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  "map_content": "There's some interesting additional content about these kinds of geometric structures and ways they represent new or emergent systems of structures of organizing complimentary components. John Baez describes some of their nature and complexity and fun aspects in this lecture. He has other really great lectures on similar topics. And he helps to educate and introduce the unique qualities of higher dimensional math models.\r\n\r\nhttps://www.youtube.com/watch?v=LKcYqMY234I",
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  "map_content": "@EquityDiamonds was one of the first people to educate me about these structures having real mathematical basis to them instead of just being philosophical abstracts like I'd been interpreting them as previously. So John introduced me to Quaternions, and I started to research them along with Maxwell's equations. \r\n\r\nHere's a bit of info about the Quaternions and their role in Maxwell's equations and used today in modern video graphics: https://www.youtube.com/watch?v=CdwxpSInhvU",
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  "map_content": "These quaternions and octonions are numerical dimensional extensions beyond the complex plane which itself is a dimensional extension beyond the real number line. These become increasingly subtle and abstract and they follow their own sets of corresponding math table logic to determine the ways to multiply and form products between them. The top of this image represents a multiplication table for quaternions in table form. But for example, the image below is the same data, but displayed differently. When you follow the direction of the arrows, you arrive at the resulting product, so multiplying i x j yields you k. But if you go in reverse, you arrive at the negatives of the product, so i x j = k but j x i = -k. This is shown in the table, where j on the left times i on the top yields -k, but you can also follow the circle using the rule that reversing the arrows yields the negative result, and you also arrive at -k.",
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  "map_content": "As extensions of the complex plane, based on the concept of i as being the square root of negative 1, j and k also follow the same principle, each themselves being the square root of negative 1, however, the -1 to which j equals for example is in an orthogonally distinct region from the -1 that i equals. This is like understanding that -1 on an X-axis is not the same as -1 on the Y-axis, but how we define these is still as the square roots of negative 1. This is why in the table, when they multiply with themselves, they result in -1 because despite the concept of the square root of negative 1 being an impossibility, when you square it, you arrive at something that is possible. And in fact when you raise the square root of negative 1 to the power of itself, it does result in a real number... Check it out: https://www.youtube.com/watch?v=55hsKQg6T_U",
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