Paul, that is a very concise explanation. I would like to say thanks for posting
that. I've been considering the question of whether the clock is in fact a CPU
as well.
I am leaning towards accepting that it is a CPU because it if I accept the
explanation provided with the 9 line program, it does have registers, it has a
comparator and it can perform jumps and loops. I suppose what remains to be
seen is if it can be programmed to perform more than one algorithm using the
machine language provided and without modifying the machine.
Great topic by the way.
Cheers,
Andrew
--- In friendsofdigicomp@yahoogroups.com, "prp_teleport" <prp@...> wrote:
>
> Some more rigorous definitions than those you found on Wikipedia might help
understand whether the clock is a CPU:
>
> Computer - In modern usage, a stored program general purpose digital
electronic computer, defined not in terms of its construction but in terms of
its capability. In particular, a computer is a machine that would be equivalent
to a "Turing Machine" if it had infinite memory. (The "electronic" aspect is not
optional in proper usage, but we can discard it for this discussion.)
>
> CPU - Central Processing Unit. Tranditionally, the "control" part of the
computer, a computer consisting of control, memory and I/O. The CPU is the
defining part of a computer and it is the part that must pass the Turing Machine
equivalency test.
>
> Harvard Architecture - A computer where the instructions and data are in
separate memory units, and the memory containing the instructions is read-only.
>
> Turing Machine - A rigorous pure mathematical construct proposed by the famous
British mathemetician Alan Turing. There is an entire field of mathematics based
on it. A Turing Machine is a very simple 1-bit device with an infinite memory.
An important early result in the field is that you can construct
(mathematically) a computing device in many different ways, and if it has the
capabilities of a Turing Machine, then it can be proved that it has exactly the
same capability as a Turing Machine, no more and no less. (Execution time is not
modelled, so there is no notion of "faster" or "slower", only whether it is the
same or not.) So, for instance, if you can show that your construct is able to
emulate a Turing Machine, then you have proved that it is exactly the same as a
Turing Machine as far as what you could do with it.
>
>
> All computers, from the tiniest microcontrollers to the largest supercomputer,
pass the Turing Machine equivalency test. There is the special case of the
Harvard Architecture designs, typical for microcontrollers, where in addition to
assuming the memory is infinite you also have to assume that, for the purposes
of the test, the instruction and data memories are combined and uniformly
accessible for read and write.
>
> The Mechanical Clock is not able to emulate a Turing Machine even if its
registers were inifitely large, so its not a computer or a CPU in itself.
>
> You could argue that the Mechanical Clock is a Harvard Architecture machine,
where the instructions are encoded in the structure of the pathways for the
ball. But this structure is not similar enough to the data memory (the
registers) to convincingly argue that they could be unified for the purposes of
testing Turing Machine equivalency. So thats out.
>
> If it is possible to emulate a Turing Machine using the 6-instruction assembly
language given, then you could argue that the instruction set combined with the
laser cutter is a computer, and the clock is one possible program. However, I
don't think the instruction set is sufficient (even though its larger than some
minimal examples I've seen) because, among possibly other things, it lacks any
kind of indirect or computed addressing mechanism. In any case, a single program
is not a computer, so the Mechanical Clock is still not a CPU.
>
> The property of Turing Machine equivalence is an extremely important concept
in Computer Science, and in my opinion cannot be discarded lightly because its
so helpful in understanding how it is that computers can do what they do. So I'm
uncomfortable seeing you call the Mechanical Clock a CPU, and more uncomfortable
seeing it used to explain what a computer is. Its a fine way to show how logic
works, and then to note that a CPU is made out of logic.
>
> I like the way you've combined a logical description (the instructions) with
the visual and tactile implementation. You had a tutelage problem you wanted to
solve, and came up with a clever approach, but it slightly missed the mark you
were ultimately aiming for.
>
> Paul Pierce
>
Thanks for the great insight.
I would “agree” with the definition
that a CPU “must pass the Turing Machine equivalency test” for it
is to be considered a CPU. But this machine, does passes the Turing
Machine equivalence test (although it does not passes the “Turing
Test” since it can not talk back :)
However, I think you are on to
something, which has to do with Universal Turing Machines.
First whether this is a Turing machine:
I say yes, and here is the proof.
