What is something that was explained to you wrong such that you could never understand it, and you received a clarifying explanation that finally made sense?
The simple mechanic of long division. I was sick from school for a couple days, when I came back they'd already gone past the instruction on long division and simply expected me to do the problems, which I couldn't because I couldn't make any sense out of them.
It was years later when I was practicing on my own that I that had an insight -- OH you have to carry the remainder and re-divide into it to get the answer. Very simple, but no one bothered to explain that to me. They just couldn't understand what i wasn't understanding.
Differential equations. Had the worst math teacher ever for LA and DE. I memorized enough to pass the class but did not really understand diff eq. Next semester, we used diff eq in my physics classes with a great professor who explained them beautifully. What form do you think the solution takes? Using an algebraic formula for that form, solve for the unknowns. Tada! If there is a solution, you’ve just solved a differential equation!
Sometimes a specific explanation works for you, but school has to be generic enough for explanation to work for most. There are probably a million videos with explanations that are utter shit.
Anything math related from before high school, it gets dumbed down too much and once you get the actual way to do it in higher math classes, it made a lot more sense to me.
Physical Chemistry. First semester of first year of university. I couldn’t understand anything that our 80+ year old professor was mumbling, and the slides he used were terrible (full of abréviations, diagrams missing steps, etc.) Although I was getting solid grades in all my other courses, I failed the first PhysChem midterm with something like 23%. I resigned myself to my fate and sheepishly told my mom (I was still living home at the time and parents were paying for my studies). She got a mad glint in her eyes, and asked for all the course materials. By next week, she had completely reworked the material and came up with new tables and diagrams to help explain the concepts. I was amazed at how simple it all really was. For example, atomic bonds aren’t static but can “wiggle” around in several ways, and we can even calculate fairly easily the amount of energy required for each wiggle.
This is very dumb, but when I was in middle school, my sister explained blow jobs to me. She said you bob your head up and down on the penis, and that you could practice on a hotdog. I did not understand. I thought she meant like nodding bob your head. Like it would be in your mouth, and you would nod and it would hit your tongue, then the roof of your mouth, then your tongue etc. I practiced on a hotdog.
In high school, I learned what she actually meant, like bob your head so it goes in and out. I was a sheltered kid.
When doing a convolution of two curves in time, you flip one of them backwards.
Our shit statistics teacher made it so complicated.
And then one day, next semester, in a lab for signals class, the TA casually said “flip one, so they both start at zero seconds” and half the class started convulsing as an entire semester worth of misunderstood math magically snapped into place.
Lots of engineering teachers, have no business being teachers.
Yeah but unless it’s directly after a preposition you sound like a stuffy asshole. “Whom did I give the ball to?” Whom is falling out of usage in general and I won’t be sad to see it go.
And in some cases it’s difficult to line up the he/him, as in “Give this to whoever needs it.” In that case the whoever is almost pulling double duty of being the object of the preposition while needing to function as the subject in the clause “[subject] needs it”. But if you see the entire clause as the object of the preposition it works out with “whoever”.
The frustrating thing is that I know this, but because the voice in my head is my voice and has my accent, “of” and “have” sound basically the same so when I’m speed typing I accidentally write “of” and when I’m proof reading it, either out loud or in my head, it sounds the exact same to read “could of” or “could have”.
I’ve gotten around this in my professional writing by proof reading everything out loud while doing a silly accent. Or getting a screen reader to read it back in a robot voice.
But for random comments on the internet, I don’t bother, so I’ll occasionally get a helpful person explaining the mistake, and they’re always polite and I appreciate it. I just wish I knew how to make it stick when I’m actually writing.
You should watch the whole series if you haven't yet; it is phenomenal. There's another one on calculus (in addition to videos on all sorts of great stuff) but the linear algebra one is just especially mind blowing.
The class notation is still meaningful. If we were talking about your particular network mask I might ask you what class it is. Telling me would give an understanding of size or hops or whatever. Granted, it is class C 99% of the time. Probably smaller. But then I’m certainly no networkologist.
A subnet is defined by its netmask. Classes are useless nowadays IMHO.
