To the Engineer, close enough is perfect. To the Artist/designer, there's no such thing as perfect. To The Mathematician, there's nothing except perfection.
And to the philosopher, they are all just opinions, and the definition of "opinion" is debatable, and the definition of "definition" is debatable, and the definition of "debatable" is debatable - but this is all just their opinion. But what actually is _their_ "opinion"? It's debatable.
Seems engineering courses have degraded since my day. Then we understood the mathematics and the physics AND how to use them practically. I often dispair of new grads; luckily most of them will spend their lives writing software!
@@markhickson9087 Ah, so it is a result of the times, not just different locations. I haven't studied engineering on a university, but what we have here are engineering schools. Usually they take 5 years to complete and the common ages for students in those schools are 14-19. I attended one of those for information technology during the 90's. (It was way more about analog things than today, minor mentions of networks ect. But we did cover electricity on an atomic level up to Radar.) We also had to do the calculations ourselves. (We had one guy in class with a calculator the price of todays expensive smartphones, his calculator could do everything. But as it would have given him an "unfair advantage" he wasn't allowed to use it in all the tests.)
@@markhickson9087 depends on the engineering course I guess, I mainly did process engineering.. But I still had to do a ton of physics stuff in my first year (which school did not prepare me for, at all, many sleepless nights were had catching up)
A mathematician, an engineer, and a statistician were out hunting in the woods. They crested the top of a hill, and saw a deer standing in the distance. Not wanting to get the shot wrong, the mathematician took some readings of the ambient air temperature, pressure, and wind speed, did a couple pages of calculations, and finally arrived at a number. Then he lifted the rifle to his shoulder, aimed to the precise angle that would hit the deer, and fired. The bullet missed, about 10 meters to the left. The engineer scoffed "Oh geez, gimme that." And he took the gun, removed the scope, bolted it back on crooked, then handed it back to the mathematician. "There." He said. "That should account for your error. Now take that exact same shot again." The mathematician fired again. The bullet landed 10 meters to the right. "We got him!" Cried the statistician.
Don’t get me started on Physicists and Mathematicians. I remember a moment in my Quantum Mechanics class in grad school the instructor paused, turned to the class and asked “are there any mathematicians in here?”. No one raised their hand. He then sighed relief and said “good, I didn’t want to have to justify what I’m about to do”. He then pulled a differential through an integral sign.
If you really want to see something that will send you over the edge, go look at feynmans path integral quantization. Where we define the propagator from the inverse of the differential operator. It will send a mathematician onto lala land and is foundational to particle physics. A nice concise example is from Zee’s book ‘Quantum field theory in a nutshell’ pgs 21-23. Another good example that’s not quite so concise is Ryder’s ‘Quantum Field Theory’ pgs 187-191.
No problem. I wasn’t tryin’ to be a dick or anything either, nor am I by pointing out that repeating the phrase “theory and practice” doesn’t make it confusing, just clunky. At least, that’s my native English speaking opinion Maybe it’s just cuz I already knew the quote tho? Idk. But it seemed easy to follow along with to me
ya boi I get where you’re going, but that doesn’t make any sense here. Because you’re saying, “In theory, there is no difference between theory and practice. In practice, there is. At least in theory, but not in practice.” which is a direct contradiction with what was just said. It doesn’t make any sense. In theory, theory is the same as practice, but in practice, theory is the same as theory (which is the same as practice)? Which means that there is no difference between theory and practice. So the whole thing is completely meaningless except to really emphasize that there is no difference between the two
Yeah I think a lot of the difference is that most engineers have to over design the hell out of things. I think from my engineering school days we we’re usually designing with a safety factor of like 2 or 3 so there’s a lot of wiggle room lol.
To a mathematician, a proposition is either true, false, undefined or unknown. This requires two bits of information. To a physicist, ANYTHING in the real world is at best approximately true. What matters is the accuracy of predictions, or more often, the order of magnitude of the relative error. This relative inaccuracy is represented by a floating point number with about 10 bits of information. For the mathematician, "Earth is a sphere", "Earth is an ellipsoid" and "the Earth is flat" are all equally false. To the physicist they are all approximations, but with radically different inaccuracies. She will pick a model based on what level of precision is need for a given situation. The engineer doesn't care either way, he does whatever the Best Practice tells him to do.
@JOSE MENDOZA it's the type of engineering they teach to kids that are so dumb they must take a major and they will fail st everything else so they get their own class at least that's how it's here the class has only 7 kids 3 of them i know to be so dumb you could give them the answers for a test and they couldn't pass
There is a joke my father told me once when I was child. He had dropped out from Physics, and is now a great carpenter. I'm now a Mathematics student. In a certain town, once was promoted a competition for the construction of bridges. One engineer, one physicist, and one mathematician were asked to make the best bridge possible, the perfect bridge. The engineer worked like he always did. He made the project, and in a few months the bridge was up. The bridge was good enough. The physicist took longer to make his bridge. By the end of the year, his bridge was up too. It was also good. The mathematician still had to hand in his project, though, so the competition was still not over. People waited for him for a long time. Days, months, years passed, and nothing from the mathematician. The people kind of just forgot about the competition, and it was left without conclusion. The town had two new bridges, and people used them in their daily lives, and they eventually payed no mind anymore to the competition that originated those bridges. Decades later, however, a student found out about the competition, and wondered "What about the mathematician?". The student went to the university, looking for the mathematician, and found his office. The student knocked on the door. A raspy voice responded "Come in.". The office was small and cluttered with paper, in piles, covering the desk, bursting out of drawers, and even piled over a couple of chairs. Sitting behind the desk, was a very old man. The student greeted him, and questioned him about the competition. "Why didn't you hand in your project? Did you forget about it? Did you give up?". The mathematician looked up to the student. "No. I've been working on it this whole time.". "And... do you already have an idea of how the bridge is going to be?", the student asked. To which the mathematician responded, excited, "No. But I know now, that the perfect bridge, it exists and it's unique!".
I feel like the physicist's bridge would be made of some absurdly expensive, practically non-existent radioactive material with a half-life of only a few hours, that would quickly collapse as the material decays but for the few moments the bridge stands it would be the closest thing possible to perfect.
The reason people hate maths is because once you sleep through fundamentals it just becomes algorithm memorisation. We did intuitive proofs at school and shit but I was immature/hated it. Cool stuff like why pi is pi and thinking about platonic solids etc.. I would say trig is what fucks most people up in calculus, I have to catch up on trig...or just use that tempting table hmmm
@@marusdod3685 I am in CompSci, I did advanced maths. Nothing on the level of a maths major, but compared to the general population...you get my point. I struggled most with trig fundamentals tbh. Many people do. Knowing it really helps your mathematical intuition- in my opinion more so than anything else in high school maths.
CS major here as well, just wanted to confirm that my lowest exam grades for calc 1 & 2 were when sections on trig were tested. Never got into it, never liked it. Must be a CS thing ¯\_(ツ)_/¯
@@WallabyWinters I'm a Practicing Civil Engineer emphasis on Structures, and I've never once integrated by hand. In fact.. I probably used integration like 2 times in the last 3 years lol. ALOT of the math you do in school you never see again depending on what your specialty is..
@@wedmunds If you're in academia yes but out in the real world not really friend. I'm saying this based on real working experience with Engineers and 'Scientist' integrating by hand is a waste of time
Engineers: Makes reasonable assumptions and approximations to make their calculations easier and more useful Mathematicians: *And we took that personally.*
Nope, we do that so there even exists a solution. Most engineering problems are simply Not solvable with Mathematics or computational Power without these assumptions and approximations. So it's the mathematicians fault for not having adequate methods to solve these problems. Sometimes they even get pesky and prove these problems are unsolvable without assumptions.
@@karlmartell7600 Pure engineers don’t solve that equation, and they don’t derive ways to compute special cases either, it’s the mathematicians coming up with ways to approximate. Most engineers only use those methods on a daily basis, but without further education in math, they can’t find legitimate new ways to “approximate”.
Engineering majors be like "what real world usage or application does this hypercomplex mathematical equation have?". Mathematicians say "None whatsoever. But aren't maths beautiful?"
@@ryanalving3785 I think I would agree with you, however my understanding of pure mathematics isn't quite as expansive as I'd like. Complex numbers and quaternions where at one point pure math with no real world application.
Yes because we all know the mathematicians aren't getting the money the engineers are. Mostly because we know how to actually apply this stuff to the real world and not some perfect ideal world.
@@tony91200211 Yes, we all know engineers are not getting the money football/soccer players are because we actually know how to apply ball mechanics and not in some "real world" computer
As an engineering student, the thing I can't stand the most in my classes is when the professor says the solution to a complex integral is "trivial". Like maybe it is to you and maybe for some students, but it'd be nice to get a reminder on how to do some calculus every now and again.