Once simple proof can be based on Church's Thesis which states that that
any algorithm can be represented as a Turing machine. And since I
have an algorithm for this clock, it is a Turing machine.
A more formal definition: A Turing
machine T has a set of 4-tuple (S,I,f,s0) (in its simplest form. I
know there are other definition, but they could all be boiled down to
this without a lose in generality). I got this from the book
“Discrete Mathematics and its applications” page 776
(http://www.amazon.com/Discrete-Mathematics-Applications-Kenneth-Rosen/dp/007289\
9050). Yes, you made me brush up my old CS book.
S is a fine set of states (in the
clock, Register A and the DTD_FLAG)
I is a finite set of alphabet (in the
clock 0 and 1)
f which is a partial function from SxI
to SxI x {R,L} (this is the program of the clock implemented by the
tracks and the flip-flops, I and L levers)
s0, which is the starting state (in our
case we can set register A and the DTD_FLAG to anything).
The “tape” is implemented by the
ball which reads register A and the DTD_FLAG and manipulates them
accordingly.
Note that I did not considered the
other registers, because they are tied together with the buss, so their state is
just the same. Also note that there is an optimization
when the INCREMENT instruction and is actually an INCREMENT and CHECK
together.
Paul Pierce wrote: “However, I don't
think the instruction set is sufficient “ (see more later)
Note that in the Turing machine
definition f can be any length (even 1) so you could have a 1
instruction Turing machine (see 1 bit Turing machines).
Therefore, this is a Turing machine.
Note that a Turing machine does not require for the tape to change!!!
However, I believe what you meant to
prove is that this is not a Universal Turing Machine (UTM), which is how we
should define a CPU (not just a Turing machine). A universal Turing
machine is one that reads the set of instructions f from the tape.
This will allow it to simulate an arbitrary Turing machine, and thus
solve an array of problems. This is why the Harvard Architecture is a
spatial case, since it has its program in a separate memory
structure. So I would argue that his clock has an Harvard
Architecture. Therefore, the only question remaining is whether this
clock reads the program from memory, and how is this memory
implemented.
I argue that the program memory is
implemented in the paths the ball takes, and is burned in using the
laser as well as the configurations of the flip-flops, so its similar
to burning the program on a ROM. (although I agree this is a far
fetch, but just for the sake of discussion). Therefore, I could
change the program of the clock by simply rotating on of the L levers
or changing the T flip-flops to an L. I could also, remake the tracks
of the C register, to check for a different number, or change the B
register to increment instead of reset (by changing the L to
flip-flops and reconfiguring the paths).
Therefore I conclude that this is a
Universal Turing machine, and thus a CPU.
Paul Pierce wrote: “However, I don't
think the instruction set is sufficient “
However,
this is not a complete proof (even if we buy the argument that the
laser cutter can cut the paths). The reason is that a universal
machine need be be able to calculate all possible functions which can
be calculated. Therefore, we need to find if this clock can do that
(even if we can reprogrammed it, by only using the instructions I
have given), which I am not able to do at this point. However, See
Wolfram's 2-state 3-symbol Turing machine
(http://en.wikipedia.org/wiki/Wolfram%27s_2-state_3-symbol_Turing_machine)
for what might be the smallest universal Turing machine, but the
proof is difficult.
Based on that, the I don't believe the DigiComp Ior II is not is a UTM, and
threfore should not be called a computer either!
However, even if you don't buy the
argument that the program is read from memory (and I agree this is
hard to swallow, even for me) or that is can not emulate a Universal Turing
machine. I still stand by the fact that this is still useful in
describing a CPU since it has all the major components of a CPU. just like the
DigiComp.
Therefore, it can help people understand what is inside a CPU and how
a CPU works in a very broad way. Remember, this is for non
computer-science people, and not for hardware designers trying to
implement a useful CPU.
________________________________
From: prp_teleport <prp@...>
To: friendsofdigicomp@yahoogroups.com
Sent: Thursday, April 19, 2012 2:50 PM
Subject: Re: [Friends of DigiComp] Mechanical CPU Clock
Some more rigorous definitions than those you found on Wikipedia might help
understand whether the clock is a CPU:
Computer - In modern usage, a stored program general purpose digital electronic
computer, defined not in terms of its construction but in terms of its
capability. In particular, a computer is a machine that would be equivalent to a
"Turing Machine" if it had infinite memory. (The "electronic" aspect is not
optional in proper usage, but we can discard it for this discussion.)
