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Whole numbers and rational numbers imply staticity whereas irrational numbers imply dynamism.
Imaginary numbers are a dimension higher than the current one. This is why we call it an aethereal constant that can be applied into various sciences, not just Physics.
- This is why Descartes called it an unreal number
While irrational numbers are on the same dimension continuing laterally, imaginary numbers are on a higher dimension acting as a template or filler for the current dimension.
i or imaginary number is the square root of -1.
- From the view of the Negative Force, this can be seen as a unit void which is probabilistic
- From the view of the Postiive Force, this can be seen as a unit spin which is also probabilistic
Superphysics Note!
In a nutshell, Math is for 1st-3rd density perceptions. Supermath is for 4th density. Qualimath is for 5th-6th density. We assume 7th density is purely intuitional and uses no logic.
In Physics, this is best seen as i in the Schrodinger Equation which is probabilistic.
The History of Imaginary Numbers:
| Year | Event |
|---|---|
| 1545 | Gerolamo Cardano publishes Ars Magna, solving depressed cubic equations. He called these results “as subtle as they are useless” and ignored them |
| 1572 | First Serious Treatment when Rafael Bombelli publishes L’Algebra. He develops rules for manipulating “plus of minus” ( ) and “minus of minus” ( ) and proving imaginary expressions could yield real results |
| 1637 | René Descartes coins term “imaginary” in La Géométrie because they were “neither nothing, nor greater than nothing, nor less than nothing” |
| 1748 | Leonhard Euler introduces notation for |
| 1799 | Gauss proves Fundamental Theorem of Algebra, requiring complex numbers. Gauss: “The true metaphysics of is elusive” |
| 1797 | Caspar Wessel(Norway) first plots complex numbers as points in plane |
| 1806 | Jean-Robert Argand independently develops same idea |
| 1831 | Carl Friedrich Gauss publishes comprehensive geometric interpretation. Complex numbers become 2D vectors: |
Application Boom
- Fluid dynamics: Complex potentials for incompressible flow (d’Alembert, Euler)
- Electromagnetism: Complex notation simplifies Maxwell’s equations
- Pure mathematics: Complex analysis becomes richest branch of analysis
Timeline Summary
| Year | Development | Significance |
|---|---|---|
| 1545 | Cardano’s cubic formula | First unavoidable appearance of √-1 |
| 1572 | Bombelli’s rules | First manipulation of complex numbers |
| 1748 | Euler’s formula | Connection to trigonometry |
| 1797 | Wessel’s geometric plot | Visualization of complex numbers |
| 1831 | Gauss’s full treatment | Complete geometric interpretation |
| 1926 | Schrödinger equation | becomes physically fundamental |
| 1948 | Feynman path integrals | Complex phases central to quantum sums |
| 1968 | Veneziano amplitude | Birth of string theory (uses complex analysis) |
| 1984 | Calabi-Yau compactification | Complex geometry essential for strings |
| 1990s | Mirror symmetry | Deep connections in complex geometry |
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