“…today we start

to pay the piper with each breath, yet love

knows not of death nor calculus above

the simple sum of heart plus heart”

In a fit of Plath love I posted a snippet from “Love is a Parallax” as a facebook status update. It kicked off an interesting conversation, conducted in a patois of poetry and maths, that I think is worth sharing, and also inviting views of the literate in both matters of the heart and pure mathematics.

Plath posits that there is a “simple sum of heart plus heart”. Reduced in its simplest form to the heart being something that can be added to another to lead to a defined outcome, and one that we may assume from her direction is qualitatively better than the component parts.

My interlocutor was in the Plath camp. Hearts are simple, and the mechanism that causes them to be combined is simple (let’s call it love for now) and leads to a defined outcome of fulfilment for both hearts.

My contention was that hearts are potentially complex, and the equation is not one of heart plus heart, but of finding where heart equals heart.

For the mathematically literate:

Plath: H1+H2 = goodness; where H1 is the heart of one person, and H2 the heart of another.

Me: f^{n}(H1) = g^{n}(H2), where the function that describes the characteristics of Heart 1 over n variables coincides with the function that governs the characteristics of Heart 2; which may be a number of outcomes which for now we can label good or bad, but which we will need to come back to later.

In fact, one may be choosing between the feasible set of outcomes for f^{n}(H1) = g^{n}(H2) and f^{n}(H1) = h^{n}(H2), and therefore in a love triangle, which partner to choose.

If the maths has lost you, think of a simple 2 axis chart, where the horizontal axis is passion, and the vertical axis is loyalty (I chose those at random). In a Plath world someone who scores 2 in passion and 2 in loyalty, joining with someone who scores 3 in passion and 1 in Loyalty leads to a partnership that scores 5 in passion and 3 in loyalty.

In comparison, I am saying that hearts are not points on that chart, they are potentially lines or even an area, and what we are really looking for is the set of results for where those points / lines / areas overlap.

Which leads to what I think is an interesting question. What are the n characteristics by which one may define a heart? I have crudely chosen passion and loyalty to illustrate the theory, but they may be irrelevant. The determinants may be something else entirely, cubic capacity perhaps, or susceptibility to chemical interference. Heart in this instance may indeed not be the muscle in the chest, but the complex group of brain parts that govern emotions and attachments.

Once we know what we think the n characteristics are what is the feasible set of values these characteristics could take? Are some binary: a person is or is not an arsehole. Are some potentially drawn from the full array of real and imaginary numbers?

When we have locked down the dimensions and their feasible sets, what form do we think the equation would take, and in solving it, do we expect to find a single point for each heart – essentially bringing us back to the simplicity of a Plath world, or a complex solution set that may or may not be continuous?

Finally, in comparing and combining two heart functions, are we in fact looking for their sum (per Plath) or where they coincide, and if there are multiple answers to the sum, or solution to the equations, on what basis could or should we choose between the results we get?

So, there is the tee up. Is the sum of heart plus heart simple, or are we looking at something infinitely more complicated?