it isn’t always stressful but it certainly can be. Especially when the one being tutored doesn’t want to be and it is being forced on them. or if the person is forced to tutor because of academic requirements perhaps.
Reltzik
The big problem is that Jason doesn’t know how to tutor. He thinks it’s just a matter of saying things how he understands them. He doesn’t really do diagnosis, or trying to grasp someone else’s current state of understanding, or trying different learning styles, or explaining something five different ways until it finally clicks.
kingleon
In all fairness to Jason, it isn’t really tutoring (its grad student TAing, which means one usually doesn’t have much time to focus on individual students, especially since their main time sink is still their thesis), and most schools put very little time into training grad students anything at all about pedagogy (and then those same individuals go on to become faculty…).
Frankly, from my perspective of what sort of time and effort the typical grad student TA will put into any given large-lecture STEM class, Jason’s attempts to personally follow-up with students easily puts him in the top percentile of actually caring. That said, that Jason has been involved with Walky’s sister, also a student, makes things entirely problematic.
BBCC
Part of his job description is office hours to talk with students. The fact he’s doing his job isn’t something I’d consider particularly praise worthy, tbh. The only time he actually did something good is when he offered Walky help when he first started falling behind. Other than that, he’s been pretty consistently shit. And sure, he’s not trained to teach, probably, but if he actually gives a rats ass about being a good teacher (like he says he does) then he needs to stop whining and do something to improve. That or be content with being shit and stop professing he cares about being a good teacher.
Emperor Norton II
He seems to give a rat’s ass about people thinking he’s a good teacher more than he gives a rat’s ass about actually being a good teacher.
BBCC
Agreed.
Reltzik
My read on him is that he does want to be a good teacher. It was in his head, part of his self-image, that he was a good teacher… or at least had that in his skillset, even if he’d never used it. (Hint: If you believe you’re good at something you’ve never done, you’re most likely wrong.)
He’s started to realize that this self-image was false, but he wants to be true. Right now he’s stuck in a mode where he thinks good intentions plus tryhard is the fix. It’s… not going well.
But none of that means he doesn’t care about being a good teacher. And it’s not really fair to blame him for that, because… as kingleon said? No one gave him significant training. The system cares more about making grad students into researchers rather than into making them into good teachers. And by “more”, I mean “only”.
Jason’s story is that of a man out of his depths who suddenly and belatedly realizes that the well-being of others rests on his own incapable shoulders. And of course he screws it up. No one’s taught him how to do anything else.
(But screwing Sal up, that’s on him.)
BBCC
I do believe he cares about being a good teacher, but I also believe that since he’s not good at it, that means he needs to put in an effort to learn to be better. I get that time and money are tight but if he wants to be a good teacher, he’s got to either learn to do that (hell, I’d take just googling ‘tutoring tips’ – at least then he’d be TRYING even if it didn’t help) or accept that’s he’s a sucky teacher and doesn’t have the time/money/energy to put into being better and so will remain so.
ischemgeek
IME as an ex-grad student who TA’d a lot: Odds are very good that by doing the minimum job description he’s putting in more time than he gets paid for. Because university fuck over grad students at every opportunity. Grad students are even cheaper than sessional instructors, and unlike sessional instructors, the grad student can’t move to a different uni or go somewhere with better pay without tanking their career, so the schools love putting grad students in charge of most of the responsibility for putting on a course (but you get no authority to go with the responsibility – you’re the one designing grading rubrics and report forms and marking and doing most of the teaching, buuut if the sessional instructor who comes in three hours a week decides you were too haaard on the student who refuses to wear PPE and spends the entire lab “jokingly” threatening to splash other students with acid, the well-deserved F the student got from being punted from your lab over safety will get overturned.
Furthermore, many unis limit how many hours grad students can work anywhere such that there’s no possible way you can keep your financial head above water (and then they offer loans and what have you for “emergencies” which they charge outrageous interest on – it’s a full on company store bullshit deal), so in order to have enough to eat and a safe place to sleep you’re usually doing something else under the table and hoping the uni doesn’t find out. All in all when I was a grad student I was working 7 AM to 9 PM, six days a week and four to eight hours the remaining day of the week.
My point here is part of Jason’s unarguable incompetence might be just sheer exhaustion if his family isn’t rich enough to support him.
