I did a thought experiment with my AI of choice and I'm absolutely flabbergasted!
I always have been fascinated by what can be done with AI so today I sat down and made up a thought experiment about popcorn (because I literally was eating popcorn) and this is how ot went:
Imagine that since the dawn of humanity (about 5 million years ago), every hominid, Neanderthal, and human had access to a microwave. Every single day, everyone pops exactly one bag of popcorn (50 kernels).
To make it a pure physics experiment, we eliminate all "noise": No dust, no skin flakes, identical humidity everywhere, and we let the popcorn cool for 24 hours so all steam has evaporated. We are looking for two bowls of popcorn that weigh exactly the same.
We calculated that throughout history, there would have been roughly 2 quintillion (2 * 10{18}) bags of popcorn made. If we measure in Micrograms (10{-6}g): There would be billions of identical pairs. If we measure in Nanograms (10{-9}g): Still millions of perfect matches.
The "Attogram Miracle":
I pushed the experiment to the limit: The Attogram (10{-18}g). An attogram is so small that it’s roughly the mass of just 50 carbon atoms. At this level, the number of possible weight increments (2 grams divided by 1 attogram) is exactly 2 quintillion.
According to the "Birthday Paradox" in statistics, since the number of bags made (2 * 10{18}) matches the number of possible weight steps (2 * 10{18}), the probability hits a tipping point.
Statistically, it is highly likely that exactly ONCE in human history, two bowls of popcorn were physically identical at the attogram level. One might have been popped by a caveman 3 million years ago, and the other by a college student in 2024.
They would be "weight-twins" down to a scale finer than anything we can measure today—a perfect symmetry across time, separated only by the mass of a few atoms.
TL;DR: If humans had been popping popcorn since we were apes, we would have produced enough bags to guarantee a 1-in-a-quintillion "Attogram Miracle"—two bowls weighing exactly the same down to the mass of 50 atoms.
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