I have the exact same feeling as you. I always go check all the details or equivalently learn the math behind it on my own. After several times I found that it's not trivial for a student, it's important for a student to learn that by themselves, however that trivial means it's trivial for engineer teachers teach those math in class or state them in engineering teaching books. As a result, you need to have really really good math backgrounds to understand what teacher says and book tells. At least it's how I understand what does trivial actually means.
@jocaguz18 More significantly, it's trivial FROM WHICH ASPECTS. Is it trivial from the aspect of precision? Is it trivial from the aspect of learn&practice because when you actually use the result you don' t need to know how they derive it 'because we already have common standard in industry level' and everyone needs to follow that meanwhile we have no need to manipulate more precisely? Have you ever understand why did teach say it's trivial?
@jocaguz18 Oh yeah, you are partially right. I see you know calculating by hands consumes lots of time, one way of how do people judge performance is efficiency, and calculator or computer may replace analytical method in the field which you know pretty much.
@jocaguz18 Well someone commended my comment and that reminds me of this conversation. We don't need to prove it everytime, yes, but we need to prove it at least once. All the AI learning algorithms have corresponding math derivation or math structures, computer only help to do logic or math operations. And I don't really care what about teachers say, you need to have your own thoughts on your attitude and methodologies about your career.
@@gianlucamolinari3490 It is supposed to be a joke about limits (the rigorous way to do a limit is with an epsilon-delta proof). The starting line of the proof is always: let epsilon>0
Sometimes I am in awe how people figured out the theorems where engineering stands so proudly of and then I hear a mathematician explain it and then I remember why I never bothered looking deeper into the foundations.
A lot of engineering theorems are just rule of thumb versions of what you get when you derive things from a lower level. Academic engineers and physicists are likely to be responsible for a lot of those, and mathematician for some of what they looked at to make those rules of thumbs.
Yeah, no girls in my classes. In my country they are heavily discouraged by teachers in high school and their parents at home so they don't study engineering.
Nissim Levy orrrr she’ll be impressed by your intelligence and be more attracted to you, sadly this is just a theory and has not been effective in practice yet 😔
See its funny, am just in first year engineering ATM, so things might change, but I have never touched a table of integrals, we either do by hand or we get out fancy engineering calculator to do it for us.
Got my BChE (Bachelor of Chemical Engineering) University of Delaware (1986), worked 2 years in Rohm & Haas Chemical Research, got my Masters (1991) in Math + PhD (2000) in Math in differential algebra. Worked my ass / brain off for all of them. But, the pure abstract math was just orders more difficult than anything I ever did in engineering, as hard as engineering was. I was not prepared for the level of abstraction for graduate level math. Ended up taking undergraduate math courses in graduate school, in spite of having taken a year of Abstract Algebra (1987-1988) at Villanova University, and one semester of Advanced Calculus (spring 1987) at Drexel University. Fell into a deep depression in first semester of graduate school (fall 1988) due to being way in over my head. I still have no idea what most professional-level mathematics is proving or saying, in spite of having seen and heard the terminology over and over. 99% of all the professional-level mathematics I see is defining spaces (of functions or maps) and maps between those spaces. Maps & spaces. Maps & spaces. Maps & spaces. The math I work on now is much more combinatorial. On an off-topic, I wish people who know NOTHING about either math or computer programming, who have done neither (I've done a LOT of math, and a LITTLE programming) would stop IDIOTICALLY equating or comparing the two. THEY ARE TWO COMPLETELY DIFFERENT ACTIVITIES! Yes, BOTH are all about MANAGING COMPLEXITY. Yes, BOTH use/apply logic formally. But computer programming is all about GETTING A COMPUTER TO DO SOMETHING. Mathematics is all about PROVING THEOREMS: STATEMENTS ABOUT WHAT IS. STATIC PROPERTIES. Even the most computational math and formula-finding does that or is that.
I still remember my first math 1 class. The professor literally said "We use exact numbers here, not like those physics ones, they like to approximate everything".
Well yeah...of course, in practical science you have to approximate everything...how accurate can these measurements be? Eventually you'll have to round because the that's just the nature of taking measurements of real-world data. Trying finding a mass scale that can do irrational numbers.
@@sulblazer my father was an EE student, he said that an approximation of even ±10 is trivial... Then when I showed him my school textbooks (yeah, in my country all first year topics in science stream, for engineering or for pure science and maths are taught in the last 2 years of high school and in every school) he was like: yeah that's ok, you people are not allowed to approximate... Remember Kalpana Chawla? She died in the upper atmosphere cause her space shuttle exploded cause THE SPEED OF ENTERING THE ATMOSPHERE WAS APPROXIMATED and it's was slightly high ... Blah blah blah... Yeah I know your gen is absolutely screwed... But anything for safety, u get me, right? 😀🙂😐😑😑😑😑
@@anirbanroy5667 that just sound like the shuttle wasn't designed well, for safety reasons most things should be able to withstand significantly more force than approximated requirements.
When a mathematician sees a formula which was obtained not through derivation, but rather through rigorous testing and analysis of data to create a model for a given property of a substance:
@@JackBlackNinja no, even in pure math, wait till they try integrating as limit of a sum for area... Or even try to find the value of π ... (This question is the worst question ever, cause as a CS student, we had code this shit up, and I will be frank, had no idea what to start with)😂
I once solved an exam question, but I was off by a factor of 2. Couldn't find where that came from for the hell of me. Then I found a cool approximation: We know that n = n+1 for large values of n. Substituting 1 in that expression teaches us that 1 = 2 for large values of 1.
@@witchBoi_Connor It's an approximation. There are very few contexts where 100,000,000,000 is meaningfully different from 100,000,000,001, so for sufficiently large numbers it's okay to act as though n=n+1 even though that isn't strictly speaking true. This person was making a joke about applying that to small numbers.
I mean either it has a dude's name attached (ohms law) or the book has a series of proofs leading up tothat equation, which my professor copied onto the slides and breezed through in 20sec. And i then copied the boxed equation into my notes and called it good enough.
Pragmatism. If your precision is going to be truncated by superfluousness anyway who cares? For example. If all you care is if a value is larger than 1 why does it matter if it's 1.2 or 1.232423874392744? Both of those things are identical in the context you care about. This is why I have not yet met a "mathematician" that was any good at engineering. Whilst I have met plenty of engineers who are great mathematicians.
I love that you and Andrew make videos in which you take stabs at each other, all in good fun. It is important to point out the frustrating differences that scholars encounter between these disciplines; more importantly, that these differences should not be allowed to be polarizing lines of division between fields that are so intrinsically cooperative. Great job guys! Please keep the content coming :)
Like my chem eng proffessor says. A scientist and a mathematician would spend weeks on one thing. While an engineer would have moved on to something more interesting.
I'm not sure if this was part of the joke, but the fact that pi² ≈ g is a historical artifact which pretty much depends on the "fundamental theorem of engineering". Namely, the meter was originally defined by the French to be the length of a pendulum of period T=2 seconds. The exact formula involves pi and g, and is derived using the small-angle approximation sin(x) ≈ x. Props to these guys, if this was thought out in advance.
One reason civil engineers are always approximate is cause the small numbers don't really matter as we will always times the required amount by a safety factor anywhere between 1.5 - 2x then use the next size up for standard construction sizes.
Yeah that’s a conservative estimate too. For concrete structures the eurocodes have a 1.5x safety factor, but then the concrete manufacturers often overshoot the required compressive strength by MILES. I worked on a construction site where the concrete structure was calculated on the basis that the concrete with a nominal 35 MPa compressive strength had a compressive strength of just 22 MPa to be safe, but the concrete used ended up having a strength of over 80 MPa. Basically 4x safety factor all in all
@@whateverreally1347 And then the mining engineers wow, they don't even know what the roof is made off so they can do like 5x or 6x safety factors wowza.
I remember being being caught by the approximation thing in university. In my pure math class we'd been looking at a formula with first order and second order terms. Most of the lesson was spent proving that the first order term approached zero. Then I walked into my physics class and the prof had the same equation on the board. "The first degree term will be swamped out by the second degree term, so we can just ignore it," he said, and simply crossed out the troublesome term.
But honestly, it takes a pure mathematician to prove that it approaches zero once, to give all physicists and engineers the "license" to cross it out whenever they feel like it. Pure mathematics has ironically been the source of all approximations applied subjects take for granted lol.
