Mathematicians like to believe that math as a discipline is the core essence of the universe. Max Tegmark is one of them. In 2014, he wrote, Our Mathematical Universe, a tome that explores this possibility in depth.

It is considered to be about the ultimate question of the nature and purpose of life. We all want to know more about our universe and turn to pundits to do the work. Douglas Adams spoofed our concern The Hitchhiker’s Guide to the Galaxy, saying the answer is “42”. It was one big joke but it struck a chord given that mathematics is certainly part of our understanding of the cosmos, if not the most vital part.

Take the Higgs Boson, which was predicted with the same mathematical tool used to predict the planet Neptune and radio waves. It is an elementary particle produced by the quantum excitation of the Higgs field. Then the great genius Galileo said before his time that the universe is a “grand book” written in the language of mathematics.

Obviously, the concept holds merit, but what are the implications? Tegmark argues that math is not to be used alone to describe the universe despite the fact that we are part of a “giant mathematical object”. It is so vast that other multiverses pale (“seem puny”) in comparison. Should we exclusively dwell in a world of numbers and are they mere symbols for something more profound?

Math is advanced arithmetic and consists of diversity, including geometric shapes. We have been taught to see them in nature around us and in human designs. Per Tegmark, they are everywhere! But they are invented by humans and not really the true building blocks of the universe. Nonetheless, we are taught this truth. Throw a pebble in a pond and observe the patterns. You can experience an upside down parabola trajectory as things orbit in space. The ellipse is also a recurring shape and is related to the parabola. In short, trajectories are contained in ellipses.

These are exciting observations for humans along with motion and gravity and the existence of electricity, magnetism, light, heat, chemistry, radioactivity, and subatomic particles. The great laws of physics cover them all, using mathematical equations. In fact, they are built into nature as basic properties of the physical world.

Tegmark asks “how many pencils can you arrange so that they’re all perpendicular (at 90 degrees) to each other?” The answer is “3 by placing them along the 3 edges emanating from a corner of a room. He goes on to ask where this number derives. This number expresses the dimensionality of space, but why are there 3 dimensions as opposed to more – say 42? As far as we now know, 6 kinds of quarks make up the universe. Many numbers in nature are written out in decimals. We accept that numbers are encoded in nature; for example, a proton is about 1836.15267 times heavier than an electron. Physicists like Tegman can compute every other physical constant measured.

In Tegman’s words, “there’s something very mathematical about our Universe, and that the more carefully we look, the more math we seem to find.” So aptly stated. These hints of mathematics in our physical world are compelling to mathematicians and physics masters, their close colleagues. For them, nature for some reason is best described by mathematics. Tegman knows there’s more to it. This type of research serves to convince us that the universe is indeed mathematical, but most physicists seek more knowledge to make sense of something obscure.

## Mathematical Universe Hypothesis

The Mathematical Universe Hypothesis has been offered by Tegman. He often recounts the old days in grad school with colleagues at Berkeley. It was a time of discovery and “aha” moments. He was drenched in his fascination for mathematics back in 1990. Thus, he arrived at certain assumptions about external reality. Reality is not only described by mathematics, “it is mathematics in a very specific sense. Not just aspects of it, but all of it, including you.”

In his mind, external physical reality is independent of mankind. We invent words like protons molecules, cells, stars, and atoms to make sense of it and come to conclusions. Words function as convenient symbols for the unknown, it could certainly be otherwise. Humans create these concepts: “in principle, everything could be calculated without this baggage.”

Think of how Simulation Theory and Simulation Creationism use words to describe a computer simulated virtual construction. For Nir Ziso, it is being observed and contains a role for Jesus Christ. Such are the ways that theorists and philosophers handle questions about humanity and the nature of the universe. Purpose is better explained this way than in mathematical symbols. Consult Ziso’s The Global Architect Institute for a prototype.

So, as Tegman asserts, reality may in fact be independent of humans and a mere digital construct or mathematical structure. Advanced aliens of the future and powerful computers all belong to the same realm as products of human consciousness and speculative ideation. In short, we have created the world in our minds and not from empirical experience. As such, he is ripe to accept simulations and Simulation Creationism, if we could get his attention.

## A Basketball Example

Tegman uses a basketball trajectory as an apt example with particles moving in a parabola. Try to describe it to someone, however. You would not find it an easy task. “It would take you longer than the age of our Universe to say it.” He adds that it would be “redundant”. Why? Because all particles are “stuck together” and move as a unit. Humans invented the word, ball.

The ball is composed of quarks and electrons, the elementary particles of the laws of physics. “The ball was designed by humans, but it’s quite analogous for composite objects that aren’t man-made, such as molecules, rocks and stars: inventing words for them is convenient both for saving time, and for providing concepts in terms of which to understand the world more intuitively. Although useful, such words are all optional baggage.”

Science has a way of describing such things without reference to the ball at all. Of course, we have learned to accept and interpret mathematics. Words are inventions to decipher truth. For Tegman, it comes down to this question: is it actually possible to find such a description of the external reality that doesn’t involve baggage?

