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Mathematics is the language that God uses to write the universe-- Galileo Galilei

We are not sure who first applied mathematics to science, but the Babylonians about 3000 years ago may have been one of the earliest. They used mathematics to understand solar and lunar eclipses, and it took 2,500 years for the advent of calculus and Newtonian physics to explain these phenomena.

Black holes, Higgs bosons and gravitational waves are all predicted mathematically, which highlights the mathematical nature of the universe. About 400 years ago, Galileo's famous assertion that the universe was a "magnificent work" written in mathematical language reflected this view. This means that our universe is not only described by mathematics, but more accurately, it is essentially mathematical. We are all part of this huge mathematical entity, which is part of a larger multiverse than the concept of multiverse that has been discussed recently.

Many people often mix mathematics with arithmetic, but in fact, mathematicians explore a wider range of abstract structures than pure numbers, including various geometric figures. To find these shapes around you, you can't just focus on man-made shapes, such as the rectangles of books.

Because nature itself is full of patterns, such as the Fibonacci series-(from the third number) the latter number is the sum of the first two numbers. Starting with 0recol 1, the first few numbers are arranged as follows: 0pr 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89144.

(we can also see this pattern in nature.) for example, when you look at a sunflower, you will find that its seeds are spirally distributed, and the number of seeds follows the law of the Fibonacci sequence.

You can find geometric patterns and shapes by observing nature. For example, when you throw a stone to observe its trajectory, you will find a beautiful and recurring arc, which is called a handstand parabola. It's the same track no matter what you throw. When we look at orbiting celestial bodies in space, we will find another common shape-an ellipse. Interestingly, the two figures-parabola and ellipse-are related to each other. The tip of an elongated ellipse is very much like a parabola (when the eccentricity of the ellipse approaches 1, the ellipse approaches parabola), indicating that all these trajectories are essentially part of the ellipse.

When we explore the world around us, we will notice that there are repeated shapes and patterns in various fields such as motion, gravity and electric current, and we summarize these laws as the laws of physics. Just as we use mathematics to describe the shape of an ellipse, we use mathematics to describe these laws.

Tegmark said, "Mathematical shapes and patterns reveal the elegant simplicity and beauty of nature, and these patterns can already be understood by our minds." Tiger Mark has such a passion for mathematics that he even hangs a lot of pictures of equations in his bedroom.

For a long time, scientists have used mathematics to describe the universe, but what if the universe is really just mathematics? This is exactly what Marx Tegmack thought about.

In a speech at Berber House on January 15th, Marx Tegmack discussed the idea that if you accept that space itself and its matter have no properties other than mathematical properties, then everything in mathematics "doesn't sound so ridiculous". He based the lecture on his book, our Mathematical Universe: my pursuit of the Ultimate essence of reality (Our Mathematical Universe: My Quest for the Ultimate Nature of Reality).

In the field of physics and cosmology, there is a speculative "theory of everything,TOE" called Mathematical Universe hypothesis (MUH) or Ultimate Unification Theory, which was put forward by cosmologist Marx Tegmack.

"you can't do anything without math. Everything around you is math, numbers." -- Sharon Tara David

Tegmark's Mathematical Universe hypothesis (MUH) theory shows that our physical world is based on mathematical structure. This means that our universe is not only explained by mathematics, but it is essentially mathematics-a special mathematical structure. That is to say, if something exists mathematically, it also exists physically. Observers like humans are considered to be the self-conscious part of this mathematical structure, and in any mathematical device in which such observers exist, they feel that they exist in the real physical world.

In the mathematical universe, some people say that the human brain is the most complex thing in the universe, and it is our human thinking that leads the great leap forward in understanding the world. One day, Tegmack says, scientists will even be able to describe consciousness in mathematics.

"the brain contains infinity with limited space"-- Carl Sagan

Tegmack stresses that the fusion of seemingly independent things often leads to major breakthroughs in physics, such as energy and matter, space and time, electricity and magnetism. Similarly, he believes that consciousness (the feeling of self-perception) will eventually be unified with the body (clusters of moving particles).

Tegmack said his hypothesis did not require additional details, which was not falsified by observers. So he thinks that according to Occam's razor principle, his theory is better than other theories of everything. He also mentioned another idea, the Computational Universe hypothesis (Computable Universe Hypothesis,CUH), which means that physical reality is a mathematical structure defined by computational functions.

Marx Tegmark's four levels of multiverse Tiger Mark's Computational Universe hypothesis (MUH) is related to his view that multiverse contains four levels. The four levels are sorted from low complexity to high complexity. They are: (level 1) the world with different starting points, (level 2) the world with different physical constants, (level 3) the world with different quantum results, and (level 4) the world with different equations or different mathematical structures.

