<p>What does art and sucking-up have to do with "developing economical and safe solutions to practical problems" for the betterment of mankind?</p>
<p>You have to convince people who like art and being flattered that they need to fork over funding to implement YOUR solutions. They don't initially know or care whether your solution is the best one out there.</p>
<p>All of the above proves to be a validation of the argument that even though the theory is useless, its application is not. I apologize if I sounded as if I were dissing humanities. I'm sure English majors found calculus and physics stupid and pointless, if not useless. The humanities are just as important as math and science, which, incidentally, also provide great examples of useless theory and exercises.</p>
<p>For example, do I really need to learn the theory that says any given number is either greater than, less than, or equal to any other given number? Yes, when the theory was developed, it was useful, but don't most geometry students already intuitively know that?</p>
<p>To provide another example from my Saxon math book, why do I care what time (to the second) it will be when the clock hands point in opposite directions from each other? How will it honestly ever help me? </p>
<p>While my examples simplify the argument to the point of absurdity, they show the faults with ignoring theory because you don't actually use it.</p>
<p>To further exemplify the argument that theory is necessary, let's take the example sentence, I is. Yes, thanks to my elementary language classes, I know that's wrong. </p>
<p>Is it really, truly enough for me to know it's wrong? Or should I know that the reason it's wrong is because the correct first person singular present indicative conjugation of the verb to be is am?</p>
<p>Doesn't knowing the reason allow me to figure out another similar problem without having to rely on someone else? Because I know the reason I can't say I is, I also know I cannot say I has.</p>
<p>To go back to the clock problems, knowing how to solve them gives me the foundation to solve other problems dealing with similar equations.</p>
<p>To sum up my lengthy argument: While theory is unimportant at face value, it provides a foundation upon which to solve similar problems without having to learn each individual case; if it works this way with this problem, it's going to work that same way with that other problem that looks remarkably simliar.</p>
<p>
[quote]
One practical application could be that, if you can measure the pressure and entropy (and some other stuff), you can figure out the internal heat. Or vice versa.
[/quote]
</p>
<p>And how exactly would one measure the "entropy" of something? </p>
<p>
[quote]
College is not just a vocation training. You learn some things because they explain why you do what you do.
[/quote]
</p>
<p>But that's exactly my point. Colleges should explain why you do what you do. The problem is, they often times don't. Instead, they toss you into a thicket of math. </p>
<p>
[quote]
1) The MR thing was to show what they're used for (which you said you never understood), not what they're used for in industry.
[/quote]
</p>
<p>Of course I understand what they are used for. What I asked was what they were used for, from the standpoint of a practicing engineer. </p>
<p>The analogy would, again, be the deep proofs of mathematics. If you are a mathematician, then sure, you do need to know Real Analysis and beyond, because you really do need to know how to rigorously prove the tenets of calculus. But if you're not a mathematician, you don't need to know that. Similarly, I can certainly agree that if you're actually going to be a thermodynamics researcher, then you obviously need to know the M.R.'s. But if you're just going to be an engineer in industry, you don't need to know that. </p>
<p>
[quote]
2) The three most industry-oriented classes in my MSE undergrad program (semiconductor, metallurgy, and ceramic processing) were all heavily dependent upon thermo. The metallurgy class is actually joked about as being a higher-level thermo class where you finally learn enough to apply it to real systems. The class is also described as you to design a steel mill.
[/quote]
</p>
<p>Then maybe that's precisely why your education was so valuable: because you took classes where somebody actually showed you how the M.R.'s are actually useful. </p>
<p>The problem is that most engineers don't get that. I certainly didn't. I wish I did, but I did not. </p>
<p>In fact, I think you just captured my frustration. You said that you took a class where you finally learned enough to apply thermo to the real world. What that implies is that your regular thermo class did not teach you how to apply it to the real world. </p>
<p>And that's the problem. There are too many engineering classes in which you aren't taught how to apply what you learn in the real world. Hence, you're just doing math for the sake of math. </p>
<p>
[quote]
3) Stop bringing up my dissatisfaction with Caltech. 80% of my classes are in non-engineering departments, and those are the ones I haven't been satisfied with. The three classes I've taken with the MS department have been pretty good, though, due to the nature of the school/department, they still have a very physics-y slant.
