2+2 = 5

My mom has had a piece of paper hanging up next to her desk for years now, saying:

2+2 = 5*

*For very large values of 2

It never made sense to me until recently, when I actually thought to look it up (shock!). Obviously, 2+2 is 4, not 5: 2 is a constant and can’t have a different value. It’s actually a joke, playing on the ideas of rounding and estimating. Say your calculator is set to show numbers to zero decimal places, so it only displays a whole number. Then if you entered 2.48 the calculator would display it as 2. If you add 2.47 (which would also only show as 2) to that, the actual answer is 4.95, which the calculator will round to and display as 5. So, 2+2=5 for large enough values of 2!

The joke is also a reminder about being aware of these rounding errors in real life. Engineers deal with this a lot, which is why we tend to approximate π as 3.14 (or 3 if we’re being really lazy!). Any number in real life has to be estimated: at some point, the measurement has to be cut off. The danger comes in rounding all your numbers, then doing the calculation, because this can lead to a final answer that is quite far away from the one you should have come up with. Rounding errors compound surprisingly quickly, and it’s something to be aware of.

In school, we usually got around this issue by storing all the values in our calculator (to however many digits it could handle) and only rounding the final answer. This usually ensured we were as close as possible to the right answer. In real life, that’s not always an option, which is when you need to start tracking significant figures. A scale that weighs to 0.1lb can’t be used to estimate to the 0.01 of a pound: it’s only accurate to the first decimal place. So, if you’re adding that weight to the weight from a scale that is accurate to 0.01lb, you still have to keep your final answer to the 0.1lb, because you can’t use more significant figures than your least accurate measurement. This ensures you’re not incorporating rounding errors into the math.

So, a very nerdy joke with a good reminder about the difficulties about existing in the real world!

What’s your favorite nerdy joke? Even better if it comes with a lesson!

Cheers,

  • H

 

http://www.straightdope.com/columns/read/1382/does-2-2-5-for-very-large-values-of-2

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