Now many of us are familiar with Moore’s law, the famous principle, according to which the development of computing power follows an exponential curve, doubling in the ratio of price-quality (that is, speed per unit cost) every 18 months or so. When it comes to applying Moore’s law to their own business strategies, even visionary thinkers did not see the huge “blind spot AI”. Even the most successful, strategically-minded business people who see their industry through and through, unable to understand what exponential development. And on this exponential curve, there is one technology that particularly benefits from exponentials: artificial intelligence.
Exponential curves on paper
One of the reasons why people don’t understand how fast artificial intelligence is developing, simple to the ridiculous: exponential curves don’t look very well when we humans try to explain them on paper. For practical reasons, nearly impossible to fully portray the steep trajectory of the exponential curve in a small space, such as a chart or slide. To visually depict the early stages of the exponential curve is easy. But since the steeper part of the rapidly building up momentum, things become complicated.
To solve the problem of inadequate visual space, we use a convenient mathematical trick — logarithm. Thanks to the “logarithmic scale”, we learned how to twist exponential curves. Unfortunately, the widespread use of logarithmic scales can also cause research myopia.
A logarithmic scale is arranged so that each tick on the vertical axis sootvetstvuet not constant increase (as in conventional linear scale), and a multiple, for example 100. Classic diagram of Moore’s law (figure 1) uses a logarithmic scale for the exponential improvement in the cost of computing power (measured in computations/second/dollar) over the past 120 years, from mechanical devices 1900s to modern graphics cards on the basis of silicon.
Logarithmic diagrams have become a valuable form of shorthand for people who are aware of visual distortion that are present on such charts. Now is a convenient and compact way to display any curve, which quickly and dramatically increases over time.
However, logarithmic charts deceiving the human eye.
Mathematically, jamming huge numbers, logarithms make exponential growth look linear. Because they compress the exponent to linear graphs, more convenient for people to look at them and talk about the impending increase in computing power.
Our logical brains know the slide rule. But our subconscious brains can see curves and configured on them.
What should I do? First, you need to return to the original linear scale.
The second diagram below the data correspond to an exponential curve, but written in a linear scale on the vertical axis. Again, the vertical scale represents the computational speed (in gigaflops), which can be bought for one dollar, and the horizontal axis represents the time. However, in figure 2 each tick on the vertical axis corresponds to a simple linear increase in only one gigaflop (no increase in 100 times, as in figure 1. Flop is a standard way of measuring computing speed which means “floating point operations per second”.
Figure 2 shows the actual real exponential curve that characterizes Moore’s law. Looking at how drawn this diagram, to our human eyes it is easy to understand how quickly the increased performance of computers over the last ten years.
But the second chart, something is wrong. It may seem that during the 20th century the value and performance of the computers do not improve. Apparently it’s not.
Figure 2 shows that the use of linear scale to demonstrate the change of Moore’s law may eventually be blind. The past seems flat, as if there was no progress. In addition, people mistakenly conclude that current point in time represents the amount of unique, “almost vertical” technological progress.
The linear scale can deceive people by making them believe that they live on top of a change.
Blind spot living in the present
Let’s take a look at figure 2. If you look out in 2018, doubling previous prices-quality that have occurred every decade throughout the greater part of the 20th century, seem flat, almost immaterial. The person studying this chart, I would say: how lucky I am to live now. I remember year 2009 when I thought my new iPhone quick. I had no idea how he’s slow. Good thing I reached the vertical part.
People say that we have been “breaking the hockey stick”. But such a transition point there.
Any form of curve in the future looks the same as it was in the past. Below, figure 3 shows the exponential curve of Moore’s law on a linear scale, but this time from the perspective of 2028. The curve assumes that the growth we have experienced over the past 100 years will continue for at least another 10 years. This chart shows that in 2028 for one dollar you can buy 200 gigaflop computing power.
But figure 3 also presents a trap for the analyst.
Look carefully where today’s computing power (2018) lies on the curve depicted in the third diagram. From the point of view of a person living and working in the future, the year 2028, it would seem, during the early 20th century, improvements to computing power practically was not. It seems that computing devices used in 2018 was a bit more powerful than those used in 1950. The observer could also conclude that the current 2028 represents the culmination of Moore’s law, where the progress of computing power, finally soars to the heavens.
Every year it would be possible to recreate figure 3, changing only the depicted period of time. The shape of the curve would be identical, would change only the ticks on the vertical scale. Please note that the form of figures 2 and 3 looks the same, except the vertical scale. Each and every chart every last moment would be flat when viewed from the future, and every future moment would be a dramatic departure from the past. Alas, such a false perception would be the result of a wrong business strategy, at least when it comes to artificial intelligence.
What does it mean?
Exponential change themes it is difficult to understand the human mind and the eye can see. Exponential curves is unique in the sense that they are mathematically self-similar at each point. This means that always doubling curve has no flat parts, has the ascending parts of the curves and bends, which people say. Its form will be the same always.
As Moore’s law continues to operate, the temptation to assume that at this moment we have reached a unique stage of great changes in the development of artificial intelligence (or any other technology that extends Moore’s law). However, as long as computing power continues to follow an exponential curve of price-quality, each future generation is likely to look to the past as an era of relatively little progress. In turn, remains true in reverse: every current generation will look 10 years into the future and will not be able to assess how much progress in the field of AI yet to come.
Thus, for anyone who is planning a future driven by exponential growth of computing, is born the challenge to overcome one’s own erroneous interpretation. You need to keep in mind just three charts to truly appreciate the power of exponential growth. Because the past will always look smooth, while the future will always look vertically.