Statistics are a lot like a bikini: what you see is interesting, but what is concealed is crucial.

When British statistician I.J. (Jack) Good was breaking Nazi codes in a mansion at Bletchley Park with Alan Turing, the father of modern computing, he had no idea that their conversations would one day nearly ruin science fiction. Yet the fascination with machine intelligence shared by Jack and his old friend Alan inspired him to pronounce in 1965 that “the first ultraintelligent machine is the last invention that man need ever make.” What he meant by that statement was that any thinking machine smarter than it’s creator could design an even smarter machine, which in turn could design one smarter still, ad nauseum. The development of a computer clever enough to design it’s own successor would result in the rapid, exponential growth of artificial intelligence.

There is a frightening assumption implicit in this argument that such an intelligence could remake the world in ways our limited imaginations could not possibly comprehend. Our brief reign as the most clever form of life on Earth would be at an end, and we would henceforth be along for the ride.

A few decades later, the mathematician and science fiction author Vernor Vinge would give this concept a name and popularize it in his award-winning science fiction novels. He referred to the point in time when progress in artificial intelligence research would reach a breakaway point as the “Technological Singularity”. Beyond this point, all things are possible, and little can be foreseen.

And thus perished science fiction. Almost.

To suggest that technology is rapidly and inevitably bringing us to a place where our most reasoned guesses about the nature of life could be no more informed than a coin toss hits every hard science fiction author where they live. It is a sobering thought for those that pride themselves at building worlds based on reasonable extrapolation of present technological trends. The Singularity is the black hole of trends, from which no prognosticator can emerge with any more credibility than a one-eyed gypsy holding a cracked crystal ball with “Made in China” stamped on the bottom.

Despite the adoption of the singularity concept (which is embraced with an almost religious fervor in some camps), it has not proven to be the end of the sci-fi franchise, obviously. You can always build fantasy worlds a long time ago in galaxies far, far away and still sell tickets, and a few authors have had great sport in trying to predict the unpredictable, but for hard science fiction authors staring into the maw of the Singularity, the future looks black indeed.

Fortunately, I have decided to come to the rescue with a very simple pronouncement of my own.

The singularity is bunk.

But don’t take my word for it. As many of my previous math teachers would be the first to point out, I am not particularly gifted at graphing equations. Fortunately, I don’t need to be, and neither do you, to see that the concept of runaway growth in artificial intelligence is unlikely to lead anywhere near where Vernor Vinge and others are pointing. To understand why, let’s examine the whole idea of the singularity a little closer, shall we?

Like most of the other frightening trends with catchy names and bestselling books devoted to them, the trend in artificial intelligence that leads to such ominous forecasts as the sinister, Hugo-devouring Singularity is one of exponential growth. Exponential growth is an impressively mathematical way of stating that the larger a quantity is, the faster it grows, assuming that it continues to grow proportionately. For example, if you take a penny and double it every day, in a month you will have amassed over a million dollars. This idea looks even more impressive on a graph, where a slowly ascending line suddenly rockets off the chart and into the darkest reaches of your imagination.

But, like most math, there is an underlying assumption that is somewhat more slippery. The assumption is that this exponential growth will continue at the same rate. The alarmists will point to the graph itself as evidence that the trend will continue. Has it not always historically done so? There is certainly no evidence that it will NOT continue…such evidence is in the future, where it has no doubt already be eaten by the ravenous, snaggle-toothed Singularity, along with several puppies.

But even if you double a penny every day, sooner or later you will run out of penny rolls. Still, it’s hard to argue with the math, at least for those of us who were enthusiastically encouraged by our math teachers to consider a career in art, so perhaps it would be better (and by better, I mean considerably less boring) if we put this idea to the test in a more graphic way. Let’s try another exponential thought experiment, and see what happens.