CPU - Central Processing Unit. Tranditionally, the "control" part of the
computer, a computer consisting of control, memory and I/O. The CPU is the
defining part of a computer and it is the part that must pass the Turing Machine
equivalency test.
Harvard Architecture - A computer where the instructions and data are in
separate memory units, and the memory containing the instructions is read-only.
Turing Machine - A rigorous pure mathematical construct proposed by the famous
British mathemetician Alan Turing. There is an entire field of mathematics based
on it. A Turing Machine is a very simple 1-bit device with an infinite memory.
An important early result in the field is that you can construct
(mathematically) a computing device in many different ways, and if it has the
capabilities of a Turing Machine, then it can be proved that it has exactly the
same capability as a Turing Machine, no more and no less. (Execution time is not
modelled, so there is no notion of "faster" or "slower", only whether it is the
same or not.) So, for instance, if you can show that your construct is able to
emulate a Turing Machine, then you have proved that it is exactly the same as a
Turing Machine as far as what you could do with it.
All computers, from the tiniest microcontrollers to the largest supercomputer,
pass the Turing Machine equivalency test. There is the special case of the
Harvard Architecture designs, typical for microcontrollers, where in addition to
assuming the memory is infinite you also have to assume that, for the purposes
of the test, the instruction and data memories are combined and uniformly
accessible for read and write.
The Mechanical Clock is not able to emulate a Turing Machine even if its
registers were inifitely large, so its not a computer or a CPU in itself.
You could argue that the Mechanical Clock is a Harvard Architecture machine,
where the instructions are encoded in the structure of the pathways for the
ball. But this structure is not similar enough to the data memory (the
registers) to convincingly argue that they could be unified for the purposes of
testing Turing Machine equivalency. So thats out.
If it is possible to emulate a Turing Machine using the 6-instruction assembly
language given, then you could argue that the instruction set combined with the
laser cutter is a computer, and the clock is one possible program. However, I
don't think the instruction set is sufficient (even though its larger than some
minimal examples I've seen) because, among possibly other things, it lacks any
kind of indirect or computed addressing mechanism. In any case, a single program
is not a computer, so the Mechanical Clock is still not a CPU.
The property of Turing Machine equivalence is an extremely important concept in
Computer Science, and in my opinion cannot be discarded lightly because its so
helpful in understanding how it is that computers can do what they do. So I'm
uncomfortable seeing you call the Mechanical Clock a CPU, and more uncomfortable
seeing it used to explain what a computer is. Its a fine way to show how logic
works, and then to note that a CPU is made out of logic.
I like the way you've combined a logical description (the instructions) with the
visual and tactile implementation. You had a tutelage problem you wanted to
solve, and came up with a clever approach, but it slightly missed the mark you
were ultimately aiming for.
Paul Pierce
[Non-text portions of this message have been removed]
It's definitely a convoluted question of whether it is a CPU or not based on
Turing and/or modern definition.
I've been writing software for decades and built 8-bit computers with Hex
Keypads back in the late 70's but I've only been really interested in CPU design
for about the last 5 - 6 years. As a result I may have a liberal idea of what
constitutes a true CPU.
My interpretation of Turing and the definition of a CPU dictates that it must
have:
1) an instruction set
2) control
3) program memory
4) accumulator
5) conditional jump
6) the ability to loop
7) the ability to be programmed
I think this unit has the first 6 but I'm not sure that the program can be
modified enough to believe that it can be programmed to do anything but be some
sort of clock.
It's not to say that it won't ever be a CPU but at the moment it is hard for me
to definitively state that it is a CPU.
That said, it's really impressive.
Cheers,
Andrew
--- In friendsofdigicomp@yahoogroups.com, Lior Elazary <lelazary@...> wrote:
>
>
> Thanks for the great insight.
>
> I would “agree” with the definition
> that a CPU “must pass the Turing Machine equivalency test” for it
> is to be considered a CPU. But this machine, does passes the Turing
> Machine equivalence test (although it does not passes the “Turing
> Test” since it can not talk back :)
> However, I think you are on to
> something, which has to do with Universal Turing Machines.
