Crossing dimensions by Wessel’s complex plane

[AntonioLao]

In 1797, the Norwegian surveyor Casper Wessel made a historic discovery for the idea of complex planes. These planes contain all the complex numbers. Each complex number is composed of a real part and an imaginary part. Each part is considered as a dimension. Therefore, the complex plane is two dimensional as implied by the definition of a plane.

In 1905, Einstein used the idea of complex planes to formulate his special theory of relativity. This is done with a subtle modification that the real 1-dimensional part is separated into three distinct dimensions comprising 3D space. But if the universe is considered as a complex plane with two dimensions (the real and the imaginary) then the 3D spaces are all linear projections onto the real axis of the complex universal plane.

In 1915, Einstein extended the complex planes into complex surfaces with their corresponding curvatures. With the idea of curvature associated to a particular complex surface, Einstein was implying the cardinality of complex numbers, i. e., one number can be determined larger than another. In truth, since the complex numbers are not points on a line, they cannot be distinguished as to which one of two complex numbers is the larger. Cardinality in complex number does not exist and is meaningless for its existence.

So, for the practical purpose of crossing from the 3D dimensions of space into the imaginary 1-dimension of time, all one has to do is to multiply oneself by the pure imaginary number i equals [math]\sqrt{-1}[/math], that is defined in mathematics as the square root of negative 1. the pure imaginary number is neither a positive number nor a a negative number. Crossing successive dimensions can be done by multiplications of power of i according to the cyclical exponents.

[math] i^0 = 1 [/math]
[math] i^1 = i [/math]
[math] i^2 = -1 [/math]
[math] i^3 = -i [/math]

[math] i^4 = 1 [/math]
[math] i^5 = i[/math]
[math] i^6 = -1 [/math]
[math] i^7 = -i[/math]

[math] i^8 = 1 [/math]
[math] i^9 = i [/math]
[math] i^{10} = -1 [/math]
[math] i^{11} = -i [/math]

each of these sets of exponential power cycles of square root of negative one comprises a Level Of Existence (LOE).

Power 0,1,2,3 comprise the 1st LOE.
Power 4,5,6,7 comprise the 2nd LOE.
Power 8,9,10,11 comprise the 3rd LOE.
so on and so forth….

[Guille]

how can something physical "multiply" by a number?


Also, just as related subject, there is a proof I read about 1=-1 via i and I wanted to ask if there is any wrong thing or fallacy in it, please tell me:

1^2=sqrt(-1*-1)
1^2=sqrt-1*sqrt-1
1^2=i*i
i*i=i^2
i^2=sqrt-1^2
sqrt-1^2=-1
-1=1=-1

[dleviwing]

Antonio;
Do you believe complex numbers have any real place in describing the reality of the universe? It is useful for electronic calculation for transmitters and RF power circuits, but not as a descriptor of real physical phenomena.
Einstein's mathematics are useful tools but should not be literally interpreted into reality.

[AntonioLao]

1^2=sqrt(-1*-1)

according to PEMDAS rule of operations, the parentheses is operated 1st, then the square root or exponentiation, then multiplication then divsion then additon then subtraction.

[AntonioLao]

Do you believe complex numbers have any real place in describing the reality of the universe?

math is a product of our imagination but most often math is used to solve various real problems like making a computer or transmitting radio signals. No communication engineers can proved the existence of EM waves, but nonetheless they can be used to do work such as relaying this message by the internet.

[Guille]

according to PEMDAS rule of operations, the parentheses is operated 1st, then the square root or exponentiation, then multiplication then divsion then additon then subtraction.

I wrote the parentheses only so it wasn't confusing.

1^2=sqrt-1*-1

(the wrong thing is that I'm using normal writing, so it is sort of confusing).

[dleviwing]

Antonio;
I can demonstrate EM radiation, can you demonstrate the square root of -1??

[AntonioLao]

can you demonstrate the square root of -1??

the complex plane is shown by the Argand diagram

http://mathworld.wolfram.com/ArgandDiagram.html

I wrote the parentheses only so it wasn't confusing.

just the same, the square root operation must be done first. multiply -1 and -1 first then square root of 1 is 1.

[Guille]

just the same, the square root operation must be done first. multiply -1 and -1 first then square root of 1 is 1.

OK, but still works because 1^2 is actually 1.

[AntonioLao]

in binary number system, infinity is equal to ...1111111111111111111111111 there are as many ones as a person can write down forever but infinity minus 1 is ...1111111111111111111111110.