Could there be a logical explanation for our universe? (# 4)

This article sets out a possible foundation for a logical explanation of the origin of our universe. The aim is to set out ideas about how a logical explanation could be developed rather than to claim discovery of THE foundation.

Modern science seems to suggest that ‘we are random fluctuations in a meaningless universe’. This implication is emotionally unappealing. The lack of appeal doesn’t make the science wrong but it does motivate a challenge to find an alternative logical explanation. The Big Bang theory suggests either the universe was created out of nothing; or the universe was born out of the ‘ashes’ of a previous universe in a cycle which has no beginning or end. A variant of such ideas is that our universe is part of a multiverse consisting of all possible universes.

None of modern science’s ideas about the origin of the universe address the issue of providing meaning to our lives. Many scientists postulate that some kind of consciousness created our universe but there is little agreement among such scientists on the origin of that consciousness or what the purpose of consciousness might be in creating our universe.

A less popular ontology is the idea that our reality emerges out of mathematics. A relative lack of discussion of this possibility may be due to the fact that there is no generally agreed explanation as to how consciousness could arise from mathematics. An aim of these articles is to contribute ideas about how and why mathematics, initially geometry, leads to consciousness and ultimately to the creation of our universe.

Does Laplace’s demon predict how the universe evolves?

Max Tegmark, Professor of Physics at Massachusetts Institute of Technology in USA, has proposed a Mathematical Universe Hypothesis (MUH) where he argues our external physical reality is a mathematical structure. According to Tegmark, in worlds that are complex enough to contain self-aware substructures, these substructures will subjectively perceive themselves as existing in a physically ‘real’ world. Sabine Hossenfelder in her popular YouTubeChannel also asks the question ‘Are We Made of Maths’? Hossenfelder concludes the idea we are made of maths is not wrong, just not scientific.

While these articles expand on the idea that our ultimate reality is mathematical, a specific explanation is proposed for the origin of the mathematical structure of reality rather than Tegmark’s idea that ‘all structures that exist mathematically also exist physically’. As a result, the consequent conclusions about the nature of our reality are not necessarily the same as Tegmark’s. With regard to Hossenfelder’s view that the idea of being made out of maths is not scientific is addressed by providing empirical evidence to support a different interpretation of dark matter.

Space-time

Einstein’s Theory of General Relativity includes a term called the Cosmological Constant. Some cosmologists suggest this term measures the curvature of space-time. According to scientists, our universe may have a very slight positive curvature. Space-time with uniform positive curvature is called De-Sitter space. Space-time with uniform negative curvature is called Anti-de Sitter (AdS) space. The curvature of space has important implications for the geometry of shapes in that space.

For thousands of years, mathematicians tried to find a set of postulates or axioms that would provide a logical, consistent basis for mathematical theory. For example, the Greek mathematician, Euclid, set out five postulates for a theory of geometry, Elementary Euclidean Geometry (EEG), but no one was able to prove that his fifth or parallel postulate is consistent with the other four.

In the early 1930s, a young mathematician, Kurt Gödel, discovered two Impossibility Theorems. He showed that, under certain circumstances, it was impossible to develop a self-consistent set of axioms as the foundation for mathematical theory. A self consistent set of axioms would not require any external assumption to prove the deductions of the theory. Gödel’s theorems raised the possibility that there could be no unique mathematical explanation for our universe.

Several years later, another mathematician, Alfred Tarski, proved that EEG is self consistent in an AdS universe. An AdS universe is describable in mathematics and EEG is describable in mathematics. A mathematical theory does not necessarily have a beginning; it may need to discover itself but it does not need to be created.

EEG includes the Platonic solids. In three-dimensional space, a Platonic solid is a regular, convex polyhedron. Each solid is: identical in shape and size; all angles are equal; all sides are equal; and the same number of faces meet at each vertex. The five Platonic solids are: a Tetrahedron with four triangular sides, a cube (Hexahedron) with six square faces; an Octahedron with eight triangular faces; a Dodecahedron with twelve faces each shaped like a five sided pentagon; and an Icosahedron with twenty triangular faces.

