Mathematical Cranks and Fallacies

[Irish Caesar]

I find math to be a waste of time, money and resources (for me atleast). All you need to know is a few applicable concepts and know how to apply them. They are all what you will need. Why do I have to learn in school all the unnecessary math when I do not even enjoy it?
I will never need to use 95% of it anyway. We have computers that can do the math for people like me (who are also the majority).

What do you do for a living?

 

[warpus]

I find math to be a waste of time, money and resources (for me atleast). All you need to know is a few applicable concepts and know how to apply them. They are all what you will need. Why do I have to learn in school all the unnecessary math when I do not even enjoy it?
I will never need to use 95% of it anyway. We have computers that can do the math for people like me (who are also the majority).

I've taken way too much math.. It's really helped me to become a better critical thinker.. and it has HUGE applications in all sorts of fields..

While I don't use the math I learned in school every day, or even every week, I'm glad that I know all that stuff.. It helps my mind think in very abstract ways.

 

[sanabas]

I liked that first one, and am amazed it snuck through review and got published.

Personal favourite is that p-->q means that q-->p. I've seen a lot of people use it, not just in maths.

 

[Erik Mesoy]

~q => ~p is the correct one, right?

 

[sanabas]

~q => ~p is the correct one, right?

yep.

 

[Mise]

We still cross multiply:

(+-1)(+-1) = (+-i)(+-i)

Since both terms on both sides of the equations are the same, we can rewrite them as:

In this step, you wrongly assume that both sides of the equation contain the same terms. Ignoring the +/- i (which should just be i by definition), there are 4 possibilities for the root of each "1":

(+1)(+1) = i*i .................. <-- this one is wrong, so we've picked the wrong roots
(-1)(+1) = i*i ................... <-- this one's correct, so is one possible solution
(+1)(-1) = i*i ................... <-- this one's also correct, and is the other possible solution
(-1)(-1) = i*i ................... <-- this one is wrong, so again we've picked the wrong roots

The first time the proof was presented, you chose only the first possibility, which was wrong. The second time, you chose the first and last possibilities, which were also wrong.

 

[pboily]

It's good to realize every once in a while that there are a whole lotta people smarter then yourself. Keeps you humble.

Manipulating symbols according to rules you make up doesn't make you smart, RedWolf, it's a game, nothing less, nothing more.

 

[pboily]

I find math to be a waste of time, money and resources (for me atleast). All you need to know is a few applicable concepts and know how to apply them. They are all what you will need. Why do I have to learn in school all the unnecessary math when I do not even enjoy it?
I will never need to use 95% of it anyway. We have computers that can do the math for people like me (who are also the majority).

Well, mathematicians aren't the ones who force you to take the course, we would much rather teach it to enthusiastic students.

Warpus said it best. But I will add that Business Schools, Engineering Schools, etc... don't insist that their students take these "useless" courses because the material they will ever apply anything they learn one day (your boss will never rush in your office, slam her hand on your desk and say: "I need you to differentiate this function, pronto!", but the same is true of just about anything you'll learn at University), rather, it's to show potential employers that you can do difficult things that you do not understand and see them through. A pretty usefull skill...

 

[Tank_Guy#3]

This one that people usually make the mistake of believing because of a common saying:

What is the shortest distance between two points? They answer "a straight line"

WRONG!!!!!!!!!!!!!!!!!!

It's a line segment. Between two POINTS.

It's really simple, but I'm a math simpleton.

 

[newfangle]

When you take the square root of something, you get two solutions, a positive and a negative one. You have assumed the positive solution, which, since you got the wrong answer, was the wrong solution to pick.

That is wrong. There is only one positive solution to sqrt(x), namely, sqrt(x). (for x positive obviously).

There are two solutions, however, to x^2 = y.

Just to be extra pendantic, here is why. Suppose we want to find sqrt(25). Well, it equals 5 obviously. But can it equal -5? Suppose it can. Then -5 = sqrt(25) = sqrt(5^2) = 5^[(1/2)*2] = 5, a contradiction. (this is assuming that power laws may be used for positive integers, which they can if Peano's axioms are assumed to be true).

EDIT: Although you were talking specifically about taking the roots of complex numbers, so I might forgive you.

 

[Mise]

You're probably right, but....

"-5 = sqrt(25) = sqrt(5^2)"

it CAN equal that, or it can equal sqrt((-5)^2), in which case there's no contradiction. What's wrong with that?

 

[Erik Mesoy]

My take on it:

-5 != sqrt(25) = sqrt(5^2)

Because:

sqrt((-5)^2) = sqrt(25) = 5

With the nonobvious element being that ^2 and sqrt are not opposite operations when applied in that order to a negative number.