Jurgen Shcmid Huber is a German computing scientist. Jurgen Shcmid Huber (J ü rgen Schmidhuber), famous for his work in the field of artificial intelligence, disagrees with Tiger Mark. He believes that it makes no practical sense for the Tiger Mark that "all mathematical structures are identical." He proposed a method with more restrictions. He focuses on the representation of the universe that can be described in constructive mathematics, such as computing programs, which are like digital libraries of mathematical functions, providing the basis for more mathematical discoveries.

Tegmark responded that even in string theory, a formal method for measuring all physical variables in the universe had not been developed, so this limitation should not be seen as a big obstacle.

More than 60 years ago, Kurt G ö del, an Austrian mathematician, put forward a theory that contradicted Tegmark's point of view. His first incompleteness theorem deals with mathematical axioms, which means that what we accept as true in mathematics cannot be proved by mathematics itself.

For example, consider the axiom of identity (Xidentity X). We believe it is correct, but we can't prove it with mathematics. Godel's theorem is that all axiom-based theories are either incomplete or self-contradictory.

Freeman Freeman Dyson, a theoretical physicist and mathematician, believes that mathematics is endless. Even if we have solved a lot of problems, we will still find more unsolved problems in the existing rules. Although this may be contrary to the "theory of everything" view, it does not mean that numbers are purely the product of human invention, or just something waiting for human beings to discover.

Some people think that the mathematical universe hypothesis (MUH) is inconsistent with Godel's incompleteness theorem. In a discussion attended by Tegmark, Piet Hut and Mark Alford, Alford argued that the methods used by formalists could not prove all the theorems in a very powerful system. He thinks that the view that mathematics is "there" is not the same thing as the view that it is based on the formal system.

Tegmack responded with a new idea: only mathematical structures that can be solved completely exist in the physical world. This view narrows down the scope of the multiverse and may explain why our universe looks so simple. He also showed that even if standard physical theories are not completely solvable, the mathematics that describe our world are still completely solvable.

In another response, Tegmark proposed an alternative to the Mathematical Universe hypothesis (MUH)-the Computational Universe hypothesis (CUH). This point of view contains only those mathematical structures that are simple enough and does not involve the unsolved or incalculable theorems in Godel's theorem. However, Tegmack acknowledges that this approach faces great challenges. For example, this assumption excludes many mathematical situations and potentially uncalculable problems, and the most successful physics theory in history is not consistent with CUH.

Stoeger, Ellis and Kircher believe that in a true multi-universe, different universes are completely separated, and one universe will not affect the other at all. They believe that the lack of this connection makes the theory of multiverse unsupported by science. Ellis particularly criticized the mathematical universe hypothesis (MUH), which he believes is almost impossible to prove except for some optimistic views.

However, Tegmack believes that MUH can be confirmed. He believes that the hypothesis predicts that in nature, matter will reveal mathematical patterns, and by assuming that we are in a particular universe in a multiverse, we can test how unique our universe is in this multiverse with a mathematical structure.

The mathematical universe hypothesis (MUH) is based on the view that mathematics is an objective existence, but some people, such as Jannes, think that mathematics is invented by human beings to some extent. He suggested that if mathematics is really an objective existence, then other intelligent creatures, such as aliens or intelligent computers, should also be able to understand mathematics well. Brian Green (Brian Greene) holds a similar view, arguing that a deep understanding of the universe should not depend on human concepts.

However, a variety of non-human entities, including intelligent life, can understand and apply basic mathematical concepts. At the same time, there are some interesting examples related to mathematical concepts in animals. For example, trained gorillas can do symbolic additions that are limited to basic arithmetic. This raises the question: does non-human intelligence exist? Can you understand advanced mathematics? So far, we have not confirmed it. Positivists believe that mathematics is developmental and does not have a fixed structure.

Various entities can understand basic mathematical concepts. Tegmark responded that mathematical structure is strictly defined, and mathematics outside human beings just looks different, because we are gradually revealing a consistent and unified mathematical picture. 'We didn't invent the language of mathematics, we just discovered its structure,'he said in his 2014 book on MUH.

Don Nelson Page, Don Page, a Canadian theoretical physicist, believes that there can only be one basic world. If mathematics can describe all possible worlds, then there must be a unique definition of mathematical structure "Reality". He believes that level 4, in which all the mathematical structures mentioned above coexist, is illogical.

Tegmark responded that Page's point of view is not completely contrary to level 4. He explained that many mathematical structures can be broken down into separate parts, but these parts can be unified. In a simpler case, even in a mathematical structure, there are seemingly separable but actually interrelated elements.

"Mathematics is the language of the universe. So the more formulas you know, the more you can communicate with the universe." Neil de Glassom Tyson

Author: Areeba Merriam

Translator: Xiao Cong

Revision: Yueyue

Original link: Is the Universe Really Built on Mathematics?

This article comes from the official account of Wechat: Institute of Physics, Chinese Academy of Sciences (ID:cas-iop), author: Areeba Merriam

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