[firebee]

	Originally Posted by Eleven To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	I find this thread horrifically depressing, because I have grown up with the firm belief that I cannot do maths. I don't know whether that's true or not, although if I were to try to actually learn some maths, it would mean going back to early high school level text books and working from there. I'm sorry to say I don't even know what calculus is.

Math, I think, is one of the major casualties of our over-emphasis on the importance of "natural talent". Supposedly, either the math fairy taps you on the head and you have an easy time getting it or she doesn't and you're doomed to perpetual struggle. In particular, I'm thinking of the idea of saying that a person is talented in verbal skills OR mathematical skills, as if the latter can't be tackled using the former.

Thing is, whatever wiring you have as far as how you learn and how you store knowledge can be adapted to learning the body of knowledge that is mathematics same as any other body of knowledge. Natural talent plays a part, but it doesn't have to stop you -- and after you've learned a thing, it doesn't matter that it took you more time and a different sort of explanation than someone else took. You've still got it just the same.

My suspicion is that early on many people pick up a lack of confidence in their mathematical abilities that produces anxiety and anticipation of failure whenever they deal with the subject. This exponentially increases the difficulty they have in dealing with it -- which pretty much guarantees more failure, which reinforces their expectation of failure even more. Interrupting this process... is pretty much how one gets tapped on the head by the math fairy.

Or more succinctly: When someone is effectively taught to spend 99% of their processing time thinking "I can't do this" and only 1% thinking "How can I do this?", the outcome is pretty much guaranteed.

[dogwoodlover]

My math education was simply horrid. It consisted entirely of me memorizing formulas and equations (which I suck at), spitting out the answers for the test, and then promptly forgetting everything the moment I walked out the door. I used to often ask the teacher to explain WHY something was the case, WHY I needed to use this or that formula, and all I ever got for an answer was "because, this is the way you're supposed to do it." I had given up on math by the time I was in high school, because I was convinced that it was just some sort of "black box" that people either never used in real life or only used without actually understanding it in the full sense of the word.

Yet, during this same period of time, I was busy at home writing software instead of doing my math homework. Go figure?

I think my story probably is more common than one would imagine, and I am inclined to believe that if colleges beefed up their remedial math courses (say, only having to spend a semester or two getting caught up to calculus, instead of having to spend a year and a half to two years in remedial math moving from HS algebra to college calculus) they would see a rather large increase in mathematical competency among the general student population.

My interests have always been of an engineering/scientific nature, but getting the kind of help I need to understand the level of math needed has just been a bitch. I've bought "For Dummies" books and studied on my own, but it's not the same as if I could simply attend a fast-paced remedial class to pull me up to speed (it seems that most remedial classes presume that if you haven't "understood it" up until now, that you're probably retarded, and they take a slow-paced approach to "remedy" this.)

Btw, does anyone know of any math books that start from say algebra and move to calculus, without breaking it down into a five-book series?

[Mozzes]

	Originally Posted by dogwoodlover To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	Btw, does anyone know of any math books that start from say algebra and move to calculus, without breaking it down into a five-book series?

You may want to look into Schaum's.


To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

[dogwoodlover]

Originally Posted by firebee To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

My suspicion is that early on many people pick up a lack of confidence in their mathematical abilities that produces anxiety and anticipation of failure whenever they deal with the subject. This exponentially increases the difficulty they have in dealing with it -- which pretty much guarantees more failure, which reinforces their expectation of failure even more. Interrupting this process... is pretty much how one gets tapped on the head by the math fairy.

I agree entirely.

It took me until my second year of college before I realized 'Hey, wait a second, I was always told I was "not a math person" or a "right-brainer" yet everything I've ever been interested in has almost entirely been math-based, so maybe this is something more than "me just sucking at math."'

[Monte314]

I am of the opinion, as I have said here before, that most problems with mathematics are the result of teaching disabilities, not learning disabilities.

The failure of my age mates to pass mathematical skills along to our children is "generational malpractice", and it's impaired our ability to compete in world markets.

However, we did do a good job of teaching ya'll how to be completely bored with life while maintaining a positive self-image.

