Modern Educayshun

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I don't think your memory is quite correct on this.

On the complex plane, there are just two square roots of any given number. But there are three cube roots, four fourth-power roots, and so on.

What I remember is that a unit circle (i.e. a circle of radius 1 in the complex plane) contains all of the nth roots of 1 regardless of what n is. But it's not so simple for numbers other than 1.

The number 4 has two square roots, both on a circle of radius 2 in the complex plane. The number 4 also has three cube roots, all of which are on a circle whose radius is the positive real cube root of 4. It also has four fourth-power roots, all of which are on a circle whose radius is the positive real fourth root of 4 (i.e. the positive square root of 2). It also has five fifth-power roots, all of which are on a circle whose radius is the positive real fifth root of 4. And so on.

Agreed that better intuitive overviews should be given before diving into the details.

These days, there are lots of educational videos out there that can give these intuitive overviews.

As far as racial inequity is concerned, I think the main problem is not the curriculum but the educational system as a whole.

One big problem, here in the U.S.A., is the way public education if funded in most places, from property taxes. That means schools in more well-to-do neighborhoods get better funding.

Another, related problem is that most teachers prefer to work in the more well-to-do, more white-dominated neighborhoods. That means the more-experienced teachers get to work in the more well-to-do, more white-dominated neighborhoods, while poorer and minority neighborhoods are stuck with those teachers who don't yet have enough seniority to choose where they work.

These problems could perhaps be fixed via financial incentives.

If those roots are scalar, of course.  Complex roots are more ... complex.

SQRT(4):
• Scalar: {-2,+2}
• Vector: {(0,-2i),(0,+2i),(-2,0i),(+2,0i),(-1.414,-1.414i),(-1.414,+1.414i),(+1.414,-1.414i),(+1.414,-1.414),...}

Have you ever worked a Smith Chart for complex impedances?



It is possible to get an infinite number of "roots" or solutions for matching impedances, but only one will actually work.

Math classes don't teach rounding? Significant figures? C'mon, I get the point you're trying to make, but since somma these kids clearly aren't even interest in pursuing the education they obviously lack, I doubt that my "dumbing down" of things is what will cause their mathematical shortcomings. They already did that to themselves.

They're not interested in an education, why should I give them one? I'm not arguing with them to teach them - I'm arguing so they're not the only voice in the room, thus creating an echo-chamber.

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I can understand how the idea that the SQRT of 4 can have more than one answer might give people the heebie jeebies, if you expect EVERY question to have ONLY one right and true answer. But if you actually STUDIED math, you'd know that once you move into and past algebra, it's fairly common to have multiple plausible answers to a given question. The fact that people can't wrap their minds around such a concept has more to do with flaws in their ability to comprehend than it does to do with some "questionable nature" about math. But even though there's more than one answer, there are still right and wrong answers.

Another wild concept that people seem to stumble on is the idea that two answers can be correct, but some answers are more correct that others. For example, "X + Y = 6", X and Y can be literally any number, so long as they're the appropriate pair to sum to 6. So, while X=2 and Y=4 is correct from a very simple point of view, a MORE correct answer would be X and Y can be any values that sum to 6, wherein 6-X=y, and 6-y=X ::: or something like that - I'm a little rusty on my proofs - I'm sure there's an even more succinct way to put it. Cos rather than one single answer, which when given as one single answer implies that there is only one single answer, it illustrates the possibilities of EVERY answer possible. The former shows that you know how to add. Yay. The latter shows that you understand the principles of mathematics.

Algebra expects you to be able to find a range of possible answers. Functions, including piecewise and stepwise functions, get even more interesting, since they can have multiple ranges of coordinating answers. Hence terms like range and domain. And so on...

So now that we have several people in here getting into the grit of math, BECUASE THEY KNOW MATH, like fnord and mona, I cant help but notice that they're talking in terms of MATH and FACTS, not discussing 40 genders or arguing that ALL answers are equally valid, or attacking each other for using "racist" variables, or any of the other things one might expect if they believed that the video represented that actuality of how college operated.

As mona pointed out, not only are schools funded by the neighborhoods they exist in, but additional funds are generally then redirected to only the "good" schools, since they're the ones that "clearly would make better use of it" under the premise that "you'd just be wasting money on those BAD schools, look how poorly they're doing" - never mind the fact that they've kinda been set up to fail. Gee, we gave this school unlimited resources, and that school $100 and some old textbooks from 1960. I WONDER WHY one is performing better than the other?!

I see your point, but there is a big difference between rounding Pi to 7 significant digits (3.141593) and saying that the value of Pi is "about three".

Just as it is one thing to give a student half-credit for writing down the answer without the decimal point after doing all of the mathwork correctly, and awarding full credit because an obviously wrong answer is "close enough".

