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'At the stroke of midnight, your brother will be hurtling sideways at an altitude of 150 meters' is a regular physics prediction about your nonmagical trebuchet, whereas 'you are cursed to build a brother-launching trebuchet' falls out of the Lagrangian.
Sadly a lot of math heavy textbooks love to present the equations and how to use them, but do a poor job explaining how those equations came to be.
Or why you'd want to use them.
I had to do a semester of learning how to deal with Fourier Transforms, with vague mentions of sine waves and slopes, before seeing Technology Connections' video on CDs and finally understanding what all that math was actually for.
This was one of my biggest issues with math myself. Sin, cos, tan, and logarithms still confuse me. Meanwhile, derivatives (a calculus concept) are pretty straightforward conceptually with the physics examples of distance, speed, and acceleration.
Derivatives are the change in something. So if you have a graph of something's distance over time, the derivative is a graph of the change in distance at any given moment, or the speed of the object. Likewise, the derivative of the object's speed is a graph of the object's acceleration, or the change in the object's speed at any given moment.
Anyway, this is also something that I used to rant about with my programming courses in college. You need an understanding of both the concept and the execution of it in order to program with a consistent amount of success, but most courses (and learning material) focus on one or the other.
I do systems admin/engineering, and I'm the team code monkey, but my co-workers want to learn. It's still the core hurdle I see my them make when they try to script. They either have the concept down with no clue how to script it, or they're flailing script snippets around without actually understanding what those parts actually do.
Logarithms confuse me too, even though I "invented" logarithms one day when I was bored before ever being taught about them. I know they're exponents in reverse, and I know they can be useful to diminish the relative weight of larger numbers, but whenever I see logs in an equation, my degree of "I can figure out what this equation does" takes a significant hit.
Whenever dealing with exponential stuff i try to just focus on the formula of what is happening in the exponent. logarithms are taking that down to "normal space". E.g. exponential functions are like in a warp drive, but you still have ships that can warp faster than others.
I wished they had taught us more context and concept in college EE classes. I guess super smart people figure that out on their own. It took me until several years after college before things started to click a little. I'm still working on it.
Electromagnetics still seems like dark magic to me though. I hated that class because it seems like it should have been the coolest topic ever but nothing made any sense.
Maybe they need to get dumber people teaching this stuff because at some point if you are too smart you take for granted leaps that elude some of us.
I have done teaching in a Corp setting for several years, and I find that all the questions from and confusion of students really push me to explain better, understand deeper, question some of the concepts, etc. (We teach both concept and execution)
I guess either our classes needed to ask more questions or the profs needed to work on their teaching or something.
Electromagnetics are dark magic and there is no way to teach it in any simpler terms that make it plausible without dark magic.
Even if you get all the concepts down. If you start asking "why". The only real answer is, because in 73 BC an egyptian, a roman and a greek magician met in a basement in Kathargo to perform the most heinous ritual. But since the roman guy had a lisp in saying his incantation, instead of unleashing the demons of hell onto earth, electromagnetics becamse what they are.
Imagine taking a line and rolling it around a circle so that it's always touching. Like a wheel on a flat surface, but from the wheel's perspective.
Sine and cosine are the X and Y coordinates of the intersection point, and tangent is the slope of the line.
You can also relate it back to acoustics!
Woah
You should pick up some civil engineering books. I did 1 year before I realized I hated it, but they're full of lovely equation that are like [Size of sand grains] x [percentage of empty space filled with water] x ([speed of water flow] + 14) x [Bill Factor]
(We add 14 to prevent the formula from breaking down)
(The Bill Factor was created by Bill Johnson and is 3.11 when it's raining and 1.70 when it's not. It is based on practical observations and has no theoretical basis)
There is also the whole formula set that adequately describes the phenomenon. It is a three dimensional set of differential equations, where you can only ever know five out of six starting conditions, so you need to iteratively adjust the sixth one until your error term is small enough. The formula set was developed 80 years after Johnsons proposal, using the advancements in computing technology, but the results are not better than what we get with the Bill Factor
So we thank Bill Johnson every day we use his Factor.
