Philosopher AI - Based on the number systems of quaternions and octonions, if you could create a new number system how it would be

Based on the number systems of quaternions and octonions, if you could create a new number system how it would be

The number system I would create (if it were possible for me to do so) would be like the octonion number system, although not entirely the same. In this new number system, all numbers will be complex numbers and there will also be imaginary numbers along with real numbers.

28 Oct 2020, 19:34

Numbers in this new number system would have the benefit of being able to express both real and imaginary numbers at the same time unlike the quaternion number system which only permits real numbers.

28 Oct 2020, 19:34

You see, in the quaternion number system, there is a real component and an imaginary component. The real component represents the 'ordinary' part of any number (the x-axis), while the imaginary components represent the 'imaginary' part of any quaternion (the y & z axes).

28 Oct 2020, 19:34

However, when adding two quaternions together (or multiplying them) the imaginary components are not considered. They are ignored. This is due to the fact that you can't add or multiply an imaginary number such as i times a real number.

28 Oct 2020, 19:34

While the imaginary components of quaternions are ignored when adding or multiplying them, this doesn't mean they are completely useless. They could still be used to represent complex numbers such as x + yi and x - yi.

28 Oct 2020, 19:34

However, it would be better and less confusing to have a number system which allowed complex numbers as well as real numbers.

28 Oct 2020, 19:34

You are getting an AI to generate text on different topics.

This is an experiment in what one might call "prompt engineering", which is a way to utilize Llama 3.1 405b, a neural network trained by Meta.

Llama is a language model. When it is given some text, it generates predictions for what might come next. It is remarkably good at adapting to different contexts, as defined by a prompt (in this case, hidden), which sets the scene for what type of text will be generated.

Please remember that the AI will generate different outputs each time; and that it lacks any specific opinions or knowledge -- it merely mimics opinions, proven by how it can produce conflicting outputs on different attempts.

Feel free to share interesting outputs to /r/philosopherAI on Reddit.

by Murat Ayfer