Jon Rich
The sex is still on him, though. Which brings to mind the question—after having slept with her, which harms his integrity less—grading her as he would have otherwise, and upholding (the remaining shreds of) his professional ethics, but at the cost of dishonoring the implicit agreement he made with Sal when he slept with her, or, on the other hand, sacrificing whatever professional ethics he might have left, but honoring the agreement with Sal?
Dr. T
It depends on the school, the department, and the class in question. I was a grad student at IU, so I have some first hand knowledge of how things work at IU for grad students. Fortunately for me, I was in the Microbiology program teaching various biology courses, which meant I got paid better than the TAs for math or the humanities. That’s not to say that was remotely fair since the university got paid the same for each credit hour of language arts than they did for microbiology lab, so the fact that I got paid noticeably more than them for the same amount of work was kind of bullshit for them.
Long story made short, I imagine that Jason is probably either pretty stressed about his finances or stressed from working a side job like some other grad students I knew. If he is working a side job, he has to be hush-hush about it lest the school find out (I only worked side jobs in between semester sessions to avoid this issue).
Mind you, this speculation requires us to assume his family isn’t rich and that he actually has money problems. There’s no guarantee in that.
BBCC
That definitely sucks, and I can definitely understand not wanting to bother in that case, but I’m still not overly impressed by doing the bare minimum.
“FUCK SCHOOL!!!!!”
“WITHIN REASON, AND NOT INTENDING DISRUPTION TO ESTABLISHED CURRICULUM”
“YEAH, AND UNLESS YOUR MUM FINDS OUT.”
*Electric guitar solo*
Honestly, he probably would/will, but he has to deal with Joe first. Then he can tutor Walky and Sal individually. He’ll probably have to be ever so slight assertive though.
Walky: So what’s up Wonderbread?
Danny: Alright first thing, don’t call me Wonderbread, only Sal gets to do that.
Walky: Why, cause you think she’s hot?
Danny: No, because she’s actually passing math.
Walky:…Dammit I don’t have a comeback for that.
Danny: Now that the sass is done, let’s get started.
Well you can but you then end up with negative numbers which are a bit harder to represent as physical objects.
William has 5 apples. The lord whose land he lives on demands 7 apples in payment. How many apples does William have? Show working.
5 apples – 7 apples = -2 apples.
As one cannot have a negative quantity of apples, and William cannot give more than he owns, William either has no apples and no home, if the lord evicts him for failing to pay in full, or needs to find other goods to trade in lieu/provide services worth two apples to somebody who can pay him. Alternatively, he may try to steal the additional two apples. If he is caught and it is a first offence, he is likely to have his hand chopped off. As we are given no indication that he has any other worldly goods or marketable skills, legal or otherwise, one must conclude that William has 0 apples and has been evicted. However, he probably has 2 hands, and may be able to gain employment helping somebody else with their landholding in exchange for food and shelter.
This is kind of a singular situation. While Danny might have some input on how to best help Dorothy handle stress, it’d only help so much in this case.
Oh true, I had forgotten Danny tutored Sal. That’d be much better.
Jon Rich
Pretty awkward, though, since Dorothy dumped Danny and then pretty immediately began a relationship with Walky.
I’m not in any way saying that it was wrong for her to do so, or whatever—Dorothy has the right to date anyone she pleases regardless of how it makes anyone else feel—but Danny probably resents Walky—or would be somewhat justified to do so—and Walky might feel awkward about it.
That said, Danny seems like he’d put that aside to help someone who needs it, and Walky really, really doesn’t want to disappoint Dorothy, so it could work out.
Yeah you don’t always want to talk right away. My biggest darkest time when i was getting help i pretty much hid in the bedroom for the whole first day. things take time.
for a STEM grad student at a large research university, being a crappy TA and/or disliking teaching will have pretty much no impact on Jason’s grad school experience. as someone who did quit grad school at a similar university in the same similar field, i was the opposite (enjoyed teaching, didn’t care enough about research to finish the phd).
sleeping with a student on the other hand, that could (or at least should) get him kicked out if it gets out. as much as i find jason entertaining, that’s pretty unforgivable for me.
BBCC
IU’s rules would agree with you. As would Jason and Penny, who both said if Jason got caught he’d be out on his ass (though apparently, they would cover it up if Jason were better liked).