I'm an engineering student and in my school, the professors will explain and show the derivation of each formulas before we can move on to the actual problem... In this way, we can understand where did it came from and it's really helpful and fun knowing how go derive the formulas rather than memorizing it hahahaha
I know this is a joke on the competition between mathematicians and engineers, but a lot of this isn't true, in my experience. In my Engineering mathematics classes at University (aerospace systems engineering), we always had to understand the derivations of equations, and why they worked. Even in fluid mechanics modules, we had to be able to derive bernoullis equation from first principles in an exam. Not a very mathematical example I know. But engineering mathematics classes were basically pure maths, with barely any actual real world uses. The one area I remember using lookup tables was Control engineering, where we used lookup tables for Laplace transformations. We had separately, previously learned the maths in the engineering mathematics module, but you don't want to be fannying about with maths when you've got a complex system to model, when you can easier and quicker just move between domains using a table.
Same. I'm studying mechanical engineering at a german university and most of the time the profs always explain the derivations of equations. In fact, it feels like we are more of a scientist than an engineer because of all the theories that we have to learn and that's also why at the end university students have a bachelor of science degree,not bachelor of engineering,which you would get if you study at a university of applied sciences i.e Fachhochschule
This was also my case, Calc 1-3 was all about understanding everything and solving by hand. Then in mechanics and other courses we could use shortcuts for the calculations needed because the focus was no more on the mathematics side of things.
My professor told me a story about a guy he used to work with. He was an ex-nasa engineer and was a senior engineer at their company. He tasked a junior engineer with creating a solution to a problem. Junior gets to it and fervently works for the next two weeks. By the end, he solved it perfectly and turned it in. The senior engineer said "Wonderful! You got it figured out. Your solution is great but let me show you something real quick." He then grabbed a note card and showed this junior engineer another solution to the problem in about 15 minutes. There are some things that you just learn through experience and getting too much into the nitty gritty will end up slowing you down when a perfectly acceptable solution could be found in only 15 minutes!
It is so cute you think you learn the derivations. But really it is just a peak in the magical world of math. I studied physics and they never proofed something rigoursly in theoretical physics except they had a co lecturer from the math department. Anyway you wouldn't be able to shuffle through the science if you are hold up math concepts your probably don't need to know in this detail.
Back in the day CS majors used HP calculator like Business majors used. Unlike the TI that the rest of engineering used. I never took any math for engineering as my department was tied to the hip with the math department. Cal 3 ruined math for me prior to that I did math in my head (number sense) still got the A. Oddly enough I struggled with Discrete had to take the course twice which was the only time in my life. I did use ML when I had difficulty, not sure it’s still used but Fortran and Cobalt are still being used by companies to this day.
There where some equations that for whatever reason where easier for me to under stand after I programed it.. I guess maybe because the breakdown was more granular? Any way I only passed calc because I pass discret mathematics
Program? More likely it's just sticking together a bunch of libraries and getting a binary that does the job in the most inneficient and cumbersome way, with a bunch of bugs that they don't even know where they come from.
Sure. Why not. Doesn't matter. You're not showing the code to anybody. You're probably going to be throwing it away after the homework is done. Feel free to make a poorly hacked together mess. It. Doesn't. Matter.
I was both but I was an engineer first. I remember in an math analysis class, no mathematician could calculate a simple Fourier transform because they were first trying to determine whether it existed. That’s pretty much the difference: engineers prove existence through calculation, possibly wasting time because it can’t be done, whereas; mathematicians don’t waste time calculating things that can’t be done. They just waste time proving existence that could have been done through calculation.
No, some people will have complaints if you do that. It is COMPLETELY unacceptable to use 3.14, you must use a builtin to prevent complaints. Complaints involve "the builtin is more precise", "the builtin is clearer", "the builtin doesn't require you to introduce a new variable", etc.
Pi squared = g is close enough in most applications. If I worked it out properly it's about a 1% error. Now all I need is for a company to bring enough mass to Earth so I can use g=10 m/s²
This video illustrates the big difference between engineering at a German university and engineering in the US. In Germany you do exactly what the "mathematician" asks, to a degree that makes you want to vomit after 4-6 semesters of engineering math. At one point, unfortunately, many people shut down and just push through the torture with a switched off brain :D because from semster 1 onwards it's all tailored to Dr.-Ing. (Ph.D) level and Dr.-Ing. habil. levels just like the programs for lawyers are still aiming for the high office of becoming a judge. German eduction can be very 19th-century-brutal in that regard.
Engineers are a special kind of people. Last day I found an old friend and we had the following dialogue: -It's been year since I don't see you mate. What are you up to? -Well, I'm in business engineering -That sounds cool, is it like economics or something like that? -iTs EnnGinEeeRinG!!!!!!!!!!! And he left, I'm still wondering what the fuck is business engineering.
From that approximation, you can derive that a pendulum needs to be 1 meter long in order to have a period of 2 seconds (like for a traditional pendulum clock, 1 swing of the pendulum = 1 second, therefore, 2 swings of the pendulum = 2 seconds = 1 period of the pendulum).
Those are the worst. I'm in physics, not math, but I hate philosophy classes. We've literally had discussions and yes, that's plural, about whether it's more morally correct to own a cat or a dog.
Andrew B; Michael J. Sandel, Professor of Government Theory at Harvard University Law School, has some TH-cam videos that helped me get through philosophy class.
Philosophy classes was the most anticipated thing for me during my time in the university. It was also the most bitterly disappointing. The only subject that actually made me feel like i'm wasting my bloody time, and that's telling something, considering we also had culturology, religious studies, psychology, ecology and history. While studying for a bachelor degree in Applied Math.
The fixation of mathematicians on deriving equations is very philosophical though. Both maths and moral frameworks rely on axioms and you can choose different axioms to see what the results are. Gödel’s Incompleteness theorems are relevant to these axioms. Both philosophy and analysis use the same notation for logic too.
I switched from pure math to mech engineering and holy shit I thought these were just jokes but they are actually so true. Engineering math course is so dumbed down it's hilarious.
I actually switched from physics to math in undergrad solely because I was tired of constantly using random formulas without being shown the derivation. Needless to say, math satisfied my curiosity but in turn made me a more curious person in general lol
As an engineer, they taught me like a mathematician and after that we were allowed to use look up tables,just because it's faster,and about most of the "complaints" of the mathematician if not all were addressed in my classes
My thermodynamics and fluidmechanics classes was only integrals and derivatives, proving control volume equations, for energy equations, momentum, and mass balance.
My favourite engineering class was when the professor taught us about eliminating variables that are unimportant. "Right, so when X gets large, 1/X approaches zero, so we can just ignore that." "And when X gets large in (X^2)/(a+X), you can just ignore "a", so that approaches X." The idea that you could go through an equation and just start eliminating variables because they were unimportant was so beautiful! After years of grinding through hideously long calculations to try to get the right answer, only to find you had made a trivial error somewhere, the ability to throw out the irrelevant bits was lovely.
It’s true though “Some trivial manipulation I’m not too interested in” proceeds to skip over 5 pages of solid working out and assumptions we’re supposed to know
As a physics student, Quantum Mechanics and Classic Electromagnetic Theory classes had a lot of hand wavy "This is some trivial integration that you should really know how to do so I won't waste class time doing it here" and hooo boy was that not trivial integration that I should really know how to do.
If you use Latex, Maple and Mathematica, you're a theorist. If you use Matlab and Latex, you're an experimentalist. If you use excel and word, you're a pleb.
To a pure mathematician, the (principal) square root of 2 is the (positive) number whose square is 2. To a computational mathematician, the square root of 2 is the sum of a Taylor series (or perhaps Fourier). To an engineer, the square root of 2 is whatever number you can measure off that comes close enough to having a square of 2 to make your object work as desired.
Well, LaTeX is just a way of typesetting text, it doesn't **do** anything but compile text to PDF documents. Maybe some LaTeX editors have spreadsheet capability, but it's not a feature of LaTeX itself.
As an electrical engineering student I can confirm that most of these are definitely true. We need good approximations to get stuff done, but precision is usually not required, especially when you have all these physical phenomena like resistor/capacitor/inductor tolerance and wire resistance which leads to inaccurate voltages and whatnot. Maths is considered a tool for design, but it's certainly not the only one, because, as stated first in the vid, we need to consider "real world applications".
I was a "pure mathematician" (well, math major, theoretical track) in Accounting 101. I completely disrespected that class, cut it all the time, the works. Got my ass handed to me on the first exam. Dropped the class with my tail between my legs. Folks, Accounting isn't Math. It's procedure. And if you don't respect it, it'll own you.
"confused by 'ANDREW's' question" -- actually just LOL'd. Having been an engineering student, I love this video. XD Thank you, Flammy, AND ZACH! for bringing us more awesome content! I'll go over to Zach's channel after I'm finished with this video to support \^^/
*glances at my small stash of Executive spare razors - counted at 3 and soon going to be 5* I shave sparingly, but when I do, they are good both in sink and in shower.
