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

[Into the Night]

The move you have to make is to open your mind to the possibility that the abstract idea of number includes more than just integers, rational numbers, and irrational numbers.

Buzzword fallacy. There is no 'abstract idea of numbers'.

The idea of infinity,

You can't understand this either. Not mathematics.

and the theorem proving that infinity comes in different sizes

Bullshit! Infinity has no size.

doesn't instantiate itself in any way in the real world.

Buzzword fallacies. Go find out what 'instantiate' means, and what 'real' means.

But what infinity and the complex plane of numbers shows is that there is an objectively real higher reality that does not instantiate itself in our physical reality.

Complex numbers are not a plane. Buzzword fallacies. 'Real' is not a value. 'Real' is not instantiation.

The fact that our mind can't make the connection with things outside of our physical experience,

Bullshit!! People have religions.

or with things seem to defy common sense, is often a limitation of our minds, not of ultimate reality.

Omniscience fallacy. You don't get to speak for everybody. Buzzword fallacy ('real', 'mind').

Your bullshitting won't work, Sybil.

 

[IBDaMann]

The move you have to make is to open your mind to the possibility that the abstract idea of number includes more than just integers, rational numbers, and irrational numbers.

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.

The idea of infinity, and the theorem proving that infinity comes in different sizes doesn't instantiate itself in any way in the real world.

I think everyone has a basic notion of the universe going off into infinity. The universe is certainly in the real world.

But what infinity and the complex plane of numbers shows is that there is an objectively real higher reality that does not instantiate itself in our physical reality.

It does not show this.

The fact that our mind can't make the connection with things outside of our physical experience, or with things seem to defy common sense, is often a limitation of our minds, not of ultimate reality.

I'll grant you this. However, you need to realize that if humans cannot conceptualize it, humans won't be modeling it. Ergo, if you are looking at a model, e.g. "infinity", complex numbers, etc., someone has conceptualized it.

 

[IBDaMann]

Bullshit! Infinity has no size.

Cypress is referring to the denumerable and the nondenumerable flavors of infinite. The set of integers and the set of rational numbers, for example, are both denumerably infinite while the set of irrational numbers is nondenumerably infinite.

Nondenumerably infinite is infinitely larger than denumerably infinite. I hope that clears everything up.

Complex numbers are not a plane.

For the purposes of analysis, the set of complex numbers are treated as a plane. When analyzing real numbers, which we describe with one variable, say R, we arrange them in the number line (i.e. one dimension), with zero being at the center, negative real numbers to the left and positive real numbers to the right. Complex numbers require two variables to be described, R for the real component and X for the imaginary component, i.e. R + Xi. So we expand on the real number line by adding a vertical axis, also centered at zero, for the imaginary component. This forms a plane and the basis for analysis.

From here we get Euler's equation that elegantly brings trigonometry to complex analysis: e^(theta * i) = sin(theta) + i * cos(theta) ... but this assumes the specific complex plane mentioned above.

 

[Into the Night]

Cypress is referring to the denumerable and the nondenumerable flavors of infinite. The set of integers and the set of rational numbers, for example, are both denumerably infinite while the set of irrational numbers is nondenumerably infinite.

Nondenumerably infinite is infinitely larger than denumerably infinite. I hope that clears everything up.


For the purposes of analysis, the set of complex numbers are treated as a plane. When analyzing real numbers, which we describe with one variable, say R, we arrange them in the number line (i.e. one dimension), with zero being at the center, negative real numbers to the left and positive real numbers to the right. Complex numbers require two variables to be described, R for the real component and X for the imaginary component, i.e. R + Xi. So we expand on the real number line by adding a vertical axis, also centered at zero, for the imaginary component. This forms a plane and the basis for analysis.

From here we get Euler's equation that elegantly brings trigonometry to complex analysis: e^(theta * i) = sin(theta) + i * cos(theta) ... but this assumes the specific complex plane mentioned above.

What imaginary component??

 

[Into the Night]

Cypress is referring to the denumerable and the nondenumerable flavors of infinite. The set of integers and the set of rational numbers, for example, are both denumerably infinite while the set of irrational numbers is nondenumerably infinite.