Oh, I know, I just think it would be an interesting story. For one thing, Jason seems pretty disillusioned about the fact that, on the one hand, he’s bad at teaching, but on the other hand it doesn’t really matter (except to his students). I find it interesting to extrapolate that further into a “what if Jason isn’t where he should be at all” train of thought. Not just because of Jason himself, but because in a large ensemble cast of university students, it seems likely that *someone* would leave their program of study, and maybe Jason could leave more easily than one of the undergrads from a storytelling perspective.
I was good at math in school. I even went to a math bee in middle school. Although i got frustrated that my teachers in highschool could never explain why imaginary numbers matter.
Remember how they used to say we had to learn because we wouldn’t have calculators all the time?
miados
yeah I recall that. Although most of the time i can do the typical math faster than many people i know can figure it out with their calculator. not always but still.
Jamie
FWIW, it’s important to be able to sanity check. If you plug in 18 x 18 and get back 342, you know you done goofed.
yeah, i’m awful at math (i have only vague seemings of spatial reasoning and managed to get Cs on the same 3d figure geometry test three times in a row no matter how much i studied) but the only time i ever tried to use a calculator for really basic stuff is the time i took an algebra 2 test doped up on super-strong cough medicine for a chronic cough. i forgot an entire page of the test and kept trying to do things like 7 x 1 on my calculator. it was terrible and i did terribly
there are lots of reasons imaginary numbers matter, it’s too bad your teachers couldn’t come up with any of them. one of the most convincing for many people, is that there are many questions that you can reasonably ask where the question and the answer are both in real numbers, but you need to use imaginary numbers somewhere during the solution. for example, some important integrals in electrical engineering and probability are computed this way.
A Scientist
It would probably help if they weren’t called “imaginary.” They’re not imaginary; they correspond to actual things. They’re extremely useful in quantum mechanics because it makes the math of wave mechanics so much easier to do, for example.
But calling them “imaginary” makes students who aren’t just naturally curious about math for math’s sake check out immediately. It conveys the absence of practicality, even though there’s so much practicality.
But it’s too late now. The name exists, and no one’s going to change it.
Yumi
To be fair, the idea that these numbers were imaginary was the only thing that made me care about them. What’s reality.
No I Haven't Had My Coffee Yet
And “real” numbers are much more abstract things than their name suggests, as anyone who has had (and passed!) a real analysis course can tell you.
Oz
Well, to be fair, imaginary numbers were a thing long before quantum mechanics was even dreamed of (like centuries earlier), so at the time the naming was pretty apt.
Also I think the main reason for imaginary numbers to be in most curriculums is that they are a pretty fine example of math being completely ridiculous and much closer to art than to engineering, but also turning out unexpectedly to be very elegant in weird ways…, I mean some guy some five hundred years ago went “hey, what we we pretended that negative numbers have square roots?” and everyone else was like “you are beng ridiculous” and he went “no seriously, just pretend for a second that what I’m saying is not complete bullshit, and suddenly we can actually solve these equations that people are literally killing each other over. Like, we alreay pretend that negative numbers make sense. Bear with me” and most people still were firmly on the “you’re ridiculous” side but a few of them were a bit “oh look, this idea actually opens a ton of new possibilities!”
The name “imaginary” was probably derogatory from the start, as a way to tell people that those ideas were kind of absurd, and a lot of that was because people found the whole concept inelegant and useless. That was in the Renaissance, before we had Calculus and long, long before we had Set Theory, and math was very much an aesthetic art, much like painting and sculpture. But centuries later Iluminists still side-eyed imaginary numbers, and I guess they only became more formally accepted when Euler ambraced them in the 18th century, and figured out a ton of really cool applications for them, including the Euler Identity. Imaginary numbers are a really great example of how letting yourself believe for a second that a completely absurd thing makes sense can eventually allow you to learn many things that are way more beautiful than you had at first imagined. Even if it takes 300 years for those things to come up.
So after that, imaginary numbers were taught in mathematics for roughly two centuries before quantum mechanics was invented/discovered, because they offered really elegant formulas and visualizations and techniques for analysis. I firmly believe that being imaginary is actually a plus, not a minus.
Sorry, I get emotional and babbly abt this stuff and I know most math teachers are undertrained and have too little time to teach history of math and make things interesting, which makes me really unhappy.
