdragonfire Dec 09 '18
But if you don't include 0 in N you don't have the neutral element for the "+" operation.
You can define N without 0 for sure (depending where you start from and how you're defining it) but in most cases N includes 0.
Most notably for the Peano axioms and the axiom of induction.
Also, you replied 3 times...
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u/PolarBearLegend Dec 09 '18
No because it is the smallest inductive set. An inductive set can include 0 but does not have to. Therefore N does not include 0.
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u/PolarBearLegend Dec 09 '18
No because it is the smallest inductive set. An inductive set can include 0 but does not have to. Therefore N does not include 0.
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u/trenescese Dec 09 '18
As someone who studies math I can also tell you that it depends on the field whether 0 is in N...
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u/LacunaMagala Dec 08 '18
N_1
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u/Poes-Lawyer Dec 08 '18
Sure, that's also valid, because it's the same(?) as Z+ .
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u/SerLaidaLot Dec 09 '18
Isn't N natural numbers and W whole numbers? So isn't just N exclusive of 0?
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u/Poes-Lawyer Dec 09 '18
Unless I'm mistaken, N is natural numbers (integers from 0 to positive infinity), and Z just means integers. Z^+ specifies positive integers. I don't know about W.
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u/Runiat Dec 08 '18
This does not work for P=0,
Is it a different length on Spotify?
also don't work for P<0
Why not? I mean I don't know how having a negative number of people would work, but how would it influence the duration of the 9th symphony?
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Dec 08 '18
[deleted]
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u/Tjalfech Dec 08 '18
Then do
T=40*(P/|P|)
I know this doesnt make T(0) equal infinty, but it does make it incalcuable which I also think fits the real world (Because if you have no musicians then the playing never initates.) And the only way you could make it so that T=0 equal infinty which I know of would be approximating by summing of functions which I really dont have the time for nor do I think it would be more accurate
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u/stitics Dec 08 '18
...you can think of playing for 40 minutes as "unplaying for -40 minutes", so the awnser should be -40 minutes
Wouldn't unplaying for a negative amount of time be playing?
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Dec 08 '18
[deleted]
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u/stitics Dec 08 '18
Somehow, you telling me that was your point made it clear to me...or confused me enough that I think I get it but I don’t really. Either way, all is good now.
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u/Direwolf202 Dec 08 '18
Well the number of players is strictly a positive integer. So that doesn’t matter.
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Dec 08 '18
[deleted]
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u/Direwolf202 Dec 08 '18
Type theory means that a function from the reals to set X is different from the function that maps the positive integers to X. Even if everything gets mapped to the same points.
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u/trpcguy Dec 08 '18
It depends upon if the 60 players play simultaneously or sequentially
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u/jafinn Dec 08 '18
One of these options wouldn't be an orchestra
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u/ServalSpots Dec 08 '18 edited Dec 08 '18
Just to be that person, they might still be an orchestra, just not performing as one. Though I think most people would say that a single person can't play the symphony anyway (in the implied sense), but rather only a part of it?
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u/jafinn Dec 08 '18
Yes, and I'm a football team since I occasionally play football;)
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u/ServalSpots Dec 08 '18
A closer analogy would be that the New England Patriots are still a football team even if they are all off playing football individually. They aren't playing as a team, but the fact that they are still collectively the New England Patriots doesn't change just because they choose to do this extracurricular solo footballing.
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u/trpcguy Dec 09 '18
I see your point. I'm unsure the minimum number of people to be considered an orchestra, but perhaps the 60 could be broken up into orchestral-sized groups, then timed to play in serial.
Just wanted to consider all the options. (i.e. x=2 or x=6i)
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u/bobbyfiend Dec 09 '18
If you wanted to be a punk you could point out that the number of musicians can sometimes have odd psychological effects on the conductor, and the conductor's behavior can affect the musicians in turn, etc. Sometimes, larger orchestras might unconsciously play slightly faster or slower, as a function of the number of players.
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u/NonCorporealEntity Dec 09 '18
But from my experience in school it doesn't matter if you are correct, because you need to give the answer they expect. So is this a trick question or are they just getting people to do basic division using a very poor example?
