Mountains are not pyramids and trees are not cones. God must love gunnery and architecture if Euclid is his only geometer.
—Thomasina, in Tom Stoppard’s Arcadia
Looking for truth in numbers presents obstacles far beyond the peculiar nature of the human thinking apparatus we carry around in our heads (and also in the rest of our bodies). There’s also the difficulty of getting true information from what some people call the real world. We only glimpse that real world through the patterns, or signals, we see in our heads. But those patterns and signals are created, at least in part, outside ourselves: Call them information, messages, signals, relationships, ideas. Whatever you call them (how’s input for a modern, computer-related analogy?), understanding anything requires getting a handle on that stuff out there and on the ways in which knowledge about it arrives on our internal radar screens.
Needless to say, the relationship between human senses and the world outside is a subject of breathtaking enormity—comprising the efforts of religion, science, philosophy, and art over many centuries. The few aspects discussed here offer just a taste of some of the glitches we may encounter in trying to add up what's going on out there, mathematically speaking.
For example, how do we measure the properties of things? How do the quantities we measure with scales and thermometers and IQ tests relate to qualities? Most of us have fallen into the long-practiced habit of believing that quality and quantity are two different kinds of properties that don’t affect each other. On the contrary, not only does quantity frequently determine quality, quantity (or, more broadly, scale) can affect the very notion of what is true, what is possible, what, indeed, exists.
Another limit imposed by reality is its sheer complexity, which makes it impossible to predict some ordinary things (like weather) at the same time that it’s possible to predict truly extraordinary things (like the fate of the universe). Astronomers can measure the distance from Earth to the Sun to the nearest centimeter. But they can’t predict the time of the sunset to the nearest minute—because at least nine different factors are involved. (Some of the most critical variables are the speed and tilt of Earth’s orbit and the layers of smog that can bend the setting rays of light like a lens.)
Yet another curious aspect of the information we glean from the outside world is that one person’s data is another person’s noise, and knowing which is which in any particular instance is not a simple matter. Indeed, what’s noise today may be viewed as an important signal tomorrow, and vice versa. Like so much else about information, the difference between signals and noise frequently depends entirely on context.