max Tegmark is a Swedish-American cosmologist who currently teaches at the Massachusetts Institute of Technology. He made important contributions to physics, such as measuring dark matter and understanding how light from the early universe affected the Big Bang model of the origin of the universe. He also proposed his own theory of everything. His theory of everything is called the ultimate set, or more strikingly known as the mathematical universe hypothesis. This assumption can be summed up in one sentence: "Our external physical reality is a mathematical structure." In this case, "mathematical structure" means a set of abstract entities, such as numbers, and the mathematical relationships between them. Thus, the mathematical universe hypothesis states that mathematics is not just a useful tool we invent to describe the universe. Instead, mathematics itself defines and constructs the universe. In other words, the physical universe is mathematics. It's a very strange and bold statement that isn't easy to understand at first glance, but let's try it.
The mathematical universe hypothesis is of a very philosophical nature. It can be seen as a form of Platonism, Plato's philosophy, where he believed that certain abstract ideas had a truly independent existence outside of our thoughts. Similarly, tegmark's hypothesis holds that mathematical entities such as numbers exist independently of us—that these abstract entities are not just imaginary; they exist as part of reality independent of the mind. In a sense, tegmark's hypothesis goes far beyond Platonism, as tegmark claims that in the end only mathematical objects exist, and nothing else exists! In his own words, "There is only mathematics; this is all there is" (Discover Magazine, July 2008). This position is known as mathematical monism.
Some may see tegmark's mathematical monism as an extreme and absurd position because we never perceive these mathematical objects, and we do perceive a physical world full of physical objects. In our experience, there seems to be no evidence of the existence of mathematical objects, while the physical world has inevitable evidence. However, in his paper "The Mathematical Universe" in Fundamentals of Physics (2007), Tegmark argues that "substructures [where the [world] is complex enough to contain self-consciousness [they] will subjectively think they exist in the physical 'real' world." So we shouldn't be surprised to learn that we perceive a physical world, because that perception is the inevitable result of a sufficiently complex mathematical universe. Ultimately, our perception of the physical world is due to the nature of our consciousness r, not to the true nature of the universe itself.
In a way, this is similar to Plato's belief that ordinary people cannot perceive or even understand the true nature of things. Plato claimed that the true nature of things can be traced back to what he called forms or ideas, which are abstract, eternal, archetypal, immaterial entities. In order to transcend the illusory appearances of things, we need to use reason to reveal their true nature, not visual or other perception. He argues that only those with philosophical training can do this.
Similarly, Tegmark believes there are two possible ways to look at reality: from the inside and outside of mathematical structures. We look at it from within and therefore see a physical reality that exists in time. However, from a (purely hypothetical) external point of view, tegmark argues that only one mathematical structure exists outside of time. Some may respond to this by saying that the idea of "out of time" and "eternal" is almost mysterious.
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In fact, Tegmark admits that he is one of the few scientists who believes in his mathematical hypothesis of the universe. It took some time for his ideas to be published in scientific journals, and he was warned that his muh would damage his reputation and career. But there are some reasons to believe it. The physicist Eugene Wigner wrote a paper entitled "The Irrational Validity of Mathematics in the Natural Sciences" (Communications on Pure and Applied Mathematics, Vol. 13, No. 1, 1960) that asked why mathematics described nature so accurately. Tegmark replied that the irrational validity of mathematics in describing reality meant that mathematics was the basis of reality.
The ancient Greek thinker Pythagoras and his followers also believed that the universe was built on mathematics. Galileo said that nature is a "great work" written in the "language of mathematics." But it's also worth reminding yourself that some people think of mathematics as purely human invention, despite its usefulness. For example, in their book Where Mathematics Comes (2001), George Lakoff and Rafael Nunez argue that mathematics stems from our brains, our everyday experiences, and the needs of human society, and that mathematics is simply the result of normal human cognitive abilities, especially the ability to conceptual metaphors—to understand an idea in another. Mathematics works because it is the result of evolution, not because it is based on objective reality: numbers or mathematical principles are not independent truths. (These authors do, however, hail the invention of mathematics as one of the greatest and most ingenious inventions ever made.) An extreme version of this evolutionary idea is the mathematical fictionalism proposed by Hartry Field in his book Science Without Numbers (1980). Field says that mathematics doesn't correspond to anything real. Instead, he argues that mathematics is a useful fiction: statements such as "2+2=4" are as fictitious as statements such as "Harry Potter lives at Hogwarts." We know what they mean, but their assertions don't correspond to any real situation.
Interestingly, tegmark's mathematical universe hypothesis is also related to the multiverse hypothesis, as he argues that all mathematically existing structures also exist physically. This means that anything that can be described mathematically actually exists. Then, with that, I don't exist in other universes, but there are countless mes in other universes.
Tegmark also wrote in his paper "Parallel Universes" in "Science and Ultimate Reality" (JD Barrow, PCW Davies, and Cl Harper, ed., 2003) that his ultimate ensemble/mathematical cosmological hypothesis covers all levels of the multiverse, which he says are of four types or levels. The first multiverse is a space-infinite universe in which there are regions that we cannot observe, but may be similar (or even identical) to our observable regions. For this type of multiverse, physical constants and laws are the same everywhere.
The second type is the multiverse, in which some regions of space form unique non-interacting bubble universes, like air bags in a rising loaf of bread. Different bubbles may have different fundamental physical constants, such as gravitational strength, electron weight, and so on.
In the third type or level of the multiverse, all possible processes of action actually take place in separate or parallel universes. For example, if I decide to take the bus instead of the train to work, reality splits the moment I make the decision, so there's another universe, and it's equally real, where I take the train to work instead of the train to work. Bus. The idea was originally Hugh Everett's multi-world interpretation of quantum mechanics, which was fairly mainstream in the physics community. The tertiary multiverse can be thought of as a tree with innumerable branches, where every possible quantum event creates a new universe and thus means the growth of a new branch.
Tegmark writes, "The only difference between i and iii is where your doppelganger is located. In the first level concept of the multiverse, my twins (copies) live elsewhere in the same universe as I do; in level three, they exist entirely in different universes.
The level iv type of the multiverse is the ultimate ensemble, which encompasses all the other levels of the multiverse, or describes all the other levels. This is why the ultimate ensemble is considered the theory of everything – because it can explain every universe that may exist. For tegmark, each different universe ends up with a different mathematical structure.