Jomon Exponentiation

Example The author considers 2 ^ 2. The author interprets 2 ^ 2 as 1 * 2 * 2, such that 2 ^ 0 becomes equal to one. Figure 1 shows 1 * 2 * 2. 1. The author gets the zero points. 2. The author adds the one point to the zero points/ 3. The author gets the one point. 4. The author adds the one point to the one point. 5. The author gets the two points. 6. The author adds the two points to the zero points. 7. The author gets the two points. 8. The author adds the two points to the two points. 9. The author gets the four points. The author rewrites the list as two sentences. 10. The author adds the one point to the first result, where the author adds the one point to the zeroth result. 11. The author adds the two points to the first result, where the author adds the two points to the zeroth result. The author rewrites the two sentences as one sentence. 12. The author adds the two points to the third result, where the author adds (the second result, where the author adds the two points to the first result, where the author adds the two points to the zeroth result) to another zeroth result. The author rewrites the sentence by multiplication. 13. The author multiplies the first result by two, where the author multiplies the one point by two. The one point is a zeroth result. The author rewrites this sentence with exponentiation. 14. The author exponentiates the two by two. Each two is unitless. Generalization There exists an exponentiation x0 ^ x1 ^ x2 ^ … ^ x(n-1) ^ xn. 15. The author exponentiates the (n-1)th result by xn, where the author exponentiates the (n-2)th result by x(n-1), …, where the author exponentiates the first result by x2, where the author exponentiates the zeroth result by x1. Definition The author defines exponentiation by multiplication. The multiplication has already been defined. Definition 1. An exponentiation of m by n is an action where the author multiplies the (n-1)th result by m, where the author multiplies the (n-2)th result by m, …, where the author multiplies the first result by m, where the author multiplies one point by m.