[/quote]
</p>
<p>I'm simply bringing it up because we both have had experiences with frustrating classes in which we don't understand the point of it all. Hence, you know how it feels. </p>
<p>Besides, I have to ask, if there are non-engineering classes at Caltech that you are not satisfied with, then why are you taking them? Is it because your program requires them? If so, then that means that your program is requiring that you take dissatisfyingly difficult classes. </p>
<p>
[quote]
I feel what's wrong is the professors that do a poor job teaching. So if you want to say engineering is tough because teaching sucks, I'll wholeheartedly agree. I'll also say that the material on its own can be quite difficult.
[/quote]
</p>
<p>What I am saying is that engineering is difficult because professors often times cannot or will not show you why the material is useful. This notion is aligned with what you said above: where you said that you had to take another class after thermo before you finally learned how thermo was useful. That begs the question: why couldn't the thermo class teach you why thermo is useful? Why do you have to wait for that in another class? </p>
<p>Now, granted, maybe the reason that professors don't teach you why the material is useful is a subset of poor teaching and hence we don't disagree by much. However, I would argue that there is more than just a simple matter of poor teaching going on. It is one thing to try to teach the practical uses of something, but to just teach it poorly. It's quite another thing to not even try to teach the practical uses at all. </p>
<p>
[quote]
I actually didn't experience any weed-out classes at CMU (the only person that switched majors switched in to math. I imagine he didn't do this because he found the math of engineering too difficult), yet my classes were still very difficult.
[/quote]
</p>
<p>Interesting. Then I have a improved opinion about CMU, as, I can tell you, the vast majority of engineering programs weed people out. The US Department of Education has published numerous studies that show that the vast majority of students who enter engineering programs won't actually finish them, either because they switch majors, or because they flunk out entirely. </p>
<p>I frankly find it hard to believe what you are saying, because CMU has only an 87% overall 6-year graduation rate (in all majors), which is even worse than Berkeley's. But if you insist that nobody gets weeded out in ChemE in CMU, I'll take your word for it, for now. I think I'll post this on the CMU section of CC and see what response I get.</p>
<p>
[quote]
The thing is, there is no explanation aside from the trivial one. Either you get it or you don't, if you don't get it is is just a mathematical equation which tells you nothing but you need to know it to solve the problems on the exams, if you do get it you understand that it is a valuable link between properties of a system that makes some things a lot easier to understand
[/quote]
</p>
<p>And what I am saying is that a good teacher should be doing everything possible to help you to "get it". Physics is not just a matter of learning a bunch of arbitrary equations, but about developing proper intuitive insight into what is happening. Somebody mentioned Feynman, and I recall reading how Feynman became such a popular teacher because he always insisted on developing simple explanations whenever he possibly could. For example, he devised the Feynman Diagrams as a simple intuitive graphical explanation of quantum field theory that even somebody with only a basic science background could understand. In fact, that was the point: he always believed that if scientists could not properly communicate their findings to the greater public and show why they're useful, then the public will eventually stop supporting science. </p>
<p>
[quote]
Or are you saying that we should stop teaching potentials just because it is an arbitrary concept and just helps with calculations? Or are you saying that since it is such an easy concept it should be taught while Maxwell relations are complex and therefore shouldn't? But then where should they draw the line?
