I've always felt the same way. The number that did it for me was i, the square root of -1. It's called imaginary, because it can't exist in the world of real numbers and yet is critical to higher math equations. I always saw that as the chink in the armor of science.
At any rate I think Wolfram, and those mentioned by others here, have hit upon a more accurate dscription of EVERYTHING because it is non-linear. Now if they can do it in about 42 dimensions, 264 colors, and modulating terabit bandwidths they might be getting somewhere. As a start.
Don't let the terminology fool you. There's nothing twilight-zone-ish about imaginary numbers, it's just an accident of word choice.
When people first started thinking about numbers, they thought in simplistic terms of whole numbers: 1, 2, 3, 4...
These are now called "natural" numbers, simply because they're naturally the first ones that come to mind when primitive peoples (or children) first start enumerating things.
Eventually people began realizing that they needed a number which referred to no things at all, and thus the zero was born. At the time it was a pretty revolutionary concept.
After a while, people started requiring numbers that could go below zero, as when accounting for money owed versus money earned. This was the rise of negative numbers.
The positive/zero/negative numbers altogether were called "integers", from the latin word for "untouched, undivided, whole".
However, the shortcomings of whole numbers became apparent, because how do you handle fractions? If you sell someone half of a butchered cow, you have to be able to include that in your accounting. So the "rational" numbers were added. Not because they were sensible, but because they were a "ratio" of one whole number divided by another (e.g. 1/2, 3/4, 99/100, etc.).
This covered most trade transactions, but eventually mathematicians began analyzing things that couldn't be expressed as a simple fraction (ratio). There were numeric quantities that fell between the rational numbers -- when written as decimals, the digits were nonrepeating (as all the rational numbers were). Because these were numbers which were not formed by a ratio (e.g. "rational"), they were dubbed "irrational" numbers.
Again, this doesn't mean that they're nonsensical, it just means that they aren't formed by a ratio of integers. The circumference of a circle (pi) is one such number out of many.
"Irrational" numbers were the first unfortunately named term, because they give the impression that the numbers are insane or something. But it's just an accident of terminology.
The entire continuum of numbers on the number line (integers, rationals, and irrationals) now filled the entire number line. There was not a spot on the number line which didn't fall into one of the above three categories (detail: the integer numbers are actually a subset of the rational numbers). The number line was complete. Because it contained every number that could be expressed to describe an actual single quantity, the set of all such numbers was rather grandiosely named the "real" number line, and the numbers were called "real" numbers.
Eventually, though, math required something more.
The square root of negative numbers, for example, didn't fit anywhere on the "real" number line. Nor did a lot of other mathematical operations which cropped up under perfectly ordinary calculations. It was discovered that if you just presumed the existence of the square root of a negative number, and used it in calculations, suddenly a of calculations became quite straightforward.
Because these new numbers didn't fall anywhere on the number line that had been labelled "real", some witty mathematician (Rene Descartes decided to humorously call them "imaginary" numbers (actually, Descartes coined the term in order to belittle the concept, but the name stuck).
But there was nothing actually imaginary about them. "Complex" numbers (formed by a combination of a "real" number quantity and an "imaginary" number quantity) are used in countless computations that have perfectly real-world applications. For example, electrical engineers use them all the time when doing AC power calculations -- the "real" component represents the instantaneous voltage, and the "imaginary" component represents the power phase. Einstein's relativity equations describe the "real" world beautifully when the three spatial dimensions are represented as "real" quantities and time as an "imaginary" quantity. Many navigation equations become dead simple when east/west is measured as a "real" number and north/south as an "imaginary" component -- and yet no one would argue that the north/south direction is not actually real. And so on.
In fact, the "reality" of imaginary numbers can be seen when you realize that the most intuitive way to understand complex (e.g., real+imaginary) numbers is as points on a *plane*, instead of on a *line*. "Real" numbers can only denote positions on a *line* (think of them as a value along the "X" coordinate). The "imaginary" part can be thought of as the value along the "Y" coordinate, which necessarily doesn't not fall on the one-dimensional "real" number line.
In short, "real" numbers are a limited form of math: one-dimensional math. "complex" numbers (which include an "imaginary" component) are TWO-dimensional math, which is much more direct and straightforward for many types of REAL-world calculations.
There's nothing "imaginary" about imaginary numbers. It's just an accident of nomenclature.