 

[newfangle]

That, being presicely what I wrote, Erik.

 

[mdwh]

I find math to be a waste of time, money and resources (for me atleast). All you need to know is a few applicable concepts and know how to apply them. They are all what you will need. Why do I have to learn in school all the unnecessary math when I do not even enjoy it?
I will never need to use 95% of it anyway. We have computers that can do the math for people like me (who are also the majority).

You could say that of every subject in school - most of it is useless if you're not doing a job that might need it. But it's good to keep options open, since many jobs may require at least some basic maths occasionally (unless you're happy flipping burgers). Note that a computer only does the arithmetic, it won't do maths in general, you have to know what sums to tell it to do.

In my opinion at least one area is important for everyone, even if they don't need it in their job: Statistics. We have statistical information thrown at us by the media and elsewhere, which influences people in all sorts of decisions such as what to buy, who to trust, which party to vote for. But it's worrying how little many people understand statistics (e.g., it's common for people to see "X% of group A are in group B" as being equivalent to "X% of group B are in group A").

Also, even simple things like numbers are important - words like "billions" are commonplace, but I do wonder how many English people mistakenly think this means "a million million" rather than "a thousand million"...

 

[Lambert Simnel]

Also, even simple things like numbers are important - words like "billions" are commonplace, but I do wonder how many English people mistakenly think this means "a million million" rather than "a thousand million"...

Well, it's not so much a case of mistaken thinking as simply a different definition. For a long time the UK definition of a billion was a million million. Nowadays I think we've just about all accepted that it's easier to use the US definition (just due to the wideness of it's use), but I think that this should be a cause for complimenting us on our reasonableness and lack of dogmatism, rather than saying that we make mistakes...

 

[Erik Mesoy]

Norway still uses the long scale, and it gives us more numbers to work with:
Thousand - million - milliard - billion - billiard - trillion - trilliard.

That, being presicely what I wrote, Erik.

But it needed to be said a second time.

 

[History_Buff]

Why do I have to learn in school all the unnecessary math when I do not even enjoy it?

Why learn math? Because you're gonna need it for all tests you're going to have to write before you finish Highschool and University. Not useful you say? This is false. It is useful for the quiz, it is useful for the midterm, it is useful for the final.

 

[kingjoshi]

You could say that of every subject in school - most of it is useless if you're not doing a job that might need it. But it's good to keep options open, since many jobs may require at least some basic maths occasionally (unless you're happy flipping burgers). Note that a computer only does the arithmetic, it won't do maths in general, you have to know what sums to tell it to do.

In my opinion at least one area is important for everyone, even if they don't need it in their job: Statistics. We have statistical information thrown at us by the media and elsewhere, which influences people in all sorts of decisions such as what to buy, who to trust, which party to vote for. But it's worrying how little many people understand statistics (e.g., it's common for people to see "X% of group A are in group B" as being equivalent to "X% of group B are in group A").

Well, many classes can be useful even if you don't go into that occupation. Making use of the knowledge is a separate issue.

Some basic chemistry classes can help you understand some of the basics in the chemicals in your house (cooking/cleaning/etc). Physics can illuminate your understanding regarding driving. Not to mention give you ideas on how to best use leverage and other ideas if you have to move large objects in your house.

Economics should give you a basic idea and help you understand some proposals by politicians (and the absurdity of some of their idea). Psychology should help you better understand how you function and how the minds of others you must deal with work. At a Civ site, I shouldn't have to explain History and you've already mentioned statistics.

It's not just being able to do something difficult or learning how to learn. Both of which are important. But the information you learn CAN be utilized and help you understand your world better. But if all you care about is just maintaining your grade or don't even show interest in the class, you won't be able to connect it to the ordinary. That's partly a failing of the education system and teachers, but responsibility falls on the student as well.

 

[Erik Mesoy]

Hey, try this link for a general perspective on this sort of debate.

 

[mdwh]

Well, it's not so much a case of mistaken thinking as simply a different definition. For a long time the UK definition of a billion was a million million. Nowadays I think we've just about all accepted that it's easier to use the US definition (just due to the wideness of it's use), but I think that this should be a cause for complimenting us on our reasonableness and lack of dogmatism, rather than saying that we make mistakes...

I mean by "mistake" that when the UK media say "billion" and mean 10^9 (as they always do, now), and someone thinks the media mean 10^12, then they are mistaken. It may be understandable and not their fault due to the confusing definitions, but they have made a mistake nonetheless