At least for me they created more confusion than anything else. Why are there classes if the netmask defines the subnet size? Because there was a time before netmasks, just ignore them
This is simplified, like it assumes routers handle everything when that’s not really the case but hopefully it still illustrates the idea.
Your network might have 5 devices connected to it. To uniquely represent those 5 devices, they need 5 addresses. If all that exists is your own network, then any 5 addresses would work, as long as they are unique. 0.0.0.0 through 0.0.0.4 would work.
But your network is connected to a larger network, probably your ISP’s network. Let’s say your ISP also has 5 clients. If they gave their clients the 0.0.0.0 through 0.0.0.4 addresses, they would clash with your own network addresses. So maybe they’d use 0.0.0.0 through 0.0.4.0 instead.
Your ISP is also connected to another network, which is connected to another one, and so on.
Each destination on the large network made up of all these smaller networks needs to have a unique address for other devices to find them. Part of the address will be assigned by higher level routers and part of it will be assigned by the router directly connected to the device.
The subnet mask (or network mask) basically lets the router know which parts of the address have been assigned to it by higher powers and which ones it can use to assign unique addresses to its own clients. It’s a bit mask where each 1 means the higher network “owns” that bit in the address (and the router can’t change it for any of its clients) and a 0 means the router can use that bit to uniquify its own clients.
So a subnet mask of 255.255.255.0 means that the first three numbers of that IP address have been assigned to the router and the last one is free for it to assign to up to 256 clients.
If ( ( myaddress xor targetaddress ) bitwise-and mask ) gives a non-zero result, then the address isn’t on the router’s client network and the packet needs to be sent upstream. If it gives a zero, then ( not ( mask ) bitwise-and targetaddress ) will give a number that can be used to look up the physical port (or wifi info) that the router needs to use to make contact with the destination.
Lemme try: an IP is the address of your computer and only a single number. If you want to group clients you have to define a way to separate these 32bit number into a part that defines the group and a part that defines the number of the client in that group. That’s what the netmask is for. Example:
IP: 10.0.0.1
Netmask: 255.255.0.0
In binary this gets more clear:
IP: 0000 1001.0000 0000.0000 0000.0000 0001
Netmask: 1111 1111.1111 1111.0000 0000.0000 0000
The netmask is always a bunch of 1 first, then 0 until you got 32 of it. 1 define the parts of the IP that define the group, 0 the client.
10.0 is the group, 0.1 is the number of the client in our example. All clients which IP begin with 10.0 are in the same group and can talk to each other without needing a router.
Taylor series approximations work because the derivatives of the taylor series expansion and the function it is approximating are the same (and the values at the given point). Likewise, the derivative of e^x is e^x because the taylor expansion of e^x is 1 + x/1! + x^2/2! + x^3/3!.. which becomes 0 + 1 + x/1! + x^2/2! + x^3/3!.. when the derivative is taken. So the derivative of the taylor expansion of e^x is itself.
Torts, which is to say the things in civil law that will get your ass sued, but aren’t contracts. Mostly your basic personal injury stuff.
My Torts professor was a local legend, and basically left the teaching of the subject to an obsolete version of a non-mandatory text. He never asked about it, and he never built his exams around it, and only occasionally mentioned the damn thing. Instead, his exams were mostly based on recitations of facts from cases and he especially delighted in including questions based on his “tangents” in lectures, well practiced over decades of southern-fried paper-chase nonsense. I was told this about the exams, and took the second years at their word. Several old exams were also freely available for review in the law library. I spent the entire year terrified and confused, holding on for dear life to remember enough to pass. I guess I did okay, getting a B on the midterm and a C (C-minus? I honestly don’t remember) overall in the class. Since it was graded on a curve, I was clearly not alone in how I approached the material, though in retrospect actually knowing anything about torts would have helped too.
