Does 2 + 2 = 5 for very large values of 2?

A STAFF REPORT FROM THE STRAIGHT DOPE SCIENCE ADVISORY BOARD

Dear Straight Dope:

Do you care to elaborate how 2+2=5 for very large values of 2? I thought 2 was a constant and had only one value, or can I toss 12 years of math out the window?

SDStaff Dex replies:

The statement is, “2 + 2 = 5 for very large values of 2.” It’s a joke about rounding and estimating. For instance, suppose you have your calculator set to round all numbers to integers (no decimal places) and the problem you’re actually computing is 2.48 + 2.47. The calculator will automatically round, so when you punch 2.48 and ENTER, it will show up on the screen as 2. When you punch in the 2.47 and ENTER, it will also show up on the screen as 2. Then when you add, the sum 4.95 will be rounded to 5. Hence, 2 + 2 = 5 if the value of 2 is large enough.

It’s a joke … but a joke with a somewhat serious point. All measurements in the real world (as opposed to the esoteric whirled of mathematics) are estimates; they’re always rounded to something. There’s no such thing as absolute precision. So rounding must come into play sometime or other, and the joke about 2 + 2 = 5 if 2 is large enough, is a reminder about the way that estimation errors compound.

Send questions to Cecil via cecil@straightdope.com.

STAFF REPORTS ARE WRITTEN BY THE STRAIGHT DOPE SCIENCE ADVISORY BOARD, CECIL'S ONLINE AUXILIARY. THOUGH THE SDSAB DOES ITS BEST, THESE COLUMNS ARE EDITED BY ED ZOTTI, NOT CECIL, SO ACCURACYWISE YOU'D BETTER KEEP YOUR FINGERS CROSSED.