Take a sheet of paper. Fold it in half. Now fold it in half again. Keep folding it until you begin to feel stupid. How far did you get? Probably not very far…maybe seven folds, if you are REALLY stubborn. The problem, of course, is that as you continue to half the area of the paper you are folding, you double the thickness of the paper you are trying to crease. Eventually, your plump little fingers simply don’t have the strength to fold the paper one more time. Or, put another way, as the area of the paper to be folded decreases exponentially, the force required to do so increases exponentially.

If this seems painfully obvious to you, it’s because we have all grown up in a universe that is very reluctant to give us something for nothing, be it pennies, paper…or intelligence.

As ephemeral as intelligence may seem to be, it doesn’t arise from thin air. It requires the organization of energy. The organization of energy is what life does best, but the universe exacts a price for it. The more organized life becomes, the higher the price. Human beings are (arguably) the smartest animal life on the planet, and the price has been high indeed. One human being consumes about as much energy as a hundred watt light bulb just to sit and think (Ironically enough, the invention of the television means we can expend even more wattage thinking less). It has required billions of people thinking together over generations to invent sophisticated ways to organize energy beyond our own native abilities by building machines to do the thinking for us. The price for this has been extraordinarily high. The average annual global energy consumption, above and beyond energy derived from food sources, is better than 15 Terawatts, or enough power to light 150 billion light bulbs. This price is so high that other forms of life have been paying in spades, and our very biome is threatened with destruction. A peek at graphs that plot the energy consumption of our species, or the quantity of pollutants produced by our machines, show the same alarming exponential curves as our technological triumphs.

It’s getting tougher to fold that paper all the time.

Many of the gains in artificial intelligence have been the result of miniaturization. Today’s pocket calculator is simply a user-friendly abacus stuffed into a much more portable package. But there is a limit to how small you can make something before its utility becomes questionable. During the days of vacuum tubes, you would have needed a city bus to carry around a fraction of the data that you can now keep on your key chain, which is by and large regarded as a good thing (although you are far less likely to lose a city bus in your couch cushions). Miniaturization produces not only improvements in portability, but speed and energy efficiency as well.

But once again, this improvement in efficiency comes at a price.

Computer manufacturers have been working steadily towards machines that offer more bang for your energy buck in an effort to make laptop batteries last longer and squeeze as many polygons as possible from your graphics card without dimming the lights in your house (or burning it down). Sadly, the efficiency improvements consumers enjoy still manage to result in a net energy loss, as landfills overflow with obsolete electronics and manufacturers go to ever greater lengths to mine the rare metals employed in the construction of all these nifty gadgets overloading our powerstrips. Energy consumption continues to outpace productivity gains, and the only appliance that threatens to open up a badly needed wall outlet is the kitchen toaster, which will soon be replaced by your laptop as continuing improvements in processing power enable you to fry an egg on it.

At this point, those of you with a skeptical bent (bless your heart) may be wondering: How does this guy know energy consumption is outpacing productivity gains? Does he have any data to back this bold assertion? Where’s the chart?

Well, no, I don’t have a chart. I don’t need one, because more brilliant men than me have long since determined that energy consumption will always outpace productivity. (They DO have charts and everything. Honest.) This inconvenient idea is known as “entropy”, and is forever enshrined in the Second Law of Thermodynamics. It is a particularly pesky property of the universe that insures that your batteries will always run down, your car will eventually rust apart and your dog will inevitably die no matter how many vitamins you feed him. It means that however much energy is put into an activity, some of it will inevitably be wasted. You need look no further than your annual tax form to see this principle in action.

