The night before defending my Masters thesis, I ran out of shampoo. I ran out late enough that I wouldn’t defend from beneath a mop like Jack Sparrow’s; but, belonging to the Luxuriant Flowing-Hair Club for Scientists (technically, if not officially), I’d have to visit Shopper’s Drug Mart.
Before visiting Shopper’s Drug Mart, I had to defend my thesis. The thesis, as explained elsewhere, concerns epsilons, the mathematical equivalents of seed pearls. The thesis also concerns single-shot information theory.
Ordinary information theory emerged in 1948, midwifed by American engineer Claude E. Shannon. Shannon calculated how efficiently we can pack information into symbols when encoding long messages. Consider encoding this article in the fewest possible symbols. Because “the” appears many times, you might represent “the” by one symbol. Longer strings of symbols suit misfits like “luxuriant” and “oobleck.” The longer the article, the fewer encoding symbols you need per encoded word. The encoding-to-encoded ratio decreases, toward a number called the Shannon entropy, as the message grows infinitely long.
We don’t send infinitely long messages, excepting teenagers during phone conversations. How efficiently can we encode just one article or sentence? The answer involves single-shot information theory, or—to those stuffing long messages into the shortest possible emails to busy colleagues—“1-shot info.” Pioneered within the past few years, single-shot theory concerns short messages and single trials, the Twitter to Shannon’s epic. Like articles, quantum states can form messages. Hence single-shot theory blended with quantum information in my thesis.
After defending said thesis, I trekked to Shopper’s Drug Mart. Planning to move out of town in a week, I decided against buying an ordinary-size shampoo bottle. A sample-size bottle, from the pharmacy’s travel section, would leave more room in my suitcase for books. Upon arriving at the pharmacy, I hailed an employee.
But I didn’t ask about sample-size shampoo bottles. Mind on my thesis, I asked about single-shot shampoo.
Then I had a single shot at convincing the employee that I hadn’t lost my marbles.
Hurrying home, I reflected (to avoid reflecting on the employee’s expression) that I’d had one shot at defending my thesis. Maybe the administration would offer second chances to students who froze in front of the chalkboard, jaw locked by stage fright, but we’d remember. Come to think of it, I considered while nipping across a street, I’d had one shot at applying to this Masters program. One shot at college, one at senior prom. At befriending a classmate. At saying goodbye to my maternal grandfather before his last surgery.
Squeezing the shampoo bottle, I froze on a curb. Isn’t each of our lives single-shot?
Loosening my grip, I crossed the street. Economics, not physics, has the nickname “the dismal science.” Physics packs meaning into my message of a life. Because I have one shot, I’m probing one-shot theory. Not that I expect to decode much. But many singles, combined, approximate Shannon’s theory. Many trials, combined, approach the infinite.
In addition to combining with other lives, this single-shot life contains many steps: the steps to my dorm and up the stairs. A thesis, a paper drawn from a thesis, and a generalization of the thesis from information theory to thermodynamics. The packing of a suitcase, a goodbye to one city, and a hello to another.
For information about single-shot theory, check out the webpage for “Beyond i.i.d. in information theory,” a conference held at Cambridge this January. For information about oobleck, check out a Dr. Seuss book.