A mathematical kōan

Imaginary numbers—‘i’ for short—are real,
the square roots of negative numbers;
impossible, true, but stay with me on this one
because now it’s getting personal.

But the biggest surprise is nothing: zero/nada/nil,
which is neither even nor odd
but more “what-it-is” than “what-it-is-not.”
And what it is, is an emptiness and a doubt,
an exhale so deep it becomes its own lasting misery
where you’re left hanging by your diminishing beliefs:
an odd looking for an even
or an even looking for an odd,
or an ‘i’, if that’s what wanders by.

Imaginary numbers are real, but not ‘real numbers’. Here’s the issue:

The square root of a number x is any number that when multiplied by itself () equals x. Thus, 2² = 4, and -2² = 4; or, put another way √4 = ±2.

Now think about -4. The issue is that -4 = -2 * 2 (or its reciprocal 2 * -2)  and -2 and 2 are different numbers, so √-4 has no solution. Not so fast! say mathematicians and engineers, who very effectively use (in the development of electronics, for example) “imaginary” or “i” numbers, where √-4 = 2i and 2i² = -4. Algebraically, that works, although there is no real sense to it. However, your electronic stuff built on the principle of imaginary numbers is, I promise you, very real. 🙂

Not that any of this matters; this is not a poem about mathematics, it is a poem about a paradoxical puzzle. (Either that or bad writing; you chose.)

Thank you for reading A mathematical kōan. I humbly appreciate your visiting the Book of Pain, and as always, I look forward to your comments.

Recently, I reviewed and archived all my poems on the Book of Pain. Some, I realized, were really two poems in one, this being such an example. The other portion of that original poem is posted separately as the poem First.

The photograph was taken in the Poconos of Pennsylvania; it is one of two ‘road’ images, one each for this poem and its sibling. To see my photography blog, please visit the Book of Bokeh.


Photograph, poem and notes © John Etheridge; all rights reserved. The poem and accompanying notes are licensed under the Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 Unported License. This applies to all original written work found on this site, unless noted otherwise. The attribution claimed under the license is: © John Etheridge, https://bookofpain.wordpress.com. The photograph is not licensed for use in any way without the expressed consent of its creator.



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4 responses to “A mathematical kōan

  1. Pingback: First | the Book of Pain

  2. Glad to have such a beautiful soul in my zone 🎀
    Loved reading ur stuff !!