[/quote]
</p>
<p>The line has clearly been crossed if regular engineers not only never even use the concepts, but don't even understand what they actually mean in a real-world sense. </p>
<p>Put another way, what you can do is poll your students after the semester is over, and ask them whether they can actually take what they just learned and apply it to real-world engineering problems. If most of them say they cannot, then clearly, you have crossed the line. </p>
<p>Again, the point is that you should be teaching why what you are teaching is useful. After all, this is not a math major here. You're not just doing math for the sake of math. This is engineering. It is supposed to be useful. It is supposed to be practical. Math is therefore just a tool to help you to understand real-world engineering projects. You shouldn't (as what happened to RacinReaver) need to take yet another class in order to finally learn why something is useful. But, hey, at least he had that other class, so at least he eventually found out why it was useful. Most engineers (like myself) didn't even get that other class, so we never learned why it was useful. </p>
<p>This gets back to the OP's question. The OP asked why engineering is hard. My response is that engineering is hard because engineering courses often times don't bother to teach you anything practical. Instead, they just toss you into the tall weeds of arbitrary math, without ever telling you why you're doing it. Even after the class is over, assuming you survived (which plenty of people don't), you still don't have a clue as to why you did it.</p>
<p>
[quote]
Grammar? When will I ever actually need to know the difference between a noun clause and an adjective clause?
[/quote]
</p>
<p>Let's extend this discussion of grammar. The analogy is that I have no problem with learning grammar. The problem is when the teaching of grammar becomes pedantic because people just learn grammar as a set of arbitrary rules rather than the intuition behind the rules of grammar.</p>
<p>Take the sentence of Jack and I went to the park.. Now, I think a lot of us, when we were kids, might have said: Jack and me went to the park, and then we got corrected that the correct grammar is actually Jack and I.</p>
<p>The problem is that many of us never learned why "Jack and I" is correct and "Jack and me" is incorrect. Hence, we end up using "Jack and I" all the time, including when it is wrong to do so. For example, the sentence of "She gave the ball to Jack and I" is wrong. It's supposed to be: "She gave the ball to Jack and me, because the word "me" is now being used as the object, not the subject of the sentence. Even Al Gore once made this mistake when he was running for President. </p>
<p>But the point simply is that many English teachers will teach grammar as just a bunch of arbitrary and pedantic rules, and not the intuition behind it, which leads to the phenomenon of hypercorrection.</p>
<p>Hypercorrection:</a> Interesting Thing of the Day</p>
<p>Hypercorrection</a> - Wikipedia, the free encyclopedia</p>
<p>Similarly, if all you are learning is a bunch of engineering equations, but not the intuition behind the equations, then you really haven't learned very much. The point of engineering education is not to teach you a bunch of equations and rules, but to teach you the logical way of thinking behind the equations and rules. The problem is that too many students will simply get lost in the equations.</p>
<p>
[Quote]
This gets back to the OP's question. The OP asked why engineering is hard. My response is that engineering is hard because engineering courses often times don't bother to teach you anything practical. Instead, they just toss you into the tall weeds of arbitrary math, without ever telling you why you're doing it. Even after the class is over, assuming you survived (which plenty of people don't), you still don't have a clue as to why you did it.
[/Quote]
I think the reason to this is because the professors are generally scientists and not engineers, in their world a formula is not useful if you can't back it up theoretically and therefore they need to teach you guys all the theory and thus also all the formulas which are only used to derive other formulas.</p>
<p>However in a way you can't just teach cookbook methods either since you need to build up their intuition on the subject or they will be very bad engineers.</p>
<p>
[quote]
However in a way you can't just teach cookbook methods either since you need to build up their intuition on the subject or they will be very bad engineers.