[reb]

i suppose this is too philosophical given the topic, but the disconnect i have observed in business is that no one in management is interested in your degree or your knowledge. they want sales performance and profit. the analysis of a mathematical model or idea is not typically valued. forecasting is always based on 'the past'; the attitude is often 'what have you done for me today?'. evaluation of the past in mathematical terms is confined to 'the back room'. in fact, much of the hard work done does not reflect future reality, as politics and finance affect 'today' more than the past frequently.

'solving simplex algorithms', accounting and stat classes were beyond the managers i had. once, i was told 'i don't pay you for opinions, i pay you to follow my orders.' when giving a presentation on learning curve for a multimillion $ contract negotiation. this was when i quit wearing a tie to management meetings...no respect, no tie.

the integration of math theory into 'real business' would be a real challenge, given the level of education of many managers and perhaps iq...yeah, yeah..now comes mbti typing lol. they may have the paper, but they don't frequently have the understanding or even the desire to understand. the commercial people i dealt with could do the equations (or have the computer do them), but they focused on the same bottom lines...their bonus and their continued employment. as i have observed, there is a complete lack of nexus between 'the real world' and academia in many cases. one has to somehow resolve this paradox in order to survive or thrive.

being a hard head, if it does not help me survive and thrive, i place a lesser personal value on it, whatever it is....art and science are nice when they put food on the table and a roof over my noggin; otherwise, they are hobbies for me. you must remember, i suppose, i obtained an mba, which got me nothing in the present but scorn, but has proved of inestimable value over the long term in a personal macro way. art for art's sake is well if one has the time and resources. long term thinking is rare in much of society.

[RichardCMongler]

	A few years ago, the undergraduate school at which I teach dropped the calculus requirement for the Computer Science degree.

To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.


WTF?!?!

[eastman]

Personally, I feel the removal of calculus is misplaced. The college should establish an IT major and let the students who aren't going to graduate school focus on relevant programming languages. You simply do not need math for programming. at the bare minimum, a programmer should master basic arithmetic, and a little bit of Boolean logic. You do not need calculus to design a website.

If it were up to me, every college should have a CS and a IT major.

[Maedhi]

Originally Posted by reb To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

i suppose this is too philosophical given the topic, but the disconnect i have observed in business is that no one in management is interested in your degree or your knowledge. they want sales performance and profit. the analysis of a mathematical model or idea is not typically valued. forecasting is always based on 'the past'; the attitude is often 'what have you done for me today?'. evaluation of the past in mathematical terms is confined to 'the back room'. in fact, much of the hard work done does not reflect future reality, as politics and finance affect 'today' more than the past frequently. 'solving simplex algorithms', accounting and stat classes were beyond the managers i had. once, i was told 'i don't pay you for opinions, i pay you to follow my orders.' when giving a presentation on learning curve for a multimillion $ contract negotiation. this was when i quit wearing a tie to management meetings...no respect, no tie. the integration of math theory into 'real business' would be a real challenge, given the level of education of many managers and perhaps iq...yeah, yeah..now comes mbti typing lol. they may have the paper, but they don't frequently have the understanding or even the desire to understand. the commercial people i dealt with could do the equations (or have the computer do them), but they focused on the same bottom lines...their bonus and their continued employment. as i have observed, there is a complete lack of nexus between 'the real world' and academia in many cases. one has to somehow resolve this paradox in order to survive or thrive. being a hard head, if it does not help me survive and thrive, i place a lesser personal value on it, whatever it is....art and science are nice when they put food on the table and a roof over my noggin; otherwise, they are hobbies for me. you must remember, i suppose, i obtained an mba, which got me nothing in the present but scorn, but has proved of inestimable value over the long term in a personal macro way. art for art's sake is well if one has the time and resources. long term thinking is rare in much of society.

I agree with this. Should a technical subject be studied if it is never going to be used in the real world? I studied calculus for 2 years in school and 1 year after. It has been 12 years since, and I have never ever had to use calculus on the job, and I have forgotten everything I ever learnt. In fact, calculus has been dropped out of the school syllabus for commerce students in my state, they study a lot more statistical analysis instead. That would have definitely been more useful for me.