I was studying the use of Laplace Transform in AC circuits for my Circuits and Systems course and it stated, "The inverse of Laplace Transform gives you the function itself. For now, we just assume that the statement is true since its proof is beyond the scope of this book". And I was like great!. This is something I love about engineering. You never bother about proving complex mathematical stuff.
This video reminded me of a course I took on optimization methods in the engineering department. I ask the professor a question and he, as soon as he found out that I was from the economics department, said: you guys from economics don't take math seriously, that's why you have this doubt (I laughed)
Somebody described it really well. "Mathematicians try to put everything into variables, applicable to any virtual situation but they don't have much concentration on a "real world" problem. Engineers work with a specific case to sole a specific problem, instead of virtualising everything for substitution."
From being a (computational) math major for undergrad that went to grad school for EE ~30 years ago, this definitely brought back some memories. 😊 I don’t remember my profs taking quite the same shortcuts….but I seemed more comfortable following the derivations than others who were the engineering undergrads. 😏
I'm studying Engineering and we don't normally see formal proofs of math concepts but often teachers give an explanation of how formulas and laws are derived which I think is really important for students to at least understand so they can apply those concepts correctly in the real world and not just try to apply something you learned by root memorization.
To the Engineer, close enough is perfect.
To the Artist/designer, there's no such thing as perfect.
To The Mathematician, there's nothing except perfection.
And to a physicist, almost everything is relative😂
@@anirbanroy5667 hahaha
@@anirbanroy5667 this is golden
And to the philosopher, they are all just opinions, and the definition of "opinion" is debatable, and the definition of "definition" is debatable, and the definition of "debatable" is debatable - but this is all just their opinion. But what actually is _their_ "opinion"? It's debatable.
@@RuyVuusen we need more subjects
To quote my professor
"We don't solve integrals, that's what mathematicians are for."
When I start engineering this Piss me off a lot but then I understand that in order to do big things you need to trust others and let go things.
Because we engineers stand on the shoulders of mathematical giants.
Seems engineering courses have degraded since my day. Then we understood the mathematics and the physics AND how to use them practically. I often dispair of new grads; luckily most of them will spend their lives writing software!
@@markhickson9087 Ah, so it is a result of the times, not just different locations.
I haven't studied engineering on a university, but what we have here are engineering schools. Usually they take 5 years to complete and the common ages for students in those schools are 14-19. I attended one of those for information technology during the 90's. (It was way more about analog things than today, minor mentions of networks ect. But we did cover electricity on an atomic level up to Radar.)
We also had to do the calculations ourselves. (We had one guy in class with a calculator the price of todays expensive smartphones, his calculator could do everything. But as it would have given him an "unfair advantage" he wasn't allowed to use it in all the tests.)
@@markhickson9087 depends on the engineering course I guess, I mainly did process engineering.. But I still had to do a ton of physics stuff in my first year (which school did not prepare me for, at all, many sleepless nights were had catching up)
“I literally hate engineering, it’s the worst shit ever.”
Hey he’s an engineering student
Yup, that's how most of us in engineering feel lmao
Lmao as a mechanical engineering student, this is so true
Unless if you're in EE: "oh hey I just made a taser, engineering is awesome!"
@@timotheeandru Oh boy I can’t wait to pursue a Masters in this field
@@MkiSaskTheGlumpSod good luck!!! But RIP to your sleep and leisure time 😭🤣
A mathematician, an engineer, and a statistician were out hunting in the woods. They crested the top of a hill, and saw a deer standing in the distance. Not wanting to get the shot wrong, the mathematician took some readings of the ambient air temperature, pressure, and wind speed, did a couple pages of calculations, and finally arrived at a number. Then he lifted the rifle to his shoulder, aimed to the precise angle that would hit the deer, and fired. The bullet missed, about 10 meters to the left. The engineer scoffed "Oh geez, gimme that." And he took the gun, removed the scope, bolted it back on crooked, then handed it back to the mathematician. "There." He said. "That should account for your error. Now take that exact same shot again."
The mathematician fired again. The bullet landed 10 meters to the right.
"We got him!" Cried the statistician.
They need be the same units. Otherwise the statistician incorrectly calculated the sample mean.
@@Grassmpl The error has been noted and corrected. Thank you for pointing it out.
I'm just posting this here for when this joke is relevant for me as it is gold
@@cheeseninja1115 same
How did he get him pls explain
"approximately is the same as equals. well, approximately. " This was glorious.
Thought you were fake until I realized you changed your profile picture 😂
≈==
So is it ≈== or ≈≈= ?
Pyth By his words: ≈==≈
Lol
Don’t get me started on Physicists and Mathematicians. I remember a moment in my Quantum Mechanics class in grad school the instructor paused, turned to the class and asked “are there any mathematicians in here?”. No one raised their hand. He then sighed relief and said “good, I didn’t want to have to justify what I’m about to do”. He then pulled a differential through an integral sign.
What? What????
Please tell me you asked him to explain that?
If you really want to see something that will send you over the edge, go look at feynmans path integral quantization. Where we define the propagator from the inverse of the differential operator. It will send a mathematician onto lala land and is foundational to particle physics. A nice concise example is from Zee’s book ‘Quantum field theory in a nutshell’ pgs 21-23. Another good example that’s not quite so concise is Ryder’s ‘Quantum Field Theory’ pgs 187-191.
I am not a mathematician but I will surely check that out.
QFT is awesome! Enjoy!🙂
The difference between theory and practice is that in theory, theory and practice are the same thing but in practice, theory and practice are not.
You kinda botched that one a bit. It’s,
“In theory, there’s no difference between theory and practice. In practice, there is.”
@@littlefishbigmountain i know, i just wanted to make it confusing haha but anyway thanks for your comment
No problem. I wasn’t tryin’ to be a dick or anything either, nor am I by pointing out that repeating the phrase “theory and practice” doesn’t make it confusing, just clunky. At least, that’s my native English speaking opinion
Maybe it’s just cuz I already knew the quote tho? Idk. But it seemed easy to follow along with to me
@@littlefishbigmountain at least in theory, but not in practice
ya boi
I get where you’re going, but that doesn’t make any sense here. Because you’re saying, “In theory, there is no difference between theory and practice. In practice, there is. At least in theory, but not in practice.” which is a direct contradiction with what was just said. It doesn’t make any sense.
In theory, theory is the same as practice, but in practice, theory is the same as theory (which is the same as practice)? Which means that there is no difference between theory and practice. So the whole thing is completely meaningless except to really emphasize that there is no difference between the two
"Actually this is what we called proof by shut the hell up"
I actually laughed when he said it 😂
aka Proof by Intimidation
LMFAO!!!
how to win an arguement 101
Actuality happened to me.
What I've learned in Engineering focused math classes about the approximately equal sign, is that it just means "close enough".
lel
Yeah I think a lot of the difference is that most engineers have to over design the hell out of things. I think from my engineering school days we we’re usually designing with a safety factor of like 2 or 3 so there’s a lot of wiggle room lol.
“Why be right when you can approximate” ~Engineers
Still trying to recover
:D
@@PapaFlammy69 can we get that on a shirt?
"why be approximate when you can assume"
- Physicist
@@alenasenie6928 "Ok, so if we assume the cow is a friction-less sphere acted on by near-earth gravity...."
To a mathematician, a proposition is either true, false, undefined or unknown. This requires two bits of information.
To a physicist, ANYTHING in the real world is at best approximately true. What matters is the accuracy of predictions, or more often, the order of magnitude of the relative error. This relative inaccuracy is represented by a floating point number with about 10 bits of information.
For the mathematician, "Earth is a sphere", "Earth is an ellipsoid" and "the Earth is flat" are all equally false. To the physicist they are all approximations, but with radically different inaccuracies. She will pick a model based on what level of precision is need for a given situation.
The engineer doesn't care either way, he does whatever the Best Practice tells him to do.
This integral is hard because its on the back of our table of integrals.
That had me dying.
I once had a thermodynamics professor tell me to never actually do integrals in his class
@JOSE MENDOZA it's the type of engineering they teach to kids that are so dumb they must take a major and they will fail st everything else so they get their own class at least that's how it's here the class has only 7 kids 3 of them i know to be so dumb you could give them the answers for a test and they couldn't pass
lmao. Imagine actually integrating lol
@@feritperliare2890 ככה זה בארץ?
@@terner1234 לפחות באויר תקשיב אני הייתי בכיתה שלהם יום לפני הבגרות וזה הרגיש כאילו מסבירים למה להתיישב על שולחן זה רעיון גרוע
There is a joke my father told me once when I was child. He had dropped out from Physics, and is now a great carpenter. I'm now a Mathematics student.
