How Do You Imagine the Multiverse?

Before my formal college background in mathematics, my vision of the infinite was a simple never-ending series of natural numbers without nothing in the way that could stop it.

Later, after getting acquainted with the theorems of Georg Cantor and his revolutionary vision of the transfinite numbers as a stair of many other super-infinities, my mind was furthermore expanded.

As time went on, a little short story titled The Book of Sand came into my hands. I never suspected that there was another twister waiting to squeeze my mind again. The simplicity of this short story by Jorge Luis Borges viewing the infinite as an incomprehensible chaos eternally randomizing and reconfiguring itself changed my mind forever. Borges’ infinity is the opposite of Cantor’s infinity; however, both are shapes of infinity.

Fortunately, the realm of infinity is not a private property of mathematics, nor of literature, nor of any field of knowledge. So, the science of physics—in its modality of cosmology—also raised its voice and said: here I am, I also have something to say about infinity! There are infinite parallel universes too! This universe is part of a multiverse!

But how do you imagine the multiverse? Do you imagine it as in Cantor-infinite style, or do you imagine it as in the Borges’-infinite-style?

The Fourth Dimension According to Charles Hinton

Surely at some time of your life, you have heard about traveling to the fourth dimension. The are many books—famous books—and many movies—famous movies—around this topic. This means that the topic is of interest to everybody, and not only for a selected group of mathematicians and physicists.

When people are confronted with the subject of higher dimensions, or when asked if they believe in it or not, their answer will vary depending on if their background is more religious than scientific or vice versa.

The fact is that for many people "the fourth dimension" is a place—similar and different to our surrounding three-dimensional world around us. Visualizing it as "place" enable us to enter or exit from it like when going to some kind of theme park. Going to such a place will enlighten and will empower us in such a way that from that experience on to forever we'll be talking about the experience like sacred events that should not be shared with anybody except those "chosen" to experience a trip like ours in the future.

For the privileged beings of this hyperworld, we are seen somewhat as toys that can be manipulated at their will.

In the literature arena of the books, Charles Hinton (1853 - 1907), a British mathematician, occupies the place of one of the initiators among the public the fourth dimension subject. He studied the topic in a reasonable systematic approach, recurring to simple examples and explaining his ideas in nonmathematical terms.

Selected Papers of Charles Hinton
about the fourth dimension

The Selected Papers of Charles Hinton about the fourth dimension is a good compilation of many of his works in a simple nonmathematical language.

Hermann Schubert Probes the Fourth Dimension

Mathematical Essays and Recreations

Hermann Schubert was a German teacher and textbook author. Mathematical Essays and Recreations is a small collection of articles ranging from the foundations of the number system, the foundations of algebra up to an extensive essay about the fourth dimension.

In the first article: Notion and definition of number, Shubert gives a brief account of how the concept of number evolved within the human mind.

In another of his essays: Monism in arithmetic, the author explores and writes about the elementary rules of algebra and about the importance that mathematical systems can operate with defined rules for any kind of number without making exceptions for some of them. For example, we can define the commutative rule of addition for the natural numbers, as in 2 + 3 = 3 + 2, and the same number should apply if instead, we use natural an imaginary numbers combined, like 2 + 3i = 3i + 2. Following his exposition, we can easily see why the class of complex numbers is such a robust field in mathematics, and how it can be derived from the natural numbers following easy and consistent steps. On the other hand, we can also see why the quaternions—when compared to the complex numbers—lack such popularity and why this class of number is so limited in applications and acceptance.

The third essay in this Datum edition is about the fourth dimension. But contrary to other science authors that rarely touch the fourth dimension from the metaphysical point of view, Schubert is not afraid to confront both doctrines. When dealing with the fourth dimension from the mathematical point of view, Schubert goes carefully from the definition of the point to the definition of dimension to a many-dimensioned space.