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Comment by ddtaylor | Hacker News Reader

I think this should be retitled to specify it's a story about the key players or the history of this subject, not so much subject matter itself.

Often I click something related to Quanta and it seems to occupy a very strange target audience. It starts with a title or link that seems lures a reader with in-depth knowledge of some subjects. I think most readers see that title and get excited about all kinds of things like a simplified introduction to subjects they weren't able to grasp in the past or someones unique perspective that might help them better understand the topic.

Instead the article is actually the story and history of some people involved. That's an interesting article as well, but I think it's a different title.

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Agree with your point. The actual title, "If the Universe Is a Hologram, This Long-Forgotten Math Could Decode It," has another issue: physicists may have "forgotten" operator algebras, but it's certainly been a very active part of mathematics.

Can someone tell me why quantmag’s coverage of these algebras is so different from

https://en.wikipedia.org/wiki/Von_Neumann_algebra#Factors ?

Wikipedia calls them by a different name! As for history, Tomita is said to be the most important guy* behind the elucidation of Type III but gets no credit…

Feels like this is a classic case of blind men and elephant

* https://en.wikipedia.org/wiki/Tomita–Takesaki_theory

>These were further developed later by Takesaki, and the theory is called the Tomita–Takesaki theory. It has great influence in statistical mechanics too. That was the beginning part, but in Tomita’s papers, he didn’t write proofs. I: Mathematicians usually like proofs. Is Tomita a mathematician? A: [Minoru] Tomita is a pure mathematician. There are a lot of algebraists in Japan, including [Masamichi] Takesaki, but Tomita is a completely different kind of person, very “singular”.

http://www.asiapacific-mathnews.com/04/0402/0012_0018.pdf

Operator algebra refers to https://en.wikipedia.org/wiki/Operator_(mathematics).

An operator can be something like the differentation operator (d/dx), the integral operator, gradient, curl, or other structure. Operators are similar to functions but work more generally, like mapping functions to other functions.

See https://en.wikipedia.org/wiki/Quantum_field_theory#Canonical... for some of the applications/definitions in quantum mechanics.

IIUC, Operator algebra is the study of the properties of operators just like real, complex, matrix, and linear algebra are the study of the properties of those objects/constructs. As such, once you have defined an operator for e.g. Schroedinger's wave equation you can manipulate and explore that using the rules and principles of operator algebra. Thus, making them easier to work with.

von Neumann algebras are operator algebras. They are algebras whose elements are operators on some Hilbert space. They also satisfy some other conditions. What I just said is not meant as a definition.

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