>
> First whether this is a Turing machine:
> I say yes, and here is the proof.
>
> Once simple proof can be based on Church's Thesis which states that that
> any algorithm can be represented as a Turing machine. And since I
> have an algorithm for this clock, it is a Turing machine.
>
> A more formal definition: A Turing
> machine T has a set of 4-tuple (S,I,f,s0) (in its simplest form. I
> know there are other definition, but they could all be boiled down to
> this without a lose in generality). I got this from the book
> “Discrete Mathematics and its applications” page 776
>
(http://www.amazon.com/Discrete-Mathematics-Applications-Kenneth-Rosen/dp/007289\
9050). Yes, you made me brush up my old CS book.
>
>
> S is a fine set of states (in the
> clock, Register A and the DTD_FLAG)
> I is a finite set of alphabet (in the
> clock 0 and 1)
> f which is a partial function from SxI
> to SxI x {R,L} (this is the program of the clock implemented by the
> tracks and the flip-flops, I and L levers)
> s0, which is the starting state (in our
> case we can set register A and the DTD_FLAG to anything).
>
> The “tape” is implemented by the
> ball which reads register A and the DTD_FLAG and manipulates them
> accordingly.
>
> Note that I did not considered the
> other registers, because they are tied together with the buss, so their state
is just the same. Also note that there is an optimization
> when the INCREMENT instruction and is actually an INCREMENT and CHECK
> together.
> Paul Pierce wrote: “However, I don't
> think the instruction set is sufficient “ (see more later)
>
> Note that in the Turing machine
> definition f can be any length (even 1) so you could have a 1
> instruction Turing machine (see 1 bit Turing machines).
>
> Therefore, this is a Turing machine.
> Note that a Turing machine does not require for the tape to change!!!
>
> However, I believe what you meant to
> prove is that this is not a Universal Turing Machine (UTM), which is how we
> should define a CPU (not just a Turing machine). A universal Turing
> machine is one that reads the set of instructions f from the tape.
> This will allow it to simulate an arbitrary Turing machine, and thus
> solve an array of problems. This is why the Harvard Architecture is a
> spatial case, since it has its program in a separate memory
> structure. So I would argue that his clock has an Harvard
> Architecture. Therefore, the only question remaining is whether this
> clock reads the program from memory, and how is this memory
> implemented.
>
> I argue that the program memory is
> implemented in the paths the ball takes, and is burned in using the
> laser as well as the configurations of the flip-flops, so its similar
> to burning the program on a ROM. (although I agree this is a far
> fetch, but just for the sake of discussion). Therefore, I could
> change the program of the clock by simply rotating on of the L levers
> or changing the T flip-flops to an L. I could also, remake the tracks
> of the C register, to check for a different number, or change the B
> register to increment instead of reset (by changing the L to
> flip-flops and reconfiguring the paths).
> Therefore I conclude that this is a
> Universal Turing machine, and thus a CPU.
>
> Paul Pierce wrote: “However, I don't
> think the instruction set is sufficient “
> However,
> this is not a complete proof (even if we buy the argument that the
> laser cutter can cut the paths). The reason is that a universal
> machine need be be able to calculate all possible functions which can
> be calculated. Therefore, we need to find if this clock can do that
> (even if we can reprogrammed it, by only using the instructions I
> have given), which I am not able to do at this point. However, See
> Wolfram's 2-state 3-symbol Turing machine
> (http://en.wikipedia.org/wiki/Wolfram%27s_2-state_3-symbol_Turing_machine)
> for what might be the smallest universal Turing machine, but the
> proof is difficult.
>
> Based on that, the I don't believe the DigiComp Ior II is not is a UTM, and
threfore should not be called a computer either!
>
>
> However, even if you don't buy the
> argument that the program is read from memory (and I agree this is
> hard to swallow, even for me) or that is can not emulate a Universal Turing
> machine. I still stand by the fact that this is still useful in
> describing a CPU since it has all the major components of a CPU. just like the
DigiComp.
> Therefore, it can help people understand what is inside a CPU and how
> a CPU works in a very broad way. Remember, this is for non
> computer-science people, and not for hardware designers trying to
> implement a useful CPU.