It was two years later, almost time to graduate, that I was having discussions with classmates and realized, “Holy shit! Torts have elements!” That is to say, there are actions and criteria that have to be satisfied: e.g., there must be (1) an action X taken with (2) mindset Y, that (3) results in damages Z, (4) ameliorated by concept AA or defense AB. Things get squishier around the edges than criminal law, but it’s basically the exact same analytical framework as that, a course that I (relatively speaking) enjoyed and did much better in. I mean, I guess I knew what most of the relevant concepts were, but the idea that they fit together in a logical way, not just as a mush of “whatever wins the case” was an epiphany.
Now, to be fair, if I’d done all the things that a properly motivated and earnest legal scholar is supposed to do, like heeding the cliched guidance to study two hours for every hour of class, to do all recommended reading, and to avail myself of office hours, I likely could have figured this out much earlier, but it happened how it happened, and in my defense, none of my other professors thought themselves too important and too bored to share the basic underpinnings of their subjects with their first-year students.
The one teaching Contracts totally fucked that second-year who rode a motorcycle, though.
College is about maximizing the knowledge given to you to yield the results you desire. There is no fucking way to read every text and study every single thing to a certainty of knowledge.
Some things are a cursory once over so IF it comes up later you know where to look. But a lot of it is just tangents. But testing you on tangents not in the text or study guides? Man. You had it rough.
American law schools are their own strange subculture of the education world, graduate school but not really research degrees (though a species of research is in some ways the heart of the exercise), professional schools but full of stuffy academics, and deeply, weirdly hierarchical and full of completely unearned egos. There are very few Richard Feynmans even in the finest law schools.
No one is (generally) allowed to represent clients without passing the Bar Exam, so professors feel emboldened to indulge their own personal quirks, whether that’s psychologically attempting to weed people out or simply washing their hands of any responsibility for their students’ success whatsoever.
I didn’t actually dislike the guy (he really was quite the character), but it’s fair to say that his idiosyncratic method of teaching didn’t resonate with me. After a rather stressful first semester of trying to play the game exactly so, I was doing okay, but as it went on I realized that the reward for spending all your time and doing well in law school is stuff that basically makes law school never end (big commercial jobs with 2000+ billable hours, judicial clerkships, etc.), and that LAW SCHOOL SUCKS. My GPA is thus like a modestly sloped roller coaster, going up at the start and fading for the rest of the ride, finally leveling out when I took my last semester pass/fail as a visiting student to make my long-distance relationship not long-distance.
I think mine was up and down too. I am not a lawyer and only have an undergraduate degree. However I have def had the professor that did not resonate with me. I can think of at least two that just did not work as intended. Luckily I passed both classes. But it was only because I figured out how to pass their class. Not because I took away a massive amount of applicable knowledge.
Trigonometry. My high school math teacher was a literal math genius and would always go deep into proofs and theory, sometimes not even getting to our homework stuff until the last 5 minutes of our 50 minute class. As a result I went from the “gifted” math group to nearly failing.
When I went to college I had to take a math placement test and ended up in Math 99 (below college level math).
It was there I was finally taught SohCahToa and everything clicked. I actually use simple trig a lot in my job now.
Interesting, I had an almost opposite experience. I was good enough with memorization and applying formulas in high school to pass with As but I never really understood what I was doing.
Taking calc again in college and watching a video of Neil Degrass Tyson talk about Newton figuring out orbits are conical sections made everything click for me. Suddenly I remembered the 3D episode of the Simpsons and those coin spinny things at the mall and put it all together.
After that, I was much more interested in figuring out how the formulas worked and it made learning way easier.
I had something similar except I actually got help in high school from a study hall teacher. I can’t remember her name but she had awful halitosis. Somehow, she just explained it in a way that clicked for me.
I was very bright when I was young, but unless I was given practical application of knowledge, it just leaked out of my ear.
I was exactly the same with trigonometry, I couldn’t understand it or why were even learning it.
As soon as I started to get into programming and I wanted to have a gun with a bullet that had a certain speed, and it was going at a certain angle, and I needed to break down the horizontal and vertical components of the motion, all of a sudden it felt like I had invented trigonometry myself.
I found that true of so many different things especially with math. No matter how much it was explain to me theoretically, it never made sense until I had a practical application and then it was just obvious to me.
I wish more of my education was that way instead of just learning theory.
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