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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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