What's one thing your learned at college/university that blew your mind?

You can calculate how long a pencil can stand on its tip before falling using quantum physics.

Basically a version of this was on our freshman accelerated physics final, and no one got it right so our professor happily explained it to us the next day.

It was pretty much the same as is described here.

https://thephysicsvirtuosi.com/posts/old/how-long-can-you-balance-a-quantum-pencil/

Whether or not an irregular verb retains its irregularity depends largely on how much it is used in everyday life. If it's a common word, it's more likely to stay irregular, because we're frequently reminded of the "correct" form. If it's a rare word, the irregularity tends to disappear over time because we simply forget. That's why "to be" couldn't be more irregular (it's used enough to retain its forms) and the past participle of "to prove" is slowly becoming regular "proved" (it's rare enough to be forgotten).

yes i like language very much

Edit: typo

It’s also interesting how the past-tense of “to dive” has changed over recent generations. “Dived” is supposed to be standard, yet people turn it into “dove” so frequently, it’s becoming the new normal.
- I resist because I'm literate enough to know that "dove" is a bird that rhymes with "love".
Wait, what's the other option for past tense 'to prove'?
- "I have proven"
- OP has just proven their point.

I learned women actually don't have the same access to higher education as men. That misogyny and rape culture is real and heavily affect people's lives in present day. And that it's about isolated incidents with bad apples, but about the structures around bad incidents, and how they systematically facilitate bad situations, don't help or silence victims.

I genuinely believed it was safe to give my peers the benefit of the doubt and assume that their ironically bigoted jokes weren't their actual views. And it was heartbreaking to realize that that is not an assumption you can make. You don't know people's values unless they tell you, seriously and genuinely, straight from the heart. You cannot infer values from ironic jokes, and you cannot assume that the nice people around you share your core values, that you'd otherwise take for granted that everyone but lunatics agree with. You don't know before you ask.

I learned that humor isn't always innocent. That not everyone who hears you make an "ironically bigoted" joke laughs because of its absurdity - they laugh because they agree. They think you agree with their bigoted views and values, and your joke further cements their worldview, that everyone thinks like them, everyone else is just too scared to say it openly. That jokes can be used as a weapon to create a culture where i.e. overt "ironic" racism is considered normal, and genuine conversations about real racism is taboo.

None of this was in the curriculum. It came from experiencing the social setting and viewing the effects of a broken administrative system at an "elite" engineering college.

I was not a feminist when I walked into my STEM education, and I was when I left.

I learned women actually don't have the same access to higher education as men.
You're right - women have significantly better access to higher education than men, and have demonstrably better education outcomes as a result.
For example, women are significantly more likely to receive scholarships and grants than men in undergrad.
Partially as a result of this lack of access, men have dropped to almost 40% of undergrad students, while women make up nearly 60%. Women also receive more doctorates than men, and almost twice as many Master's degrees as men.
I'm not trying to minimize the bigotry that you observed (or faced), but it's objectively false to claim that women have worse access to higher education than men.
- OP didn't indicate their gender.

One of the most accurate and successful theories in physics contains the single worst prediction and isn't mathematically rigorous at all.

Doing calculations with it feels like doing vibes based maths, and you spend a lot of time doing things like: "oops divided by zero guess I'll cancel it out by multiplying by zero" and it works.

Physics in general has not caught up to the fact that locality isn't a thing. Nobel prizes were handed out for this in I think 22... And people still think the notion of spacetime can be taken seriously. It can't.
- What does that mean?

That Earth was in fact way older than 6000 years.

Did you believe otherwise growing up?
- Some religious people do.
  I was a jehova witness an I believed science class was all wrong and that my job was to just get through it without believing it.
- Not the person you asked, but it's commonly taught as science in a lot of Christian themed curriculums, including a lot of homeschool programs. Source: friends who believed it, and seeing the homeschool program of my step-kids. We had to teach facts on the side and introduce them age appropriately to real science.
  "It" being Creationism.
  Here's something fun to learn more: https://en.m.wikipedia.org/wiki/Creation_Museum
- Yes. I grew up in the Dutch Bible Belt, with very strict evangelical parents. They sent me to a Christian school that taught a literal interpretation of the Bible. So I was taught at home, in church, and in school that Earth was created about 6000 years ago.

Shale tastes like mud, yes, but it has the consistency of a chocolate bar if you eat a little.

Honestly not bad. Great experience.

