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”
That would be the past participle wouldn’t it?
Yeah, that’s what I said earlier.
Ah, duh. Interesting that it’s moving to the more typical “ed” ending
Exactly, that’s the expected path: the irregular form disappears as more and more speakers forget it and instead, “on the fly”, apply the general rules of word formation in their language. Over time the “regularised” form becomes the accepted, “correct” one.
OP has just proven their point.
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.
In engineering we have a simmillar thing for some cases where we replace 0 with a variable that is 0 at the limit but not 0 itself then continue on like nothing happened. It all cancels out at the end but feels so wrong.
π=√10
π=√10=√g=3=e=c*10^-8
It’s truly the universal constant
Can you give an example?
In control dynamics u have a transfer function and need to determine the Routh-Hurwitz criterion it will sometimes give u division by 0 errors so u sub in a variable and say its almost zero but not quite and continue on like nothing happened.
Eg determining the stability of a system with characteristic eq of A(s) = 3s4+6s3+2s^2+4s+5=0
If u do a RH array u will end up with a zero which then will give u (4*0−30)/0 so u sub in 𝜀 for 0 giving (4𝜀−30)/𝜀 and continue on. That eq obviously evaluates to negative infinity. U are essentially just saying 𝜀 is an infinity small positive number ie it is the number next to 0 on the positive side.
EDIT: If the markdown is messed up the eq should be
A(s) = 3s**4+6s**3+2s**2+4s+5=0When using ** as super notation
control dynamics
Well, that’s a relief! That’s a completely different kind of engineering than I studied, so I can stop being worried that there was something I was supposed to have learned but didn’t.
Its general mechanical background stuff
My degree is in civil.
Ahh. Mechanical before shit starts to move.
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?
Which part
locality. what was it supposed to be? and why doesn’t it actually exist? what model “replaces” it, if any?
maybe the meaning of spacetime isn’t obvious either, and I just misunderstand what it means
In short locality states that things are only directly affected by their immediate surroundings. This is provably untrue in quantum mechanics.
Thanks!
You know how you get COVID from being in the same room as someone who sneezes on you or something? It’s that.
Non locality is when you get COVID from someone the next state over.
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.
Thanks, good point. I’ve edited my comment.
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.
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.
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
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
I know it’s a week later but this has been weighing on my mind.
It has to be such right? I wouldn’t develop Krudler Fuel, with the hopes that in a couple years I will have completed development on the new Krudler Engine.
That scenario would make no sense and illustrates that the naming of the fuel must have come later.
Shale tastes like mud, yes, but it has the consistency of a chocolate bar if you eat a little.
Honestly not bad. Great experience.
My highschool friends weren’t really friends, just people who’d been temporarily thrown into the same unfortunate position as me.
Relevant: https://youtu.be/rGDBTLT9__s
(if I’m honest, this is not his finest work. his videos are usually way funnier than this)
That I am way stupider than I thought I was. No seriously, constantly failing and seeing how little I actually know made me question my life choices.
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
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.
That sounds like something news worthy with name and everything
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.
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
she was an older teacher, so makes sense it was the ideal she grew up with
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.
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.
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 :)
It’s also false. Take any pair of points on the graph of sin(1/x) using the domain (0,1] that you just gave. Then we can write these points in the form (a,sin(1/a)), (b,sin(1/b)) such that 0 < a < b without loss of generality. The map f(t)=(t,sin(1/t)) on [a,b] is a path connecting these two points. This shows the graph of sin(1/x) on (0,1] is path connected.
This same trick will work if you apply it to the graph of ANY continuous map from a connected subset of R into R. This is what my graph example was getting at.
The “topologists sine curve” example you see in pointset topology as an example of connected but not path connected space involves taking the graph you just gave and including points from its closure as well.
Think about the closure of your sin(1/x) graph here. As you travel towards the origin along the topologists sine curve graph you get arbitrarily close to each point along the y-axis between -1 and 1 infinitely often. Why? Take a horizontal line thru any such point and look at the intersections between your horizontal line and your y=sin(1/x) curve. You can make a limit point argument from this fact that the closure of sin(1/x)'s graph is the graph of sin(1/x) unioned with the portion of the y-axis from -1 to 1 (inclusive).
Path connectedness fails because there is no path from any one of the closure points you just added to the rest of the curve (for example between the origin and the far right endpoint of the curve).
A better explanation of the details here would be in the connectedness/compactness chapter in Munkres Topology textbook it is example 7 in ch 3 sec 24 pg 157 in my copy.
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.
This is fine. I stated boundedness as an additional assumption one might require for pragmatic reasons. It’s not mandatory. But it’s easy to imagine somebody trying to be clever and pointing out that if we allow the domain or range to be unbounded we still have problems. For example you literally cannot draw the identity function in full. The identity map extends infinitely along y=x in both directions. You don’t have the paper, drawing utensils or lifespan required to actually draw this.
Yes, you are right, topologists’ sine curve includes the origin point, which is connected but not path connected. I guess I didn’t do very well in my point-set topology. I will change that in my answer :)
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.