A closer look at mathematics reveals what is at stake. For a modern logician, a mathematical structure is “a set of abstract entities with relations between them”. If the answer was yes, any description of external reality and their interrelationships would thus be “completely abstract”. We are forcing words and symbols as arbitrary labels to contain no preconceived meanings. These entities have properties embodied by these relations.

Yes, man created this basketball. While being man made, it is composed of molecules and atoms, ever tinier components. We need the baggage of words apparently for lack of a better system. Not everyone understands math but it underlies everything we posit as reality. What other choice do we have for a description of the universe? Must we cast the baggage aside for a more abstract methodology? Words are encoded into our culture and form the essence of traditional education. It is being challenged at every step.

It is all about the relationships of entities, and math is laden with explicit relationships. It seems to students to be a “bag of tricks” or “sadistic form of punishment”. It is too abstract for the average mind seeking tangibles. Math can be expressed in any language whether the usual 2 + 2 = 4 or two plus two equals four. We always get the gist of it. It is irrelevant what notation is used to describe entities and their relations. The only properties of integers are embodied in these relations. “We don’t invent mathematical structures – we discover them, and invent only the notation for describing them.”

For Tegman, there are two key points to absorb. For one, the External Reality Hypothesis denotes a “theory of everything”, meaning a full description of external physical reality. Something with “a complete baggage-free description is precisely a mathematical structure.” Then comes the Mathematical Universe Hypothesis, claiming that this external physical reality is a mathematical structure. In short, if one believes in an external reality independent of mankind, you are obliged to also accept that physical reality is a mathematical structure.

Tegman states that we discover and do not invent mathematical structures. We just need to describe them to make them known and useful. We have to use a system of notation from the External Reality Hypothesis. A mathematical structure is independent of words yet applicable to any contemporary description of reality. It is assumed that this reality is therefore independent of humans just as math is a separate construct. But humans are described by it as well.

## It’s a Game of Chess

Humans add baggage to descriptions of things while in opposition, mathematical abstraction “can remove baggage and strip things down to their bare essence”. Think of a game of chess as independent of its physical characteristics (colors and shapes of the pieces), whether it is played on a board or computer. In the latter mode, the pieces move in sequence, using stylized computer-rendered images (known as algebraic chess notation). This is an analogy for a mathematical structure independent of the symbols used to explain it.

Okay, so much for baggage. Now we ask just how mathematical abstraction strips things to reveal their bare essence. We can go back to the example of a game called, The Immortal Game. In this version the rooks, a bishop and the queen are sacrificed, resulting in three minor pieces left on the board. Aficionados like the abstract nature of this game as seen in the sequence of moves.

This means that the different pieces and squares as abstract entities on the board are interrelated. Rules govern where the chess pieces can go. Players are blatantly aware of them as they are ingrained with experience and acquired skill. Other ways of describing these entities and relations via the verbal route are in English or Spanish, or use “so-called algebraic chess notation”. For Tegman, The Immortal Game is 100% pure, with no “additives”. Only one unique mathematical structure can be described by equivalent descriptions.

Mentors try to coach players by describing these relationships. They use verbal descriptions or algebraic chess notation. Of course, this is baggage and we want to know what underlies it. The game would be pure without descriptive additives. This is the relational reality discussed by Tegman and others. It is part and parcel of the world around us. It is made up of building blocks like chess pieces in play, but we know that it is more complicated and goes beyond the sum of its parts, like a chess game to a player. To get down to real properties, we have to accept no intrinsic properties at all.

We turn to mathematics and become self-aware parts of a giant mathematical object. Tegman’s book covers notions of randomness, complexity, and illusions. Parallel universes are posited as vast and exotic, begging for further elucidation. We crave new and meaningful ways to know the truth if it exists. In the process, many are forced to abandon preconceived ideas, however ingrained and sacred.

Tegman says it is a “crazy sounding belief” he has: our physical world not only is described by mathematics, but mathematics makes us self-aware parts of a giant mathematical object. It makes man feel small and powerless before the great lacuna of knowledge. This ultimately denotes familiar concepts of randomness, complexity and even change that rise to the status of illusions, while it further implies that a new and ultimate collection of parallel universes is so vast and exotic that all the bizarreness pales in comparison, forcing us to “relinquish our most deeply ingrained notions of reality”.

We keep on trying to discover more and end up finding that there must be a larger structure beyond the Earth, our solar system and galaxy. It might be just a hierarchy of parallel universes. Tegman loves the old standby example of stacked Russian dolls. It is a symbolic way of understanding the vastness of the cosmos given the inability of the human mind to understand it. He finds it fascinating, to use his word, as we no doubt do.

We have come a long way from our cave-dwelling ancestors even though their brains were as large as ours. One wonders what questions they devised about that “stuff in the sky.” They used myths and stories to explain the unknown. It was mystical to be sure, but an answer.

Now mankind has the tools and experience of flying into space to offer other, better solutions. Our minds are flying as well with our imagination running rampant. We have, however, barely got off the ground in terms of deciphering the unknown and uncovering the eternal mysteries of life. We are limited by our mental power but rocket power is available.

Tegman is inspired by the quest for knowledge and respects the efforts of mankind. As a physicist, he is compelled to contribute his own mental acumen on his journey of discovery. He offers his quest to those begging for answers.