But let’s forget about the unfortunate fate of your dog for a while and think about speed. Not of processors this time, but of another technological marvel, the airplane. If you plot the maximum speed of cutting edge flying machines over the past hundred years, you will get a curve remarkably similar to the exciting ski slope of other, more apocalyptic charts. From poking along in an open cockpit at highway speeds to scraping the edge of space at three times the speed of sound in the SR-71, we’ve come a long way. Recently developed technology demonstrators have travelled faster and higher still. Yet where are all of these blazingly fast aircraft today? The SR-71 Blackbird and the Concorde are museum pieces, and the scramjet is little more than a high-flying model. Fighter planes and air traffic alike move along at more stately…and sustainable…speeds, for the simple reason that it is just too damn expensive to build them to go any faster. During World War Two, American factories cranked out tens of thousands of fighter planes. Sixty years later and considerably further along the gee-whiz curve, our Air Force can barely scrape together enough money for a hundred F-22’s, despite a budget that rivals or even exceeds WW2 levels.

If you consider that money is representative of physical resources (when money stops representing physical resources, it becomes valueless little pieces of paper that the rioting peasants like to light their torches with), and that the cost of a resource is a fair approximation of the energy required to extract/provide/create it, then it is clear that the exponential increase in aircraft performance has a corresponding exponentially-increasing energy cost.

If you follow these flying machines off the ground and into space, you can see the same exponential cost increases slowing down our speedy ambitions. We can neatly sidestep the obstacles to our ambitions for a while by throwing more and more energy at them, but sooner or later, the energy-requirement curve slopes up to infinity. Nuclear rockets are faster than chemical ones, and antimatter-propelled spacecraft can theoretically take us even closer to the speed of light…but the closer we get, the more energy is required, until even the fastest of hand-waveum powered spaceships are pulled over by the relativity police. And the accountants are likely to pull the plug long before the police get there.

If you are looking for trends, I think you can see one emerging here. Exponential curves have a lot of trouble making it off the chart, thanks to other exponential curves. This applies to every field of technology, be it artificial intelligence, aviation, or biology.

Speaking of biology, I suspect that there are still more hidden curves lurking beneath the bikini.

Ponder the reliability of intelligence. A decent calculator, though simple-minded, will infallibly give you the correct answer to your multiplication problem every time. Not so a human being, whose sophistication and intelligence greatly exceeds that of any pocket calculator. Why?

As machines grow increasingly complex, they become more vulnerable to error, partly owing to the indeterminacy that inevitably accompanies events on such a small scale, and partly owing to the increasingly unpredictable behavior of so many processes running at once. For an example of smaller not necessarily meaning better, I offer this factoid that I read-somewhere-and-have-long- since-forgotten-where-so-don’t-even-ask: it is estimated that the average computer user experiences a half dozen or more “soft fails” a month…that is, errors produced by little more than free radiation bumping bits of data around on a quantum level. So when you PC seems to crash for no apparent reason, it probably did. At least the cosmic ray got it and not your DNA.

For an example of how multiple processes can compromise intelligence, the average PC offers another real-life lesson. Every PC runs a number of pieces of software concurrently, including some the user didn’t want there in the first place. Some are part of its operating system, some are nifty bits of crapware designed to make toasters fly across your screen when you forget to turn your computer off and a few of them like to produce annoying pop-up ads at embarrassing moments. None of them get along very well and often result in persistent crashes and ever-growing landfills.

But for the best example of why ultraintelligent machines may be a problematical idea, look no further than the most intelligent living thing on the planet, the human being. Despite one of the most ruthless and efficient quality control systems in existence (which often penalizes stupidity with death), the smartest animal mother nature has been able to produce after millions of years of selective breeding is…us. Given that a fair portion of us are undeniably error-prone, if not completely loopy, this does not bode well for advances in artificial intelligence. I suspect any sufficiently advanced machine intelligence will be just as crazy as your average human being, if not crazier, and prove to be far less useful than we might have hoped. You can only endure so many pop-up windows before losing your mind completely.

So fear not. While there may be little hope for the human race getting smarter any time soon, there is no need to fear for the future of science fiction. There are dangerous curves ahead, but for every remarkable curve you see, there are likely to be some equally impressive ones you can’t see.

There is nothing like a bikini to let your imagination get the better of you.

Finis