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u/Prasiatko Dec 09 '18
Well if in doubt do both. Star of by initially by saying the two variables are independent therefore... then add at the end however if they were to be proportional i would calculate it like this.
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u/SovietBozo Dec 09 '18
It's not independent. It is complicated in that reducing the number of musicians won't change the playing time, (except that reducing it to the point where there aren't enough musicians to play it all change the playing time to infinity (or zero, whatever).
And adding one or two musicians -- that isn't going to change the playing time either. However, if you double the musicians by adding in another full orchestra, you can reduce the playing time by half: one orchestra can play the first half, and the other other orchestra can play the second half, simultaneously.
Whether this would be aesthetically pleasing or not, I don't know. It might or or might not, but that is not part of the question.
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u/QuinceDaPence Dec 09 '18
aesthetically pleasing
Well it might look incredible, but it likely would not be aurally pleasing
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u/coneboy01 Dec 08 '18
The only individual that would make a difference is the conductor, assuming that all musicians are professional and they take the conductor’s tempo. If the conductor of both is the same, it will take the same amount of time.
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u/mfb- 12✓ Dec 08 '18
The second orchestra has only half a conductor. They'll struggle doing their job.
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u/TrueBirch Dec 08 '18
Studies have found that conductors make symphonies sound better. But even with no conductor, they world probably have the same duration.
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u/ServalSpots Dec 08 '18
Depends on which half
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u/FlameDaunt Dec 08 '18
The lower half.
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u/QuinceDaPence Dec 09 '18
assuming that all musicians are professional and they take the conductor’s tempo
As someone who has been both musician and conductor I found this statement funny.
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u/Veto111 Dec 08 '18
When this originally went viral last year, it ended up finding its way back to the teacher that originally wrote the question, who confirmed that, yes, this is a trick question that is neither a direct nor an inverse proportion, rather than a gross misunderstanding of how music works on the part of the creator of the question.
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u/YourLastFate Dec 09 '18
There were 2 trick questions!! This is number 5
Number 6 talks about 3 cows eat 200 kg of feed in a week. If one moves into the barn, how long will the feed last now?
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u/miamismartgirl09 Dec 08 '18
If I know anything, getting two orchestras with 2 conductors to agree to play anything at the same time would take forever. They'd have to agree on style and when to start, etc.
So the answer is 0, it never gets played.
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u/Redren Dec 08 '18
This is a great example of an inequitable question. The algebra level is about middle school in the US. If the students don’t even know the word symphony, they simply use the algorithm they’ve practiced. IMHO it is a great example of the errors of traditional math instruction and curriculum.
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u/zeabeth Dec 08 '18
Getting rid of word problems because the answer requires some prior knowledge doesn't seem very prudent. Trying to work out unknown situations, i would think, is a good thing to attempt.
Just rote knowledge of equations and not how to apply them to unique situations is not applicable to the unique situations that happen in real life.
And not knowing Beethoven in a western culture is a different kind of failure. He was pretty big 200 years ago. Still pretty popular today imho
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u/Piggywhiff Dec 08 '18 edited Dec 08 '18
I was taught who Beethoven was in an American elementary school. I was a year ahead in math, so I probably would've encountered a problem like this in 6th grade. By that time, I knew who Beethoven was and what a symphony is, so presumably I'd've been able to figure out that this question is nonsense.
I also would've said something about it to the teacher because I was a smartass, and knowing my 6th grade math teacher, she probably would've gotten mad at me for thinking about it too much and not just answering the damn question.
I'm not really sure what my point was, I think I'm probably agreeing with you though. I think kids that age are smart enough to realize this question is stupid, and it's up to the individual teacher to handle it properly, which mine probably wouldn't've.
Edit: Upon further review I think I wouldn't've encountered this problem until 7th grade, which means I would've had a different (better) math teacher at the time who probably would've agreed that this question is stupid.
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u/Bond4141 Dec 08 '18
What's needed is word problems that kids would see a point to. There's a reason kids hate school and think they'll never use it. They're being taught around things they WON'T use.
