Microsoft Word Kurzweil, Ray The Singularity Is Near doc

 
Information, Order, and Evolution: 
The Insights from Wolfram and Fredkin's Cellular Automata: 
 
As I've described in this chapter, every aspect of information and information technology is growing at an 
exponential pace. Inherent in our expectation of a Singularity taking place in human history is the pervasive 
importance of information to the future of human experience. We see information at every level of existence. 
Every form of human knowledge and artistic expression—scientific and engineering ideas and designs, 
literature, music, pictures, movies—can be expressed as digital information. 
Our brains also operate digitally, through discrete firings of our neurons. The wiring of our interneuronal 
connections can be digitally described, and the design of our brains is specified by a surprisingly small 
digital genetic code.
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Indeed, all of biology operates through linear sequences of 2-bit DNA base pairs, which in turn control 
the sequencing of only twenty amino acids in proteins. Molecules form discrete arrangements of atoms. The 
carbon atom, with its four positions establishing molecular connections, is particularly adept at creating a 
variety of three-dimensional shapes, which accounts for its central role in both biology and technology. 
Within the atom, electrons take on discrete energy levels. Other subatomic particles, such as protons, 
comprise discrete numbers of valence quarks. 
Although the formulas of quantum mechanics are expressed in terms of both continuous fields and 
discrete levels, we do know that continuous levels can be expressed to any desired degree of accuracy 
using binary data.
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In fact, quantum mechanics, as the word "quantum" implies, is base on discrete values. 
Physicist-mathematician Stephen Wolfram provides extensive evidence to show how increasing 
complexity can originate from a universe that is at its core a deterministic, algorithmic system (a system 
based on fixed rules with predetermined outcomes). In his book 
A New Kind of Science
, Wolfram offers a 
comprehensive analysis of how the processes underlying a mathematical construction called "a cellular 
automaton" have the potential to describe every level of our natural world.
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(A cellular automaton is a 
simple computational mechanism that, for example, changes the color of each cell on a grid based on the 
color of adjacent nearby cells according to a transformation rule.) 
In his view, it is feasible to express all information processes in terms of operations on cellular 
automata, so Wolfram's insights bear on several key issues related to information and its pervasiveness. 
Wolfram postulates that the universe itself is a giant cellular-automaton computer. In his hypothesis there is 
a digital basic for apparently analog phenomena (such as motion and time) and for formulas in physics, and 
we can model our understanding of physics as the simple transformation of a cellular automaton. 
Others have proposed this possibility. Richard Feynman wondered about it in considering the 
relationship of information to matter and energy. Norbert Wiener heralded a fundamental change in focus 
from energy to information in his 1948 book 
Cybernetic
and suggested that the transformation of 
information, not energy, was the fundamental building block of the universe.
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Perhaps the first to postulate 
that the universe is being computed on a digital computer was Konrad Zuse in 1967.
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Zuse is best known 
as the inventor of the first working programmable computer, which he developed from 1935 to 1941. 
An enthusiastic proponent of an information-based theory of physics was Edward Fredkin, who in the 
early 1980s proposed a "new theory of physics" founded on the idea that the universe is ultimately 
composed of software. We should not think of reality as consisting of particles and forces, according to 
Fredkin, but rather as bits of data modified according to computation rules. 
Fredkin was quotes by Robert Wright in the 1980s as saying, 
There are three great philosophical questions. What is life? What is consciousness and thinking 
and memory and all of that? And how does the universe work? ... [The] "information viewpoint" 
encompasses all three....What I'm saying is that at the most basic level of complexity an 
information process runs what we think of as physics. At the much higher level of complexity, life, 
DNA—you know, the biochemical function—are controlled by a digital information process. Then, at 
another level, out thought processes are basically information processing....I find the supporting 