That's really something, that a student with a BSEE degree would not understand the Pythagorean theorem or basic trig.

First, I wonder how many of these degrees are outright fakes. Have you looked into that question?

Insofar at they are not outright fakes, have you looked into the curricula of the colleges these people got their degrees from?

Or perhaps there are just a lot of college students out there who may study hard for their exams but then promptly forget it all when the semester is over?

Not personally, but the screening services I use would not allow a fake degree to get through.The poor performers are mostly from the California State University at Long Beach (CSULB) and the University of California at Irvine (UCI).Considering the colleges in question, I think the answer is "Yes".

"Woo-HOO!  I done been gradiated!
Now I doesn't gots to think no more!
Huh-HYUCK!"

I was talking about complex roots. For example, the four complex fourth-power roots of 1 are: 1, i, -1, and -i, which can also be written as 1+0i, 0+1i, -1+0i, and 0-1i, respectively.


By "(0,-2i)," do you mean the same thing as (0 - 2i)?

If I understand your notation correctly, you've made a list of complex numbers for which the absolute value (amplitude) of the square is equal to 4, but the square itself is not necessarily equal to 4.

The square of (0 - 2i) is -4, not 4. The square of (-1.414 - 1.414i) is 4i, not 4. The square of (-1.414 + 1.414i) is -4i, not 4.


It's been a long time since I worked as an EE and a long time since I saw a Smith Chart, but a quick review I found via Google just now brought me back up to speed. There's only one point where an actual complex value matches, it seems to me.

So rounding 3.1415... to the nearest whole integer isn't "3"? That may lose accuracy, as does ANY rounding, but it's still accurate in the context it's referring to. I could go bananas and say "No, Pi is NOT 3.141593, it is 3.14159265", to which you could then reply "Noooo, it's 3.1415926454" and so on ad infinitum, literally, since Pi is an irrational number.

Pi IS "approximately three", it's just that that doesn't help when it comes to mathematical accuracy. And surely you've encountered instances where problems allowed you to use either 3.1415 OR 22/7, which is most definitely NOT 3.1415926, but rather 3.1428571. Yet both are used to teach geometry.

Again, I get where you're coming from, exact questions have exact answers - usually - even if the answer is a correctly defined range of answers, such as "any value greater than -3 but less than or equal to 7". "4" is A correct answer, since it is part of the solution set, but it's not the complete answer. To some extent it is correct, far more so than say, "12", which isn't part of the solution set at all. But you're last statement of people getting full credit for obviously wrong answers isn't something that happens, so much as it's something some people seem to WANT or EXPECT. That's their failing as an individual.

Now, I DO see things like partial credit, where you do get some credit for what you did do right, but it's usually HALF credit, at MOST, for just the single part you got right. And half credit for a "perfect score" is still a nice solid "F" at 50%. Nobody passes REAL college on partial credit. Having said that, some people do pass, who clearly don't deserve the credit they give themselves. The "C-" students of the world. The ones who pass by ace-ing easy electives to offset their garbage grades in the primary courses.

And, unfortunately, "Clown Colleges" do exist, and some people get their honka honka degrees thinking they're actually worth something - while also not knowing how much (or little) weight or clout even a real degree, by itself, actually carries. Since you do hiring, you already know that the degree means very little when the person walks in and instantly sounds like an idiot, not knowing even the simplest terminology of the job they're applying for. I totally get that. If I ask someone whether they favor investing in CapEx or OpEx, and they say they usually use FedEx, they can kindly leave my office. If I tell someone to get a UPS for a computer, and they come back with a shipping label, even if they're kidding, I'm not thrilled that they're wasting time.

It's true that "almost correct" is still wrong. In war, if you "almost hit" you still missed. But, if I'm hiring an employee that's motivated and willing, and can do everything 90% correct, I'm willing to train them that last 10% as an investment in their future potential. Particularly if I believe that the 90% person, with a little training, will eventually outperform the the person who got it 100% right, but as a result, may not be as motivated, or adaptive, or other such intangibles.

I also get that we're going to have different perspectives on this, since you strike me as a Type-X, whereas I fall more on the side of a Type-Y. Neither is more right or wrong as far as I'm concerned, since all types of people exist. I do certainly agree that being too loose, too lenient, devalues the nature of the work. But at the same time, sometimes being too strict or rigid can have just as negative an effect.

While math itself doesn't change, the context in which it is used does. It's all well and good to point out that the average family has 2.4 kids. But you can't actually have 0.4 of a kid without some very messy results. You might be able to build 127.8 cars a day, but you can't sell that 0.8 of a car until it's a whole 1.0 car. And even though rounding up to 128 cars a day is "mathematically accurate", I can't actually SELL 128 cars a day, regardless of how close that decimal place rounds to the next integer. In that case, I do need you to know that .8 is there, but you do also have to ignore it, to some extent, despite it's weight.