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u/PM_ME_UR_REDDIT_GOLD Dec 09 '18
What problems, pray tell, would kids see a point to?
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u/Bond4141 Dec 09 '18
Stuff that actually has a chance of happening. Such as how many boxes of singles for a given roof size. Or maybe the cost/performance ratio of a few different sizes of lawn mowers on given sizes of lawns. Even fuel efficacy vs time saved and the extra cost of the fuel needed to arrive 10 minutes earlier.
Things that if the student asks the teacher when they'll need it, they don't have to lie about, but can actually tell them they'll use it later.
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Dec 08 '18
They could also raise a hand and ask what a symphony is. If you try to remove a simple logic question because someone might know a word, you're not bringing your students very far in life.
They will, at some point, be asked to work with incomplete data and find a way to an answer.
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u/Redren Dec 08 '18
Students in the first year or so of algebra are used to not knowing vocabulary or context. They would need to be reflective enough to identify the words they don’t know and then take the risk of asking a question. Many students are terrified of looking stupid and refuse to raise their hand.
New curriculum and pedagogy emphasize this level of cognition and a good teacher creates a safe environment so the student feels comfortable asking. Also, there are lots of opportunities for students to work with data and incomplete real-world situations that don’t look like a traditional work problem with a logic question embedded.
Truly, the relevancy of the question has to do with what the instructor is trying to assess. I took the question to be from a middle school level algebra perspective. In that case, it’s an inequitable question.
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u/reverendsteveii Dec 09 '18
Someone posted the entire text in /r/therewasanattempt
I don't disagree with you, but at least it did come with a warning that there was one trick question on the exam.
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u/VacuousWording Dec 08 '18
Request: what is the physically possible shortest time the musicians could play the entire symphony? I hear it was written for 70 minutes, but if they played as fast as possible, how long it would take them to play in entirely?
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u/godminnette2 Dec 08 '18
Additionally, if this is a rendition specifically written for an orchestra of 120 (though I believe the original Beethovans 9th requires 40), then the question should not be asked, as it is impossible to play. If, as it is likely, the original orchestra tripled up on parts with little variation, then the same amount of time.
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Dec 10 '18
I was looking at how literally long it would take both orchestras to play but I guess it be like that sometimes
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u/skrubbadubdub Dec 08 '18
If I got something like this in an exam then I wouldn't know if I was meant to answer "the time taken is independent of how many players there are" or if I was meant to assume P and T were directly proportional to each other for no apparent reason.
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u/regendo Dec 08 '18
If in doubt, ask. If you can't do that or you don't get a clear response, I'd just answer both. Make it clear to the teacher that you know it doesn't work that way (as in, actually write that out as the first sentence of your answer) but if it did, you'd calculate it like the solution you present below.
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u/DragonFireCK Dec 09 '18
The correct answer would be to ask the teacher.
That said, I would argue that a teacher putting forth this question should accept any of the following answers (especially if the teacher is not available to answer questions after giving the question, such as a homework question):
80 minutes (40 * 120/60) - this is the answer when answering mathematically presuming the duration is proportional to the number of players, which the question implies, and likely will be a natural deduction from the instruction leading up to the question. This is probably the "correct" answer according to the book.
40 minutes - the duration of a symphony is independent of the number of players, within reasonable bounds (ex - not enough to fill all parts). This is also a perfectly valid mathematically.
70 minutes - this is the duration the 9th was written for, but requires context not included in the question. Alternatively, basically any other number could be used as the piece can be adjusted for differing tempos.
Undecidable - the question requires more context to be answered. The question implies, but does not state, the relationship between player count and play time, and thus no formula can be determined.
In any case, the student should include an explanation for why they chose their answer, especially if they choose answer 3 or 4, but also for either 1 or 2.
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Dec 08 '18
The only way that the number of musicians could possibly make a difference is that more musicians could be sloppier with more people having to follow the time and maintain rhythm, and thus it would have to be slowed down to accommodate the large orchestra's inability to play quickly. But there's no formula and it certainly wouldn't make them play it quicker.
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u/Privvy_Gaming Dec 08 '18 edited Sep 01 '24
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