One reason why people don't understand how fast AI develops is simple, even ridiculous: when we try to capture them on paper, the exponential curve does not perform well. For practical reasons, it is almost impossible to narrow. The steep trajectory of the exponential curve is fully described in space (such as a chart or slide). It is easy to visually depict the early stages of the exponential curve. However, as the steep part of the curve begins to appear and the numbers increase rapidly, things become More challenging.
Capture index curve
To solve this problem of insufficient visual space, we used a simple mathematical technique called logarithm. Using the so-called 'logarithmic scale', we learned to compress the exponential curve. Unfortunately Yes, the widespread use of the 'log scale' also leads to short-sighted results. The logarithmic scale works by the fact that each scale on the vertical y-axis does not correspond to a constant increment (such as a typical linear scale). It's a multiple, say 100 times. The classic Moore's Law chart below uses the 'log scale' to describe the cost-exponential growth of computing power over the past 120 years, from mechanical equipment in 1900 to today's powerful silicon-based GPUs.
Figure 1: Index change in the logarithmic scale showing the cost of calculation over the past 120 years
Today, logarithmic graphs have become a very valuable shorthand for those who are aware of visual distortion. In fact, the 'log scale' is a simple and compact method that can be used to describe over time. Any curve that rises in a rapid manner. However, the logarithmic graph hides a huge price: they fool the human eye. By mathematically large numbers, the logarithmic graph makes the exponential growth appear linear. Because they compress the irregular exponential growth curve into a linear shape, the logarithmic graph makes it easy for people to be satisfied with the exponential growth rate and scale of future computing power, and even complacency.
Our logic brain understands the logarithmic graph. However, our subconscious mind sees a linear curve and chooses to turn a blind eye to its defects. So, how to effectively eliminate the strategic short-sight caused by the logarithmic graph? Part of the solution is to return The original linear scale. In Figure 2 below, we use the data to fit the exponential curve and then plot it with a linear scale on the vertical axis. Similarly, the vertical axis represents the processing speed (in gigaflops) that can be purchased for one dollar. The horizontal axis represents time.
However, in Figure 2, each scale on the vertical axis corresponds to a simple linear increase trend (equivalent to 1 gigaflops instead of 100 times as shown in Figure 1). The word 'FLOP' is the standard method for measuring calculation speed. , represents the floating point operation per second, other units include megaFLOPS, gigaFLOPS and teraFLOPS.
Figure 2 shows the true exponential curve describing Moore's Law. The way this chart is drawn is easy for our eyes to understand: In the past decade, how fast the price/performance ratio has changed. However, the same is true in Figure 2. There are serious errors. For the naive readers of this chart, it seems that the computer's price/performance ratio has not improved at all in the 20th century. Obviously, this is wrong.
Figure 2 shows that when using linear scales to prove that Moore's Law changes over time, there is also considerable blindness. It can make the past seem unremarkable, as if it has only recently progressed. In addition, the same linearity The scales also lead people to mistakenly believe that their current strengths represent a unique, 'almost vertical' period of technological advancement. This brings me to the next main reason for the emergence of charts that lead to AI blind spots: Linear Degree charts can deceive people and make them believe that their lives are at the peak of change.
Short-sightedness living in the moment
Let us look at the following table 2: From the situation of 2018, the doubling of the price/performance ratio that occurs every ten years in most of the 20th century seems to be unremarkable, even seemingly irrelevant. People who saw Table 2 may I will say to myself: 'Child, I am very lucky to live today? I remember 2009, when I thought my new iPhone was very fast! But actually I don’t know how slow it is, now I finally arrived excited. Vertical part! '
I heard people say that we just passed the 'elbow of the hockey stick'. But there is no such transition point. Any exponential curve itself is similar, that is, the shape of the future curve and the curve of the past are almost not too Big change. Figure 3 below shows the exponential curve of Moore's Law on the linear scale chart, but this time from the perspective of 2028. This curve assumes that we have experienced at least the growth in the past 100 years. It will last for 10 years. This chart shows that in 2028, one dollar will purchase about 200gigaflops of computing power.
Figure 3: Moore's Law on a Linear Scale
However, Figure 3 also represents a potential analytical dilemma. Take a closer look at the position of the curve shown in Figure 3, which represents today's computing power (2018). For those who live and work in 2028, even at 21 At the beginning of the century, there was hardly any substantial improvement in computing power. It seems that the computing devices used in 2018 were only slightly stronger than the computers used in 1950. Observers can also conclude that 2028 is the culmination of Moore's Law, the year The progress of computing power has finally begun.
Every year, I can recreate chart 3, changing only the description of the time category. The shape of the curve is very similar, only the scale on the vertical scale will change. Please note that in addition to the vertical scale, the shape of Figure 2 and Figure 3 looks It is the same. On each such chart, from the perspective of the future, every point in the past is flat, and every point in the future seems to be completely different from the past. Views are being introduced into flawed business strategies, at least in terms of AI.
What does this mean?
Exponential speed of change is incomprehensible to human minds and eyes. The exponential curve is unique because, from a mathematical point of view, they are similar at every point. This means that The doubled curve has no flat part at all, and there is no rising part; there is also no business person who is used to talking about the 'elbow' and 'hockey stick' bending. Even if you zoom in on any part of the past or the future, its shape looks like it's the same.
As Moore's Law continues to work, we can't help but think that at this moment, we are in a unique period of development of AI (or any other technology that relies on Moore's Law). However, as long as processing power continues to follow exponential price/performance curves, the future Each generation may look back and think that this is a relatively small era of progress. In turn, the situation will be like this: Each generation will look forward to the next 10 years, but can not predict how much room for improvement in AI.
So for anyone planning to drive the future by computer exponential growth, the challenge is to fight the misinterpretations in their brains. Although this sounds difficult, you need to remember these three graphs simultaneously – the logarithmic graph The visual consistency, the deceptive scale of dramatic and linear graphs, so that you can truly understand the power of exponential growth. Because the past always seems bland, and the future will always be full of great changes.