In 1996, when I was seven-and-a-half, approximately sixty miles north of Seattle, I counted bald eagles on the Skagit river. In that one morning, in about two hours, I saw 126 eagles. I know this because I kept count.

For the purpose, my dad had given me a clicker, a small sleek shiny metal device whose entire job was to be a number. The clicker had a satisfactorily cool feel to it and felt dense owing to its durable metal construction. On the right hand side was a silver knob with ridges. Twist the knob, and four centered analog dials with stenciled white Courier New numbers behind a centered crystal display would satisfactorily click-click-click and advance from 0000 to 9999 to reset the clicker. Further up, and closer to the side of the clicker, was a metal lever that looked something like a gas pedal that had been bent out of shape. It stuck out enough from the rest of the clicker that any absentminded flick of the fingers would advance the count by one. On the left hand side you could put your thumb through a rotating metal ring to make sure that the clicker did not fall out of your hand. Hence your number would stay with you, always a palm away at your fingertips.

I remember that first counting experience vividly because it was the beginning of a long indoctrination of the certainty that numbers provide. In the sixteen years since that time I could sleep soundly knowing exactly how many eagles I saw that crisp fall morning. Knowing was a satisfactory feeling. Counting seemed simple at the time, but my days of naïveté were numbered.

Are numbers really as certain as we make them out to be in school? From an early age we are taught to deal with numbers. Perhaps we learn how to count things we know the answer to, like the number of bananas or cookies on a Sesame Street set, because it is the easiest way to see how a three dimensional object can be represented, first by two dimensions (describing the object as a word), and then by something even simpler: a number. Flip through any children’s book, and you will also see collections of animals that are very countable and verifiable.

Numbers can take on a different property when we get older. Their most important use shifts from quantifying something that we can already easily characterize, such as the amount of money in a bank account, to trying to help us figure out what is not already obvious enough to know. This is a new use of numbers. We now express our uncertainty with a range of numbers, a percentage mark, and a distribution about which sets of numbers are more likely to yield what we are trying to count.

Using numbers in this new way is difficult and full of pitfalls: measurement error, statistical uncertainty, and context. For some numbers, such those used to infer politician popularity, these difficulties are overlapping: the polling error margin from extrapolating from several hundred phone calls, voting uncertainty from hundreds of thousands of voters only being separated by several hundred votes (a statistical insignificant margin given even a small measurement error), whether the type of people answering the phone represent a scaled down subset of all eligible voters (or are even eligible to vote), the question of what defines popularity in the first place.

Extending the political polling example, when we reach the limit of what we can measure sometimes we cannot determine a winner. In this sense, numbers fail us. In both the 2000 presidential election of Bush vs. Gore and the 2004 Washington State gubernatorial race of Gregoire vs. Rossi, the “margin of victory” was only several hundred votes out of several million cast. Who won? We do not know, since for hundreds of years we have known that certain methodologies have measurement error attached to them.

When the difference between two candidates is smaller than the possible variance of the technique we use to infer the winner, there is no winner. Conspiracy theorists point to “underlying patterns” behind why the outcome turned out to favor the Republican in one case, and the Democrat in the other. But a good null test in either case is comparing the results to the expected variance if everyone voted by chance: a 50/50 coin flip for each cast vote. And in instances of super close races, whether it is a recount, a court decision, or some other method of determining an outcome, the political process does not help us infer who actually won. Trying to find more resolution out of a process where you are already at the limits of resolution is foolish and useless, akin to turning up the volume on the radio and trying to hear words out of static. Fittingly, in both of these cases votes were recounted in an arbitrary manner: partial recounts and continual recounts until a court finally put a stop to it. Flipping a coin, or waiting until the political preference was no longer statistically deadlocked, would have been simpler.

Even numbers that are more physically grounded, such as figuring out how many wildebeest occupy a particular patch of acacia woodland, require numerical assumptions to get the answer. In other words, we have to make stuff up. This is okay, we say, because we are able to calculate uncertainties and confidence intervals in the event that we do not know exactly how many whatever-it-is there are. Yet by using numbers yet again, we return to the same difficulties we tried to get away from in the first place. Oftentimes, when we use more numbers to explain our numbers, it does not help us understand the problem any better; it merely shifts the uncertainty away one step further removed from what we are trying to measure. If we do not delve into the details of an assumption, but gloss over it without a critical eye, we can pretend like the unknowns of our assumption are inconsequential.

If we were scientists, we would say that our assumption is not “grounded” in what we know about the world, something I learned in my geophysics and data modeling training. Most of us are not scientists, however. Judging by the lack of statistics in my early education and contextualizing information in newspaper facts and figures (sample size, r squared values, distribution used for error margins in our political polls), the answer is that we seldom finish what we start. We are left with only numbers, not the toolset and framework of what to make of them. In essence, the numbers are naked.

Finally, a numerical answer needs to have meaning. Science fiction author Douglas Adams jovially raised this point in A Hitchhiker’s Guide to the Galaxy. The mice had finally figured out the “Answer to the Ultimate Question of Life, the Universe, and Everything” after much effort and many computers (and just before the destruction of Earth). The answer? Forty-two.

Despite our problems with numbers today we live in a world obsessed with them. In many public schools we are ranked against our classmates. Our English essays on standardized tests are converted to percentiles. Our letter grades, which are used to determine academic performance, are converted into numbers for the purposes of a grade point average. In sports, we are evaluated by movements and exercises which are expressed in percentages, distance, time. Cameras are first talked about in terms of the number of megapixels, and televisions the highest resolution offered. In computing, the concept of a “binary world” is not just a metaphor. The quantification of information is seemingly inescapable.

Numbers are a relatively recent innovation in human history and much of what they are trying to describe is even more recent (capitalist markets, currency exchange rates, an output from a scientific instrument). It is understandable, but not excusable, that we do not have a good grasp on how to educate ourselves about how to use numbers in these novel situations.

Ironically, it is hard to say whether we are abusing numbers without the data, a Catch-22 conundrum. However, I have a sneaking suspicion that my speculation of the “fudge factor” is much more than a smear of our current way of doing things. For all of the precision a final number can afford us, I think little of this potential precision is actually meaningful (which is why scientists round to “significant figures”).

We need more cautious, careful constructions of how numbers are used in order to increase our quantitative understanding. If we do not keep track of what numbers are supposed to represent they are meaningless, something that is painfully apparent to a cryptographer but not to the ninety-nine percent of us who do not know what that job even is. The key to using numbers is knowing how to interpret them. When we cannot do that or are not willing to put forth the effort to do so, we have reached the limits of our numerical literacy.