In a certain town, once was promoted a competition for the construction of bridges. One engineer, one physicist, and one mathematician were asked to make the best bridge possible, the perfect bridge.
The engineer worked like he always did. He made the project, and in a few months the bridge was up. The bridge was good enough.
The physicist took longer to make his bridge. By the end of the year, his bridge was up too. It was also good.
The mathematician still had to hand in his project, though, so the competition was still not over. People waited for him for a long time. Days, months, years passed, and nothing from the mathematician. The people kind of just forgot about the competition, and it was left without conclusion. The town had two new bridges, and people used them in their daily lives, and they eventually payed no mind anymore to the competition that originated those bridges.
Decades later, however, a student found out about the competition, and wondered "What about the mathematician?". The student went to the university, looking for the mathematician, and found his office. The student knocked on the door. A raspy voice responded "Come in.". The office was small and cluttered with paper, in piles, covering the desk, bursting out of drawers, and even piled over a couple of chairs. Sitting behind the desk, was a very old man.
The student greeted him, and questioned him about the competition. "Why didn't you hand in your project? Did you forget about it? Did you give up?". The mathematician looked up to the student. "No. I've been working on it this whole time.". "And... do you already have an idea of how the bridge is going to be?", the student asked. To which the mathematician responded, excited, "No. But I know now, that the perfect bridge, it exists and it's unique!".
😆
This story takes the phrase "non-constructive proof" to the extreme! (ba dum tss)
I feel like the physicist's bridge would be made of some absurdly expensive, practically non-existent radioactive material with a half-life of only a few hours, that would quickly collapse as the material decays but for the few moments the bridge stands it would be the closest thing possible to perfect.
@@Jacob-ge1py It works perfectly for t=0, and well enough when t ~ 0
@@Pao234_ so beautiful
Mathematicians: "Do...do you approximate and round everything?"
Engineers: "You get used to it."
Forgot the second part of the quote from MiB: "Or you have a psychotic episode."
We had a simiar joke :You know youre a physics major if u approximate a horse as a sphere to make the math easier"
Ain't that the truth
Pi = 5
Except for Electronics, did that for 4 years, and now I’m an accountant.
“This one is pretty tricky, yep the solution is on the back of the table of integrals”
The reason people hate maths is because once you sleep through fundamentals it just becomes algorithm memorisation. We did intuitive proofs at school and shit but I was immature/hated it. Cool stuff like why pi is pi and thinking about platonic solids etc.. I would say trig is what fucks most people up in calculus, I have to catch up on trig...or just use that tempting table hmmm
@@abdulmalikjahar-al-buhairi9754 sounds like you never did any math past high school
@@marusdod3685 I am in CompSci, I did advanced maths. Nothing on the level of a maths major, but compared to the general population...you get my point. I struggled most with trig fundamentals tbh. Many people do. Knowing it really helps your mathematical intuition- in my opinion more so than anything else in high school maths.
@@abdulmalikjahar-al-buhairi9754 I personally think trigonometry is interesting.
CS major here as well, just wanted to confirm that my lowest exam grades for calc 1 & 2 were when sections on trig were tested. Never got into it, never liked it. Must be a CS thing ¯\_(ツ)_/¯
“but why do I have to know how to integrate by hand?”
“you won't walk around with MATLAB in your pocket all the time.”
Wolfram Alpha:
When in your life will you ever have to integrate by hand outside of school?
@@justina8143 It's not common, but some people do science for a living.
@@justina8143 in engineering duh
@@WallabyWinters I'm a Practicing Civil Engineer emphasis on Structures, and I've never once integrated by hand. In fact.. I probably used integration like 2 times in the last 3 years lol. ALOT of the math you do in school you never see again depending on what your specialty is..
@@wedmunds If you're in academia yes but out in the real world not really friend. I'm saying this based on real working experience with Engineers and 'Scientist' integrating by hand is a waste of time
*≈ = =*
such extremely important formula this is
Where's the t-shirt
≈ ≠ =
:===
:|≠| = =
:[≈] = =
=.=
C==3
Ah, yes. The basis of all engineering
Gawd, I never thought I'd encounter a context where the engineers would become viewed as the jocks. Everything is relative.
Ikr. It's like a miracle.
Me chilling as a premed
if you watch a lot of math channels and videos people make fun of the formulas
Wrong field my dude
The more you know
Engineers: Makes reasonable assumptions and approximations to make their calculations easier and more useful
Mathematicians: *And we took that personally.*
Nope, we do that so there even exists a solution. Most engineering problems are simply Not solvable with Mathematics or computational Power without these assumptions and approximations.
So it's the mathematicians fault for not having adequate methods to solve these problems. Sometimes they even get pesky and prove these problems are unsolvable without assumptions.
@thompsguy Navier Stokes. Unsolvable, as was mathematically proven.You need to make assumptions to solve them.
@@karlmartell7600sigh, have you ever heard of numerical analysis? They are considered math, not engineering. At most, it is applied math.
@@brightlin777 What has that to do with my comment?
@@karlmartell7600 Pure engineers don’t solve that equation, and they don’t derive ways to compute special cases either, it’s the mathematicians coming up with ways to approximate. Most engineers only use those methods on a daily basis, but without further education in math, they can’t find legitimate new ways to “approximate”.
Engineering majors be like "what real world usage or application does this hypercomplex mathematical equation have?". Mathematicians say "None whatsoever. But aren't maths beautiful?"
Yes but math is really beautiful, very and if you can solve them you get free hugs and a high IQ test :)
"Math is just like playing a video game!" said one mathematician, impervious of the world around him
aka my math teacher
I'm convinced that all equations that have "no practical application" are merely places where science has yet to catch up to mathematics.
@@ryanalving3785 I think I would agree with you, however my understanding of pure mathematics isn't quite as expansive as I'd like. Complex numbers and quaternions where at one point pure math with no real world application.
"Is this an engineering joke I'm too sophisticated to understand." So this is the mathematician's version of the rich meme.
Yes because we all know the mathematicians aren't getting the money the engineers are. Mostly because we know how to actually apply this stuff to the real world and not some perfect ideal world.
@@tony91200211 yes but we all know that engineers are 3rd rate mathematicians, they're not dedicated nor smart enough to became mathematicians.
@@tony91200211 Yes, we all know engineers are not getting the money football/soccer players are because we actually know how to apply ball mechanics and not in some "real world" computer
Osu! Top Replays unrelated but Osu! is a great game
@@tony91200211 In my country 90% engineers are unemployed so... mathematicians are rich bruh...
If engineers wasted their time proving everything and being accurate, we would have stuck with technology from 18th century.
*sigh* if only
It was a joke. Ofc it’s good engineers are doing their own thing, otherwise they’d jus be mathematicians
LOL
15th*
@@ellevasc good engineers are just mathematicians that like money
As an engineering student, the thing I can't stand the most in my classes is when the professor says the solution to a complex integral is "trivial". Like maybe it is to you and maybe for some students, but it'd be nice to get a reminder on how to do some calculus every now and again.
I have the exact same feeling as you.
I always go check all the details or equivalently learn the math behind it on my own.
After several times I found that it's not trivial for a student, it's important for a student to learn that by themselves, however that trivial means it's trivial for engineer teachers teach those math in class or state them in engineering teaching books.
As a result, you need to have really really good math backgrounds to understand what teacher says and book tells.
At least it's how I understand what does trivial actually means.
@jocaguz18 More significantly, it's trivial FROM WHICH ASPECTS. Is it trivial from the aspect of precision? Is it trivial from the aspect of learn&practice because when you actually use the result you don' t need to know how they derive it 'because we already have common standard in industry level' and everyone needs to follow that meanwhile we have no need to manipulate more precisely? Have you ever understand why did teach say it's trivial?
@jocaguz18 Oh yeah, you are partially right. I see you know calculating by hands consumes lots of time, one way of how do people judge performance is efficiency, and calculator or computer may replace analytical method in the field which you know pretty much.
@jocaguz18
Well someone commended my comment and that reminds me of this conversation.
We don't need to prove it everytime, yes, but we need to prove it at least once.
All the AI learning algorithms have corresponding math derivation or math structures, computer only help to do logic or math operations.
And I don't really care what about teachers say, you need to have your own thoughts on your attitude and methodologies about your career.
If your in your 3rd year and you can't integrate literally everything then you fucked up in calc 2
Let's get a moment of silence for the engineers who just realized they chose epsilon < 0 on their pre-lab.