That the diesel engine wasn’t originally ran on diesel fuel. (In college I was led to believe that it was hemp oil). It was actually peanut oil and later they tried hemp oil.

I'm not trying to be a smartass, but wouldn't the name "diesel fuel" be assigned after a certain substance was found to be the optimal fuel for a diesel engine?
- Honestly, good question and I actually don’t know

Nothing mind blowing? Only mind blowing course was Sociology. My professor worshipped Bernie Sanders and I appreciated him engaging his students to do better.

But also, That succeeding in college/university just shows that someone can learn, follow instructions, work in a group, etc. It really is to prepare someone to show up and do the work. I mean everyone is different and there's just more likelihood of someone being a better person to work with than someone who doesn't have that structure or ability to absorb info and think.

I don't think necessarily that people need higher education but it helps. I tell people I think careerwise it helps to have at least two of the three:

skills
networking/network
higher education

Know college isn't for some people and the people I know that are successful are often very skilled or/and have connections, can make connections to get employed where they are.

Oh and STEM though, I think people 100% need college/university for more specialized fields and STEM like medical professionals, physicists, etc.

My polisci teacher day 1 really hammered in that literally everything is political, that it is unavoidable, and all you do by avoiding politics is giving up your own agency when it comes to the things that you care about. It was 2017, so a lot of political apathy at the time, idk it reallly made it click that every single thing is poltical, based on it or decided by it.
Like not caring about politics is just not caring about how you live your life and giving up any control you have to others. People only realize when they lose something they care about like porn games lol
- https://en.wikipedia.org/wiki/The_personal_is_political
It really depends on the line of work if you need higher education or not.
In my work, where we create software in the automobile industry, Only 1% or so don't have higher education, and even if they can work around it, it shows pretty fast once you look at how they organize their work, code, documentation, etc.

That teaching isn't the point. It's getting research grants or funding. So much energy was spent on that. Students came 2nd.

Students came 2nd.
Right. Yes. At least second. For sure.
There's not like, another kind of research we should save a spot for? No? Okay. 2nd is good.

Just how greedy some professors can be.

Like the one that had a publishing deal with Pearson. He wrote his own textbook, charged $700 for it, then made you remove parts from the book so it made used copies of the book worthless.

I'd be switching classes during drop/add if that happened.
I'm very grateful of having a publicly funded university. I pay around 70€ a year for the student union and another around 70€ for student health care. That's all I pay, includes the school, materials, and free healthcare.

It has been proven that each mathematical reasoning system* either has a statement that cannot be proven true or false, or a statement that can be proven both true or false. In simpler terms, it has been proven that we can't prove everything.

Gödels incompleteness theorem if anyone wants to look it up.

only holds for reasoning systems that can reason about numbers

I know people's experience varies on this but I absolutely hated high school, and only discovered that I enjoyed learning as a process because of uni. And I'd probably still be small minded and somewhat bigoted if I hadn't gone. Simply because it forced me to critically evaluate my own views and also exposed me to a number of types of people I wouldn't have encountered otherwise.

It's a shame it's so expensive in some countries, because I think it's important to have a well-educated society more broadly.

Functions on real numbers are incredibly werid.

There are continuous but nowhere differentiable functions.

There are continuous and monotonically increasing function that goes from 0 to 1 (i.e. surjective function [0,1] →[0,1]), that "almost never" increases; specifically, if you pick a point at random, that point will be flat on said function with probablity exactly 1 (not almost 1, but exactly 1, no approximation here).

More impressively, you can have function that is continuous, but you cannot find a connected path on it (i.e. not path connected). In plain word, if anyone told you "a function is continuous when you can draw it without lifting your pen". They have lied to you.

EDIT: the last one (crossed out) is wrong. Intuitively "topologists' sine curve" contains two parts; you can neither find a distinct seperation for them (i.e. "connected"), nor can you draw a path that connects the two part (i.e. not "path connected"). However, topologist's sine curve is not the graph of a continuous function.