[/quote]
</p>
<p>Which is precisely what I have been saying throughout this entire thread. The goal of an engineering curriculum should be to develop intuition. But sadly that often times does not happen. Certainly, my intuition as to how thermodynamics works was not improved by hacking and slashing through the M.R.'s. I suspect most engineers would agree. </p>
<p>I think many of you have misinterpreted what I have said. I have never said that engineers should not have to learn rigorous mathematical methodologies. What I am saying is that the goal of those methodologies is to help you to develop and codify intuition, and it is intuition that is the ultimate goal. In other words, within the context of engineering, math is just a means to an end-goal. You shouldn't be teaching math equations just for the sake of math equations. Sadly, that is what actually happens.</p>
<p>Let me put it to you this way. Take 2 guys. One guy has a lot of engineering intuition. But he's not good at the math. The other guy has no intuition, but is very good at manipulating the math. The first guy will end up with a far worse grade than the second guy. In fact, the first guy will probably flunk. But if anybody should flunk, it's the second guy. After all, he's not going to be a good engineer because he doesn't have the intuition. Sure, he can play all kinds of games with the equations, but put him in an actual engineering setting, and he will perform poorly, because real-world engineers don't go around manipulating equations all day long. </p>
<p>But the second guy will get good grades on his exams. Hence, engineering programs reward strong mathematicians over strong engineers. That's the main difference between being an engineering student vs. being an actual engineer. I wish it wasn't true, but it is true.</p>
<p>
[quote]
Let me put it to you this way. Take 2 guys. One guy has a lot of engineering intuition. But he's not good at the math. The other guy has no intuition, but is very good at manipulating the math.
[/quote]
</p>
<p>Does guy #1 really exist? I think that if he does, he must be smart as hell. Guy #1 must have quite a brain if he can visualize complex objects without having the luxury of abstracting away details with mathematics. </p>
<p>I don't see mathematics as some burden on engineering students, but rather as an useful, and probably necessary tool. Mathematics is an aid--without it, talking about complicated things would take a lot of time and be difficult to do. For example, If I had to explain the phenomena of E&M without using vector calculus, I'd have a pretty hard time. Without being able to talk about div and curl and the Green-Gauss-Stokes theorem (when viewed with these tools, the relations between and properties of E & B fields are pretty simple), electricity and magnetism would seem like quite a mess.</p>
<p>I do agree with you with respect to providing motivation for the mathematics. That is very important, and I can see professors skimping on this.</p>
<p>
[quote]
Does guy #1 really exist? I think that if he does, he must be smart as hell. Guy #1 must have quite a brain if he can visualize complex objects without having the luxury of abstracting away details with mathematics.
[/quote]
</p>
<p>I give you arguably the greatest engineer in world history: * Thomas Edison*. Edison had such trouble with math that modern experts speculate that he may have suffered from dyscalculia (which is a condition similar to dyslexia, but affects your ability to understand numbers rather than words). </p>
<p>*Edison's mother, who had been a schoolteacher, took Edison out of school to home-school him herself. Fortunately for Edison, his mother let him study subjects he was interested in. She allowed him to create his own experiments, read a lot, and avoid subjects like math. *</p>
<p>*Edison chose assistants he thought knew more about a subject than he did. For example, he hired a mathematician because he had never learned math. *</p>
<p>Students:</a> History: Thomas Edison</p>
<p>Thomas Edison was kicked out of school when he was 12 because teachers said that he was too dumb. He was bad at mathematics, had trouble with words and speaking. Later he overcame his dyslexia and went on to patent more than 1000 inventions including the electric light bulb</p>
<p>Alexander</a> Graham Bell, Thomas Edison, Beethoven with Learning Disability Fookem and Bug</p>
<p>Now, certainly, I agree with you that Edison was indeed a brilliant individual, and his life's body of work proves that to be the case. Nevertheless, I think we can also agree that he would never have been able to have completed an engineering degree. </p>
<p>But think about how sadly absurd that really is. I doubt there are too many engineers today - who have earned actual degrees in engineering - who would actually claim to be better engineers than Edison was. Heck, I can only wish I was just a tiny fraction of the engineer that Edison was. </p>
<p>Yet the fact is, he was terrible at math. Hence, if he was alive today, any engineering program would have flunked him out post-haste. No engineering company would have therefore even deigned to have hired him, because they would have considered him to be 'too stupid' and 'too unskilled at engineering': an utterly ridiculous concept if I have ever heard one. After all, we're talking about Thomas Edison here. </p>
<p>
[quote]
I don't see mathematics as some burden on engineering students, but rather as an useful, and probably necessary tool. Mathematics is an aid--without it, talking about complicated things would take a lot of time and be difficult to do. For example, If I had to explain the phenomena of E&M without using vector calculus, I'd have a pretty hard time. Without being able to talk about div and curl and the Green-Gauss-Stokes theorem (when viewed with these tools, the relations between and properties of E & B fields are pretty simple), electricity and magnetism would seem like quite a mess.
