Suppose politicians were free to spend money in ever increasing amounts, and that the only rule they had to follow is that each additional expenditure they make would have to be exactly one dollar more than their previous highest expenditure. So, if they started off with a $1 expenditure, they would spend $2 for their next line item in their budget, then $3 for the next item, and so on, until they've spent an infinite amount of money.
Now, what would we have to show for all that spending if we added it all up?
Well, to do that, we'd first have to sum up all that spending. Believe it or not, after doing the math, we would have less than nothing, which is to say that we are all worse off than we were before all that spending was allowed to happen. And that is just another way to say that all that spending wasn't anything other than an infinite waste of money. Here's the math that proves it:
Jason Kottke comments:
This is, by a wide margin, the most noodle-bending counterintuitive thing I have ever seen. Mathematician Leonard Euler actually proved this result in 1735, but the result was only made rigorous later and now physicists have been seeing this result actually show up in nature. Amazing.