I’ve got a T-Shirt where
i says to pi (sorry, no Greek keyboard)
“Be rational”
And pi answers “Get real”
Only one of my friends gets it.
I must have a bad geek ratio.
290 thoughts on “Abstract”
Ana Chronistic
WITH REAL MATHS ACTION
thebombzen
Have you heard of 0x0.st? Could be useful for your anachronistic purposes
truk2
With real maths action
https://imgs.xkcd.com/comics/existence_proof.png
truk2
With IMAGINARY Math action
https://imgs.xkcd.com/comics/complex_conjugate.png
miados
tutoring can be stressful on both sides
Reltzik
I’ve hardly ever found it to be that way, and it was my primary income for a while.
….
…. then again, Jason just don’t know how to tutor.
miados
it isn’t always stressful but it certainly can be. Especially when the one being tutored doesn’t want to be and it is being forced on them. or if the person is forced to tutor because of academic requirements perhaps.
Reltzik
The big problem is that Jason doesn’t know how to tutor. He thinks it’s just a matter of saying things how he understands them. He doesn’t really do diagnosis, or trying to grasp someone else’s current state of understanding, or trying different learning styles, or explaining something five different ways until it finally clicks.
kingleon
In all fairness to Jason, it isn’t really tutoring (its grad student TAing, which means one usually doesn’t have much time to focus on individual students, especially since their main time sink is still their thesis), and most schools put very little time into training grad students anything at all about pedagogy (and then those same individuals go on to become faculty…).
Frankly, from my perspective of what sort of time and effort the typical grad student TA will put into any given large-lecture STEM class, Jason’s attempts to personally follow-up with students easily puts him in the top percentile of actually caring. That said, that Jason has been involved with Walky’s sister, also a student, makes things entirely problematic.
BBCC
Part of his job description is office hours to talk with students. The fact he’s doing his job isn’t something I’d consider particularly praise worthy, tbh. The only time he actually did something good is when he offered Walky help when he first started falling behind. Other than that, he’s been pretty consistently shit. And sure, he’s not trained to teach, probably, but if he actually gives a rats ass about being a good teacher (like he says he does) then he needs to stop whining and do something to improve. That or be content with being shit and stop professing he cares about being a good teacher.
Emperor Norton II
He seems to give a rat’s ass about people thinking he’s a good teacher more than he gives a rat’s ass about actually being a good teacher.
BBCC
Agreed.
Reltzik
My read on him is that he does want to be a good teacher. It was in his head, part of his self-image, that he was a good teacher… or at least had that in his skillset, even if he’d never used it. (Hint: If you believe you’re good at something you’ve never done, you’re most likely wrong.)
He’s started to realize that this self-image was false, but he wants to be true. Right now he’s stuck in a mode where he thinks good intentions plus tryhard is the fix. It’s… not going well.
But none of that means he doesn’t care about being a good teacher. And it’s not really fair to blame him for that, because… as kingleon said? No one gave him significant training. The system cares more about making grad students into researchers rather than into making them into good teachers. And by “more”, I mean “only”.
Jason’s story is that of a man out of his depths who suddenly and belatedly realizes that the well-being of others rests on his own incapable shoulders. And of course he screws it up. No one’s taught him how to do anything else.
(But screwing Sal up, that’s on him.)
BBCC
I do believe he cares about being a good teacher, but I also believe that since he’s not good at it, that means he needs to put in an effort to learn to be better. I get that time and money are tight but if he wants to be a good teacher, he’s got to either learn to do that (hell, I’d take just googling ‘tutoring tips’ – at least then he’d be TRYING even if it didn’t help) or accept that’s he’s a sucky teacher and doesn’t have the time/money/energy to put into being better and so will remain so.
ischemgeek
IME as an ex-grad student who TA’d a lot: Odds are very good that by doing the minimum job description he’s putting in more time than he gets paid for. Because university fuck over grad students at every opportunity. Grad students are even cheaper than sessional instructors, and unlike sessional instructors, the grad student can’t move to a different uni or go somewhere with better pay without tanking their career, so the schools love putting grad students in charge of most of the responsibility for putting on a course (but you get no authority to go with the responsibility – you’re the one designing grading rubrics and report forms and marking and doing most of the teaching, buuut if the sessional instructor who comes in three hours a week decides you were too haaard on the student who refuses to wear PPE and spends the entire lab “jokingly” threatening to splash other students with acid, the well-deserved F the student got from being punted from your lab over safety will get overturned.
