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

IBDaMann said:
Self-defense, as in defensiveness.
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I assume you mean defense of his ego. He can't defend it. He doesn't seem to know how.
IBDaMann said:
Exactly, but he has to appear as though he is "too smart for you, and too important to bother with you."
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The very nature of The Elite attitude. All it shows, of course, is that he is quite ignorant and illiterate.
IBDaMann said:
Exactly. He just issues curt cryptic quips (did you notice my use of alliteration?) as a facade of participating in a value-added manner. Please recall his claims of having a degree in math as well as in science and in whatever else he has initiated discussions.
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Again, The Elite attitude. He is a nothing, as both you and I recognize.
IBDaMann said:
Yep, that's what I mean. His greatest fear is the "Cypress Bane", i.e. that people will recognize someone else as the authority on some subject.
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...and his ego suffers greatly because of it. He can't defend it.
 
Cypress said:
I haven't posted anything that is beyond what somebody who took math in 11th grade couldn't intuitively grasp.

The fact you believe this knowledge could only come from sophisticated AI software programs is a comment on your level of education.
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So you figure that everyone that took 11th grade math is a bullshitter like you? What makes you think that, Sybil?
 
AProudLefty said:
  • Wavefunctions and Probability Amplitudes:
    In quantum mechanics, wavefunctions (denoted by ψ) are complex-valued functions that describe the state of a quantum system. The square of the magnitude of the wavefunction ( |ψ|² ) gives the probability density of finding the system in a particular location or state. Using complex numbers allows for the inclusion of phase information, which is crucial for describing interference phenomena in quantum systems.

  • Linear Algebra and Superposition:
    Quantum systems are linear, meaning that any solution to the Schrödinger equation can be multiplied by a complex number, and any two solutions can be added together, and the result is still a solution. This allows for the concept of superposition, where a quantum system can exist in a combination of multiple states simultaneously.

  • Spin and Half-Integer Spin Particles:
    The spin of particles, a fundamental property in quantum mechanics, is often described using complex numbers. Half-integer spin particles (like electrons) require complex numbers for their rotation and other transformations.

  • Mathematical Convenience and Generalization:
    Complex numbers provide a more compact and convenient mathematical framework for describing quantum phenomena, including the evolution of quantum states over time. They also allow for the generalization of concepts from classical physics to the quantum realm.

  • Experiments Reveal Necessity:
    Recent experiments have shown that a quantum theory based on real numbers alone cannot fully reproduce experimental results, further solidifying the need for complex numbers in quantum mechanics.
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And....
 
Bai Lan said:
How many not numbers are there?
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There are infinite not numbers, nondenumerably so.

How many numbers are there?

The answer depends on the kind of number. If you are talking about integers (3, 85,104,17, etc), for example, then that quantity is denumerably infinite. If, on the other hand, you are talking about real numbers (2.6, 17.785, 2678.91, 0.0034, etc.), then that quantity is nondenumerably infinite.
Denumerable means discrete, or countable, whereas nondenumerable means nondiscrete and uncountable. Nondenumerably infinite is infinitely more infinite than mere denumerably infinite.

The set of real numbers is comprised of two sets of numbers, 1) rational numbers and 2) irrational numbers. The rational numbers are denumerably infinite while the irrational numbers are nondenumerably infinite. Ergo, the set of real numbers is nondenumerably infinite, owing to the irrational numbers.

Bai Lan said:
A gazillion.
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Roughly.
 
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