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> In the approach from the article it seems as you are picking a mathematical structure in the middle of nowhere Quaternions were very popular way of expressin
by sannee 8y ago
> In the approach from the article it seems as you are picking a mathematical structure in the middle of nowhere
Quaternions were very popular way of expressing the "classical" physics around the 19th century (and the vector algebra we know today is in some ways just a derivative of quaternion algebra). Complex numbers are extremely useful in many fields even today. It's hardly in the middle of nowhere.
- danbruc 8y agoBut the article is not really talking about quaternions - which are surly a useful tool, probably best known for the nice way in which they can describe rotations - but about R⊗C⊗H⊗O. And it's at the very least not obvious that this thing is anywhere close to where they journey is hopped to lead to.
- sannee 8y agoOctonions are to quaternions as are quaternions to complex numbers (and complex numbers to reals). This is called "Cayley construction" iirc.
- danbruc 8y agoSure, but the structure the article is about is the tensor product of the four algebras which is an algebra with 64 real dimensions.
- simcop2387 8y agoYep complex numbers get used extensively for doing calculations with electronics when doing analysis. https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-ac-analysis/v/ee-complex-numbers https://www.khanacademy.org/science/electrical-engineering/e...
- danbruc 8y agoMuch closer to the topic of the article are quantum mechanics and quantum field theory which make extensive use of complex numbers. But that really does not say much about the usefulness of the structures discussed in the article for modeling the universe, complex numbers are just a rather simple and general tool and can therefore be used for a lot of applications.