Before we go into questioning what we are taught, I think we should focus on how we are taught. I was never told why I had to learn calculus, other than it was required to clear exams. As a result, I never knew the applications of calculus despite studying it for 3 years. I also don't see why calculus should be taught to people who are not capable of much simpler math. As part of my job as a financial analyst, I handled training for newly recruited Finance MBAs. Most of them had trouble understanding why a profit of 33.33% on cost would be 25% of selling price. They knew how to calculate percentages, but didn't understand them. Funnily enough, in an increasingly process driven world this is not a handicap. A few well educated people can reduce complex tasks to a series of small steps which can be carried out by a large number of people who are less educated, for a much lower cost. I consider this a better utilisation of human resources.

I don't agree that calculus needs to be taught to everyone, or that a person cannot be considered well educated unless they have studied calculus. This attitude is fairly common in those who teach a subject and have a great deal of passion for it. I hear similar rants from my Mom, who holds a Ph.D in Nutrition and Dietetics and has held a bunch of very impressive academic posts for her subject. She would scoff at the importance you give calculus, pointing out that eating right has a much bigger impact on the human race than an ability to differentiate or integrate. I agree with her, but not to the point of gaining more knowledge about food and diets, the topic doesn't interest me and that is what we have dietitians for.

Specialisation makes us more efficient at what we do, the human race has to operate at a very high level of efficiency to sustain an ever increasing population with limited resources. This means that some people need to learn calculus, and many people don't.

[Rudy]

	Originally Posted by Maedhi To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	I don't agree that calculus needs to be taught to everyone, or that a person cannot be considered well educated unless they have studied calculus.

I think what Monte said, at least what I understood him to say, is that a person should understand why calculus is important to be considered educated, not necessarily that they need to learn it.

[Monte314]

	I also don't see why calculus should be taught to people who are not capable of much simpler math. I don't agree that calculus needs to be taught to everyone, or that a person cannot be considered well educated unless they have studied calculus. This means that some people need to learn calculus, and many people don't.

Well, the misrepresentation of my OP is now complete.

I did not suggest that people who had not "studied" calculus are not well-educated. Nor did I suggest that it should be taught to everyone, or people who aren't capable of handling it.

What I said is WRITTEN IN BOLD AT THE BOTTOM OF THE OP. I suppose I should have put it in 48-point type, too.

I *explicitly* quantified my suggestion in my second post as "10 minutes" in a "history class" to explain what calculus is, and what it does.

Somehow you have morphed me into a calculus nazi!

[Undead Bonzi]

Originally Posted by Mozzes To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

There's absolutely no reason why all college students shouldn't take a semester of calculus and I think high-schools are a big part of the problem. I, once again, go back to balance. In high school I had to take an English class every year. Why should students not be required to take a math class every year in high school (you know, like the high school students in the rest of the first world...)? They could take algebra freshmen and sophomore years, analytic geometry junior year, and senior year take a class on functions and trig and then they're ready for a calculus class upon entering college. As it is now, however, most students' math proficiency is abysmal. I've tutored plenty of students who didn't even know what they were supposed to have learned in high school. Thus our problem. I think the people who set the curriculum know that most students enter university with pathetic math skills and that requiring a calculus course or sequence would require 2-3 semester of remedial math for a lot of students which isn't a tenable option when the goal is to graduate as many students as possible as quickly as possible.

Is this the state of most high schools? Granted I graduated six years ago but I don't remember such inbalance in my high school.

In my school, starting at the end of middle school (8th grade) you had the option to take algebra or pre-algebra. That choice pretty much determined your path in high school. People who took algebra in 8th grade took algebra 2 in 9th grade, 3 in 10th, 4 in 11th and then your Senior year you could take Calc 101? and Finite Math for college credit or you could take Buisness Math and Accounting. People who took prealgebra in 8th were basically just a year behind and never had to take algebra 4 and could not take college credit classes, their Senior year they could take Buisness Math and Accounting. Thus no matter what you did in my high school you took math each year. The same with science and english. The only real options we had was languages where you only had to take 2 years or arts which were largely optional. This was in a tiny high school in Iowa with each year consisting of roughly 30-40 people.