[/quote]
</p>
<p>You guys are all agreeing with me; you just don't know that you are. </p>
<p>Again, my problem is not with the use of mathematics per se. Obviously there are many cases where mathematics makes concepts easier to understand.</p>
<p>But - you said it yourself - mathematics is just a tool. It is just a means by which you can understand complex engineering topics. But math is not the end goal in itself. Math is just the mediating language that you use to convey the concepts. The object is not to learn the language, but to learn those concepts. </p>
<p>It is precisely that second step that often times goes missing. Many engineering professors don't bother to teach you the actual concepts. They don't teach you the intuition. Instead, they obsess over the math. Hence, students just end up learning a bunch of math without ever understanding why they are learning it or how to use it to understand real-world engineering problems. During the weeders especially, they're thrown into a situation where they don't know what the equations are actually talking about, and they don't have time to find out. All they know is that they have such-and-such homework due on this day, a lab report due on another day, and an exam after that, and consequently they don't have the time to absorb what the equations actually mean. </p>
<p>It also doesn't help when the profs don't tell you what the math means. RacinReaver himself admitted that he didn't learn what thermo actually meant until he took the advanced class that was after basic thermo. That begs the question of why they couldn't tell him that during that basic thermo class. But hey, at least he did eventually have a class that taught him what it all meant, even if it was a little late. Unfortunately, not all other engineers can say the same. I certainly never took an advanced class where I could finally learn what the basic class actually meant. Maybe that's a personal problem with me, or maybe that's a problem with my program's curriculum in not requiring such a class. Either way, it is still an open question as to why the basic course couldn't have taught you what the equations actually meant.</p>
<p>
[quote]
I give you arguably the greatest engineer in world history
[/quote]
</p>
<p>Of course! Leonardo DaVin... Wh... Thomas Edison?!? No way, dude...</p>
<p>
[quote]
Many engineering professors don't bother to teach you the actual concepts. They don't teach you the intuition.
[/quote]
</p>
<p>They <em>try</em> to teach you the intuition. It's incredibly difficult to stand up in front of one person and say something to evoke their discovery and mastery of a complex concept, let alone with a full lecture hall of forty people. It's incredibly difficult to come up with a lab experiment that forty people can follow and end up with the discovery and mastery of a complex concept. Same with class projects, same with problem sets.</p>
<p>I've found that the only way that I, and all the people I've talked to about this, know of to really understand engineering concepts is to slam one's head against them time and time again. I don't think you're taking that into account. Professors <em>try</em>, heaven help them, but it's not as idealized as you seem to think.</p>
<p>
[quote]
Of course! Leonardo DaVin... Wh... Thomas Edison?!? No way, dude..
[/quote]
</p>
<p>You prefer we talk about Leonardo?</p>
<p>Three signs of the dyslexia of Leonardo: He did "mirror writing", his spelling was peculiar, and most importantly, he described himself as a "man without letters"</p>
<p>Hexmaster's</a> Factoids: Famous dyslectics</p>
<p>
[quote]
They <em>try</em> to teach you the intuition. It's incredibly difficult to stand up in front of one person and say something to evoke their discovery and mastery of a complex concept, let alone with a full lecture hall of forty people. It's incredibly difficult to come up with a lab experiment that forty people can follow and end up with the discovery and mastery of a complex concept. Same with class projects, same with problem sets.</p>
<p>I've found that the only way that I, and all the people I've talked to about this, know of to really understand engineering concepts is to slam one's head against them time and time again. I don't think you're taking that into account. Professors <em>try</em>, heaven help them, but it's not as idealized as you seem to think.