Furthermore, many unis limit how many hours grad students can work anywhere such that there’s no possible way you can keep your financial head above water (and then they offer loans and what have you for “emergencies” which they charge outrageous interest on – it’s a full on company store bullshit deal), so in order to have enough to eat and a safe place to sleep you’re usually doing something else under the table and hoping the uni doesn’t find out. All in all when I was a grad student I was working 7 AM to 9 PM, six days a week and four to eight hours the remaining day of the week.
My point here is part of Jason’s unarguable incompetence might be just sheer exhaustion if his family isn’t rich enough to support him.
Jon Rich
The sex is still on him, though. Which brings to mind the question—after having slept with her, which harms his integrity less—grading her as he would have otherwise, and upholding (the remaining shreds of) his professional ethics, but at the cost of dishonoring the implicit agreement he made with Sal when he slept with her, or, on the other hand, sacrificing whatever professional ethics he might have left, but honoring the agreement with Sal?
Dr. T
It depends on the school, the department, and the class in question. I was a grad student at IU, so I have some first hand knowledge of how things work at IU for grad students. Fortunately for me, I was in the Microbiology program teaching various biology courses, which meant I got paid better than the TAs for math or the humanities. That’s not to say that was remotely fair since the university got paid the same for each credit hour of language arts than they did for microbiology lab, so the fact that I got paid noticeably more than them for the same amount of work was kind of bullshit for them.
Long story made short, I imagine that Jason is probably either pretty stressed about his finances or stressed from working a side job like some other grad students I knew. If he is working a side job, he has to be hush-hush about it lest the school find out (I only worked side jobs in between semester sessions to avoid this issue).
Mind you, this speculation requires us to assume his family isn’t rich and that he actually has money problems. There’s no guarantee in that.
BBCC
That definitely sucks, and I can definitely understand not wanting to bother in that case, but I’m still not overly impressed by doing the bare minimum.
Doctor_Who
Their death metal band, on the other hand, is coming along great!
Van Jealous
Yeah…”Jason And The ArgueNauts”!
Individual Lies
I very nearly spit tea all over my screen.
Thanks for that.
Valerie
That is goddamn beautiful. You deserve a cookie. Go buy yourself a cookie.
VanVelding
Amazing.
ellernock
oh my god i keep grinning despite myself, damn you van jealous
Anowan
This is wonderful. Put some rose petals on your bed tonight. You deserve it.
Eldritch Gentleman
Where is the upvote button when you need one. This is sweet XD
Rukduk
I do believe that for the next thirty minutes, you own the Internet. Because that joke definitely paid for a half hour of universal internet control.
NelC
Where’s the “Like” button? Why is there no “Like” button?
Tacos
Nice.
BP
MARRY ME
Bagge
“FUCK SCHOOL!!!!!”
“WITHIN REASON, AND NOT INTENDING DISRUPTION TO ESTABLISHED CURRICULUM”
“YEAH, AND UNLESS YOUR MUM FINDS OUT.”
*Electric guitar solo*
butts
and then they start kamehameha’ing each other, it’s brutal
TamiDOA
I’m expecting more of the comical dog-paddling slap fight from these two.
Cattleprod
So the real reason for the time skip was so we wouldn’t have to sit through several weeks of Walky and Jason powering up?
C.T Phipps
Walky, stop cheating on Dorothy! We know you had hate-sex with Bowtie! It’s a family failing.
Rocketboy1313
So the tutoring is gonna be on slipshine then?
I think I will make this joke about everything that happens off panel at this point.
Yumi
I’d suggest that Walky try asking Danny, but that might be a bit…uncomfortable for them.
But, hey, he’s New Danny now, so maybe it’d work out.
Doctor_Who
New Danny will teach math skills via soulful ukulele tunes!
fogel
He’s a good egg, so he’d help for sure!
Rukduk
Honestly, he probably would/will, but he has to deal with Joe first. Then he can tutor Walky and Sal individually. He’ll probably have to be ever so slight assertive though.
Walky: So what’s up Wonderbread?