That one choice I made in 8th grade to take algebra has made all the difference in the world. I was done with my math reqs. before I even went to college. Of course since then I've had to take around three engineering and one physics and materials class which showed me what a math dunce I am, but I am still glad I took the path I did in high school.

[Monte314]

I have noticed that the level of preparation of incoming freshman in many areas (math, ability to write cogently, ability to express their ideas verbally, spelling, grammar, etc.) has fallen quite a bit in the last 10 years.

It has become relatively common for students to take more than four years to complete a bachelor's degree, owing at least in part to the raft of remedial courses students must take to make up for the damage done by our ineffective system of secondary education. (Of course, we don't actually call these "remedial" courses... but, for example, pick up any textbook titled "college algebra" and explain to me how it differs from what should be taught to 10th graders.)

[Maedhi]

My mistake, I apologise. However, I still don't see how a person is supposed to know what calculus is and what it does without being taught calculus. Also, why should I know what calculus is and what it does if I don't use it? Are you suggesting that a man is not yet educated if he cannot answer questions in a trivia quiz? Because any knowledge that is not of use is trivial isn't it? Most (if not all) of the farmers in my country do not have much access to schooling, they wouldn't get your '10 minutes in History class'. They wouldn't know what calculus is, and what it does. Do I take it that I am to consider them uneducated because I live in a modern, technological society where the knowledge of seasons, cycle of nature, and an indepth understanding of getting life enabling sustenance from the earth is nothing compared to being able to say 'I know what calculus is and what it does'? I wouldn't. They may have received a very different education from the one you have received, and in a totally different field, but that does not mean I value their knowledge any less than I value yours. I might value it more, because I can easily compare those who are hungry with those who are ignorant of calculus, and see who suffers more.

I am not suggesting that you are a calculus Nazi. I am merely pointing out that those who love a subject tend to be evangelical about it and believe that everyone should know something about it, but it isn't really necessary.

[Rudy]

Maedhi, I would consider myself uneducated if I did not know the basics of how food was grown, a rough history of agriculture, and the differences in different types of crops. This does not mean that I need to know how to farm.


Your vision of society where everyone knows what they "need" to know sounds rather bleak, and ominously dystopian, to me. We cannot predict what knowledge someone will need, or whether they will react and grow due to receiving a certain type of knowledge.

[reb]

Monte, is it possible that 'understanding calculus' in your op is really 'understanding how concrete things in the world work'? this is a winding trail, thinks i.

i think it is important to understand theory, and yet, it is also important to udderstand process. even more so, to achieve results. in reading wikipedia for an update, i got to the point where i went ' omg, this is gobbledygook':


To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.


they go on at length discussing what 'it' does, and never synthesize simply. to me, genius is truly coalescing a subject that might take pages into a clear explanation. calculus allows us to understand more precisely the world around us and theorize about more expandable issues. however, early man could and did over time observe and develop ideas of what occurred in the world. was it truly important to put 'a man on the moon' or to develop nuclear energy? would we have not been better off to have never calculussed at all? lol!

educate me. you are obviously intelligent and erudite...what is the lesson you are trying to impart? i am rather a simple person...survival=success in my world. what is it that i miss in calculus that i should be getting? i agree that a broad knowledge base gives one perspective on matters that one would otherwise not understand at all. a limited perspective is frequently what leads to a person being highly boorish. yet i know some with 'paper' who are obnoxious to experience for short periods, and others with no paper at all who are highly entertaining and thought provoking.

'calculus nazi'! lol! this is so ironic, it is lovely. this would make me a 'results nazi'....funny i have been reading shaara's 'the steel wave'. the 'real' nazis were not so good at overall results and perspective, and yet were highly knowledgeable and 'scientific' in certain ways.

[Max T]

This thread may be suffering from "man with a hammer syndrome"- to the man with a hammer (maths), every problem looks like a nail (a mathematical issue).

	Originally Posted by Monte314 To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	every person who wants to be regarded as educated should know what calculus it is, what it does, where it came from, and why it is important.