What is epsilon? 😅😂
@@gianlucamolinari3490 It is supposed to be a joke about limits (the rigorous way to do a limit is with an epsilon-delta proof). The starting line of the proof is always: let epsilon>0
F
Ive made this mistake once
💀
Sometimes I am in awe how people figured out the theorems where engineering stands so proudly of and then I hear a mathematician explain it and then I remember why I never bothered looking deeper into the foundations.
A lot of engineering theorems are just rule of thumb versions of what you get when you derive things from a lower level. Academic engineers and physicists are likely to be responsible for a lot of those, and mathematician for some of what they looked at to make those rules of thumbs.
My math teacher once said: "Math is a strong, independent subject that ain't need no applications!"
Tfw ur prof been listening to too much beyonce
Sounds like a feminist
@@InsertTheCoin1997 Lmfao
@@InsertTheCoin1997 That's the joke
@mrdoe97 Nice try, but math ain't need no boys to work., It needs man!
My professors were never like that, usually when someone asks for where an equation comes from they just put it as an exercise on the homework
I hate when that happens. Makes you want to strangle the nerd that asked.
F
"Any questions?"
*raises hand
"Ok! We have our first question for the assignment."
*lowers hand
@@masteranimation2008
I always wanna strangle the nerds that beg for more homework.
So they learn to never ask again xD
>Instantly leaves at “Real World Applications.”
It’s adorable.
Welcome to Electrical Engineering, where numbers are imaginary and so are the women. 😭
Especially in the Black Magic (radio frequency) specialization
😆
Hey! I'm pretty sure I'm not imaginary haha
Though it sure is quite hard to find other girls in EE 😔
Don't forget mechanical engineering
@@niloofarjamshidi7731 there are not that many girls in engineering in general haha
Yeah, no girls in my classes. In my country they are heavily discouraged by teachers in high school and their parents at home so they don't study engineering.
“Hey we found the virgin, already! That was pretty quick”
-anyone who hears someone ask to do actual integration in ENGR
Nissim Levy orrrr she’ll be impressed by your intelligence and be more attracted to you, sadly this is just a theory and has not been effective in practice yet 😔
@Nissim Levy yeah okay
See its funny, am just in first year engineering ATM, so things might change, but I have never touched a table of integrals, we either do by hand or we get out fancy engineering calculator to do it for us.
Michael Gonzalez my bf and I are studying physics
Hahahahahhahaha so trueee
Got my BChE (Bachelor of Chemical Engineering) University of Delaware (1986),
worked 2 years in Rohm & Haas Chemical Research,
got my Masters (1991) in Math + PhD (2000) in Math in differential algebra.
Worked my ass / brain off for all of them. But, the pure abstract math was just orders more difficult than anything I ever did in engineering, as hard as engineering was. I was not prepared for the level of abstraction for graduate level math.
Ended up taking undergraduate math courses in graduate school, in spite of having taken a year of Abstract Algebra (1987-1988) at Villanova University, and one semester of Advanced Calculus (spring 1987) at Drexel University.
Fell into a deep depression in first semester of graduate school (fall 1988) due to being way in over my head.
I still have no idea what most professional-level mathematics is proving or saying, in spite of having seen and heard the terminology over and over. 99% of all the professional-level mathematics I see is defining spaces (of functions or maps) and maps between those spaces. Maps & spaces. Maps & spaces. Maps & spaces. The math I work on now is much more combinatorial.
On an off-topic, I wish people who know NOTHING about either math or computer programming, who have done neither
(I've done a LOT of math, and a LITTLE programming) would stop IDIOTICALLY equating or comparing the two.
THEY ARE TWO COMPLETELY DIFFERENT ACTIVITIES!
Yes, BOTH are all about MANAGING COMPLEXITY. Yes, BOTH use/apply logic formally.
But computer programming is all about GETTING A COMPUTER TO DO SOMETHING.
Mathematics is all about PROVING THEOREMS: STATEMENTS ABOUT WHAT IS. STATIC PROPERTIES.
Even the most computational math and formula-finding does that or is that.
The fundamental theorem of engineering is actually π = e = 2.
actually its 3
or actually 2 works pretty much the same
aasy jepale Or 10
Mike Durbin Both are the fundamental theorem of engineering, because sin(x) = x = 3
3 = Pi = e = sqrt(g)
aasy jepale why not just 2=3? Sounds pretty solid to me. Basically the same number, three just has an extra bump or whatever.
I still remember my first math 1 class. The professor literally said "We use exact numbers here, not like those physics ones, they like to approximate everything".
Aproximation always depends on instrument used to measure.
Well yeah...of course, in practical science you have to approximate everything...how accurate can these measurements be? Eventually you'll have to round because the that's just the nature of taking measurements of real-world data. Trying finding a mass scale that can do irrational numbers.
@@sulblazer my father was an EE student, he said that an approximation of even ±10 is trivial... Then when I showed him my school textbooks (yeah, in my country all first year topics in science stream, for engineering or for pure science and maths are taught in the last 2 years of high school and in every school) he was like: yeah that's ok, you people are not allowed to approximate... Remember Kalpana Chawla? She died in the upper atmosphere cause her space shuttle exploded cause THE SPEED OF ENTERING THE ATMOSPHERE WAS APPROXIMATED and it's was slightly high ... Blah blah blah... Yeah I know your gen is absolutely screwed... But anything for safety, u get me, right?
😀🙂😐😑😑😑😑
@@anirbanroy5667 that just sound like the shuttle wasn't designed well, for safety reasons most things should be able to withstand significantly more force than approximated requirements.
@@antarachatterjee4299 yep, always add a margin for safety. 20%+ at minimum.
I can confirm the words "lookup table," "approximately," and "assume" are quite frequent in engineering classes
When a mathematician sees a formula which was obtained not through derivation, but rather through rigorous testing and analysis of data to create a model for a given property of a substance:
Wait until they find out about dragforce, most things in thermodynamics and electrical resistancy. It Will be hilarious!
@@dinamosflams any mechanics/dynamics really
@@JackBlackNinja no, even in pure math, wait till they try integrating as limit of a sum for area... Or even try to find the value of π ... (This question is the worst question ever, cause as a CS student, we had code this shit up, and I will be frank, had no idea what to start with)😂
@@dinamosflams Due to statistical mechanics most of thermodynamics can be derived from first principles
@@Smitology quantum electrodynamics too for everything electromagnetism
I once solved an exam question, but I was off by a factor of 2. Couldn't find where that came from for the hell of me. Then I found a cool approximation:
We know that n = n+1 for large values of n. Substituting 1 in that expression teaches us that 1 = 2 for large values of 1.
It's valid in QCD, since 3 is close to infinity.
That's amazing.
My brain is screaming!!😂😂
I have a high school education and have no fucking clue how n = n+1, wtf. How can 1=2?!
@@witchBoi_Connor It's an approximation. There are very few contexts where 100,000,000,000 is meaningfully different from 100,000,000,001, so for sufficiently large numbers it's okay to act as though n=n+1 even though that isn't strictly speaking true. This person was making a joke about applying that to small numbers.
'Proof by shut the hell up' is definitely going to be a groundbreaking invention.
Like where it is derived from.
.
.
This textbook😂
It is actually derived from the previous edition of the same book and so on, ad infinitum.
Yeah, that one got me
Heard that part just as I read this lmfao
I mean either it has a dude's name attached (ohms law) or the book has a series of proofs leading up tothat equation, which my professor copied onto the slides and breezed through in 20sec. And i then copied the boxed equation into my notes and called it good enough.
and the textbook derived from?
well... its made of paper .... so from trees?
“Why be right when you can approximate?” I love it, that’s it...that’s engineering
Pragmatism. If your precision is going to be truncated by superfluousness anyway who cares?
For example. If all you care is if a value is larger than 1 why does it matter if it's 1.2 or 1.232423874392744? Both of those things are identical in the context you care about.
This is why I have not yet met a "mathematician" that was any good at engineering. Whilst I have met plenty of engineers who are great mathematicians.
Also, why be right when you can build a prototype to be sure that you haven't approximated too much?
I love that you and Andrew make videos in which you take stabs at each other, all in good fun. It is important to point out the frustrating differences that scholars encounter between these disciplines; more importantly, that these differences should not be allowed to be polarizing lines of division between fields that are so intrinsically cooperative.
Great job guys! Please keep the content coming :)
Andrew?
Like my chem eng proffessor says. A scientist and a mathematician would spend weeks on one thing. While an engineer would have moved on to something more interesting.
That's exactly what everyone would've done if they were all engineers lmaaoooo
"Real-world applications"
*leaves the class*
HAHA, extremely relate-able.