Danny: Alright first thing, don’t call me Wonderbread, only Sal gets to do that.
Walky: Why, cause you think she’s hot?
Danny: No, because she’s actually passing math.
Walky:…Dammit I don’t have a comeback for that.
Danny: Now that the sass is done, let’s get started.
Chris Phoenix
Hooray for new math, New Math!
It won’t do you a bit of good to review math!
It’s so simple, so very simple,
That only a child can do it!
You can’t take three from two, two is less than three, so you…
http://www.lyricsfreak.com/t/tom+lehrer/new+math_20138395.html
Miri
Well you can but you then end up with negative numbers which are a bit harder to represent as physical objects.
William has 5 apples. The lord whose land he lives on demands 7 apples in payment. How many apples does William have? Show working.
5 apples – 7 apples = -2 apples.
As one cannot have a negative quantity of apples, and William cannot give more than he owns, William either has no apples and no home, if the lord evicts him for failing to pay in full, or needs to find other goods to trade in lieu/provide services worth two apples to somebody who can pay him. Alternatively, he may try to steal the additional two apples. If he is caught and it is a first offence, he is likely to have his hand chopped off. As we are given no indication that he has any other worldly goods or marketable skills, legal or otherwise, one must conclude that William has 0 apples and has been evicted. However, he probably has 2 hands, and may be able to gain employment helping somebody else with their landholding in exchange for food and shelter.
Times were tough back then.
Shiro
This is kind of a singular situation. While Danny might have some input on how to best help Dorothy handle stress, it’d only help so much in this case.
Yumi
I…meant about the math tutoring thing. I don’t think “Dorothy advice” would be on the list of topics that would make things LESS uncomfortable.
Shiro
Oh true, I had forgotten Danny tutored Sal. That’d be much better.
Jon Rich
Pretty awkward, though, since Dorothy dumped Danny and then pretty immediately began a relationship with Walky.
I’m not in any way saying that it was wrong for her to do so, or whatever—Dorothy has the right to date anyone she pleases regardless of how it makes anyone else feel—but Danny probably resents Walky—or would be somewhat justified to do so—and Walky might feel awkward about it.
That said, Danny seems like he’d put that aside to help someone who needs it, and Walky really, really doesn’t want to disappoint Dorothy, so it could work out.
CJ
Well, he could always resort to alternative math and bully his way through 😉
Somebro
ORA ORA ORA ORA ORA ORA ORA ORA ORA ORA ORA!
MUDA MUDA MUDA MUDA MUDA MUDA MUDA MUDA!
AGV
Walky’s Bizarre Adventure: Maths are Unteachable
MK15
Like Willis, she would rather not talk about it right now 🙁
miados
Yeah you don’t always want to talk right away. My biggest darkest time when i was getting help i pretty much hid in the bedroom for the whole first day. things take time.
RacingTurtle
Hmm, this reminds me that I thought Jason might be a good candidate for “The Story of someone who quits [grad] school.”
s
for a STEM grad student at a large research university, being a crappy TA and/or disliking teaching will have pretty much no impact on Jason’s grad school experience. as someone who did quit grad school at a similar university in the same similar field, i was the opposite (enjoyed teaching, didn’t care enough about research to finish the phd).
s
sleeping with a student on the other hand, that could (or at least should) get him kicked out if it gets out. as much as i find jason entertaining, that’s pretty unforgivable for me.
BBCC
IU’s rules would agree with you. As would Jason and Penny, who both said if Jason got caught he’d be out on his ass (though apparently, they would cover it up if Jason were better liked).
Temperaryobsessor
First they would need to change Sal’s math class.
RacingTurtle
Oh, I know, I just think it would be an interesting story. For one thing, Jason seems pretty disillusioned about the fact that, on the one hand, he’s bad at teaching, but on the other hand it doesn’t really matter (except to his students). I find it interesting to extrapolate that further into a “what if Jason isn’t where he should be at all” train of thought. Not just because of Jason himself, but because in a large ensemble cast of university students, it seems likely that *someone* would leave their program of study, and maybe Jason could leave more easily than one of the undergrads from a storytelling perspective.
