An xkcd comic showing the breathtaking ranges for lifetime and mass covered by physics

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

On March 10, 2025 Randall Munroe’s xkcd web comic had the cartoon shown above titled Water Balloons. It uses two logarithmic scales to show a range of lifetimes in seconds from ten to the minus twentieth power to ten to twentieth power, and a range of masses in kilograms from ten to the minus thirtieth power to ten to thirtieth power. Wikipedia says a Logarithmic scale is:

 

“… a method used to display numerical data that spans a broad range of values, especially when there are significant differences between the magnitudes of the numbers involved.

 

Unlike a linear scale where each unit of distance corresponds to the same increment, on a logarithmic scale each unit of length is a multiple of some base value raised to a power, and corresponds to the multiplication of the previous value in the scale by the base value. In common use, logarithmic scales are in base 10 (unless otherwise specified).”

 

An article at Explain xkcd on March 10, 2025 describes this comic:

 

“The comic graphs the mass vs the lifetime of three objects: mesons, water balloons and planets. Mesons, which are subatomic particles, have a very low mass and a very short lifetime, as they naturally decay into other fundamental particles.

 

‘Flying water balloons’ are depicted as having a mass centered around 1 kilogram, but the area outlined covers a very broad range of mass (from grams to hundreds of kilos), and a lifetime centered around 1 second (but the area outlined covers from fractions of a second to a couple of hours), indicating the approximate amount of time that a water balloon is expected to be in the process of being thrown through the air. Not all water balloons break on impact, and they may be prepared well in advance, so specifying ‘flying’ indicates that it isn't the lifetime of the intact (and water-filled) balloon. Additionally, some are thrown directly into someone's face, thus their flight time would be extremely short, or non-existant if 'planted' before even being released.

 

Finally, planets have a very large mass and a very long lifetime, as they tend to exist for billions of years.”

 

Back on January 13, 2020 I blogged about How thin is “extremely thin”? I described using nine powers of ten in centimeters to step down from one (a finger) to ten to the minus eighth (an   atom).