Nondenumerably infinite is infinitely larger than denumerably infinite. I hope that clears everything up.

Infinity is not larger or smaller than infinity. Boundary error.

 

[Trumpet]

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.


I think everyone has a basic notion of the universe going off into infinity. The universe is certainly in the real world.


It does not show this.


I'll grant you this. However, you need to realize that if humans cannot conceptualize it, humans won't be modeling it. Ergo, if you are looking at a model, e.g. "infinity", complex numbers, etc., someone has conceptualized it.

Oh WOW!!!!!! The Great Thinker is an expert mathematician , and now he's giving Cypress a lecture.

 

[Trumpet]

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.


I think everyone has a basic notion of the universe going off into infinity. The universe is certainly in the real world.


It does not show this.


I'll grant you this. However, you need to realize that if humans cannot conceptualize it, humans won't be modeling it. Ergo, if you are looking at a model, e.g. "infinity", complex numbers, etc., someone has conceptualized it.

"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.

 

[Cypress]

Bullshit! Infinity has no size!

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

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

"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]

it is never permitted to take the square root of a negative number.

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

I think everyone has a basic notion of the universe going off into infinity. The universe is certainly in the real world.

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

I'll grant you this. However, you need to realize that if humans cannot conceptualize it, humans won't be modeling it. Ergo, if you are looking at a model, e.g. "infinity", complex numbers, etc., someone has conceptualized it.

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

 

[Cypress]

"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.

Thanks for explaining how that works in electromagnetism.

 

[IBDaMann]

What imaginary component??

If you'd prefer to put the word "imaginary" in quotes, that works, or you can use the word "cyclic". It's math so you can use whatever words or labels (or language) you wish ... but that means that Cypress and others get to use whatever words they wish.

I think you understand that as long as the formal expression is unambiguous, it doesn't matter what words are used when spoken. In fact, deaf mutes can work with complex numbers just fine.

 

[IBDaMann]

"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.

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

 

[IBDaMann]

Thanks for explaining how that works in electromagnetism.

He didn't explain anything. What explanation did you see?

 

[AProudLefty]

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

And yet it is done.

 

[IBDaMann]

Infinity is not larger or smaller than infinity. Boundary error.

Infinity, as a quantity, can be larger than another infinite quantity.

 

[AProudLefty]

Infinity, as a quantity, can be larger than another infinite quantity.

Wow. You said something that is factual, Dum-dum Boy.

I'm proud of you.

 

[IBDaMann]

And yet it is done.

What happens when an error is produced? Who's responsible? Do you remember the Space Shuttle explosion of '86? Maybe someone tried to take the square root of a negative number. Sometimes when engineers make insidious errors, people die, or there are electrical disasters, or devastating fires. Is that sufficient concern?

 

[IBDaMann]

Wow. You said something that is factual, Dum-dum Boy. I'm proud of you.

You should try it. It's excellent.

 

[AProudLefty]

What happens when an error is produced? Who's responsible? Do you remember the Space Shuttle explosion of '86? Maybe someone tried to take the square root of a negative number. Sometimes when engineers make insidious errors, people die, or there are electrical disasters, or devastating fires. Is that sufficient concern?

 

[IBDaMann]

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

Nope.

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.

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

That is where imaginary numbers and the complex plane of numbers enters into the history of mathematics.

I get it, but you still cannot take the square root of a negative number, even in complex analysis. Why are you, of all people, giving me, of all people, pushback on this? Why don't you simply research the mathematical proof for why it is never permissible to take the square root of a negative number? You could have already done this.

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

1. You didn't say that.
2. Infinite sets have been conceptualized, as has the value of "infinity".

It comes down to whether you believe mathematics is created or discovered.

Mathematics is created. Every theory is a set of axioms riding on logic. Sure, things are discovered, but humans have to create the models for those things that are discovered.

I believe most professional mathematicians think it is discovered.

There isn't a methematician alive who thinks that any math just somehow created itself, and that it somehow hung out in a cave awaiting to be discovered.