More impressively, you can have function that is continuous, but you cannot find a connected path on it (i.e. not path connected). In plain words, if anyone told you "a function is continuous when you can draw it without lifting your pen". They have lied to you.
You are misrepresenting an analogy as a lie. Besides that, in the context where the claim is typically made, the analogy is still pretty reasonable and your example is just plain wrong.
People are talking about continuous maps on subsets of R into R with this analogy basically always (i.e., during a typical calc 1 or precalc class). The only real issue are domain requirements in such a context. You need connectedness in the domain or else you're just always forced into lifting your pen.
There are a couple other requirements you could add as well. You might also want to avoid unbounded domains since you can't physically draw an infinitely long curve. Likewise you might want to avoid open endpoints or else things like 1/x on (0,1] become a similar kind of problem. But this is all trivial to avoid by saying "on a closed and bounded interval" and the analogy is still fairly reasonable without them so long as you keep the connectedness requirement.
For why your example is just wrong in such a context, say we're only dealing with continuous maps on a connected subset of R into R. Recall the connected sets in R are just intervals. Recall the graph of a function f with domain X is the set {(x,f(x)) : x is in X}. Do you see why the graph of such a function is always path connected? Hint: Pick any pair of points on this graph. Do you see what path connects those two points?
Once you want to talk about continuous maps between more general topological spaces, things become more complicated. But that is not within the context in which this analogy is made.
- Sure, I have no problem with analogy. I called them lie simply to peak people's interest, but in research and teaching, lies can often be beneficial. One of my favorite quote (I believe from Mikołaj Bojańczyk) is "in order to tell a good story, sometime you have to tell some lies".
  At the begining of undergrad, "not lifting pen" is clearly a good enough analogy to convey intuition, and it is close enough approximation that it shouldn't matter until much later in math. I can say "sin(1/x) is a continuous function on (0,1] but its graph is not path connected", which is more formal, but likely not mean anything to most of the reader. In that sense, I guess I have also lied :)
  However, I like to push back on the assumption that, in the context of teaching continuous function, the underlying space needs to be bounded: one of the first continuous function student would encounter is the identity function on real, which has both a infinite domain and range.
Can you please elaborate on that second one, or drop a name so I can look into it? Sounds very counterintuitive and like something I wanna know
- The second one is the cantor function, also known as devil's staircase; the third one is topologist's sine curve.

Being able to communicate effectively is critical in a public speaking role. Sadly, I learned this in the inverse - class was taught by a TA who didn't speak English, professor was never available, whole class failed, no one cared. Still fills me with rage to this day. But, it did make me a better public speaker, so I guess that's something.

At a certain point, you need to be force which pushes you forward. I saw a lot of intelligent people fail because they no longer had the external stimulus to go to class.

Also, it is easier to manipulate people in positions of power, but you have to understand how they think and are rewarded. There is a reason why a lot of liberal arts education is focused on having people understand others.

Also, the liberal arts education of a century ago was basically a degree which was intended to make managers. Along with it, the extra-curricular activities were an important part of the education, but just what happened in class.

Why is it easier to manipulate people in power? What makes them more vulnerable to manipulation?
- A lot of the official liberal arts college education goes into understanding the perspectives of others, with a bias to people in power and their power structures. While not an explicit thing they are teaching you, college is teaching you how to understand power structures and the people within them.
  If you have a better understanding of power structures, it becomes easier to push said structures to achieve your own goals since you can speak to power structures in their language instead of your own in order to get what you want.
  Also, a lot of the clubs and other extra-curricular activities are designed to create small power bases to practice these techniques on.
  It is a lot easier to get what you want when you can speak on other people's terms.

A lot of things from my Philosophy and Literature class:

In the Old Testament (or at least Genesis) a man’s semen is literally a bunch of little hims and thus impregnating a woman with a son is creating a new him, and something went wrong if it’s a daughter. Obviously that’s wrong, but if I pretend to go back in time to when nobody knew anything about biology beyond the super obvious, it makes a very basic sort of sense. More importantly, it has provided me with a lot of context for why Abrahamic religions have (or have had) the views they have on masturbation, abortion, and patriarchy.

Gulliver’s Travels is a bunch of satirical metaphors that go right over the head of someone lacking the cultural context of the time it was written. The Lilliputians are at war with other tiny people because of how they eat their egg delicacies (I think they eat it out of a bowl while the others eat out of a cup or something). This is making fun of the schism between Catholics and Protestants taking communion where one believes the bread they eat becomes the literal body of Christ while it’s more figurative for the other. End of the day, they both eat bread to worship God and cleanse their souls, but they’ll kill each other (at the time anyway) for how the other does it.

