Excerpt from Quaternions as the Result of Algebraic Operations
Beginners in the subject of Quaternions are generally bewildered by the arbitrary manner in which the subject is developed. They are forcibly introduced into a new domain where the familiar rules of combination of symbols are not valid. New magnitudes are arbitrarily assumed, subject to arbitrary laws. The reader finds the logic consistent and the results concordant with those of his previous courses, but he hardly knows why. He finds himself in a new country, but thoroughly and bewilderingly uncertain as to how he got there.
It is in the attempt to avoid this uncertain journey, to lead the student from the known to the unknown by familiar steps, by steps which require no arbitrary limitations of former laws, but merely their adaptation to new circumstances, that these class notes have grown into their present shape.
The backbone of the method of presentation is the use of a one-to-one correspondence between the mathematical concept and what I have ventured to call its idiographic symbol, that is, a symbol whose spatial properties are the same as the mathematical properties of the concept it symbolizes. From this similarity of properties there exists a one-to-one correspondence between the results of spatial operations upon the symbols and the corresponding mathematical operations upon the concept.
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