I suggest the maths for anyone to be considered "educated" would instead be:
- Arithmetic
- Basic elementary algebra (i.e. invert things, isolate variables, functional equivalents and linear/squared/cubic relaionships)
- Basic combinatorial maths (permutations etc.)
- Probability (and basic sets, decision trees and basic Bayes and basic game theory)
- Normal distribution (skewness, statistical significance and law of large numbers)
- Compounding
- Power law/ 80:20 rule basics.

Wouldn't even bother with precalculus (although the above list has bits of it), never mind calculus itself.
That list surely captures the vast bulk of useful maths for a person to be considered "educated".


Besides, work with any complex adaptive systems (much of business, economics, social research... anything involving people (excluding actuarial output)) and false precision is rapidly reached. Keep the Greek letters to yourselves.

What IS important is to use the above list on a very regular basis, as skills attenuate with disuse. Regular enough usage to synthesise and analyse using maths (instead of only banging it out through rote learning). A good teacher like Monte would agree with that.

Could someone explain in <30 words the single most frequently useful 'thing'/ rule derived from calculus? That would enable the rest of us to judge whether we should remember the rule.

[dVdT]

I haven't parsed through every single reply here, but I (and others here who teach, either as a living or a side-job tutoring) can explain to someone with fairly rudimentary math skills what calculus IS, why it's important historically and in the physical sciences, and what sort of situations call for this level of analysis, in less than 1/2 an hour.

I'm NOT talking about teaching someone about triple integrals, to derive the power rule, to tell my why d/dx ln(x) is 1/x as long as x is >0...

I'm talking about relating things like "what does velocity mean? How is it related to position, and acceleration? " "what did Newton accomplish, and what sciences were able to flourish as a result?"
stuff like that.

Just like...to be a good engineer at what I do (MEMS mostly), I don't need to know the entire history of the semiconductor industry, who developed what and when, why Moore's law has held true and what the future holds for it. I certainly don't need to know things like the history of the Russian Revolution, how the Soviet regime stimulated some aspects of the physical sciences, etc while horribly repressing others...

But I think knowing those things makes me a more...complete person, in a way, and knowing lots of things (I hold more trivia in my head than several boxes of trivial pursiut cards) has been an aid in my life & career for those 'think outside the box' moments. In fact, that's one thing i'm quite good at, and while I don't attribute it 100% to my voracious appetite for knowledge on just about any topic, that hasn't hurt any either.

[Rudy]

	Originally Posted by Max T To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	This thread may be suffering from "man with a hammer syndrome"- to the man with a hammer (maths), every problem looks like a nail (a mathematical issue).

Did you read any of the thread, Max T? It's been established, several times, that we are talking about the need for an educated person to know why calculus is important, not their need to actually know how to do it. Consider it part of a proper history education.

[dVdT]

	Originally Posted by reb To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	Monte, is it possible that 'understanding calculus' in your op is really 'understanding how concrete things in the world work'? this is a winding trail, thinks i.

Seeing as this thread started with a quote of mine from a different post, I'm chiming in again.
That's pretty much what I said- "in my ideal world, everyone would know basic calculus, as it's such an aid in understanding how the physical world works". Or something like that. As an ME, I was thinking about things in my field...things like gravity, friction, normal force, centripetal 'force', kinematics. F= ma, and derive back to position, & how they're related. Velocity, translational, tangential and rotational, and acceleration. Electrical components- current/ resistance/induction, etc. Stuff like that, that really don't take a HUGE amount of study to just say "oh, cool, that's how it works"- not in-depth years of study. That's what I meant, and I think monte is getting at also.

[Max T]

	Originally Posted by RudyHenkel To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	Did you read any of the thread, Max T?

Yes, I read the thread. We are talking about:

	Originally Posted by Monte314 To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	every person who wants to be regarded as educated should know what calculus it is, what it does, where it came from, and why it is important.

My point is that a person should be articulate in far more elementary maths, well before calculus, to be considered "educated".


Could someone explain in <30 words the single most frequently useful 'thing'/ rule derived from calculus, or is this just some idle pontificating (of very little use to most people)?

[Rudy]

	Originally Posted by Max T To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	Could someone explain in <30 words the single most frequently useful 'thing'/ rule derived from calculus, or is this just some idle pontificating (of very little use to most people)?