Sometimes "knowing math" is more than just being able to crunch the numbers accurately. Being able to apply it in practical and meaningful ways is just as important. You can be great at math, but still be a terrible engineer, simply by not effectively applying it. I do largely agree with you - I just differ on the extent of rigidity necessary. I like what you do and I like where you come from, generally. Even things like math and physics have nuance. Like, generally the units are irrelevant in math, so long as they're consistent. Unless you're doing trig, in which case, you're using radians, end of story. You can convert it to degrees later, but the math generally still needs to be crunched in radians. Or even in algebra, multiplication rules that ONLY apply to 9's, or 3's. In physics, it matters whether you're talking about planetary systems or atomic structure, even though they're both just things spinning and orbiting around other things. Newtonian vs Einsteinian physics. The very nature of relativity.

As for this particular discussion, here in this forum and this thread, if they so badly want to avoid a college "edjookayschun", far be it from me to try to force one upon them. I wouldn't want to be too accurate in what I say, lest some of my college-ness rub off on them against their will, and they spontaneously sprout hipster glasses and a 3rd gender as a result.

But I feel that the point has been well-made, thanks to you and mona, that maybe educated people are in fact educated. Some dummies slip through, but not because the curriculum has taken to pandering to feelings. Every math class I've taken in the last 25 years has focused exclusively on math, and math alone, and the proper application thereof. No history, no clever interpretation, no free passes. I know this from having failed a math class or two in my time. I failed it cos I didn't grasp the material yet.

The biggest problem there I had was that the maths I learned in high-school fell short from where college math picked up. Apparently, that's a common problem, where even high-scoring high-school students are in need of remedial math upon entering college. And from what I understand, that has to do with the kneecapping of public schools via underfunding and being buried under "standardized competency test" requirements that keep getting changed every few years anyways, so it's kinda impossible to get good at something that's going to be replaced with an entirely new thing in short order. It's like being set up to fail.

As for making math more "appealing", the idea that things have to be made "appealing" sounds like it comes from the "feelings are important" crowd, not the actual intellectually curious crowd. Knowledge seekers find knowledge appealing in and of itself. The problem isn't that math isn't "appealing". Part of the problem is videos like this making an active effort to make education look overtly UNappealing. DON'T EVEN GO! Part of the problem is the inherent hostility and dismissiveness towards women and minorities because of tropes that drive the false narrative that women and minorities just don't have the brains for such complex concepts as math or some similar garbage, and based on that assumption, conclude that any minorities or women that ARE there are must only be there cos of "minority quotas", at the expense of a genuinely deserving applicant. People still believe the "women are worse drivers" crap, you better believe there's people who think women can't be engineers and mathematicians and such. You still have people that believe that minorities are less intelligent - even if they try to save face by adding the qualifier "but I'm sure some of them are just as smart", they still fall to the side of believing they aren't by default.

Lets not forget, Harvard, Yale, and Princeton are all older than slavery is. People didn't stop being racist just cos slavery ended any more than slave states just up and freed the slaves willingly when the government told them to, and totally didn't start the civil war over it. Laws clearly don't stop all criminals. You really thing ending slavery made racism magically evaporate along with it? Why do you think we criminalize things like being poor and homeless? Where do you think crimes like "vagrancy" and "loitering" came from? It was an excuse to arrest (certain) people for simply existing in public.

And as for feelings, even the psychology and behavioral classes I've taken, and am taking, don't pander to feelings. Even the philosophy classes I've taken weren't anywhere near the nonsense proposed by the video. It wasn't some free-for-all of free thinking where every opinion is equally valid. It was Socrates, Calvin, Kant, Nietzsche, Plato, Hobbes, Sartre, and their like. Consequence, the veil of ignorance, the allegory of the cave, types of reasoning and knowledge, cognitive fallacies, that kinda stuff.

Not everyone puts the same effort in, and not everyone gets the same returns on their effort. Even allowing for the people who do slip through and don't deserve their degrees, the content of the video is still sufficiently detached from reality that there may as well have been a singing and tapdancing gorilla and a space alien in class, too.

Doesn't it concern you that math gives irrational solutions to finite problems?

I'm more concerned with people trying to act smart, but failing to realize that in math, "irrational" just means "cannot be expressed as a ratio of two integers". Numbers are irrational. Solutions are what they are. If the solution happens to be an irrational number, that doesn't make it an "irrational solution". That's both a math failure AND a language failure. See my previous comment above re: CapEx, OpEx, and FedEx. You can leave my office now...

Where's Inigo Montoya when you need him...? "I do not think it means, what you think it means."