Many have heard of Plato’s allegory of the cave. Some men are in a cave and shadows are cast representing real things, but only in an illusory way. They then leave the cave and discover the reality of those things. But what I didn’t know is who was casting the shadows. In ancient Greece around this time there was a group called the Sophists who basically told people what to think/know, ‘soph’ being the root term meaning “knowledge/to know.” Literally the knowers. These Sophists are the ones casting the shadows, claiming to give knowledge while only giving the illusion of it, trapping the men in a cave of falsehoods. What enables them to leave is what Plato calls philosophy, again ‘soph’ but also ‘philo’ meaning “love of/to love.” Essentially to escape the false illusions given by sophists and discover reality one can’t just claim to know things or be told things and take them at face value, they must have a love for knowledge that will lead them to seek it out and try to learn the best ways to seek it out.

Big-endian versus little-endian. i.e. which end to crack a boiled egg to scoop out the contents with a spoon. (The other end goes in the egg cup). Gets some use in computer science due to the way certain numbers are stored in memory, and also with date formats. US format is middle-endian. Got to wonder how Swift would have run with that observation.
The allegory of the cave is deeper than that. Sure, perhaps there are unseen others guiding your world view, but it can go the other direction into the concept of qualia and the nature of perception itself. Perhaps some façades are necessary as we wouldn't be able to perceive anything otherwise.

Bit too busy with the ole undiagnosed adhd and a hankering for world of Warcraft

You can tell from my transcript the exact week Elder Scrolls Oblivion came out.
- For me it was might and magic III, yes I'm very old...
  My roommate, RA for the dorm, and I played for 3 months straight on my computer. It was never turned off 24/7 ....

Higher education is a waste of money for the vast majority of degrees, even STEM ones.

Let me guess, you went to uni in the U.S.A.?

That I spent years developing proficiency in my language and expanding my vocabulary to get accepted, only to be told to write simplified English in journalism school. Then they doubled down in my business classes to write for a 6th grade education and those who don't speak natively.

That if you're an international student at a small, struggling school, you can miss half your classes and bullshit your way through most assignments and they'll still give you a degree.

In other words: I learned nothing.

We are all pretty much screwed

If you were to put a big fan on a sailboat and point it at the sail, it would move the sailboat in a similar way as if the wind was pushing the sail.

Which actually makes sense if you understand it's not the wind pushing but the generated updraft at the sail.
(also not point at, but sideways)
😁
- Even if you are sailing directly downwind, it works. That was actually the professor's demonstration. He said that at the time it was accepted as a physical phenomenon, there were many physicists who said it wasn't possible, but it was being actively used by some engineers to make jets go in reverse.

Using physics (mechanic) you can become better at playing billiards and snooker.

There is no god. No amount of looking for it would be enough. I was already doubtful beforehand. Having grown up conservatively, I kind of already knew it was all fake, but the deprogramming took a while.

I wasn't doubtful, unfortunately. I went in a true-believer, expecting to get a Religious-Studies degree. But I left early as an Atheist. I'm glad that I did, but fundamentally shifting my life like that really messed me up. Deprogramming myself was the hardest, but best decision that I ever made.

That although there are many wonderful professors, the average professor does not know their ass from a hole in the ground.

High School is just busy work to keep you off the streets until you're ready for a job or college.

