Opinions Aren't Facts: Math Doesn't Care What you Think

I almost had a math-induced heart attack. I blame Facebook.

Browsing my feed, I came across one of those "bet you can't solve this math problem" posts. It was a brief order of operations problem, one of those where you have to do the multiplications and divisions before you the additions and subtractions. I learned the rule of thumb for this back in high school as "Please Excuse My Dear Aunt Sally," but the mnemonic may have changed since then.

Anyway, I have an engineering degree, so (as you can see) I couldn't help myself. I solved the problem and then started browsing the comments, some offering correct answers and others erroneous ones. I have no judgment about that, by the way -- we all have our strengths and weaknesses. But it was as I was about to leave the whole post and move along that I came across the response that nearly stopped my heart:

"The answer is either 50 or 56. It depends on how you do the problem."

I've written before about how social media encourages us to confuse opinions with facts. By constantly asking what people think, even when it's unnecessary or disruptive, too many companies waste resources and distract themselves from more useful endeavors. But, as my heart recovered, I realized that this comment took the inappropriate intermixing of facts and opinions to the next level.

"Hey Frank, how long should I cut the shelf so that it fits across the closet?"

"Either 6 feet or 10 feet. It all depends upon how you choose to measure it."

The thing is, it doesn't. Math is not negotiable; it is not subject to whim. Opinions and interpretations, like whether or not it would be better for the shelf to occupy the entire width of the closet, are born from an objective reality, the closet itself. And those opinions lead right back to that same reality -- once you've made the decision to span the closet, you're going to have to measure and cut. If the closet is six feet wide, it's not 10 feet wide. It doesn't matter what you think. It doesn't matter what you prefer. It doesn't matter what you believe. There is a right answer and a wrong answer. And any one of us can be wrong. If you don't believe me, try fitting a 10-foot shelf into a six-foot closet by explaining to the closet that you chose a different way of doing the problem.

To say that a mathematical equation is subject to personal approach is to say that opinions are equivalent to facts, rather than being born out of them and destined to return. It's simply not true. And being unable to differentiate your opinions from the factual reality in which they exist is, well, dangerous.

Why? Put bluntly, it makes you dumber. If you let an opinion about what your customers want dictate your discovery of what's actually true about them, you're likely to get the wrong answers, and waste efforts on products or services that don't resonate. If you use an opinion about what your company should pay for a job function in place of market data for what it is actually worth, you're probably going to pick the wrong pay rate, and have some recruiting and hiring woes. And, if you let an opinion about how to do a math problem dictate your answer, you're at risk for making a real, factual error, and ending up with shelves that are too long, optical systems that don't align, or bridges that fall down.


So, when you find yourself -- as we all occasionally do -- feeling abject frustration at the idiocy of those who don't see the world the way you do, take a pause. There's a good chance you're mixing up objective reality with your opinions about it. And, when you find yourself using opinions-masquerading-as-facts as the basis for further factual investigation, take an even longer pause. Unlike real facts, which tend to raise questions and drive accurate discovery, opinions used in this way lead to one-sided results that always support the pre-existing bias -- feeling exactly right, all the way up to the moment the shelf doesn't fit in the closet.

Avoid the demise of your own intelligent decision-making. Be as explicit as possible, with both yourself and others, about what constitutes an opinion and what constitutes a fact. If you find the line to be fuzzy, one good rule of thumb is that while opinions lend themselves to lively debate and use words like "should," facts tend to rather dull and use words like "is." Remember: You could argue for hours with a spouse or friend about how you "should" design the interior of your closet, but the question of how wide that closet actually "is" will be answered, definitively, in about 10 seconds with a tape measure.

If you'd like an even clearer separation, below is a video that draws bright lines between what's actually going on in objective reality, and how our own leanings and preconceptions drive our opinions about it. You may find it helpful in your attempts to separate your opinions, and the opinions of those around you, from the facts upon which they are based.

Please try. The brain you save may be your own. The heart you save may be mine.