It's easy to be "clever" in the absence of knowledge. No pesky "facts" to interfere with imagination. It's the same level of problem-solving as "if people are starving in africa, they should move to france..."

I'm also not bothered by the fact that science "changes". As we learn more, we UPDATE and CLARIFY our understanding of things. Science doesn't radically reshuffle like some grand game of musical chairs where nothing is knowable. We just gain more insight as to what is or isn't the next logical conclusion. If science seems like it's all over the place, you probably don't understand science either.

"I have a theory...!" NO, YOU have a HYPOTHESIS, and I have my doubts as to whether or not it is in fact an "edjookated" guess...

Life isn't static. The Real World isn't an RPG overworld, where the way it is, is the way it always will be. Life changes every day. But change and uncertainty is SCARY! Concrete facts make people feel better. Nuance makes people uncomfortable. Unfortunately, pretty much everything involves nuance.

Someone may not NEED a formal education to succeed in life, but that doesn't mean they can't still benefit from it.

Last edited by uncommondenominator on 19 Mar 2021, 2:16 pm, edited 1 time in total.

Not when math also gives transcendental solutions to many of the same problems.

When asked a question, you cite an abstraction of "cannot be expressed as a ratio of two integers", and berate the asker.

Saying something is NOT X, doesn't tell us what IT IS.

So the abstraction you cited is the problem, because explaining an abstraction with another abstraction is confusing.

This topic is about efforts to simplify math.

Irrational numbers appear to be the space in between real numbers based on a made-up modeling technique that assumes there is infinite divisible space between two numbers.

https://brilliant.org/wiki/history-of-i ... l-numbers/

Most people, like me, are likely already confused.

Me: Hey, where do you get this infinite divisible space idea from?

Teacher: (hopefully) Well, we made it up.

Me: Now we're getting somewhere ....

If you think there are parts of math that are just "made up", you can kindly leave my office...

You don't get to talk for other people just to make yourself look better. Just say it. YOU'RE confused. No need to drag other people along just so you're not standing alone.

It's cute to make an imaginary situation wherein a math teacher "admits" that they just "made it up".

In REALITY, the conversation would go more like:

Me: Hey, where do you get this infinite divisible space idea from?

Math Teacher: (Honestly) Through years of trial and investigation we have found that no numerical denomination yet exists that cannot be subdivided into smaller sections. We used to believe that this equally applied to the measure of distance as well, thus leading to Zeno's paradox. However, we now have strong evidence that space / spacetime is granular, and of finite reducibility, much like our current understanding of the electron or other members of the lepton family. Just because a concept is abstract doesn't mean it's "made up".

Explaining an abstraction with another abstraction is called "building knowledge". If you don't understand it, that means you need to learn more first. Math builds upon itself. If the definition of an irrational number baffles you, that means you need to go study THOSE terms.

There are two kinds of people. Those who can extrapolate from incomplete data.

So, ALL numbers on a number line are real numbers. Even the numbers between them are real numbers. Even irrational numbers are real numbers, as they can exist on a number line. So you're already off the mark. From there, it's not "made up modeling". It's based on the observable fact that mathematically, you can always divide by two. Just like you can always add one. Since pure numbers are not bounded by physical constraints. What you are referring to are INTEGERS, which are the whole numbers. So an irrational number is a number that is so complex in length and composition, that you can't get it from dividing two integers.

And that's a very different animal than simply saying that it's "not X". Just because the description or definition contains a negative qualifier doesn't mean it's a negative definition. There's a big difference between saying "he's not Steve" (which leaves any name but Steve available), versus saying "he's not single", which by elimination means he's involved in some manner. So while you may find it confusing in verbiage, I'm not defining it by one random thing that it can't be among a horde of other alternatives - but rather by what it must be, by elimination, within a finite category of options. It's not a whole number, and it can't convert to a fraction by using whole numbers.

People who are good at math spend years learning it and practicing it. I'd probably give you more credit for trying to understand math if you spent less time trying to argue about what you think math is, and more time learning things rather than flexing what you think you already think you know.

Everything in life is the exact opposite of how you think it is.

There are more species of parasitic animals than there are of free living animals (the tapeworms and leeches are the majority).

There are more porno movies than there are non porno movies.

And... there are more irrational numbers than there are rational numbers (both numbers are infinite in number but the infinity of irrational numbers is a bigger infinity than that of the rational numbers).

Most numbers have an infinite sequence of digits to the right of a decimal point that never have any pattern, rhyme, or reason (like Pi). Only the few are stolid like integers (1,2,4), or are fractions that yield a repeating pattern to the digits (like one third is 1.333333...).

Thats just the way it is.

So thats what math, and mankind, hafta deal with.