My math literacy improved tenfold when I discovered the Springer Verlag historical approach math books in college.
I have some sort of learning disability when it comes to math. I barely passed math classes in high school. I had one required math class in college, took the "anyone can pass this class" one and still got a C.
So basically, once math is involved, it's all magic to me.
Hooray ~~magic~~ science!
You might have dyscalculia. It's best described as 'math dyslexia' and heavily impacts a person's ability to do math
It could be, but I don't mix up numbers, I just can't grasp concepts. Equations mystify me.
I wonder if I have this. Edit: no I don't think I do.
One of the symptoms of ADHD, as I understand it, is difficulties with symbol decoding (I think that is what it is called). I think it may be related to poor working memory. Say you want to decode a substitution cypher. With ADHD you have to keep referring back to the decoding chart more often than those without. (I took a test on this as part of my diagnosis and I sucked at it).
I think maybe that affects understanding equations with all the symbols and Greek letters and such?
That may be my problem. My daughter was diagnosed with ADHD and although I've never gotten an official diagnosis, her symptoms are pretty similar to my experiences, so it's entirely possible I have ADHD and this is an ADHD thing.
ADHD is very heritable, almost as much as height. So it is pretty likely, indeed.
PS: I can grasp math concepts if explained in certain ways. I had to take a below grade level math class in middle school and needed a tutor for algebra. I blame the teachers lol. I somehow managed to get through all the math in my engineering degree (wtf was I thinking?).
Later on in life I struggled to understand Kalman filters until an online course explained it in a really accessible way, and related it to another class that was well taught on Bayesian statistics. It all clicked. But if I stare at typical math textbooks, it might as well be written in hieroglyphics. It just doesn't sink in.
I felt the same way until I had to take a statistics class for a second bachelors I'm working on as a middle aged person. The class was "statistics for non STEM majors" and the extremely chill, aging surfer dude prof approached it like we were all easily spooked horses and math was a snake.
He didn't even tell us when we took our midterm, he told us it was a quiz that he was offering lots of extra tutoring sessions for. He didn't tell us until weeks later when someone asked when the midterm would be. He really went out of his way to explain down to the roots of each equation about how and why it works.
By the end of it I didn't feel like I was missing the part of my brain that can do math anymore.
A lot of math involves just moving things around until the problem is easier. It's just a bunch of tricks that work for relatively simple reasons. But you just memorize them to make it easier.
Statistics is more like magic than other kinds of math. Like when you have more than 30 random unbiased selections from a population you can start guessing at the composition of the whole, no matter how large it is. The explanations require someone who really knows what's going on.
Then you have modern LLMs that use statistics to produce the next word in a sentence. They can be so complex the designers don't really know why they do what they do. It's just trial and error testing the outcomes.
Biology bs required 5 units of physics, physics was 3+1 for the lab. I haaaaate physics, love my chemistry, I'm pretty bad at higher math, physics just tries to be as tricky as possible while hiding behind the shroud of "this is how it works in life". They made a "physics for biologists"class which was as much practical application of physics as they could put into a 1 unit 1 night per week course. I learned more, better, talking point physics in that class than any other.
Finals week was an optional "sasquatch" lecture that was open to anyone we wanted to bring, it was attended by more people than were actually in the class.
We learned how drag coefficients worked, how a great white child swim from California to Japan in 1 bite of food, how a blue whale and a bacteria both use the same amount of energy to move a distance. How terminal velocity means you can't drop a mouse to it's death. The optics of eyes.. greatest physics course ever.
There is a real good argument to be made that math is a language.
So you didn't fail math you are just illiterate. Not really sure if that is better though...
I'm terrible with human languages too. I barely made it through French.
And computer languages. I've tried learning C and Python and Java multiple times and it just baffles me.
So yeah, apparently the language center of my brain is entirely devoted to English.
I really love science and I do try my best to understand it, but I realize I can only ever do so at a superficial level.
"I'll take 'I am not good at math so ELI5 the joke to me' for $100, Alex."
Magie ist Physik durch wollen.
Muss man Wissen!
DIE REICHSFLUGSCHEIBEN!!
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