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In the approach from the article it seems as you are picking a mathematical structure in the middle of nowhere with the universe faintly visible at the horizon
by danbruc 8y ago
In the approach from the article it seems as you are picking a mathematical structure in the middle of nowhere with the universe faintly visible at the horizon and then you start wandering around hoping that you will stumble across a path leading to the horizon.
But there don't seem to be many reason to believe that such a path exists, there are countless mathematical objects you could pick as a starting point and almost none of them have a path leading to the universe at the horizon. And even even of those with path going roughly into the right direction many will take a turn before you arrive at your destination.
So it seems much more promising to me to start at the universe and the mathematical structures describing our observations in a straight forward way and then explore from there the surrounding mathematical structures to see if they are a better fit, suggest new ideas, or whatever.
- 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.
- pishpash 8y agoThe article briefly alluded to this, that C, R, H are both already seen in features of the universe, so it's not "middle of nowhere."