Sacred Geometry

The discovery that Platonic solids can be self-consistently described in AdS space provides support for the belief in Sacred Geometry as the origin of the universe. According to Wikipedia:

Sacred geometry ascribes symbolic and sacred meanings to certain geometric shapes and certain geometric proportions. It is associated with the belief that a god is the geometer of the world.

While Sacred Geometry is usually associated with belief in a god, the idea advanced in these articles is that Sacred Geometry may explain the origin of a god. In other words, some form of god arises out of Sacred Geometry rather than god being the geometer.

Sacred Geometry is not only concerned with geometric shapes but also certain geometric proportions. One of these proportions is also known as the Fibonacci sequence. Starting with 0 and 1, each subsequent number in the sequence is the sum of the two previous numbers. As the numbers get larger, the ratio of two adjacent numbers converges to the Golden Ratio of 1.618033… In other words, as the numbers get large, there is a nearly constant relationship between two adjacent numbers.

One description of AdS space-time consists of three physical dimensions (up/down, right/left and front/back) as well as a time like dimension. The Fibonacci sequence is consistent with a time-like dimension. The sequence constantly increases although the rate of increase converges toward a constant value. Individual numbers in the sequence can be characterised as ‘before’ and ‘after’. AdS space-time could consist of Platonic solids with a time-like dimension consisting of Platonic solids increasing in size in the same proportion to the numbers in the Fibonacci sequence.

At the moment, this is all mathematics. Mathematicians, however, have researched AdS space-time in some detail because such research could lead to an understanding of what happens inside a black hole in De-Sitter space when a mathematical singularity is encountered. Cosmologists have discovered that a mathematical relationship, a correspondence, could exist between what happens in AdS space-time and De-Sitter space-time; this is called the AdS/CFT correspondence where the letters CFT stand for Conformal Field Theory.

This mathematical research shows an AdS universe could have features significantly different to our De-Sitter universe e.g. AdS universes have imaginary boundaries something like mirages or rainbows in our world. A boundary in AdS space is a hologram displaying the contents of the AdS space in one less dimension. Another feature of an AdS universe is that it could contain black holes (mathematical singularities) where the content inside the black hole has an extra time-like dimension compared to the space-time surrounding the black hole.

These features will be examined in more detail in subsequent articles. To explain how the features are relevant to the origin of our universe, some ideas are needed to explain how unknown properties could emerge in a universe. Furthermore, there is a need to explain the origin of features in AdS space. To assist in understanding the logic behind these articles, the next article provides a brief synopsis of the subsequent twelve articles.

Sacred Geometry provides a geometry for space-time but assumes there is a God or consciousness, a divine geometer. Modern physics describes where consciousness comes from but does not explain where either space-time or the laws of physics come from. The aim of these articles is to combine insights from both these points of view. Sacred Geometry explains where the laws of physics i.e. geometry, come from; and modern physics explains why there may be a divine geometer. Some implications of this consolidation are also discussed.

Testing truth value

As discussed in the previous article, analogous to Wheeler’s game of 20 questions, each of these articles will end by asking a question. These questions are intended to help shape ideas consistent with a reality that provides our life with some kind of meaning. There are many ways of testing the truth value of an answer to a question, for example watch this YouTube Video How to Muscle Test YOURSELF. For some people, muscle testing may only be applicable once they have acquired an understanding about it could work. Quite possibly, muscle tests will not work for everyone. Until the ideas behind these tests have been discussed, the answers to the questions could be based on your conscious opinion.

The question to be tested in this article is:

Could our universe have been created inside a universe with physical laws different to ours?

A more specific question is:

Could cosmologists be misguided in assuming the fabric of our universe has positive curvature?

To obtain a copy of the book ‘Orbiting Stars’ which contains the first drafts of all these articles, please visit www.amazon.com

To view the headings of all the articles to be published in this series please click on https://readmedium.com/orbiting-stars-and-origin-of-our-universe-338906930f51