For real? A lot of high school subjects were pre requisites for enrolling in my degree here and it'd be quite tough to get through the degree without the foundation laid in those subjects. At the very least they'd have to extend the university course by probably a year or so.
- Yeah not seeing how you could go into any form of STEM and lesson 1 is matrix math, but you flunked math 300 and don't know what a quadratic equation is.
- Probably varies largely on where you're talking about, and even then, which university program you're looking at enrolling in. If you go and look at universities in the UK, for example, a BA studying a foreign language generally seems to assume that this is a language you've already been studying for several years in secondary education. You're meant to be entering the program with roughly a B1 level in the language, and allegedly develop up to C1 over the course of 3 years of study. Meanwhile, in the US, you can rock up to a university and be a Japanese language major with nothing more than "Well, he says he likes anime and his grades are okay." and the degree program will start you off in a 100-level class that expects negligible prior knowledge, if any.
  Then again, having attempted university in the US, and now doing it at a UK school, university education is pretty drastically different. The US schools take 4 years to grant the same degree, and you spend almost the whole of the first year and a good chunk of the second just doing general education requirements that are, at best, only tangentially relevant to your chosen field of study. If I were doing my current degree program for a BA in French and Spanish as a first time student in the US, unless I did a bunch of AP courses or took night classes at a community college on the side, I'd need to do a general English composition class, a few math classes, probably get to pick between a biology or chemistry course, something to do with world cultures or music and the arts, and a handful of other electives I'm forgetting about. For that degree in the UK, from start to finish over the course of 3 years, I exactly 2 modules that aren't either French or Spanish, with one being the "Hey, we need to make sure you can actually write in English competently, too" module, and the other being a free choice of an introductory language module for something else.
  I'd also assume the US' lack of a national curriculum also plays into how things work out with universities here, as well. Since things can be so variable at a regional and local level, not only in terms of the established curriculum, but what courses your particular secondary school has the funding to offer, universities can't really assume much of incoming students' education. You can have a kid from one state whose school was a Spanish language immersion school offering bilingual education from day 1 of Kindergarten, and later offering French, German, Japanese and Arabic as a third language for the final 4 years of compulsory education sat side-by-side with another from a different part of the country who only had the chance to take 2 years of Spanish classes. Even for subjects with a better baseline, someone whose studies covered all the available math classes up to geometry and algebra is going to have a totally different starting point from another whose school partnered with a local college to offer college level courses in calculus and statistics in high school.
- And the first thing they teach you in college is "High School was bullshit, here's the real way to do it..."
Unfortunately, that’s becoming more and more true, and the quality of college classes has to adapt to a student population that is more and more divided depending on the quality of their high schools.
Students coming from good high schools have already internalized effective studying mechanisms, and often the basics of many topics in the first years of college, while others coming from worst high schools have no clue how to organize themselves to be successful. Often, they lock themselves up and spend unreasonable amount of time trying to make sense of things they don’t have the perquisite for. A good read in this direction is Whistling Vivaldi. Obviously, high school quality is very connected with the whiteness and affluence of their location, putting poorer and minority students at a disadvantage even before the starting block.

How low the expectations are for a putatively “adult” level of education

The Twin Paradox (special relativity). Every time I wrap my head around the idea I lose it a few weeks later an it's a mystery all over again.

Twin Paradox TL;DR: Identical twins—one stays on Earth, the other rockets off near light speed and returns. Relativity says time slows for the traveler, so they age less (e.g., returns 20 while sib is 50). "Paradox" cuz from traveler's view, Earth seems to move, but acceleration/turnaround breaks the symmetry, so no real contradiction. Mind-bendy Einstein stuff. 🚀

That all the shit I was told about making 60k out of college and doubling it in 4 years, how I would need college to get a cushy desk job, how without college I would never afford a house or a car, that my loans would be paid off in 10 years or forgiven in 20... All of that was a fucking lie.

Colleges will happily take 80 grand from teenagers and give them absolutely nothing for it.

Making a counter which scoud count up to 10 and loop back just with soma cables and electricity.

That a diploma doesn't mean shit beside someone being able to say what their teacher want them to say... but that was not really new, it was just a lot more sad to experiment as naive me was hoping for something more.

I think this depends entirely on the subject.
I was in a STEM degree and I learned a lot of technical skills. (Super early internet, no YouTube) In the extra classes like marketing, English Lit, I basically learned how to deal with people because of the professors like you describe, group projects, and trying to see the perspectives that didn't make sense to be initially so I could pass the damn class.
It seemed incredibly stupid at times, but making you think in ways that challenge you in ways you hate and think are stupid is actually excellent training for dealing with the myriad of brain-breaking people on this planet.
High School did this too, but less in your interest. High School was "shut up and do it this way, because that's how it's done." This benefits the Institution.
College was "sure, argue, but here's why you're wrong, or if not wrong, you need to be able to see this differing perspective, understand, and navigate it. The world is fucked, there is so much that is morally gray, that you need to learn flexibility. Show me you understand by explaining back to me what I'm teaching you. Don't just entrench your whole being in what you've been taught before coming here."

That I had to study.

That when actually challenged I couldn't justify eating meat. It was just a part of a long conversation with another meat eating woman in completely unrelated majors.

Honestly that sort of thing is one of the most valuable parts of college imo. I was in a place dedicated to learning and thinking, surrounded by people also dedicated to it and it meant that I had a lot of deep intellectual conversations. Those years didn't just give me a career, they molded me into someone genuinely educated

How completely stupid a professor can be. My parting words to him were basically "You have no idea what you are talking about." And everyone in the room but the professor knew I was right.