You are here: Home & Blog » Anticipating the Future » Moore’s Law, Kings, Paupers, Lilies, and Exponents

Moore’s Law, Kings, Paupers, Lilies, and Exponents

by Langdon on September 20, 2015

Sept 2015 V2 rice

In 1965, computer scientist and Intel co-founder Gordon Moore calculated the year to year progress that had been made during the brief history of computer chips, and he realized that as a result of scientific and technological innovation, the capacity of chips to perform computing functions was doubling roughly every year. This progress was instigated on the scientific side largely by academic and industry researchers, who had continually found new ways to put more switches onto a single chip, and on the commercial side as a result of the market environment in which the chip makers were competing, where they had strong incentive to improve their products to sustain or improve their market position.

As a result of his calculation and the article he published about it, this rate of improvement got a name, Moore’s Law, by which it is still known today.

The combination of scientific progress applied in a commercial context describes not only the history of computer chips, but it indeed illuminates much of the broader history of civilization. Not every breakthrough was motivated by commercial concerns, but a great many were. Gutenberg was a business man, and his printing press was built specifically to support a commercial venture; it went on to transform the religions of central Europe, and then the entire world of scholarship, and then the entire world. Watt and the steam engine transformed transportation, Whitney and his cotton gin the basic factory, Ford and the Model T further transformed transportation, and countless millions of other advances are central to our lives today.

Moore charted the progress of computer chips on a graph, and wondered how much longer the progress shown on the graph could be sustained. A long time, as it turned out, since its’ now 50 years later and the progress is still proceeding along the same line.Slide1This is one of the most important curves that describes the modern world, for the technological improvement it visualizes is the enabler and provocateur of so many other changes that have occurred during the last five decades.

The sustained rate of progress that Moore’s Law describes is also historically unprecedented, as computer chips have been made progressively smaller, progressively more powerful, and progressively less expensive for all these decades. Throughout the entirety of the history of human industry going back hundreds of thousands of years, no other industry has a sustained rate of progress that is anything even close to the computer chip industry.

Hence, computer scientists like to joke that if the auto industry had made improvements as steadily as the chip industry has, a top-of-the-line BMW would cost something like $20 and get about 5000 miles per gallon. The numbers in the joke vary, but the point is precise and correct: sustained progress has a compounding effect, which results in the J-Curve.

The Pauper and the King and the Exponents

The compounding effect embedded in exponential progressions is worth further exploration here, because it is central to one of the key and ongoing themes of our work, which is the acceleration of change. The technical definition of an exponential process is one that doubles repeatedly at a fixed interval. For some reason which is not entirely clear, humans are exceptionally poor at recognizing the full impact and consequences of exponentially-growing trends, and as a result we are often confounded when they appear. In fact, we seem to be consistently bad at recognizing and interpreting quantities that are very large, those that are very small, and those that change in non-linear ways, which is in fact what exponents do.

Here are two examples of how we are often fooled by exponential rates of change. The first is a fairy tale.

Long ago in a distant land, the king was out in the forest riding on his favorite white horse, which he preferred to do alone to the consternation of his closest advisors. Nevertheless, the king refused their entreaties to take a guard along, and on a clear but cold winter’s day as he was enjoying the forest trails, his horse was spooked by a snake, and took off at a sprint that left the poor king barely holding his place in the saddle. Alas, in its panic the horse soon ran far off the trail and among the trees, and the king was crashed into a large limb. Falling off the horse, he hit his head on a rock and fell unconscious.

While the horse eventually made it way back to the castle, the king lay there for some time, until an old man who lived in a small hut nearby happened upon the king, who will still unconscious on the ground. The old man half-carried and half-dragged the poor king back to his hovel, and there, he bandaged the king’s head, set his broken leg, and fed him small sips of tea. Eventually the king awakened, but his condition was obviously too poor for him to attempt to leave the hovel.

After some weeks of rest under the care of the old man, during which time the entire army was unsuccessfully combing the forest in search of the king, the king decided at last that he was strong enough to return home.

The old man led him back through the snow-covered forest to the main trail, upon which the king was then easily able to find his way home to the castle. Upon parting, the king thanked the old man profusely and told him that should he so desire, he could at any time visit the castle, and the king would have the pleasure of bestowing upon the man anything his heart desired. And so they parted, the king to his throne, and the old man to his hut in the forest.

Some months later, when winter had turned to spring, and spring to summer, and the snow was melted and the weather was fair, the old man presented himself at the castle and requested an audience with the king. However, not knowing of the king’s promise, he was rudely turned away by the king’s guard, and so the old man sat down at the gate and waited. The next day when the king came out on his horse the old man called to him, and the king did indeed recognize him, and had him brought into the castle and given a fine meal.

Finally the king asked what it was that the old man wished as his reward, to which the old man replied, “Your highness, I am but a simple man. I only need a small bit of rice to tide me through my days.”
“Then you shall have it,” the king replied. “How much shall it be?”
“Only a small amount, your majesty. Do you have chess board?”
“Of course I do,” replied the king.
“Then on it can you please place one grain of rice on the first square, and two on the second square, and four on the third, and 8 on the fourth, and so on?” asked the old man.
The king laughed at the foolish old man who was asking for nearly nothing when we could have had nearly anything!
“So it shall be,” replied the king. “Bring out the rice,” he instructed his advisors, and so they did.