>
>
>
> ________________________________
> From: prp_teleport <prp@...>
> To: friendsofdigicomp@yahoogroups.com
> Sent: Thursday, April 19, 2012 2:50 PM
> Subject: Re: [Friends of DigiComp] Mechanical CPU Clock
>
>
>
> Some more rigorous definitions than those you found on Wikipedia might help
understand whether the clock is a CPU:
>
> Computer - In modern usage, a stored program general purpose digital
electronic computer, defined not in terms of its construction but in terms of
its capability. In particular, a computer is a machine that would be equivalent
to a "Turing Machine" if it had infinite memory. (The "electronic" aspect is not
optional in proper usage, but we can discard it for this discussion.)
>
> CPU - Central Processing Unit. Tranditionally, the "control" part of the
computer, a computer consisting of control, memory and I/O. The CPU is the
defining part of a computer and it is the part that must pass the Turing Machine
equivalency test.
>
> Harvard Architecture - A computer where the instructions and data are in
separate memory units, and the memory containing the instructions is read-only.
>
> Turing Machine - A rigorous pure mathematical construct proposed by the famous
British mathemetician Alan Turing. There is an entire field of mathematics based
on it. A Turing Machine is a very simple 1-bit device with an infinite memory.
An important early result in the field is that you can construct
(mathematically) a computing device in many different ways, and if it has the
capabilities of a Turing Machine, then it can be proved that it has exactly the
same capability as a Turing Machine, no more and no less. (Execution time is not
modelled, so there is no notion of "faster" or "slower", only whether it is the
same or not.) So, for instance, if you can show that your construct is able to
emulate a Turing Machine, then you have proved that it is exactly the same as a
Turing Machine as far as what you could do with it.
>
> All computers, from the tiniest microcontrollers to the largest supercomputer,
pass the Turing Machine equivalency test. There is the special case of the
Harvard Architecture designs, typical for microcontrollers, where in addition to
assuming the memory is infinite you also have to assume that, for the purposes
of the test, the instruction and data memories are combined and uniformly
accessible for read and write.
>
> The Mechanical Clock is not able to emulate a Turing Machine even if its
registers were inifitely large, so its not a computer or a CPU in itself.
>
> You could argue that the Mechanical Clock is a Harvard Architecture machine,
where the instructions are encoded in the structure of the pathways for the
ball. But this structure is not similar enough to the data memory (the
registers) to convincingly argue that they could be unified for the purposes of
testing Turing Machine equivalency. So thats out.
>
> If it is possible to emulate a Turing Machine using the 6-instruction assembly
language given, then you could argue that the instruction set combined with the
laser cutter is a computer, and the clock is one possible program. However, I
don't think the instruction set is sufficient (even though its larger than some
minimal examples I've seen) because, among possibly other things, it lacks any
kind of indirect or computed addressing mechanism. In any case, a single program
is not a computer, so the Mechanical Clock is still not a CPU.
>
> The property of Turing Machine equivalence is an extremely important concept
in Computer Science, and in my opinion cannot be discarded lightly because its
so helpful in understanding how it is that computers can do what they do. So I'm
uncomfortable seeing you call the Mechanical Clock a CPU, and more uncomfortable
seeing it used to explain what a computer is. Its a fine way to show how logic
works, and then to note that a CPU is made out of logic.
>
> I like the way you've combined a logical description (the instructions) with
the visual and tactile implementation. You had a tutelage problem you wanted to
solve, and came up with a clever approach, but it slightly missed the mark you
were ultimately aiming for.
>
> Paul Pierce
>
>
>
>
> [Non-text portions of this message have been removed]
>
I think number 7 needs to be defined more. So we will need a definition of what
does reprogramming means. For example, I believe that the clock can be
reprogrammed (even without re-burning the tracks).
For example, we can make it add two numbers (only up 4 bits) by doing the
following.
* Reprogram the clock by disconnecting the 3 buss wires from register C to
register A (register C is the check).
* Place the first number in register A
* Run the clock for the second number of times
* The result will be in register A
Similarly, subtraction can be made by taking the compliment of the number.
We can also produce other programs by replacing the T flip-flops with L or I.
So this clock can be reprogram. However, this does not mean that it can simulate
any program (or any Turing machine).
So I think it is not a Universal Turing Machine (although it will need to be
proven) and thus not a True CPU.