[/quote]
</p>
<p>No they don't. Or at least, they're not trying very hard. If they were, you wouldn't have quotes like the following:</p>
<p>*Why do students drop out? Student surveys say because the first year of an engineering program is all foundational theory and they don't see the connection to a career in engineering. The second most common complaint is poor quality teachers that are more interested in their own research than in teaching undergraduate students. *</p>
<p>Don</a> Dodge on The Next Big Thing: 50% of US engineering students dropout - Why?</p>
<p>
[quote]
You prefer we talk about Leonardo?</p>
<p>Three signs of the dyslexia of Leonardo: He did "mirror writing", his spelling was peculiar, and most importantly, he described himself as a "man without letters"</p>
<p>Hexmaster's Factoids: Famous dyslectics
[/quote]
</p>
<p>Maybe I'm reading this wrong, but doesn't the link you posted offer evidence that Leonardo wasn't dyslexic?</p>
<p>* Here are some people claimed to be dyslectic who weren't...</p>
<p>Why do people who write like me write from left to right? Because the hand moves across fresh paper, so you won't mess up your writing - provided you're using your right hand, that is. So there is a good reason for left-handed people to write from right to left...</p>
<p>As for the errors, you can only spell wrong if there is a spelling considered right. Such norms didn't exist in those days, at least not for common languages - dictionaries and grammars existed for latin and greek, not for e.g. italian...</p>
<p>What is un uomo di lettere? Someone who can write? No, it's precisely the same thing as spanish hombre de letras and french homme de lettres, that is, "a man of letters". When Leonardo used the expression he didn't mean he couldn't read or write, he just meant that he lacked formal education. It's the very same argument you use when dealing with experts: "I'm no expert, but..." </p>
<p>*</p>
<p>Actually, no, I'm pretty sure that the evidence shows that Leonardo probably was a dyslexic. Consider the last sentence:</p>
<p>*Since he never went to school he never got the opportunity to show off his dyslexia, so to speak, but the current evidence should do well enough. *</p>
<p>Now, granted, we'll never really know, as the guy has been dead for centuries. </p>
<p>Nevertheless, the point stands that there is a big difference between engineering intuition and mathematical acumen. Yet the fact is, to survive an engineering program, you have to be a very good mathematician. Thomas Edison would sadly have not been able to complete an engineering program, yet the fact is, he's far more of an engineer than most of us could ever hope to be.</p>
<p>This all gets to the original question of why is engineering so hard? My reply is that engineering - as a degree program - is hard because it isn't really engineering. Meaning that it's not really engineering in a real-world sense. It's basically an applied math program, with a smattering of real-world engineering tossed in only at the very end (i.e. the senior design project). Granted, the mathematics is supposed to be connected to real-world engineering uses, but that often times gets lost in the translation. Hence, you often times end up wading in the thickets of mathematics just for the sake of mathematics, leading many of my colleagues to proclaim that if they had wanted to do this, they would have just majored in math.</p>
<p>I understand your overall point sakky, but education can only go so far in teaching true intuition. Also, education is geared towards the masses; therefore, it is difficult to remove the convoluted math because the math is the basic foundation and standard of how scientists and engineers break down our complicated world into what they consider to be simple mathematical, empircal models.</p>
<p>BTW, it would be a shame in today's world if let's say a Thomas Edison went to an engineering program and flunked out, hindering his entrance into the mainstream industry. But then again, would Thomas Edison have given up just because he failed? Edison is the one quoted saying, "I have not failed. I've just found 10,000 ways that won't work."</p>
<p>Possibly what sakky is trying to say is that education must evolve to better suit the minds of the time. However, learning science and engineering has involved mathematics for as long as the empirical model has been in existence. And while it is true that some inventions and ideas were based more on intuition than on math, the world has advanced in the areas of science and technology that inventions built off of intuition and the advancement of current technology require heavy mathematical proofs in order to be actualized in almost all cases.</p>