AnvilPro
I need more Jason and Walky comics in my life
Gojira
Dorothy doesn’t know trauma! Math tutoring, that’s the real deal!
miados
I was good at math in school. I even went to a math bee in middle school. Although i got frustrated that my teachers in highschool could never explain why imaginary numbers matter.
timemonkey
Remember how they used to say we had to learn because we wouldn’t have calculators all the time?
miados
yeah I recall that. Although most of the time i can do the typical math faster than many people i know can figure it out with their calculator. not always but still.
Jamie
FWIW, it’s important to be able to sanity check. If you plug in 18 x 18 and get back 342, you know you done goofed.
Needfuldoer
Dun goofed indeed.
(18 x 20) – 36 = 324
ellernock
yeah, i’m awful at math (i have only vague seemings of spatial reasoning and managed to get Cs on the same 3d figure geometry test three times in a row no matter how much i studied) but the only time i ever tried to use a calculator for really basic stuff is the time i took an algebra 2 test doped up on super-strong cough medicine for a chronic cough. i forgot an entire page of the test and kept trying to do things like 7 x 1 on my calculator. it was terrible and i did terribly
s
there are lots of reasons imaginary numbers matter, it’s too bad your teachers couldn’t come up with any of them. one of the most convincing for many people, is that there are many questions that you can reasonably ask where the question and the answer are both in real numbers, but you need to use imaginary numbers somewhere during the solution. for example, some important integrals in electrical engineering and probability are computed this way.
A Scientist
It would probably help if they weren’t called “imaginary.” They’re not imaginary; they correspond to actual things. They’re extremely useful in quantum mechanics because it makes the math of wave mechanics so much easier to do, for example.
But calling them “imaginary” makes students who aren’t just naturally curious about math for math’s sake check out immediately. It conveys the absence of practicality, even though there’s so much practicality.
But it’s too late now. The name exists, and no one’s going to change it.
Yumi
To be fair, the idea that these numbers were imaginary was the only thing that made me care about them. What’s reality.
No I Haven't Had My Coffee Yet
And “real” numbers are much more abstract things than their name suggests, as anyone who has had (and passed!) a real analysis course can tell you.
Oz
Well, to be fair, imaginary numbers were a thing long before quantum mechanics was even dreamed of (like centuries earlier), so at the time the naming was pretty apt.
Also I think the main reason for imaginary numbers to be in most curriculums is that they are a pretty fine example of math being completely ridiculous and much closer to art than to engineering, but also turning out unexpectedly to be very elegant in weird ways…, I mean some guy some five hundred years ago went “hey, what we we pretended that negative numbers have square roots?” and everyone else was like “you are beng ridiculous” and he went “no seriously, just pretend for a second that what I’m saying is not complete bullshit, and suddenly we can actually solve these equations that people are literally killing each other over. Like, we alreay pretend that negative numbers make sense. Bear with me” and most people still were firmly on the “you’re ridiculous” side but a few of them were a bit “oh look, this idea actually opens a ton of new possibilities!”
The name “imaginary” was probably derogatory from the start, as a way to tell people that those ideas were kind of absurd, and a lot of that was because people found the whole concept inelegant and useless. That was in the Renaissance, before we had Calculus and long, long before we had Set Theory, and math was very much an aesthetic art, much like painting and sculpture. But centuries later Iluminists still side-eyed imaginary numbers, and I guess they only became more formally accepted when Euler ambraced them in the 18th century, and figured out a ton of really cool applications for them, including the Euler Identity. Imaginary numbers are a really great example of how letting yourself believe for a second that a completely absurd thing makes sense can eventually allow you to learn many things that are way more beautiful than you had at first imagined. Even if it takes 300 years for those things to come up.
So after that, imaginary numbers were taught in mathematics for roughly two centuries before quantum mechanics was invented/discovered, because they offered really elegant formulas and visualizations and techniques for analysis. I firmly believe that being imaginary is actually a plus, not a minus.
Sorry, I get emotional and babbly abt this stuff and I know most math teachers are undertrained and have too little time to teach history of math and make things interesting, which makes me really unhappy.
CJ
I’ve got a T-Shirt where
i says to pi (sorry, no Greek keyboard)
“Be rational”
And pi answers “Get real”
Only one of my friends gets it.
I must have a bad geek ratio.
Yumi
I get it, but if I knew you in real life and saw you wearing that shirt, I would absolutely pretend I had no awareness of it whatsoever.