Microsoft Word Kurzweil, Ray The Singularity Is Near doc

 
Fractal Dimensions and the Brain 
 
Note that the use of the third dimension in computing systems is not an either-or choice but a continuum 
between two and three dimensions. In terms of biological intelligence, the human cortex is actually rather 
flat, with only six thin layers that are elaborately folded, an architecture that greatly increases the surface 
area. The folding one way to use the third dimension. In "fractal" systems (systems in which a drawing 
replacement or folding rule is iteratively applied), structures that are elaborately folded are considered to 
constitute a partial dimension. From that perspective, the convoluted surface of the human cortex represents 
a number of dimensions in between two and three. Other brain structures, such as the cerebellum, are 
three-dimensional but comprise a repeating structure that is essentially two-dimensional. It is likely that our 
future computational systems will also combine systems that are highly folded two-dimensional systems with 
fully three-dimensional structures. 
Notice that the figure shows an exponential curve on a logarithmic scale, indicating two levels of exponential 
growth.
36
In other words, there is a gentle but unmistakable exponential growth in the rate of exponential growth. (A 
straight line on a logarithmic scale shows simple exponential growth; an upwardly curving line shows higher-than-
simple exponential growth.) As you can see, it took three years to double the price-performance of computing at the 
beginning of the twentieth century and two years in the middle, and it takes about one year currently.
37 
Hans Moravec provides the following similar chart (see the figure below), which uses a different but overlapping 
set of historical computers and plots trend lines (slopes) at different points in time. As with the figure above, the slope 
increases with time, reflecting the second level of exponential growth.
38 

---

If we project these computational performance trends through this next century, we can see in the figure below 
that supercomputers will match human brain capability by the end of this decade and personal computing will achieve 
it by around 2020—or possibly sooner, depending on how conservative an estimate of human brain capacity we use. 
(We'll discuss estimates of human brain computational speed in the next chapter.
39 

---

The exponential growth of computing is a marvelous quantitative example of the exponentially growing returns 
from an evolutionary process. We can express the exponential growth of computing in terms of its accelerating pace: it 
took ninety years to achieve the first MIPS per thousand dollars; now we add one MIPS per thousand dollars every 
five hours.
40 

---

IBM's Blue Gene/P supercomputer is planned to have one million gigaflops (billions of floating-point operations 
per second), or 10
15
calculations per second when it launches in 2007.
41
That's one tenth of the 10
16
calculations per 
second needed to emulate the human brain (see the next chapter). And if we extrapolate this exponential curve, we get 
10
16
calculations per second early in the next decade. 
As discussed above, Moore's Law narrowly refers to the number of transistors on an integrated circuit of fixed 
size and sometimes has been expressed even more narrowly in terms of transistor feature size. But the most 
appropriate measure to track price-performance is computational speed per unit cost, an index that takes into account 
many levels of "cleverness" (innovation, which is to say, technological evolution). In addition to all of the invention 
involved in integrated circuits, there are multiple layers of improvement in computer design (for example, pipelining, 
parallel processing, instruction look-ahead, instruction and memory caching, and many others). 
The human brain uses a very inefficient electrochemical, digital-controlled analog computational process. The 
bulk of its calculations are carried out in the interneuronal connections at a speed of only about two hundred 
calculations per second (in each connection), which is at least one million times slower than contemporary electronic 
circuits. But the brain gains its prodigious powers from its extremely parallel organization in three dimensions. There 
are many technologies in the wings that will build circuitry