<p>For example, I can't say exactly which mathematical model or scientific idea the scientists/engineers used to develop the transistor, but much has to be accredited to the scientists that laid the foundation in order for it to be created. And although many of the scientists used thought experiments to formulate parts of their models, math was used to explain most of it. Einstein applied his theory of light being photons to Max Planck's quantum hypothesis to explain the photoelectric effect. Although it was mostly theory, it had to be proven mathematically by Millikan through experimentation, who was in fact trying to disprove Einstein's idea that light was a photon. Schrodinger was able to use these ideas to develop his model, the equation named after him. The developers of the transistors, whether they knew it or not, were basically applying the scientific ideas and mathematical proof for these ideas to make the transistor. The developers of the transistor also had to know how to calculate or understand the Hall Effect, the photovoltaic effect; not to mention the ideas of Faraday and Maxwell on static electricity/electro-magnetism.</p>
<p>Basically my point is this: we have the computer now because all of that convoluted math and science was able to come together in the minds of those that developed the idea of the transistor and those that used that idea of the transistor to make it a reality. Now, just because I now have the luxury of the advanced microprocessor, shall I ignore to learn the basic concepts that got us to this point. Yes. Of course. I am not an electrical engineer or a computer engineer, so let them learn it. But really, no. it would be nice to either learn everything that is relevant to our interests or to just focus our attention on what we believe is most important. But education was made to educate the masses. The engineering curriculums believe that what they are teaching include some of the important concepts that all engineers in each specific discipline must attempt to learn. Many will not have the innate intuition to take those concepts and apply to the real world, either by advancing current technology or inventing new ones. But it will create a basic foundation of knowledge that most engineers can rely on when they face a situation in the real world which helps spark intuition into their minds.</p>
<p>Can education improve? I sure hope so. But getting rid of tedious mathematics and relying solely on computer technology or whatever practical applications there are at this moment doesn't seem to be the answer. There will always be anamolies where the few with great intuition will jump away from the education model and create their own great inventions/discoveries (again, education is geared towards masses; of course as you go higher up it is geared towards specialists). But can you really say that Thomas Edison did not benefit from those before him that understood the theories of electric current and the need for a vacuum tube in making the prototype for the light bulb? Could Einstein have correctly predicted that light had properties of a photon without analyzing Max Planck's quantum hypothesis and other mathematical models? I believe that these great minds and great inventors benefit from the many that try to understand the math behind phenomenons of the world. If everyone or most everyone was just sitting around trying to invent a light bulb, while only a few were trying to understand what current actually is, could we have come to the same conclusion? Possibly. But I think it is because there were so many learning the concepts of current in a time when electricity was not understood that helped lead to the invention of the light bulb. Not everyone can be great, but we can all try to reach greatness. And maybe on the way, we might actually be inspired or we might actually inspire someone with innate intuition to do great things.</p>
<p>I don't remember exactly which book I read this, but I remember reading that over 90% of bridges built by man (and woman) over the course of history have failed catastrophically.</p>
<p>It takes intuition to devise a pathway to travel over water without getting wet or getting caught in the downdrift, or between two adjacent cliffs without falling to your demise, but intuition alone cannot guarantee success. The idea is simple. Something flat and hard that extends the length of the obstacle and something to hold it up and in place. But before mathematics and the understanding of loading conditions, etc., many have tried to build bridges, but few have been successful in keeping it upright.</p>
<p>This example is explicitly one that is of a real world example. I brought it up because those with pure intuition can build a bridge. Some will even stay upright through the test of time. But the damage and risk of getting it wrong, which is more often than not if math is not involved, is too great to allow it to continue. Therefore, a student learns Statics to understand analyzing forces and moments, Mechanics of Materials to understand how beams deflect and bend, and so on and so forth in the first years in undergrad. But are these concepts really necessary? I mean, there are engineering handbooks that have all the calculations for the moments of area, etc. for all different types of steel beams set up. Why even learn the concepts? There are computer programs where you can design bridges and where the program analyzes stresses/strains/forces/various loadings, etc. automatically. Why not just learn how to use the computer programs instead of going over the mathematical concepts?</p>
