According to new research, if we try to leave them out of quantum mechanics, our description of nature becomes faulty:

“Without imaginary numbers, the device on which you are reading this article probably wouldn’t even work. As science writer Padavic-Callaghan points out, When you set out to try and capture a quantum state in the language of mathematics, these seemingly impossible square roots of negative numbers are an integral part of your vocabulary. Eliminating imaginary numbers would highly limit how accurate of a statement you could make. The discovery and development of quantum mechanics upgraded imaginary numbers from a problem seeking a solution to a solution that had just been matched with its problem. As the physicist and Nobel laureate Roger Penrose noted in the documentary series Why Are We Here? (2017): ‘[Imaginary numbers] were there all the time. They’ve been there since the beginning of time. These numbers are embedded in the way the world works at the smallest and, if you like, most basic level.’ – Karmela Padavic-Callaghan, “Imaginary Numbers Are Real” at Aeon (July 14, 2022)”

News, “Recent research: Imaginary numbers are part of the real world” atMind Matters News(July 17, 2022)

*Takehome:* Perhaps the universe is bound to seem mysterious, in part because it is not wholly material. It keeps the rules but the rules are not always what we expect.

*You may also wish to read:* *You may also wish to read:* Yes, you can manipulate infinity in math. The hyperreals are bigger (and smaller) than your average number — and better! *(Jonathan Bartlett)*

As to the Aeon headline; “Imaginary numbers are real”,

The finding that “Imaginary numbers are real” makes what was already an intractable problem for Atheistic Materialists that much worse still.

To start off with, Atheistic Materialists simply have no clue why mathematics should even be applicable to the universe in the first place.

This is because mathematics is profoundly immaterial in its foundational essence,

In fact, no less than Eugene Wigner and Albert Einstein are both on record as to regarding the applicability of mathematics to the universe to be a miracle.

Eugene Wigner, (who received a Nobel prize for his work in the foundations of quantum mechanics, and after rightly calling into question the ability of Darwin’s natural selection to produce our ‘reasoning power’), stated that, “It is difficult to avoid the impression that a miracle confronts us here,,, and “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.,,”

Likewise, Albert Einstein himself is also on record as to regarding the applicability of mathematics to the universe to be a ‘miracle’. Einstein even went so far as to chastise ‘professional atheists’ in the process of calling it a ‘miracle’.

And the last time I checked, miracles are considered to be the sole province of God:

What is so interesting in particular about “Imaginary Numbers” being found to be “Real” is that imaginary numbers, particularly the square root of negative one (i), is essential for understanding the ‘wave packet’ in quantum mechanics prior to measurement, and/or prior to the ‘collapse of the wave function’, (but is not required after the ‘collapse of the wave function)

Moreover, to make the dilemma even more vexing for Atheistic Materialists, the wave function, prior to collapse of the wave function, is mathematically described by an ‘infinite dimensional’ Hilbert space,

Moreover, this ‘infinite dimensional’ Hilbert space takes an infinite amount of information to describe properly,

To point out the obvious, the ‘infinite dimensional’ Hilbert space corresponds to the Theistic attribute of omnipresence. Whereas the infinite information that is required to describe the ‘infinite dimensional’ wave function prior to collapse corresponds to the Theistic attribute of omniscience.

In short, the finding that “Imaginary numbers are real” makes what was already an intractable problem for Atheistic Materialists that much worse still since it is rather stunning confirmation of the Christian’s contention, (via Neoplatonic philosophy and Augustinian theology), that the (higher dimensional) mathematics that are found to describe this universe really are “God’s thoughts”. Just as was originally held by the Christian founders of modern science.

Verse:

Of supplemental note, not only do Atheistic Materialists have no realistic clue why mathematics should even be applicable to the universe in the first place, they also have no clue how we can comprehend this immaterial world of mathematics.

In 2014, a group of prominent Darwinists, who are leading experts in this area of research, authored a paper in which they honestly admitted that they have, “essentially no explanation of how and why our linguistic computations and representations evolved.”

No less than Alfred Wallace, Darwin’s contemporary, considered our ability ‘do math’, among other things, to be proof that man must have an immaterial soul.

Of note:

H’mm, how about the 2-d vector approach?

Such are relevant to the phenomena of quantum mechanics, and of course we get exponential forms too.

This is a small part of why I argue that for any distinct possible world, we find N,Z,Q,R,C,R* etc, with structures and relations, so a core of the logic of structure and quantity is trans-world applicable, giving Mathematics its universal, actually trans-universal, power.

That answers Wigner of course but is huge: we have a mental tool pivoting on logic that extends to any possible world.

Worlds and minds are powerfully connected.

KF