The Breath of Life: Computation
Life is a process. Death is the cessation of this process.
Or perhaps they are both parts in a bigger process of which we are yet unaware…
Can the process of Life be abstracted from its machinery (the cell)? Before we can answer this question, we need to think deeply and clearly about what we mean by “process.”
A process is in effect, an algorithm that describes how something is done. It is possible in many cases to separate the process from the physical medium in which it initially resides and to then re-implement this process in another medium.
Charles Babbage pondered the question of process and developed the idea of what would later become known as “software.” Software is an abstract representation of the process of a machine, distinct from its physical components (its “hardware“). Using the concept of software, machines could ultimately be used for purposes that were not foreseen when the machine was built.
Babbage came to believe that it was possible to create a machine capable of performing any intellectual process. He called his attempt the “Analytical Engine.” His software consisted of punched cards (shown at left).
Alan Turing addressed the question of process in computational terms. He described a mathematical model of computation through a hypothetical device he called the “Turing Machine” (or TM). He then went on to prove that the Turing Machine was capable of performing any intellectual process, given that the process relied upon the logical manipulation of Symbols.
Machines perform mechanical processes. All mechanical processes can be defined in terms of the manipulation of symbols since a “mechanical process” is by definition one in which the events in the process progress according to “mechanical” rules. A particular state and situation leads inexorably to the next state. States and inputs can be encoded using symbols.
Therefore, if a Turing Machine can perform any process that involves the manipulation of symbols, then it can simulate any machine.
Turing proved the theoretical existence of a “Universal Turing Machine” (or UTM) – a Turing Machine capable of emulating any other Turing Machine. By interpreting the encoded process for a given machine, a UTM can simulate the behavior of any machine. Alonzo Church had independently and by another method also proved the computability of process steps. Turing and Church‘s combined proof, known as the “Church-Turing Thesis,” provides the theoretical underpinnings for the stored program computer – a truly “Universal Machine.”
Turing came to believe that machines would one day be able to emulate the linguistic output of a typical human being. Since this is a way that we communicate intelligence among ourselves, if machines ever possess this capability, then by necessity we would seem to have to grant that they also exhibited some intelligence. He created a test for this capability which is known as “The Turing Test of Machine Intelligence.”
Our minds also operate on Symbols, not on reality. At a low level, the Symbols are electrical and chemical and serve as representations of reality. We somehow abstract patterns from this electro-chemical soup, form conceptions, and make judgements. All of these processes can be thought of as further abstractions involving the manipulation of various layers or levels of symbols.
But is our mind based on purely mechanical processes? Where does this leave “free will?”
It seems interesting that the story of the “Fall of Man” described in Genesis concerns the apparent unlawful acquisition of free will. If the mind is in some sense a machine, does this mean that we are incapable of innovation or choice?
Stephen Wolfram‘s research into another branch of computer theory – automata theory (specifically cellular automata or CAs), seems to indicate that even if the steps in a process are completely deterministic, we still may not be able to predict the behavior or outcome of the process.
Wolfram found that some simple forms of automata, specifically certain 1-dimensional cellular automata, seemed to exhibit evolving complex behavior that could not be predicted in advance. The only way to find out future states of some of these automata appears to be to run them and find out.
Wolfram was so enthusiastic about his findings, he felt that he had discovered a “New Kind of Science” (published in 2002). In point of fact, there was a long history of research into cellular automata (including work by Stanislaw Ulam, John von Neumann, and John Horton Conway). In his 1969 paper “Calculating Space,” computer pioneer, Konrad Zuse inaugurated the field of digital physics when he speculated that reality itself might be a massive cellular automata computer and that the laws of physics might be modeled using cellular automata.
Wolfram had intuited that some elementary cellular automata might be “Turing Complete.” Turing-completeness is an implication of the Church-Turing Thesis and proves that if a system can duplicate the processes of a Turing Machine, then that system is computationally equivalent to the Turing Machine and hence theoretically capable of Universal Computation.
One of Wolfram’s graduate students, Matthew Cook proved that the cellular automata identified as Rule 110 (according to Wolfram’s CA numbering scheme) is Turing Complete.
Cellular automata are grids of automata that change state based on the states of their neighboring cells. This is only one type of automata. Any process (or machine) can be thought of as an automata, in having states that the machine (or process) progresses through based on inputs to the system.
Finite state automata or finite state machines (FSMs) are generalized mathematical models that can be used to model an automata and hence a process (aka an algorithm). Finite state machines can be described using a diagram in which nodes represent states and directed edges are associated with symbols that tell when the FSM is to transition to the connected node/state.
Another way to think about finite state machines is to look at the set of symbols that are accepted by the machine. This field of inquiry is known as Formal Language Theory which examines production rules or formal grammars that can be used to generate a particular language which may be accepted by an FSM.
Programming languages are a type of formal language. The process of writing a compiler or interpreter requires a detailed specification of the acceptable symbols (or tokens) along with the formal grammar of the language.
Noam Chomsky defined a set of categories of formal grammars that is known as the “Chomsky Hierarchy” in which categories are divided based upon the type of machines that accept the languages generated by a grammar. Chomsky has also written extensively on the uniqueness of human language generation and acquisition.
Other researchers whose work is important in considering the implications of computational processes are Norbert Weiner (Cybernetic Theory) and Claude Shannon (Information Theory). Both researchers examined abstract machines containing “feedback loops” used to exhibit self-regulating behavior in a system. These behaviors can appear “Life-like” in that cybernetic systems adjust their states (and hence their behavior) based on the inputs they receive.
Inventor and Futurist Ray Kurzweil believes that we will eventually infuse all matter with computational capabilities. If the process of Life is computable then is this the same as imbuing all matter with Life?
“As we gradually learn to harness the optimal computing capacity of matter, our intelligence will spread through the universe at (or exceeding) the speed of light, eventually leading to a sublime, universe wide awakening.” (Ray Kurzweil)
“The Singularity,” Kurzweil‘s mystical/scientific vision of a computationally infused apocalypse (which he discusses in his documentary “Transcendant Man”), resonates with an ancient idea within the ancient Hebrew mystical system known as Kabbalah. The Hebrew term “Tikkun ha-Olam” means “Restoration of the World,” and is concerned with bringing order back into the chaotic material world by “raising of the sparks” of the formerly shattered and disconnect reality that we inhabit.
What forms will computation take in the future when nanoscale engineering becomes commonplace? Will machines ever be able to think like we do? Many researchers have made the point that asking this question may be similar to asking if planes will ever fly like birds do.
With planes, we abstracted the process of flight and can now implement that process in a variety of material forms.
The enigma that we call “computation” touches on the mysteries of language, thought, humanity and ultimately of the process of Life itself. The only Life we can experience directly is our own. The only way we experience the lives of others is through shared symbolic interchanges the root of which we refer to (for lack of a better term) as “computation.”
What is a computation? The simple answer is: deriving a desired output from inputs by manipulating symbols according to processing rules. The deeper answer is perhaps…
Everything.
