Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.
Surely you have heard all some amazingly wild theories about the Universe. It’s a computer simulation and we are all subject to our programmers. We are just holograms on the surface of a supermassive black hole. Everything around you is just a figment of your imagination. But how about this one: the Universe is made up of math. Not just described by it, but is math. Sorry, that may be scaring for the math-sensitive crowd out there, with terrors unspeakable brought back to the mind. But let’s look deeper into this and hopefully quash those fears away.
Talking the Talk
Work by Max Tegmark shows that the properties we associate with reality such as mass, time, space, and so on are just mathematical structures. He came to this idea based on the mathematical patterns we have seen appear in nature, like the Golden Ratio or the Fibonacci Sequence, but also with more common place things like conics. Math describes natural phenomena extremely well but Tegmark says this isn’t enough. We sometimes mistake the notation of mathematics with that of reality. Instead, think of that as a convention we adapted to decribe the true mathematical reality around us We ourselves are substructures made of math (otherwise known as a self-aware substructure), uncovering the landscape all around us by formalizing them in equations and theorems. This is a new philosophical position known as mathematical monism, implying the singular source of our reality. If true, then anything could be described by math, which has amazing inter-connections between its disciplines. It also shows a beauty to the fine-tuning of our Universe, whose numerous constants are just perfect to allow for our existence. A natural consequence of the theory is a multiverse of other mathematical structures, i.e. universes, in existence (for more on that, see my hub on multiverses) (Lewis, Woolfe, Tegmark “Is,” Tegmark 2014).
It would be a shift in our thinking, to say the least. If everything could be reduced to a single mathematical structure, then all of our sciences are currently limited based on the vocabulary we use to describe them. But it’s a necessary evil, because without that vocab we lose a relational quality that helps us see the connections between disciplines. As we get to the more overarching theories, we find that words don’t cut it and the math grows – a sign of the overarching structure. The key will be our ability to abstract concepts and remove the associations we currently have. They will need to change, just as we do. One aspect is the viewpoint we can take in science of a system: Being a participant versus an omnipotent observer. Relativity and quantum mechanics depend greatly on this, and it would be hard to gain an understanding of the two without it, so an adaptation will likely be required (especially if we hope to merge them someday). Math has done such a good job of describing (and predicting) science that this hypothesis gains solid footing if we can make that hurdle in our communication over it (Tegmark “The,” Piet).
Challenges to the hypothesis are numerous. How this can be reconciled with theories that contradict this precision (like the incompatibility of quantum mechanics and general relativity or Gödel’s Incompleteness Theorem) remains to be seen. We all hope that someday the relation between them could be uncovered. Also, why do we see reality the way we do and not as just a bunch of math? Tegmark reconciles this by pointing out how subjective our perception can be, and so we see reality in the way that makes most sense to us. Is it even science, able to be proven false, and can we make predictions from it? Statistical analysis points to yes. Some also argue that math is just a tool that gives us our communicative ability to describe it, but is nothing more than. An even more intriguing question is what caused the structure in the first place. Was it a deity, or something different? Tegmark postulates that the physical reality which is true math has to be independent of us...and historically, this has been challenging, if not impossible to accomplish (Tegmark “Is,” Murphey).
It is ultimately the metaphysics that can really get one going on this. Roger Penrose developed the Mind-Matter-Math triangle to describe a potential layout to think about universal dynamics. In it, matter impacts us, we impact math, and math impacts matter, creating a cycle. It seems reasonable, but what could alternatives bring to the table, especially with the notion that math may just be everything we mentioned? If you do subscribe to this, a fundamentalist position, then the link of mind causing math would be wrong because math is the fundamental structure of the Universe, and our minds are made of matter which is a mathematical structure. Tegmark avoids this problem by emphasizing how reality must be mind-independent, that it exists regardless of our evaluation or labeling of it. Its a priori to everything. Then again, as Paul Austin Murphey echoes Einstein in the idea that we may be projecting the idea that the Universe should follow these laws because we assigned that value. We may think we are making things independent of us, but we can come to that with preconceived notions.. But our understanding is constantly in flux, and just because a correlation appears apparent, it certainly cannot satisfy all causation requirements. That's why this is a difficult scientific postulation to defend. And if we need math to describe math but its all math anyway...(Piet, Jaanes, Murphey).
Hut, Piet and Mark Alford, Max Tegmark. “On Math, Matter, and Mind.” arXiv:physics/0510188v2.
Jannes, Gil. “Some comments on ‘The Mathematical Universe.’” arXiv:0904.0867v1.
Lewis, Tanya. “Universe is Made of Math, Cosmologist Says.” Huffingtonpost.com. Huffington Post, 02 Feb. 2014. Web. 15 Jan. 2019.
Murphey, Paul Austin. "Max Tegmark, Our Universe is Not Mathematical." paulaustinmurphypam.blogspot.com. 10 Feb. 2019. Web. 14 Sept. 2020.
Tegmark, Max. “Is ‘the theory of everything’ merely the ultimate ensemble theory?” arXiv: 9704009v2.
---. “Is the Universe Made of Math?” Scientificamerican.com. Springer Nature America, Inc. 10 Jan. 2014. Web. 10 Aug. 2020
---. “The Mathematical Universe.” arXiv: 0704.0646v2.
Woolfe, Sam. “The Universe is Made of Mathematics.” Philosophynow.org. Philosophy Now, 2016. Web. 16 Jan. 2019.
© 2019 Leonard Kelley