Non the less, its still useful in explaining CPU concepts.
Lior.
________________________________
From: awasson2001 <no_reply@yahoogroups.com>
To: friendsofdigicomp@yahoogroups.com
Sent: Thursday, April 19, 2012 10:22 PM
Subject: [Friends of DigiComp] Re: Mechanical CPU Clock
It's definitely a convoluted question of whether it is a CPU or not based on
Turing and/or modern definition.
I've been writing software for decades and built 8-bit computers with Hex
Keypads back in the late 70's but I've only been really interested in CPU design
for about the last 5 - 6 years. As a result I may have a liberal idea of what
constitutes a true CPU.
My interpretation of Turing and the definition of a CPU dictates that it must
have:
1) an instruction set
2) control
3) program memory
4) accumulator
5) conditional jump
6) the ability to loop
7) the ability to be programmed
I think this unit has the first 6 but I'm not sure that the program can be
modified enough to believe that it can be programmed to do anything but be some
sort of clock.
It's not to say that it won't ever be a CPU but at the moment it is hard for me
to definitively state that it is a CPU.
That said, it's really impressive.
Cheers,
Andrew
--- In friendsofdigicomp@yahoogroups.com, Lior Elazary <lelazary@...> wrote:
>
>
> Thanks for the great insight.
>
> I would “agree” with the definition
> that a CPU “must pass the Turing Machine equivalency test” for it
> is to be considered a CPU. But this machine, does passes the Turing
> Machine equivalence test (although it does not passes the “Turing
> Test” since it can not talk back :)
> However, I think you are on to
> something, which has to do with Universal Turing Machines.
>
> First whether this is a Turing machine:
> I say yes, and here is the proof.
>
> Once simple proof can be based on Church's Thesis which states that that
> any algorithm can be represented as a Turing machine. And since I
> have an algorithm for this clock, it is a Turing machine.
>
> A more formal definition: A Turing
> machine T has a set of 4-tuple (S,I,f,s0) (in its simplest form. I
> know there are other definition, but they could all be boiled down to
> this without a lose in generality). I got this from the book
> “Discrete Mathematics and its applications” page 776
>
(http://www.amazon.com/Discrete-Mathematics-Applications-Kenneth-Rosen/dp/007289\
9050). Yes, you made me brush up my old CS book.
>
>
> S is a fine set of states (in the
> clock, Register A and the DTD_FLAG)
> I is a finite set of alphabet (in the
> clock 0 and 1)
> f which is a partial function from SxI
> to SxI x {R,L} (this is the program of the clock implemented by the
> tracks and the flip-flops, I and L levers)
> s0, which is the starting state (in our
> case we can set register A and the DTD_FLAG to anything).
>
> The “tape” is implemented by the
> ball which reads register A and the DTD_FLAG and manipulates them
> accordingly.
>
> Note that I did not considered the
> other registers, because they are tied together with the buss, so their state
is just the same. Also note that there is an optimization
> when the INCREMENT instruction and is actually an INCREMENT and CHECK
> together.
> Paul Pierce wrote: “However, I don't
> think the instruction set is sufficient “ (see more later)
>
> Note that in the Turing machine
> definition f can be any length (even 1) so you could have a 1
> instruction Turing machine (see 1 bit Turing machines).
>
> Therefore, this is a Turing machine.
> Note that a Turing machine does not require for the tape to change!!!
>
> However, I believe what you meant to
> prove is that this is not a Universal Turing Machine (UTM), which is how we
> should define a CPU (not just a Turing machine). A universal Turing
> machine is one that reads the set of instructions f from the tape.
> This will allow it to simulate an arbitrary Turing machine, and thus
> solve an array of problems. This is why the Harvard Architecture is a
> spatial case, since it has its program in a separate memory
> structure. So I would argue that his clock has an Harvard
> Architecture. Therefore, the only question remaining is whether this
> clock reads the program from memory, and how is this memory
> implemented.
>
> I argue that the program memory is
> implemented in the paths the ball takes, and is burned in using the
> laser as well as the configurations of the flip-flops, so its similar
> to burning the program on a ROM. (although I agree this is a far
> fetch, but just for the sake of discussion). Therefore, I could
> change the program of the clock by simply rotating on of the L levers
> or changing the T flip-flops to an L. I could also, remake the tracks
> of the C register, to check for a different number, or change the B
> register to increment instead of reset (by changing the L to
> flip-flops and reconfiguring the paths).