They quickly discovered, however, that the old man was not so foolish as he appeared.

What the old man asked for, of course, was for the rice to be given to in an exponentially increasing rate. With each increment the amount doubled, which is exactly what an exponential trend such as Moore’s Law indicates.

For a while the numbers were indeed quite modest, but when they sustained the exponential trend toward the 64th iteration, which is of course the number of squares on a chess board, then something happened that was quite surprising to most people, including to the king and his advisors.

Here is a table showing the progression of numbers.2015 Sept Exponent TableUpon the last square, the 64th, we have attained a value of 9 to the 18th, or 9.2 quintillion, and this is, of course, a number far larger than all the grains of rice in the kingdom, and indeed in the entire world. It is a veritable Mt. Everest of rice, one that no one could eat even in a million years.

But of course by the time the advisors had reached even the third row of the board they foresaw what was coming because the pile of rice was already spilling out all over the place, and the king saw it as well, and understood that he had been fooled by his own ignorance. Being the king, he was not obliged to carry through the promise, which was in any event impossible, and so the advisors bundled up a great many bags of rice, and some soldiers carried them back to the hut in the forest. And in the end, of course, the rodents ate most of the rice, but the point was made, and the king and his advisors had learned a powerful lesson, the same lesson that the computer industry would learn a few hundred years later, that exponential trends lead to outcomes that are difficult to foresee, but which are utterly transformative when they do arrive.

So over the course of fifty years since Moore first made his calculation, the computing power of chips has doubled about 25 times, and the table above shows us that today’s computers are probably therefore about 16 million times more powerful than the computers of 1965. This by any standard a tremendous accomplishment.

And what if the progress underlying Moore’s Law is sustained for another decade? Then look at what’s likely to happen! For a computer a decade hence is likely to be 32 times more powerful that the computer of today, and a gargantuan 530 million times more powerful that the computer of 1965!

The second story now becomes fully relevant. It is a story told by the late Donella Meadows, who was one of the world’s prominent systems scientists and teachers of the modern era. She related the following story in her book Thinking in Systems, which I will paraphrase.

Being a professor at Dartmouth, she was very familiar with the small New England farm, which typically consisted of a farmhouse, a barn, some acreage, perhaps a small forest of Maple trees kept largely for their beauty as well as for their winter firewood and their spring syrup, and almost inevitably a pond. On the pond, in some years, would grow lilies, which could eventually choke off the oxygen and kill the fish. Hence, pond owners had to keep them mostly cleared.

So let’s say that on your own pond you notice a small patch of lilies, but it’s not enough to bother with, and anyway you’ve got a busy week ahead. Each day the patch doubles in size (the hidden exponent), but in this situation it’s going to be a finite trend, because the pond is only so large.

In any case, you come and go throughout the week, and by Friday when you return home you decide that you’ll have to get busy and do something about the lilies because they’ve now covered about a quarter of the pond. In a week’s time, you promise yourself, you’ll clean the pond. Too bad for you, because by then everything below the surface will be choked off and probably dead, for if the pond is one-quarter covered today, by tomorrow it will be one half, and the day after it will covered 100%. Your weekend is ruined by the unforeseen exponent.

This is the insidious nature of the exponential trend … that it appears rather insignificant for quite some time until quite suddenly, it seems to explode out of control. We are surprised by these types of trends, even when we shouldn’t be. Often this happens because we don’t recognize that the exponential pattern is what we’re confronted with. Hence, during the 1960s a group systems scientists including Donella Meadows rose to prominence when they pointed out that the human population was growing exponentially, and since they were among the few who understood what that actually meant, they did the rather simple math to help everyone else grasp the frightening consequences.

A successful and influential book of that era was The Population Bomb, by Paul Ehrlich, and the term “population explosion” was coined to warn us about the terrible resource shortages that were coming. The world took the warning to heart, and in fact the rate of population growth slowed significantly, and it is still slowing today.

But the progression we know as Moore’s Law is not slowing, at least not yet, and the power of exponential growth it describes underlies a great many of today’s business success stories. Powerful and inexpensive computer chips are the core of the iPhone and Android phones, today’s laptops, the internet, the massive arrays of servers that power the internet, and thus it is central to today’s digital lifestyle. Without this trend there would be no Google, no Facebook, no Netflix… no NSA, no Snowden, and no cyber wars.

So where is all this headed?  It’s a great question, and one we will explore in subsequent blog posts, where we’ll examine robots, genetic engineering, artificial intelligence, and solar energy, all of which are dependent on digital technology, and all of which are bringing major change as a result of the continuing trend of exponential transformation.


This blog post is adapted from Langdon Morris’ forthcoming book, Mega Risk, which we expect to publish in Q1 2016.

As always, we welcome your thoughts and comments.

Main Content

Be Sociable, Share!

Previous post: Creating Tomorrow, Geopolitics and Innovation

Next post: 20 Million Ideas to Greatness