What he was talking about is the infinite possibility of a finite symbol system, but that's all software. First you need a machine.
...sometime sooner or later...
The primitive physical components of any physical computer; the Memory and a Comparator. The physical functions of Memory is to load or store and for the Comparator it is to evaluate input and provide output. This computing model most closely resembles a string rewriting system such as a Markov algorithm or Lindenmayer system.
There is a direct relationship between these components and their purpose. The Comparator is the Algebra and the Memory is the Algorithm. The Algebra is where the input and output is evaluated and Algorithm has the state and program.
The program is compiled beforehand to create compound conjunctions of program, input, state, and output and provided a stream of symbols that are suited to a particular physical medium. It doesn't matter what you make your Memory from, or how you Compare it, if can make some memory or a some sort of interpreting comparator then, there you go! You've got an instant, add water computer. It might be easier than you think...
I promise an updated version of the Grey Goo Game soon. ...I have like time for games lately...
notes:
add mechanical symbol manipulation core diagram
drosophila melanogaster; fruit fly behavioural conditioning
I've got some laser guided fruit flies in store for you. ;-)
...sometime earlier...
I could tell you that it took years and years of research and development to create a theory of computation that could be implemented in wood, but alias it would be untrue. The idea was formed after only a few reductions and one night when I couldn't get to sleep. You see, computers are much simpler than our teachers might of taught us in school. You don't even need the Boolean logic primitives to create a computer. These so called primitives are merely symbolic.
The most primitive computer is comprised of only two parts and from these two parts we can create all others. Those two parts are memory and a comparator. Some may claim that any practical computer must also have input and output, but that just is memory, or registers, memory again, or an ALU, nope that's a comparator.
We can further delineate memory into two types, read-only and read-write. We need the read-write type of memory to store temporary values for comparison. For example, read-write memory could be a toggle or counter. Read-only memory is convenient for storing tables or a program, however these two examples are symbolic and not necessary for computation. An example of read-only memory is pegs in a disc, where the presents of a peg represents a symbol.
The true heart of a computer is the comparator. A comparator simply compares two values. One of those two values was read from memory previously and the other value is read at the current position in memory.
Now that we have our fundamental blocks we can start creating all the other complications that are common to modern computers. However, I'm out of time now so that will have to wait until later.
... some time later...
Now that we've taken efforts to separate a "computer" as in a computing device, from symbolic logic or software, we can launch into building a computer from whatever we can implement these two primitive components in. To introduce the idea I suggest we play a game.
Would you like to play a game?
Ooh! Let's play, Grey Goo!
It's a card game where the rules keep changing. The basic rule is draw one, play one, but watch out! The deck might be loaded.
I'll post a set of cards so that you can play along at home.
Update!!!
See the first edition of "Grey Goo" here!
Learn more about how it all works.
http://fractalclockwork.blogspot.com/2012/04/aryabhata-and-coordinate-rotational.html
http://fractalclockwork.blogspot.com/2012/04/bit-serial-computers.html
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