Last weekend, as I was munching away on a sweet home grown carrot from our own backyard, I let my mind wander with the wind and ponder pointless profoundities. An interesting, but totally useless statistical question occurred to me.
That we are all ultimately made of dust from the distant stars is indisputable. But what, I pondered, might be the odds that an atom of carbon in my crunchy carrot was the same atom in a molecule of CO2 I had exhaled earlier?
To clarify, this is how the cycle works - We eat food. Our body oxidizes the food we eat and burns the carbon in it to produce Carbon dioxide (CO2), which we exhale. Plants in sunshine absorb CO2, and make carbohydrates that they store as food for themselves, and as it happens, for us too.
Of course, I couldn't possibly have been looking for an answer to this question had I been consuming a carrot from Trade Joe's, our local grocery store. Those carrots would have come from miles away, and what are the chances that my breath from Palo Alto would have blown onto a distant carrot field from which the very carrot that chose to make its sugar from my sweet breath found its way into our Trader Joes, and thence into my home and my hands? Vanishingly small indeed.
Hence, it was only the sudden realization of the effect of home-grown-ness that tantalized me with the prospect of finding a reasonable guesstimate to the odds. If I had a greenhouse, then the odds would be even greater. But I don't. I could have improved the odds somewhat by breathing over my carrots as they photsynthesized. But I chose to spare them this ordeal. So I am left to make various liberal approximations to arrive at my answer.
If you were in this situation, what would you say the odds might be? Make any approximation assumptions you deem necessary. Also remember that plants respire too. So you must factor into your calculation the odds that an atom of carbon from your breath that was incorporated into your carrot's sugar, was oxidized by the plant itself at night (and that the resultant molecule of CO2 was lost to the wind.)
Your answer indicates the odds of communing with your carrot in a special, albeit totally bizarre way!