Exponential Growth and the Technological Singularity

exponential growth

Is Technology Exponential Growth a Fairy Tale?

A few years ago, I published a blog article explaining how a recursively self-improving AI would create a runaway exponential growth effect and used the fairy tale story of the peasant child, the King and a chessboard full of rice to explain it.

Unfortunately, the term ‘exponential growth’ gets banded about a lot these days, and quite often it’s misapplied to situations where it simply doesn’t apply.

So, this article is going to hopefully set the record straight on the question of exponential growth, and what you need to understand when thinking about it in terms of AI, Automation and Robotics.

exponential growth explained

Exponential Growth Explained

The story of the child, King and rice is not the only fairy tale that’s spoken around exponential growth. Unfortunately, many AI writers and commentators are also carried away by such stories, I believe they are misguided in doing so.

The famed technologist and transhumanist Ray Kurzweil for example:

"An analysis of the history of technology shows that technological change is exponential, contrary to the common-sense “intuitive linear” view. So we won’t experience 100 years of progress in the 21st century — it will be more like 20,000 years of progress (at today’s rate). The “returns,” such as chip speed and cost-effectiveness, also increase exponentially. There’s even exponential growth in the rate of exponential growth. Within a few decades, machine intelligence will surpass human intelligence, leading to The Singularity — technological change so rapid and profound it represents a rupture in the fabric of human history. The implications include the merger of biological and nonbiological intelligence, immortal software-based humans, and ultra-high levels of intelligence that expand outward in the universe at the speed of light."

While I believe there is absolutely a need to plan and prepare for the threat of an AI singularity which one day might induce a runaway technology to move out of our control, I don’t share the view that such singularity is inevitable in the coming decades because of exponential growth.

To explain why I’m going to tell another story, it's called the New York Card Trick.

The New York Card Trick

new york card trick

I was at an event a few years ago where the speaker was excitedly talking about exponential growth and its seemingly magical properties. The story he gave was that of playing cards in New York.

Imagine you stood on Houston Street and Broadway (basically the spot where the East Village becomes Lower Manhattan). You place a playing card on the street and walk a block.

At the junction of 2nd Street and Broadway, you place two cards on the sidewalk and walk the next block where you place four cards on the ground. Each block you walk, you double the number of cards you place on the ground.

By the time you reach Union Square Park, the stack of cards would be higher than any skyscraper in Manhattan. As you cross the park and place another stack of cards, your stack would be higher than any skyscraper in the world.

By Madison Square Park (where the famous Flatiron building is situated), your stack would be higher than Everest.

By Times Square it would reach the moon!

So too with technology, he said. We’re currently standing on the corner of 10th Street on Broadway, where the street suddenly starts making its dramatic diagonal across the length of Manhattan island.

We can see Houston Street where we’ve walked from, Grace Church where we’re standing outside, and Union Square Park ahead of us.

We look at the technology we have today, how much we’ve achieved – but have no way of grasping what we’re going to achieve with the next few steps.

That’s where exponential growth has its impact. It’s where its immense power gets felt. 

Or does it?

There are two reasons why this is an illusion, read on to find out.

new york broadway

The true shape of the curve

The first is the simple truth that while it might seem impressive to imagine this hockey stick curve growth ahead of you, especially compared to the rather mundane progression until that point; the feature of exponential growth is that when plotted on a chart, the curve looks the same no matter what point you sit.

Let me say that again in big text this time:

... when plotted on a chart, the curve looks the same no matter what point you sit.

Take the perspective of where you are after just 5 steps:

exponential curve

At 5 steps, you are at the point where just over half the pack (32 cards) is piled up at your feet. The previous piles are puny, and the next few ones are immense in comparison.

Now compare this to the shape of the curve after 9 steps: 

exponential curve

Notice something?

That’s right.

The shape of the curve is the same, at this point.

The past few piles look puny compared to the 512 cards that are now stacked in front of you. The next few steps look immense by comparison.

In fact, the shape of the curve looks exactly the same at any point you take.

Actually, at every point.

Here again, imagine you are at the 22nd step.

The road behind looks light compared to the steps ahead.

Notice here how the scale has changed - we’re now counting in millions – but the shape is the same.

exponential curve

You see, exponential growth is a fascinating mathematical property – but so often it is misunderstood and misapplied, with the same rhetoric.

“What we’ve accomplished until now, is nothing compared to what we’re about to accomplish”.

This statement would be true of something that is recursively self-improving (where the measure of progress can be described as a proportion of its current state), but until we reach recursive self-improving AI – we can only look backwards and report on the shape of the curve – we can’t look forward.

The true shape of the curve might not even be exponential after all – S-Curves look exponential until the gradient reaches a limit point after which progress starts slowing down.

If you’d like to read more about S-Curves, then you’ll need to wait for my forthcoming article on the subject coming soon.

Recursive self-improving AI is a problem we need to prepare for, but not because we’ve suddenly reached the step before take-off like Ray Kurzweil believes. 

It surely is better to be prepared, but equally – the next 100 years of technological progress might be the same as the past 20,000.

Until we reach the singularity or recursive self-improving AI – we simply cannot predict what the future brings.

Contempt for Complexity

The other illusion painted by proponents of exponential growth is that they overlook the complexity of the problem that they believe will be solved by the next few jumps.

When you stand outside Grace Church and see the pile of cards stacked to your knees, it must seem unimaginable to believe that by the time you get to Union Square Park the pile will be higher than any Manhattan skyscraper.

That’s because it is unimaginable.

The laws of physics prevent it.

The person who told this story at the event I was at picked 10th and Broadway as the arbitrary point of today not because that is where Broadway suddenly kinks to the left, nor because that’s where a recognisable landmark is standing.

It’s also the point of the story where it changes from reality to fantasy.

You see, the tallest structure ever created by a pack of playing cards is a little over 10 metres (30 feet)! 

And so, while you might succeed in building your tower of cards on 11th Street, you’re unlikely to at 12th, and almost certainly never will at 13th.

new york

So too, beware of ever-increasing complexity challenges posed by the underlying human skills and abilities that the Artificial Intelligence, Automation and Robotics industries are trying to replicate.

What we can achieve today is truly impressive, and I firmly believe that most if not all of human skills and abilities will one day be capable of being performed by machines.

At the same time, I think we should be cautious of those who claim that the rapid advances we’ve seen in AI abilities in the past few years indicate that we’re on the beginning of the hockey curve of progress.

It’s not.

house of cards

The reason we’ve made such progress in a short period of time is partially down to the cheap computational power that keeps following Moore’s Law in doubling approximately every two years and is also partially down to the explosion of data being created and consumed in the ‘Big Data’ revolution of the last decade.

But it’s also because we’re able to for the first time meaningfully apply mathematical techniques that have been in existence since the 1950s and 1960s.

Innovators are also applying these solutions to an ever-increasing set of problems. But to say that the capabilities that researchers are succeeding in are following an exponential trajectory is misleading.

Just as misleading as to say that the amount of capital flowing into AI investment is also following an exponential trend.

So in summary – when we reach the point of building recursive self-improving AI, then we will be on the road to exponential growth; but until then – it’s just as likely that technological progress will plateau along an S-curve shape.

There is nothing special about where we are today compared to the past, but until we reach a consensus of how we want our future AI systems to operate – we should be very wary of recursive self-improving AI; for if we don’t heed these warnings – we could find ourselves sitting on top of a house of cards, and not with a fairy tale ending.

Now it's Your Turn

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