:D
I'm not sure if this was part of the joke, but the fact that pi² ≈ g is a historical artifact which pretty much depends on the "fundamental theorem of engineering". Namely, the meter was originally defined by the French to be the length of a pendulum of period T=2 seconds. The exact formula involves pi and g, and is derived using the small-angle approximation sin(x) ≈ x. Props to these guys, if this was thought out in advance.
One reason civil engineers are always approximate is cause the small numbers don't really matter as we will always times the required amount by a safety factor anywhere between 1.5 - 2x then use the next size up for standard construction sizes.
Yeah that’s a conservative estimate too. For concrete structures the eurocodes have a 1.5x safety factor, but then the concrete manufacturers often overshoot the required compressive strength by MILES.
I worked on a construction site where the concrete structure was calculated on the basis that the concrete with a nominal 35 MPa compressive strength had a compressive strength of just 22 MPa to be safe, but the concrete used ended up having a strength of over 80 MPa. Basically 4x safety factor all in all
@@whateverreally1347 beautiful
@@whateverreally1347 What kind of structure was it? Cause that's way too overdesigned
@@bruhbruh-uv5fl Apartment building
@@whateverreally1347 And then the mining engineers wow, they don't even know what the roof is made off so they can do like 5x or 6x safety factors wowza.
I remember being being caught by the approximation thing in university. In my pure math class we'd been looking at a formula with first order and second order terms. Most of the lesson was spent proving that the first order term approached zero. Then I walked into my physics class and the prof had the same equation on the board. "The first degree term will be swamped out by the second degree term, so we can just ignore it," he said, and simply crossed out the troublesome term.
But honestly, it takes a pure mathematician to prove that it approaches zero once, to give all physicists and engineers the "license" to cross it out whenever they feel like it. Pure mathematics has ironically been the source of all approximations applied subjects take for granted lol.
@@Smitology yes
"I don't even have a calculator here."
I felt that one, as a math minor.
"OH is this an engineering joke I'm too sophisticated to understand?" I'm dead 😂😂
I thought you were pertaining to Hydroxide (OH)...
@@arianbehnami1050 don't get me start3d on chem majors...
2:49
420 points for 69%
real smooth 😂
Groovy
Niiiiiice bro.
I was wondering if this comment would exist
Nice
Cha cha
I'm an engineering student and in my school, the professors will explain and show the derivation of each formulas before we can move on to the actual problem... In this way, we can understand where did it came from and it's really helpful and fun knowing how go derive the formulas rather than memorizing it hahahaha
I know this is a joke on the competition between mathematicians and engineers, but a lot of this isn't true, in my experience. In my Engineering mathematics classes at University (aerospace systems engineering), we always had to understand the derivations of equations, and why they worked. Even in fluid mechanics modules, we had to be able to derive bernoullis equation from first principles in an exam. Not a very mathematical example I know. But engineering mathematics classes were basically pure maths, with barely any actual real world uses. The one area I remember using lookup tables was Control engineering, where we used lookup tables for Laplace transformations. We had separately, previously learned the maths in the engineering mathematics module, but you don't want to be fannying about with maths when you've got a complex system to model, when you can easier and quicker just move between domains using a table.
Same. I'm studying mechanical engineering at a german university and most of the time the profs always explain the derivations of equations. In fact, it feels like we are more of a scientist than an engineer because of all the theories that we have to learn and that's also why at the end university students have a bachelor of science degree,not bachelor of engineering,which you would get if you study at a university of applied sciences i.e Fachhochschule
Same. I'm studying Computer Science Engineering and I am proving everything literally every math class and much much more than that.
This was also my case, Calc 1-3 was all about understanding everything and solving by hand. Then in mechanics and other courses we could use shortcuts for the calculations needed because the focus was no more on the mathematics side of things.
My professor told me a story about a guy he used to work with. He was an ex-nasa engineer and was a senior engineer at their company. He tasked a junior engineer with creating a solution to a problem. Junior gets to it and fervently works for the next two weeks. By the end, he solved it perfectly and turned it in. The senior engineer said "Wonderful! You got it figured out. Your solution is great but let me show you something real quick." He then grabbed a note card and showed this junior engineer another solution to the problem in about 15 minutes. There are some things that you just learn through experience and getting too much into the nitty gritty will end up slowing you down when a perfectly acceptable solution could be found in only 15 minutes!
It is so cute you think you learn the derivations. But really it is just a peak in the magical world of math.
I studied physics and they never proofed something rigoursly in theoretical physics except they had a co lecturer from the math department.
Anyway you wouldn't be able to shuffle through the science if you are hold up math concepts your probably don't need to know in this detail.
And then the computer scientist is like "Can I just program my math homework away?"
I have a library that can solve that.
Back in the day CS majors used HP calculator like Business majors used. Unlike the TI that the rest of engineering used. I never took any math for engineering as my department was tied to the hip with the math department. Cal 3 ruined math for me prior to that I did math in my head (number sense) still got the A. Oddly enough I struggled with Discrete had to take the course twice which was the only time in my life. I did use ML when I had difficulty, not sure it’s still used but Fortran and Cobalt are still being used by companies to this day.
There where some equations that for whatever reason where easier for me to under stand after I programed it.. I guess maybe because the breakdown was more granular? Any way I only passed calc because I pass discret mathematics
Program? More likely it's just sticking together a bunch of libraries and getting a binary that does the job in the most inneficient and cumbersome way, with a bunch of bugs that they don't even know where they come from.
Sure. Why not. Doesn't matter. You're not showing the code to anybody. You're probably going to be throwing it away after the homework is done. Feel free to make a poorly hacked together mess. It. Doesn't. Matter.
5:06 the “I just learned how much engineers are paid” moment.
Are we seriously going to ignore this legendary Nintendo Mii lobby music?
You don’t have the music playing on loop in your STEM classes?
Kazumi Totaka :)
I really love how everyone uses Dotson last name 😂
4:10 Mathematician: „A calculator for sure doesn’t have that much *overcalculation*“
CS and CE students: „pfffft“
“Anyone else confused by *Andrew’s* question?”
Lmfao you guys are like the 3 Musketeers
Pretty sure it’s him, Dotson and epic flame
This guy is probably the 4th one
lol "here approximately equals equal well.... approximately
I was both but I was an engineer first. I remember in an math analysis class, no mathematician could calculate a simple Fourier transform because they were first trying to determine whether it existed.
That’s pretty much the difference: engineers prove existence through calculation, possibly wasting time because it can’t be done, whereas; mathematicians don’t waste time calculating things that can’t be done. They just waste time proving existence that could have been done through calculation.
Meanwhile in programming: And now we make Pi equal to 3.14 as a double and go from there. lol
No, some people will have complaints if you do that. It is COMPLETELY unacceptable to use 3.14, you must use a builtin to prevent complaints. Complaints involve "the builtin is more precise", "the builtin is clearer", "the builtin doesn't require you to introduce a new variable", etc.
@@AAA-de6gt True. I've never set a variable equal to 3.14 since high school.
No, you just use the macro from a header, don't you dare use magic numbers
@@janisir4529 Macros? They technically are magic numbers with token substitution :)
@@HyperMario64 Half of programming is naming shit. Having a good name for constants and variables makes all the difference.
"Why be right when you can approximate" - every programmer when they notice 0.1 does not equal 0.1 thanking engineers
Then there's me, a physicist writing C code for the first time, not getting why 1/3 is not the same as 1.0/3.0
one does not simply == floating point numbers
Pi squared = g is close enough in most applications. If I worked it out properly it's about a 1% error. Now all I need is for a company to bring enough mass to Earth so I can use g=10 m/s²
"and by small, I mean equal to zero" LMFAO 😭😭
“That’s what we call proof by shut the hell up” I give this response 420/69 stars, which is exactly equal to 6.1 stars.
@iMagUdspEllr that's the joke
I'd call it exactly 5 stars
As physics student, i have an existential crisis because i have to adopt both these mentalities
EXACTLY
The one dislike is Andrew
Well now there are 2 so his 2nd account
"Where does this equation come from?"
>The textbook
-Every math teacher I have ever had
Most relatable comment here
This video illustrates the big difference between engineering at a German university and engineering in the US. In Germany you do exactly what the "mathematician" asks, to a degree that makes you want to vomit after 4-6 semesters of engineering math. At one point, unfortunately, many people shut down and just push through the torture with a switched off brain :D because from semster 1 onwards it's all tailored to Dr.-Ing. (Ph.D) level and Dr.-Ing. habil. levels just like the programs for lawyers are still aiming for the high office of becoming a judge. German eduction can be very 19th-century-brutal in that regard.
Engineers are a special kind of people. Last day I found an old friend and we had the following dialogue:
-It's been year since I don't see you mate. What are you up to?
-Well, I'm in business engineering
-That sounds cool, is it like economics or something like that?
