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Tue Sep 22 11:18:02 EDT 2009
The Computer Merit Badge: how I'd complete the requirements NOW;
part 2
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This installment is part 2 of my series, answering some of the
questions in the Boy Scout's Computer Merit Badge as I would
knowing what I know now.
Requirement 1: Give a short history of computers. Describe the
major parts of a computer system. Give four different uses of
computers.
A) Give a short history of computers (continued)
In part 1 of answering this question, I discussed the fact that a
computer device's power is tied directly to its ability to remem-
ber what it has seen before. There are 3 main possibility:
1) a device has no memory (finite automata)
2) a device has a single "stack" of memory, able to access what
is on the stack using only a series of 'push' and 'pop' opera-
tions
3) a device that has random access to some memory (Turing Ma-
chines)
So, let's look at the history of computing devices from the per-
spective of function (i.e., what the device does), rather than
the technologies used to put these devices together. This is not
an exact or complete chronology, but covers some major devices
seen over the years.
a) the Abacus - of course, how could I not start with this. It
was a board with pegs and beads that allowed humans to count.
Similar to any other counting device of the time, it had no real
memory. It was a glorified clicker. So under what class would it
fall? It can be modeled exactly as a finite automata - so it is
in class 1. The "state" of the device is defined by the posi-
tions of the beads. The positions of the beads contain all of the
information one needs to determine the current count. The "input"
consists of the reconfigurations required to increment the cur-
rent count by 1.
b) the Antikythera mechanism - this amazing device was found in
1901 at the bottom of the sea. It is an ancient Greek device es-
timated to be built around 150-100 BC. A lot more detail regard-
ing its precision and construction can be viewed on Wikipedia,
but it is sufficient to say that it is absolultely stunning that
something this well designed was done so that long ago. It is the
oldest analog "computer" known, and its sophistication clearly
indicates that it is not a "first generation" device created by
the Greeks. It alludes to some lost knowledge that we'll probably
never recover from ancient tomes. But I digress. So what does it
do? Well, after a lot of detailed investigation and painstaking
analysis, it was determined that it is used to calculate the po-
sitions of celestial objects, like the Sun and Moon. I will dis-
cuss, later, how Humans are really bad at discovering what un-
known "machines" actually do.
As complex and sophisticated as it is, I propose that it is still
no more powerful than a device than can be modeled by a finite
state automata. Why do I say this? Because the celestial patterns
are predictable, and were clearly known to the creator of the de-
vice. The input for the device is the turning of the knobs. The
state of the device consists of the positions of the gears and
other moving devices internally. From each state, the turning of
a knob provides the input needed to transistion to the next
state. Only the information encoded in the state itself is re-
quired to go to the next of many potential states, depending on
the input provided by the knobs. Also note, the Antikythera mech-
anism contains no MEMORY for the storing of temporary values. And
why would it? Its functionality did not require memory since the
relations among the bodies were known, and thus encoded into the
gears and their ratios (like a Swiss clock of the 18th Century!).
c) Automatons - these were devices, probably first created by the
people who created the Antikythera mechanism, that were designed
to resemble the actions performed by animate objects. They were
robots in the most basic sense, and were used by the ancients in
much the same way that Disney uses its animatronic characters at
its theme parks. The ancient Automatons were also of class 1
computing devices. They consisted of gears, levers, pullies, and
other simple mechanical devices - BUT NO MEMORY. Why did it have
no memory? They didn't need it in when "computing" their next mo-
tion or movement. The computation was built into the states im-
plicitly.
d) the Difference engine - according to Wikipedia, this device
is, "an automatic, mechanical calculator designed to tabulate
polynomial functions. Both logarithmic and trigonometric func-
tions can be approximated by polynomials, so a difference engine
can compute many useful sets of numbers." There's something very
special about this. These computations require MEMORY! So where
does this machine fit in terms of the classes we've discussed?
Well, the answer to this is a bit tricky, but here it goes. It
is more powerful that class #2 (push down automata), but is not a
general purpose and programmable machine like the Turing Machine
is meant to be. It does, however, represent a PROGRAM that can be
(when written in a context sensitive language), be recognized and
executed by a Turing Machine. The Difference engine therefore
represents a mechanical program, or in otherwords, a special pur-
pose (as opposed to general purpose) computer. The distinction is
subtle, but the key to understanding this is to realize that a
Turing Machine (general purpose) can be programmed to act as a
special purpose computing machine. This is what programs really
are - they are instructions needed by a general purpose to emu-
late the actions of a special purpose machine. In otherwords, a
general purpose machine could be programmed to act exactly (in
function) as the Difference engine, but the difference engine
(being a special purpose machine) is unable to be programmed to
emulate the action of any other valid machine.
It should be noted that, also according to Wikipedia, "an engi-
neer in the Hessian army conceived the idea in a book published
in 1786, but failed to find funding to progress this further."
e) the Analytical engine - although never completed by Charles
Babbage, this machine was intended to be a GENERAL PURPOSE ME-
CHANICAL DEVICE! In otherwords, if this device had been built, he
could have "programmed" to be functionally equivalent to his Dif-
ference engine. The ramifications of a working Analytical engine
would have been far reaching. In particular, it would have given
Humans computational powers not to be seen for over 100 years.
There are whole "alt history" book series premised on the success
of this machine called, "cyber punk" and "steam punk." The point
of the books is, what would have happened in the World and to Hu-
manity had we developed computational powers a century before?
It's an incredibly interesting thought experiment.
Conclusion:
It took 100 years after the failed completion of Babbage's Ana-
lytical engine before another device was created. Starting in
1941, not very long after Church and Turing formalized their the-
ories on computability, the Germans created a equivalently power-
ful machine called, the "Zuse Z3." Interestingly, modern comput-
ers did not follow on its design or methods for programming. It
was programmed using a language called, "Plankalkul." During the
remainder of the decade came other attempts, some not as computa-
tionally powerful as the Zuse Z3. Among them are the ones typi-
cally discussed when speaking of the history of computing de-
vices.
The deviced highlighed above were chose to make the point regard-
ing the development of computational power. It is not close to an
exhaustive or chronological list. For example, textile looms
were complex and sophisticated to be "programmed" as early as
1725. Still earlier, countless people and cultures were experi-
menting with various other machines such as calculators and
clocks.
History of Computing Hardware (Wikipedia)
History of Computing (Wikipedia)
Timeline of Computing (Wikipedia)
This concludes this section on history of computers, but I do
hope to write further on the history of computing devices with
respect to computational power. In closing, do not forget that
modern computers are not more powerful than computer designs from
a long time ago. As illustrated with the Antikythera mechanism,
there is no reason to believe that computing devices as powerful
as Babbage's Analytical engine (and therefore modern computers)
were not created by ancient people. There's a lot of "modern"
knowledge that we are fooled into thinking is ours alone, but
people thousands of years ago were just as smart as we were. And
remember, power is all about the memory - no matter how it is im-
plemented: gears, vacuum tubes, transistors, stacks, or not at
all.
Until the next installment, please stay tuned.
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