> Therefore I conclude that this is a
> Universal Turing machine, and thus a CPU.
>
> Paul Pierce wrote: “However, I don't
> think the instruction set is sufficient “
> However,
> this is not a complete proof (even if we buy the argument that the
> laser cutter can cut the paths). The reason is that a universal
> machine need be be able to calculate all possible functions which can
> be calculated. Therefore, we need to find if this clock can do that
> (even if we can reprogrammed it, by only using the instructions I
> have given), which I am not able to do at this point. However, See
> Wolfram's 2-state 3-symbol Turing machine
> (http://en.wikipedia.org/wiki/Wolfram%27s_2-state_3-symbol_Turing_machine)
> for what might be the smallest universal Turing machine, but the
> proof is difficult.
>
> Based on that, the I don't believe the DigiComp Ior II is not is a UTM, and
threfore should not be called a computer either!
>
>
> However, even if you don't buy the
> argument that the program is read from memory (and I agree this is
> hard to swallow, even for me) or that is can not emulate a Universal Turing
> machine. I still stand by the fact that this is still useful in
> describing a CPU since it has all the major components of a CPU. just like the
DigiComp.
> Therefore, it can help people understand what is inside a CPU and how
> a CPU works in a very broad way. Remember, this is for non
> computer-science people, and not for hardware designers trying to
> implement a useful CPU.
>
>
>
> ________________________________
> From: prp_teleport <prp@...>
> To: friendsofdigicomp@yahoogroups.com
> Sent: Thursday, April 19, 2012 2:50 PM
> Subject: Re: [Friends of DigiComp] Mechanical CPU Clock
>
>
>
> Some more rigorous definitions than those you found on Wikipedia might help
understand whether the clock is a CPU:
>
> Computer - In modern usage, a stored program general purpose digital
electronic computer, defined not in terms of its construction but in terms of
its capability. In particular, a computer is a machine that would be equivalent
to a "Turing Machine" if it had infinite memory. (The "electronic" aspect is not
optional in proper usage, but we can discard it for this discussion.)
>
> CPU - Central Processing Unit. Tranditionally, the "control" part of the
computer, a computer consisting of control, memory and I/O. The CPU is the
defining part of a computer and it is the part that must pass the Turing Machine
equivalency test.
>
> Harvard Architecture - A computer where the instructions and data are in
separate memory units, and the memory containing the instructions is read-only.
>
> Turing Machine - A rigorous pure mathematical construct proposed by the famous
British mathemetician Alan Turing. There is an entire field of mathematics based
on it. A Turing Machine is a very simple 1-bit device with an infinite memory.
An important early result in the field is that you can construct
(mathematically) a computing device in many different ways, and if it has the
capabilities of a Turing Machine, then it can be proved that it has exactly the
same capability as a Turing Machine, no more and no less. (Execution time is not
modelled, so there is no notion of "faster" or "slower", only whether it is the
same or not.) So, for instance, if you can show that your construct is able to
emulate a Turing Machine, then you have proved that it is exactly the same as a
Turing Machine as far as what you could do with it.
>
> All computers, from the tiniest microcontrollers to the largest supercomputer,
pass the Turing Machine equivalency test. There is the special case of the
Harvard Architecture designs, typical for microcontrollers, where in addition to
assuming the memory is infinite you also have to assume that, for the purposes
of the test, the instruction and data memories are combined and uniformly
accessible for read and write.
>
> The Mechanical Clock is not able to emulate a Turing Machine even if its
registers were inifitely large, so its not a computer or a CPU in itself.
>
> You could argue that the Mechanical Clock is a Harvard Architecture machine,
where the instructions are encoded in the structure of the pathways for the
ball. But this structure is not similar enough to the data memory (the
registers) to convincingly argue that they could be unified for the purposes of
testing Turing Machine equivalency. So thats out.
>
> If it is possible to emulate a Turing Machine using the 6-instruction assembly
language given, then you could argue that the instruction set combined with the
laser cutter is a computer, and the clock is one possible program. However, I
don't think the instruction set is sufficient (even though its larger than some
minimal examples I've seen) because, among possibly other things, it lacks any
kind of indirect or computed addressing mechanism. In any case, a single program
is not a computer, so the Mechanical Clock is still not a CPU.
