With a sufficiently broad definition of mathematics, the ERH implies the Mathematical Universe Hypothesis (MUH) that our physical world is a mathematical structure.
This means that our physical world not only is described by mathematics, but that it is mathematical (a mathematical structure), making us self-aware parts of a giant mathematical object.
Swedish-American physicist and cosmologist
Max Tegmark (born May 5, 1967) is a Swedish-American physicist, cosmologist and machine learning researcher. He is a professor at the Massachusetts Institute of Technology and the scientific director of the Foundational Questions Institute. He is also a co-founder of the Future of Life Institute and a supporter of the effective altruism movement, and has received research grants from Elon Musk to investigate existential risk from advanced artificial intelligence.
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But why has our physical world revealed such extreme mathematical regularity that astronomy superhero Galileo Galilei proclaimed nature to be “a book written in the language of mathematics,” and Nobel Laureate Eugene Wigner stressed the “unreasonable effectiveness of mathematics in the physical sciences” as a mystery demanding an explanation?
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[W]hat I had been missing... and what Feynman realized: physics is the ultimate intellectual adventure, the quest to understand the deepest mysteries of our Universe. ...[I]t makes us see more clearly, adding to the beauty and wonder of the world ...[T]he lens of physics adds more beauty to the world ...
The various approximations that constitute our current physics theories are successful because simple mathematical structures can provide good approximations of how a self-aware substructure will perceive more complex mathematical structures. In other words, our successful theories are not mathematics approximating physics, but mathematics approximating mathematics!
We don't know for sure that the Schrödinger equation is actually that accurate a description of nature either. That's why it's so exciting to see what's going to happen with the quantum computer efforts... Will they ultimately fail because physics isn't fully described by the Schrödinger equation, or will they actually succeed... This is where ultimately our experimental friends will... give us crucial insights...
Evolution endowed us with intuition only for those aspects of physics that had survival value for our distant ancestors, such as the parabolic orbits of flying rocks (explaining our penchant for baseball). A cavewoman thinking too hard about what matter is ultimately made of might fail to notice the tiger sneaking up behind and get cleaned right out of the gene pool. Darwin’s theory thus makes the testable prediction that whenever we use technology to glimpse reality beyond the human scale, our evolved intuition should break down. We’ve repeatedly tested this prediction, and the results overwhelmingly support Darwin. At high speeds, Einstein realized that time slows down, and curmudgeons on the Swedish Nobel committee found this so weird that they refused to give him the Nobel Prize for his relativity theory. At low temperatures, can flow upward. At high temperatures, colliding particles change identity; to me, an electron colliding with a and turning into a Z-boson feels about as intuitive as two colliding cars turning into a cruise ship. On microscopic scales, particles schizophrenically appear in two places at once, leading to the quantum conundrums... On astronomically large scales... weirdness strikes again: if you intuitively understand all aspects of black holes... put down this book and publish your findings before someone scoops you on the Nobel Prize for quantum gravity… [also,] the leading theory for what happened [in the early universe] suggests that space isn’t merely really really big, but actually infinite, containing infinitely many exact copies of you, and even more near-copies living out every possible variant of your life in two different types of parallel universes.
The DQN AI system of Google DeepMind can accomplish a slightly broader range of goals: it can play dozens of different vintage Atari computer games at human level or better. In contrast, human intelligence is thus far uniquely broad, able to master a dazzling panoply of skills.
A healthy child given enough training time can get fairly good not only at any game, but also at any language, sport or vocation. Comparing the intelligence of humans and machines today, we humans win hands-down on breadth, while machines outperform us in a small but growing number of narrow domains, as illustrated in figure 2.1. The holy grail AI research is to build “general AI” (better known as artificial general intelligence, AGI) that is maximally broad: able to accomplish virtually any goal, including learning.
Physicists, we have a sort of arrogance... which has harmed us a lot. ...We forget that we're in a bubble and ...that there's actually a science of how you persuade people ...of how to communicate, and other people have studied that at great length. ...[T]he average person who works making cigarette ads is much more scientific about the way they get their message out than the average physicist. ...[I]t comes not from stupidity ...but from arrogance ...We're not going to stoop so low that we're going to be scientific about how we communicate... about how we advocate. We have to get off our high horses... If you get invaded by Hitler's army, you shouldn't just say... "Tanks are immoral, we're going to fight them with swords." We have to be scientific also about standing up for ourselves and our ideas... A second mistake... spending much more time infighting within our community of physicists, or... having one science pitted against another... for a few more tax dollars... losing sight of the fact that there's a tiny trickle of money that flows to all of the sciences combined... compared to... generic fruits of... corporate lobbying and random waste... So, get out of our bubble again. If we look at the big picture, it's kind of pathetic... that you have physicists, biologists, chemists, who together have built up most of the wealth of the world, and managed to be so incredibly navel-gazing and busy with infighting, and old-fashioned in how they communicate, that they have to come begging for money, and people don't listen to them.