Collecting a Complete Set: From Baseball Cards to Disease and Denial of Service

In these an attacker repeatedly sends packets of partial information (parts of a file, say) to a site in order to flood it and make it unavailable.

The site reassembles these randomly arriving packets into a complete file when at least one of each of the packets is received.

How long it takes a complete file (or many complete files) to travel from the attacker to the destination site can be computed using roughly the same mathematics as that used in the examples above.

The math can also help the victim locate the attacker.

If each of the routers along the path the information packets take marks them electronically, then how long it takes the destination site to receive the complete set of marked packets can be calculated and the attacker's location sometimes inferred from the marked path taken.

Another possible example is that of a disease that requires at least one of a number of different independent, continually occurring assaults on the body. Once these have all been collected, as it were, the disease develops.

Dice, children, baseball cards, denial of service attacks, disease together testify to the imperialist nature of mathematics. It sends out colonies to almost disciplines and endeavors.

John Allen Paulos, a professor of mathematics at Temple University in Philadelphia, is the author of several best-selling books, including "Innumeracy," "A Mathematician Reads the Newspaper" and "A Mathematician Plays the Stock Market." He's on Twitter and his "Who's Counting?" column on appears regularly here.

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