Ummm... "physics"

Again, though, no one is saying that you have to be able to use Calculus, just as you don't have to use anything you learn in any history class that you've ever taken. They both still help you understand the world better.

[reb]

i'm digging in order to put forth examples:

1. the method of exhaustion led to calculations of 'pi', without which we would be in deep doggy do today....a convenient and necessary method for calcluations of circle area and diameter. very useful in machining, building, design.

2. the relationship of calculus to physics has enabled us to predict and design both small and large machines of infinite type. no 'man on the moon', no faster trains, perhaps no internet without calculus. trial and error is greatly more costly in developing these objects, especially to the poor fool who is shot towards the moon in an ill designed rocket...wonder why they used monkeys in the first 'manned' flights, and not politicians?

3. wonder why the brakes on your vehicle are the size they are? the drums/pads are sized using coefficient of friction along with a calculation of force (including the hydraulic lines) to determine 'stopping power'. the pins and bolts, likewise. the brake actuator leverage, the compression of the hydraulic fluid...all available by calculation and projection from known criteria. plus a 'fudge factor', also calculable. trial and error for brake size doing 70 mph with a loaded 18 wheeler is not an option i want to consider.

so, flesh it out, someone with more math background than i. but does everyone need to know? most people are doing good to know to change their oil...they have no idea about additives, or refinery process....there is a simpler form of life. it does not require nor desire calculus...and i'm not one to say 'they must have it in order to have worth'. there is intelligence among the non-technological, as well asthere are those who lack intelligence. the intelligent among them are interesting, speculative, curious people...

[Trenchant1]

Interesting. I finished studying maths at school when I was 16 and got as far as algebra. Now, thirty something years later, I am getting books from the library on algebra, trigonometry and calculus, just because it's fun to learn. It is a source of regret to me that I took the wrong courses when I was at school and that I had crappy maths teachers. I have had questions in my head all that time about the kind of things that calculus helps to explain but daily life and idleness stopped me from trying to answer them. Also, I didn't believe I would be able to understand even the basics because of my poor results as a youth. Now, I love it. It's hard work because my brain isn't as young as it was and I tend to forget things much more easily than I did as a kid, but it's worth learning just for the sake of it.

Several people have spoken about the failure of secondary schools in teaching maths. I think the problem starts earlier, in primary schools. Many teachers have very little ability in maths and here in the UK the methods of teaching it seem to change every couple of years, causing confusion among teachers and children. If children are not taught the absolute basics properly at a very young age, they will not progress well at secondary level. Maths, more than any other subject, requires that you build from the bottom up. To move to level three, you have to go through levels one and two. Unfortunately, lots of kids turn up for lessons at level one but don't, for one reason or another, learn everything they need to. The system requires them to move up to level two but, because they haven't fully understood level one, they understand even less of level two. This gets worse as they continue and by the time they get to leave school, they hate maths because they're 'not maths minded' and they still need to learn what they should have learned five years earlier.

The responsibility for a child learning anything should lie with the teacher, not with the child. The teacher is there to teach, not just to turn up and talk. My daughter has occasionally come home from school and mentioned something that she didn't understand. I have usually managed to explain it to her within a couple of minutes, yet her teacher could not, despite being asked several times. In this country, it is estimated that there are around 15,000 teachers who are incompetent. How they came up with that figure, I have no idea. And if they can identify them, why don't they get rid of them, like they would if they worked for a company?

I agree that giving children an idea of what calculus can do is very desirable. They can then decide if they want to pursue their studies in that area. Even if they don't, they will at least have an idea of what other people are talking about if they mention calculus. I wish I had done it when I was young.

[Max T]

Very interesting examples, Reb.
Based on a personal once-in-a-decade need for calculus (I recently used it to figure the axial force needed on a cone clutch to resist a given amount of torque), my little view is that a guy does not need to know what calculus is, does, came from and why important… to be considered educated.

Sure it's important but not a requirement for labelling as "educated".

Wait long enough and a biologist will post “every educated person should know taxonomic ranking of organisms to be regarded as educated”.
Natural selection yes, taxonomy no.

It’s human nature to distort the importance of our own profession.