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evidence for my beliefs in ten thousand different places....And to me it's just totally overwhelming. 
It's like there's an animal I want to find. I've found his footprints. I've found his droppings. I’ve found 
the half-chewed food. I find pieces of his fur, and so on. In every case it fits one kind of animal, and 
it's not like any animal anyone's ever seen. People say, Where is this animal? I say, Well, he was 
here, he's about this big, this that, and the other. And I know a thousand things about him. I don't 
have in hand, but I know he's there....What I see is so compelling that it can't be a creature of my 
imagination.
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In commenting on Fredkin's theory of digital physics, Wright writes, 
Fredkin ... is talking about an interesting characteristic of some computer programs, including many 
cellular automata: there is no shortcut to finding out what they will lead to. This, indeed, is a basic 
difference between the "analytical" approach associated with traditional mathematics, including 
differential equations, and the "computational" approach associated with algorithms. You can 
predict a future state of a system susceptible to the analytic approach without figuring out what 
states it will occupy between now and then, but in the case of many cellular automata, you must go 
through all the intermediate states to find out what the end will be like: there is no way to know the 
future except to watch it unfold....Fredkin explains: "There is no way to know the answer to some 
question any faster than what's going on. "... Fredkin believes that the universe is very literally a 
computer and that it is being used by someone, or something, to solve a problem. It sounds like a 
good-news/bad-news joke: the good news is that our lives have purpose; the bas news is that their 
purpose is to help some remote hacker estimate pi to nine jillion decimal places. 
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Fredkin went on to show that although energy is needed for information storage and retrieval, we can 
arbitrarily reduce the energy required to perform any particular example of information processing. and that 
this operation has no lower limit.
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That implies that information rather than matter and energy may be 
regarded as the more fundamental reality.
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I will return to Fredkin's insight regarding the extreme lower limit 
of energy required for computation and communication in chapter 3, since it pertains to the ultimate power of 
intelligence in the universe. 
Wolfram builds his theory primarily on a single, unified insight. The discovery that has so excited 
Wolfram is a simple rule he calls cellular automata rules 110 and its behavior. (There are some other 
interesting automata rules, but rule 110 makes the point well enough.) Most of Wolfram's analyses deal with 
the simplest possible cellular automata, specifically those that involve just a one-dimensional line of cells, 
two possible colors (black and white), and rules based only on the two immediately adjacent cells. For each 
transformation, the color of a cell depends only on its own previous color and that of the cell on the left and 
the cell on the right. Thus, there are eight possible input situations (that is, three combinations of two colors). 
Each rules maps all combinations of these eight input situations to an output (black or white). So there are 
2
8
(256) possible rules for such a one-dimension, two-color, adjacent-cell automaton. Half the 256 possible 
rules map onto the other half because of left-right-symmetry. We can map half of them again because of 
black-white equivalence, so we are left with 64 rule types. Wolfram illustrates the action of these automata 
with two-dimensional patterns in which each line (along the 
y
-axis) represents a subsequent generation of 
applying the rule to each cell in that line. 
Most of the rules are degenerate, meaning they create repetitive patterns of no interest, such as cells of 
a single color, or a checkerboard pattern. Wolfram calls these rules class 1 automata. Some rules produce 
arbitrarily spaced streaks that remain stable, and Wolfram classifies these as belonging to class 2. Class 3 
rules are a bit more interesting, in that recognizable features (such as triangles) appear in the resulting 
pattern in a essentially random order. 
However, it was class 4 automata that gave rise to the "aha" experience that resulted in Wolfram's 
devoting a decade to the topic. The class 4 automata, of which rule 110 is the quintessential example, 
produce surprisingly complex patterns that do not repeat themselves. We see in them artifacts such as lines 
at various angles, aggregations of triangles, and other interesting configurations. The resulting pattern, 
however, is neither regular nor completely random; it appears to have some order but is never predictable. 

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Why is this important or interesting? Keep in mind that we began with the simplest possible starting 
point: a single black cell. The process involves repetitive application of a very simple rule.
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From such a 
repetitive and deterministic process, one would expect repetitive and predictable behavior. There are two 
surprising results here. One is that the results produce apparent randomness. However, the results are more 
interesting than pure randomness, which itself would become boring very quickly. There are discernible and 
interesting features in the designs produced, so that the pattern has some order and apparent intelligence. 
Wolfram include a number of example of these images, many of which are rather lovely to look at. 
Wolfram makes the following point repeatedly: "Whenever a phenomenon is encountered that seems 
complex it is taken almost for granted that the phenomenon must be the result of some underlying 
mechanism that is itself complex. But my discovery that simple programs can produce great complexity 
makes it clear that this is not in fact correct." 
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I do find the behavior of rule 110 rather delightful. Furthermore, the idea that a completely deterministic 
process can produce results that are completely unpredictable is of great importance, as it provides an 
explanation for how the world can be inherently unpredictable while still based on fully deterministic rules.
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However, I am not entirely surprised by the idea that simple mechanisms can produce results more 
complicated than their starting conditions. We've seen this phenomenon in fractals, chaos and complexity 
theory, and self-organizing systems (such as neural nets and Markov models), which start with simple 
networks but organize themselves to produce apparently intelligent behavior. 
At a different level, we see it in the human brain itself, which starts with only about thirty to one hundred 
million bytes of specification in the compressed genome yet ends up with a complexity that is about a billion 
times greater.
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It is also not surprising that a deterministic process can produce apparently random results. We have 
has random-number generators (for example, the "randomize" function in Wolfram's program Mathematics) 
that use deterministic processes to produce sequences that pass statistical tests for randomness. These 
programs date back to the earliest days of computer software, such as the first version of Fortran. However, 
Wolfram does provide a thorough theoretical foundation for this observation. 
Wolfram goes on to describe how simple computational mechanisms can exist in nature at different 

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levels, and he shows that these simple and deterministic mechanisms can produce all of the complexity that 
we see and experience. He provides myriad examples, such as the pleasing designs of pigmentation on 
animals, the shape and markings on shells, and patterns of turbulence (such as the behavior of smoke in the 
air). He makes the point that computation is essentially simple and ubiquitous. The repetitive application of 
simple computational transformations, according to Wolfram, is the true source of complexity in the world. 
My own view is that this is only party correct. I agree with Wolfram that computation is all around us, 
and that some of the patterns we see are created by the equivalent of cellular automata. But a key issue to 
ask is this: