I am intersecting here the oft-repeated example of Ceasar's dying breath (link) with a Scouting tradition (link) that dates back to at least the first World Jamboree, held 1920 in London, of spreading ashes from prior campfires on each new campfire, and collecting the ashes the next morning. It is absolutely unquestioned Scouting wisdom that every campfire carries the spirit, comraderie, and memories from every other campfire which shares the ashes tradition. But what about the physical matter?
With the following assumptions:
- My old ashes and the ashes of other attendees were sprinkled on the fire just as it began to pick up,
- The fire burned for several hours, being stoked and stirred occassionally,
- I returned to the cold pile of ashes in the morning, and used my pocket knife to scoop some into my vial,
- I have done this repeatedly, having at least once crossed paths with Scouts claiming unbroken chains back to the first World Jamboree.
What is the probabilty that my vial of ashes contains at least one molecule from the first World Jamboree campfire? Or even my prior campfire?
Can the Ceasar logic be applied? Is this a 'Kolmogorov zero-one law' example?