"The true metaphysics of the square root negative 1 remains elusive." - C.F. Gauss

[AProudLefty]

Irrelevant. You can't take the square root of a negative number.

And yet it is done. And a field is created out of it. Many applications.

 

[IBDaMann]

And yet it is done. And a field is created out of it. Many applications.

Great pivot into a subjuctive fallacy to EVADE my question.

 

[AProudLefty]

Great pivot into a subjuctive fallacy to EVADE my question.

Imaginary question.

 

[IBDaMann]

Imaginary question.

Nope. The reason you cannot take the square root of a negative number is that it can give the wrong result, i.e. it's bad math, it produces errors and yes, as you noted, this is nonetheless done. So who is responsible for the damages and deaths caused by people who insisted on using bad math?

 

[Trumpet]

You aren't allowed to take the square root of a negative number, even if you have a j operator.

You need to get an education, before you start lecturing, and you might start here.

https://www.electronics-tutorials.ws/accircuits/complex-numbers.html

 

[Cypress]

You need to get an education, before you start lecturing, and you might start here.

https://www.electronics-tutorials.ws/accircuits/complex-numbers.html

It's like beating a dead horse, eh?
Some people are incapable of learning. From your link:

"But real numbers are not the only kind of numbers we need to use especially when dealing with frequency dependent sinusoidal sources and vectors. As well as using normal or real numbers, Complex Numbers were introduced to allow complex equations to be solved with numbers that are the square roots of negative numbers, √-1.

In electrical engineering this type of number is called an “imaginary number” and to distinguish an imaginary number from a real number the letter ” j ” known commonly in electrical engineering as the j-operator, is used. Thus the letter “j” is placed in front of a real number to signify its imaginary number operation."

 

[Trumpet]

Nope. The reason you cannot take the square root of a negative number is that it can give the wrong result, i.e. it's bad math, it produces errors and yes, as you noted, this is nonetheless done. So who is responsible for the damages and deaths caused by people who insisted on using bad math?

It's like beating a dead horse, eh?
Some people are incapable of learning. From your link:

"But real numbers are not the only kind of numbers we need to use especially when dealing with frequency dependent sinusoidal sources and vectors. As well as using normal or real numbers, Complex Numbers were introduced to allow complex equations to be solved with numbers that are the square roots of negative numbers, √-1.

In electrical engineering this type of number is called an “imaginary number” and to distinguish an imaginary number from a real number the letter ” j ” known commonly in electrical engineering as the j-operator, is used. Thus the letter “j” is placed in front of a real number to signify its imaginary number operation."

He's not the sharpest knife in the drawer.

 

[Cypress]

You can't take the square root of a negative number.

That's only true for the set of real numbers, i.e. the integers, rational numbers, and irrational numbers on the real numbers line.

1. You didn't say that.

I've only been talking about numbers, in that context I was obviously referring to the infinite sets of numbers. I wasn't referring to the size of the universe, which is unknown and speculative.

As per Gregor Cantor, you can prove things about the infinite sets of numbers. You can't prove anything about the size of the universe, so it's not even relevant to the discussion.

 

[Bai Lan]

The researchers cited in the article claim that the underlying math for quantum systems requires imaginary numbers, and cannot be duplicated with real numbers.

That seems to imply that while imaginary numbers are a convenience in classical physics, they are an inherent part of the description of quantum reality.

I have no reason at this point to doubt what these researchers published.

quantum physics is all wrong.

electrons are not even negative.

every "electron" is a dipole magnet.

terrence Howard has solved the three body problem.

Eric weinstein is a fool.

 

[Cypress]

quantum physics is all wrong.

A bold claim.

electrons are not even negative.

Pick any word you for the charge, just make it the opposite charge of a positron.

every "electron" is a dipole magnet.

All moving electrically-charged particles create a magnetic field.

terrence Howard has solved the three body problem.

Eric weinstein is a fool.

They don't ring a bell for me.

 

[Bai Lan]

A bold claim.

Pick any word you for the charge, just make it the opposite charge of a positron.

All moving electrically-charged particles create a magnetic field.

They don't ring a bell for me.

thanks for your irrelevancies and stupidity.

 

[Cypress]

Infinity is not larger or smaller than infinity!

1) "There are actually many different sizes or levels of infinity; some infinite sets are vastly larger than other infinite sets."

2) "Strange but true: infinity comes in different sizes."

3) "As German mathematician Georg Cantor demonstrated in the late 19th century, there exists a variety of infinities—and some are simply larger than others."

Here's the simple proof that there must be multiple levels of infinity

A crucial concept in mathematics.

www.businessinsider.com

Strange but True: Infinity Comes in Different Sizes

If you were counting on infinity being absolute, your number's up

www.scientificamerican.com

 

[Cypress]

If Cypuss was actually serious about discussing this he wouldn't be here.

You have no idea how many discussion groups I am in.

More importantly, this thread reached 300 responses precisely because people here who are engineers, science majors, or just interested laypersons contributed to this thread.

If 11th grade math makes you flustered, and you don't have any interest in science, don't click on threads like this

 

[Cypress]

So, if the solutions aren't real, are they surreal? I mean, is that why Salvador Dali's clocks melted, for example?

I think some people elected to take auto shop and gym class in high-school, rather than preparing for college with advanced algebra and precalculus in 11th and 12th grade.

 

[anonymoose]

Same as you’ve amused so many others over the years.You have no idea how many discussion groups I am in.

I’m mildly curious. About how many?

If 11th grade math makes you flustered, and you don't have any interest in science, don't click on threads like this

I lost interest in 11th grade math in the 12th grade.
The only reason I clicked on this thread is because you amuse me.
Same as you’ve amused so many others over the years.

 

[T. A. Gardner]

I think some people elected to take auto shop and gym class in high-school, rather than preparing for college with advanced algebra and precalculus in 11th and 12th grade.

Good choices. The world needs mechanics and ditch diggers too. From what I can tell, only about a third of the population of any country, at most, is college material. Another third or so are people who can do skilled trades that are every bit as important to a modern society as skills derived from college. Then there's the last third. The world needs hairdressers and janitors too...

 

[Into the Night]

"My grasp of complex analysis is quite solid. You need to open your mind to the reality that math is not subjective and that it is never permitted to take the square root of a negative number"

Then how do you explain the J operator which is used in electronics?????? Such has for complex impedance, such as 70-J350.

I already did. He accepted it, and prefers to use i anyway. One letter is like like any other here. YOU can use z for all I care.

 

[Into the Night]

"There are actually many different sizes or levels of infinity; some infinite sets are vastly larger than other infinite sets."

Infinity is not a set. Infinity has no size, Sybil.

 

[Into the Night]

That's only true for the real set of integers, rational numbers, and irrational numbers.

So all numbers.

It was discovered centuries ago that certain polynomial equations had no solutions on the real number line, and required a new concept of number for solutions to be found. That is where imaginary numbers and the complex plane of numbers enters into the history of mathematics.

Complex numbers are not a plane. Polynomials are not complex or imaginary numbers and don't need them. The number line is not a 'solution'.

I was talking about the abstract mathematical concept of infinite sets, not the three dimensional space of the cosmos.

The Universe is infinite. There are no known boundaries to the Universe. There is no 'mathematical concept of infinite sets'.

It comes down to whether you believe mathematics is created or discovered. I believe most professional mathematicians think it is discovered.

Mathematics is created. We wrote the axioms of mathematics, a closed functional system.

 

[Into the Night]

Thanks for explaining how that works in electromagnetism.

He didn't.