<p>Why? I think it is because there is no point in having a bunch of engineers that know how to use a computer program to build bridges when they don't understand why something works and why something does not work. That is a liability. That is an engineer that builds a levee and doesn't question whether it is sufficient to hold up against a Category Five hurricane. That is a bridge that I will never set my foot on even if millions have done so already, because the engineer does not understand why the bridge will fail.</p>
<p>Granted, the math behind building bridges might not be too difficult to visualize or understand. But that is the whole point. If something that is supposedly simple to understand and can be designed with not much intuition requires so much learning and preparation, how is it possible to think that something that is complex and hard to understand does not? It might be harder to find real world connections, but that doesn't mean it is not there. As I said in the previous post, something that is harder to find in the real world probably requires more learning so that a foundation can be set for the fit and few to utilize that knowledge towards doing big things. The rest of us? We do our thing and try our best to apply what we learn towards doing big things in our lives, however great or small it may be.</p>
<p>I understand that it is unfair to those that may have trouble with courses that have little relevance to them (and they very well may have been great engineers in their own respects), but maybe there are just some things that most everyone should get exposure to in their field that these students have to overcome. Or they can choose a school that is more hands on in teaching. But avoiding courses with tedious math is probably not the answer.</p>
<p>P.S. I hated taking these classes as much as the other guy or gal. I also received below median grades in some of these courses. But I still do not believe that what I had to learn was trivial in any way, no matter how much I said that it was a load of bull crap while studying for the exams.</p>
<p>
[quote]
I don't remember exactly which book I read this, but I remember reading that over 90% of bridges built by man (and woman) over the course of history have failed catastrophically.
[/quote]
</p>
<p>Reminiscent of To Engineer Is Human: The Role of Failure in Successful Design, by Henry Petroski. If that's not the book you're referring to, I recommend it. It's a good read.</p>
<p>Hoping to contribute to the conversation here.</p>
<p>I was a shipboard electrician in the Navy, worked mostly on 440 volt industrial equipment; such as generators, motors, switchboards, motor controllers and transformers. The training I went through with the navy was very vocational. The only theory taught was pretty much electrons move and we call that electricity and here's how to use a voltmeter. These are technical skills on a ship, far from engineering yet, I came across people in the Navy who were in fact engineers from lots of practical experience and intuition.</p>
<p>There was a guy in my shop who could look at electrical blueprints that come with equipment manuals and figure out exactly what was going on. These are not simple drawings to understand, in fact they were created by the manufacturers and engineers that designed the equipment. On top of that every drawing is different, with different parts labeled differently or adhering to different standards, yet this guy could fix and locate problems in very complex solid state frequency converters, motor rewindings and even generator rewinding. Of course lots of it was from hands on layman's experience but he intuitively understood how electrical equipment operated. We had one of our generator windings burn out. This guy literally sat there for two days and cleaned out the inside of generator and rewinded the coils and got it working again. He later went on to do the same job for the navy as a civilian making much more money but that's outside the story.</p>
<p>What I'm driving at here is that this guy probably didn't have much more understanding of electricity and magnetism other than magnetic fields induce current in wires. One of my division officers who was a EE grad couldn't tell a motor from a pump, let alone rewire a simple transformer and the guy from my shop was assembling motor controllers with three different emergency operation modes and variable speeds using salvaged components.</p>
<p>I think today's engineering programs lack the connection between the real world and hands on. Granted my example is a little unique and outside of designing new ideas and inventions, I think there could still be more focus on learning to APPLY pure and advanced theory to physical things that benefit humanity. After all isn't R/D the end all purpose of engineering?</p>
<p>
[quote]
I've found that the only way that I, and all the people I've talked to about this, know of to really understand engineering concepts is to slam one's head against them time and time again. I don't think you're taking that into account. Professors <em>try</em>, heaven help them, but it's not as idealized as you seem to think.
[/quote]
</p>
<p>I agree. It is very difficult to teach intution period, let alone in a classroom setting. I think it's unfortunate that there isn't more time in a general engineering curriculum for the type of regular one-on-one instruction that students of dance, music, art, etc. have.</p>