-iTs EnnGinEeeRinG!!!!!!!!!!!
And he left, I'm still wondering what the fuck is business engineering.
Sure he didn't mean financial engineering? That's more like statistics. Or is business engineering like datascience and process optimization?
Engineering must just be code for undergraduate ;^)
Probably just putting engineering at the end just to desperately try and make business and economics to be a science
It's garbage
I totally get the business engineering guy. Just like him I drive my business to work every morning as well.
π²=g Laughed everytime I see that
g ≈ 10
e ≈ 3
π ≈ 3
... 4 ≈3
From that approximation, you can derive that a pendulum needs to be 1 meter long in order to have a period of 2 seconds (like for a traditional pendulum clock, 1 swing of the pendulum = 1 second, therefore, 2 swings of the pendulum = 2 seconds = 1 period of the pendulum).
Hehe
The thing is, *it's correct*
Well, approximately
@@VndNvwYvvSvv wait my teacher said that π = 5
I've never seen a derivative or integral lookup table in engineering school. It was derive it by hand every time.
"Is Anyone else confused by Andrew's Question?" Had me dying of laughter! Awesome work!
@@PapaFlammy69 Yeah! xD
You should do mathematician in a philosophy class next.
Those are the worst. I'm in physics, not math, but I hate philosophy classes. We've literally had discussions and yes, that's plural, about whether it's more morally correct to own a cat or a dog.
Andrew B; Michael J. Sandel, Professor of Government Theory at Harvard University Law School, has some TH-cam videos that helped me get through philosophy class.
Philosophy classes was the most anticipated thing for me during my time in the university. It was also the most bitterly disappointing. The only subject that actually made me feel like i'm wasting my bloody time, and that's telling something, considering we also had culturology, religious studies, psychology, ecology and history. While studying for a bachelor degree in Applied Math.
The fixation of mathematicians on deriving equations is very philosophical though. Both maths and moral frameworks rely on axioms and you can choose different axioms to see what the results are. Gödel’s Incompleteness theorems are relevant to these axioms. Both philosophy and analysis use the same notation for logic too.
@@andrewb378 i mean there are differences in circumstances in how these pets are sourced
vegans adopt instead of shop for a reason
As an engineering teacher, I can say that this fundamental theorem of engineering is glorious
I switched from pure math to mech engineering and holy shit I thought these were just jokes but they are actually so true. Engineering math course is so dumbed down it's hilarious.
I'm not great at math so I became a physicist instead lol
I'm not great at math, nor physics that's why I'm an engineering student lmao
I think of engineering more as an art than science, sometimes you just do it how you feel its right
Andrew B if you want to do real physics you must have a good understanding of advanced math
I actually switched from physics to math in undergrad solely because I was tired of constantly using random formulas without being shown the derivation. Needless to say, math satisfied my curiosity but in turn made me a more curious person in general lol
4:40 I feel this so hard, I'm the only engineering student who regularly uses LaTeX on all my assignments 😅
@Nissim Levy that's based as fuck
As an engineer, they taught me like a mathematician and after that we were allowed to use look up tables,just because it's faster,and about most of the "complaints" of the mathematician if not all were addressed in my classes
My thermodynamics and fluidmechanics classes was only integrals and derivatives, proving control volume equations, for energy equations, momentum, and mass balance.
*When you love math*
*When you're also in Engineering*
*sweats in nerd*
Wtf, this video is all about my conversation and unnecessary quarrel with my math professor
My favourite engineering class was when the professor taught us about eliminating variables that are unimportant.
"Right, so when X gets large, 1/X approaches zero, so we can just ignore that."
"And when X gets large in (X^2)/(a+X), you can just ignore "a", so that approaches X."
The idea that you could go through an equation and just start eliminating variables because they were unimportant was so beautiful! After years of grinding through hideously long calculations to try to get the right answer, only to find you had made a trivial error somewhere, the ability to throw out the irrelevant bits was lovely.
It’s true though “Some trivial manipulation I’m not too interested in” proceeds to skip over 5 pages of solid working out and assumptions we’re supposed to know
As a physics student, Quantum Mechanics and Classic Electromagnetic Theory classes had a lot of hand wavy "This is some trivial integration that you should really know how to do so I won't waste class time doing it here" and hooo boy was that not trivial integration that I should really know how to do.
@@andrewb378 "Classical" not "Classic".
@@michaeljorgensen790 my bad
If you use Latex, Maple and Mathematica, you're a theorist.
If you use Matlab and Latex, you're an experimentalist.
If you use excel and word, you're a pleb.
What if you use Matlab, Latex, Maple and Excel? Haha
Python > Matlab
Matlab’s totes for plebs
@@tobias7043mils Checkmate
U use google sheets and google docs for my physics class lol
What if you use Latex, Python and R? :thinking:
To a pure mathematician, the (principal) square root of 2 is the (positive) number whose square is 2.
To a computational mathematician, the square root of 2 is the sum of a Taylor series (or perhaps Fourier).
To an engineer, the square root of 2 is whatever number you can measure off that comes close enough to having a square of 2 to make your object work as desired.
Wait, you can use LaTeX for spreadsheets? My whole life was a lie...
Yeah please enlighten us unholy heathens on this magnificent technology
Well, LaTeX is just a way of typesetting text, it doesn't **do** anything but compile text to PDF documents.
Maybe some LaTeX editors have spreadsheet capability, but it's not a feature of LaTeX itself.
Real mathematicians program their own spreadsheets software
On C
@@omerresnikoff3565
Or assembly... 😂 😂
@@Invalid571 Or simply take a hex editor and type the opcodes yourself
As an electrical engineering student I can confirm that most of these are definitely true. We need good approximations to get stuff done, but precision is usually not required, especially when you have all these physical phenomena like resistor/capacitor/inductor tolerance and wire resistance which leads to inaccurate voltages and whatnot. Maths is considered a tool for design, but it's certainly not the only one, because, as stated first in the vid, we need to consider "real world applications".
I was a "pure mathematician" (well, math major, theoretical track) in Accounting 101. I completely disrespected that class, cut it all the time, the works. Got my ass handed to me on the first exam. Dropped the class with my tail between my legs. Folks, Accounting isn't Math. It's procedure. And if you don't respect it, it'll own you.
"confused by 'ANDREW's' question" -- actually just LOL'd. Having been an engineering student, I love this video. XD Thank you, Flammy, AND ZACH! for bringing us more awesome content! I'll go over to Zach's channel after I'm finished with this video to support \^^/
As an Engineer, I’m glad that Dollar Shave Club sponsored this video...because we all know, they are Brilliant!
*glances at my small stash of Executive spare razors - counted at 3 and soon going to be 5*
I shave sparingly, but when I do, they are good both in sink and in shower.
I was studying the use of Laplace Transform in AC circuits for my Circuits and Systems course and it stated, "The inverse of Laplace Transform gives you the function itself. For now, we just assume that the statement is true since its proof is beyond the scope of this book". And I was like great!. This is something I love about engineering. You never bother about proving complex mathematical stuff.
“Choosing epsilon to be less than zero at the start of an e-d proof”
Yeah I really hate it when that happens
i lost it on "Why be right when you can approximate"
NGL pretty often ‘unique up to unique isomorphism’ has EXACTLY the same energy as ‘approximately equal equals equal’ 😂
This video reminded me of a course I took on optimization methods in the engineering department. I ask the professor a question and he, as soon as he found out that I was from the economics department, said: you guys from economics don't take math seriously, that's why you have this doubt (I laughed)
:DDD
1:20 I thought he said " we found the virgin already" LMAO
Somebody described it really well. "Mathematicians try to put everything into variables, applicable to any virtual situation but they don't have much concentration on a "real world" problem. Engineers work with a specific case to sole a specific problem, instead of virtualising everything for substitution."
'"why be right when you can approximate" - Engineers'😂
I HAD THAT EXACT CONVERSATION WITH MY PROF ABOUT SIN(x) = x 😂😂😂😂
From being a (computational) math major for undergrad that went to grad school for EE ~30 years ago, this definitely brought back some memories. 😊 I don’t remember my profs taking quite the same shortcuts….but I seemed more comfortable following the derivations than others who were the engineering undergrads. 😏
I'm studying Engineering and we don't normally see formal proofs of math concepts but often teachers give an explanation of how formulas and laws are derived which I think is really important for students to at least understand so they can apply those concepts correctly in the real world and not just try to apply something you learned by root memorization.
We literally never used a look-up table except for laplace transforms lol
And Fourier transforms too :D
@@darkfinal9964 Fourier transform is just a special condition if Laplace transform
I have had enough machinist jobs to know that if you're unsure add an inch.
As an engineer, I consider this useless and I'm afraid of it.