"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.