### Signal-to-noise

My closet, National Enquirer magazine and Homeland Security alerts – what could they possibly have in common? How about a scary-sounding but very useful math concept called Signal-to-noise ratio.

At the beginning of a new weather season, when the contents of your wardrobe need to be swapped, you sort clothes by colors or type or style, and neatly fold them on shelves and bins in your closet. If your family is similar to mine, in a matter of days you will observe that the closet has a life of its own. It has rejected your naive intentions of order: someone has placed your son's sports T-shirt into your long sleeve shirt bin, or mixed pajama bottoms and sports pants, or even rolled a dirty red sweater into a shadowy corner.

When would you officially call this a mess and order re shelving? How about utilizing mathematics to define a measure of order versus mess? All the literature says that children and husbands need very clear instructions. So, let's create closet clean-up guidelines for them. We can define a ratio of the number of correctly shelved items to the number of misplaced items. Signal-to-noise ratio (SNR) is the scientific term. Assume we have 50 articles in the closet. At the beginning of the season the SNR is very large: all items neatly ordered; nothing is misplaced. In two days we still have 47 ordered items and only 3 misplaced. SNR is 47/3 = 15.6. Doing well so far. Two weeks later you spend 30 minutes searching for your shirt and realize that half of the items have been misplaced. SNR is 25/25 = 1! Time to re-organize before SNR sinks even lower and your mess overpowers your order.

The original Signal-to-noise concept derives from the field of electrical engineering, where it is used to measure the strength of a signal compared with the strength of a background noise. For example, your phone has high SNR unless you get occasional interference from neighbors' calls or a static line noise. Informally, SNR started to be used as a ratio of useful information to false or irrelevant data. Homeland Security Information Center uses this concept to define how many of the daily received security alerts and leads should be pursued.

To me signal-to-noise sounds like a perfect way to measure the trustworthiness of friends or magazines. I love catching up with the latest gossip while standing in line at the store, but doubt that most magazines I glance at would get a SNR above 1. Wouldn't it be great to use SNR to define an official trustworthiness approval rating and stamp it on each printed or aired piece? Otherwise how on earth would we know if Madonna really had a fling with Yankee's Rodriguez?

Would you like to try something else from TheMathMom? See how math can help you test awareness level of your teenager remotely.

1. I think you overlooked one of the most common usages of signal-to-noise ratios which is in consumer electronics.

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