>
> The property of Turing Machine equivalence is an extremely important concept
in Computer Science, and in my opinion cannot be discarded lightly because its
so helpful in understanding how it is that computers can do what they do. So I'm
uncomfortable seeing you call the Mechanical Clock a CPU, and more uncomfortable
seeing it used to explain what a computer is. Its a fine way to show how logic
works, and then to note that a CPU is made out of logic.
>
> I like the way you've combined a logical description (the instructions) with
the visual and tactile implementation. You had a tutelage problem you wanted to
solve, and came up with a clever approach, but it slightly missed the mark you
were ultimately aiming for.
>
> Paul Pierce
>
>
>
>
> [Non-text portions of this message have been removed]
>
[Non-text portions of this message have been removed]
Hello Folks,
(Slightly off topic, but related): "Norelco Electronic Educational Kit EE20"
Yes, I still have my Digicomp I received as a gift when I was a kid. The box
still has one of those postal stamps dated 1966.
But we are cleaning out the garage. I knew I had this electronics kit, but
haven't opened it in decades. It appears to be complete, only 1 missing part
that I can tell. It has the breadboard, wiring diagrams, the instruction book.
I put a couple of pictures here:
http://groups.yahoo.com/group/friendsofdigicomp/photos/album/2101722262/pic/list
You can build a 3 transistor radio, automatic night light, a light meter, a
Morse code trainer, electronic organ, and whoo-hoo!
Couldn't find much on the web, just:
http://ee.old.no/20/http://ee.old.no/library/
Anyway, I thought some people here in the Digicomp group might be interested to
see this.
Roland
They're still around. Radio Shack has them, also there's Snap Kits.
Neil
From: rmelzer
But we are cleaning out the garage. I knew I had this electronics kit, but
haven't opened it in decades.
[Non-text portions of this message have been removed]
Mine was a Raytheon Lectron Series Two kit. Each component was mounted inside a
1-inch square block with magnetic sides. Each block was capped with a component
symbol marking.
To build a project, all you had to do was match the printed symbols on the
blocks with the schematic, and slap the magnetic blocks together. No
breadboarding, clips, springs, or wires needed.
Sadly, I had to cannibalize the parts in a deperate attempt to finish a college
project. I still have the instruction manual, which is now nestled next to my
DigiComp I manual.
CMcF
--- In friendsofdigicomp@yahoogroups.com, "rmelzer" <rmelzer@...> wrote:
>
> Hello Folks,
>
> (Slightly off topic, but related): "Norelco Electronic Educational Kit EE20"
>
> Yes, I still have my Digicomp I received as a gift when I was a kid. The box
still has one of those postal stamps dated 1966.
>
> But we are cleaning out the garage. I knew I had this electronics kit, but
haven't opened it in decades. It appears to be complete, only 1 missing part
that I can tell. It has the breadboard, wiring diagrams, the instruction book.
>
> I put a couple of pictures here:
>
http://groups.yahoo.com/group/friendsofdigicomp/photos/album/2101722262/pic/list
>
> You can build a 3 transistor radio, automatic night light, a light meter, a
Morse code trainer, electronic organ, and whoo-hoo!
>
> Couldn't find much on the web, just:
> http://ee.old.no/20/
> http://ee.old.no/library/
>
> Anyway, I thought some people here in the Digicomp group might be interested
to see this.
>
> Roland
>
I had the Radio Shack version which was awesome but a buddy of mine had that
Raytheon kit which I thought was top notch. I really liked the block idea. I
haven't seen one of those since then and that was the mid-seventies.
Andrew
--- In friendsofdigicomp@yahoogroups.com, "Courtney" <abcmcfarren@...> wrote:
>
> Mine was a Raytheon Lectron Series Two kit. Each component was mounted inside
a 1-inch square block with magnetic sides. Each block was capped with a
component symbol marking.
>
> To build a project, all you had to do was match the printed symbols on the
blocks with the schematic, and slap the magnetic blocks together. No
breadboarding, clips, springs, or wires needed.
>
> Sadly, I had to cannibalize the parts in a deperate attempt to finish a
college project. I still have the instruction manual, which is now nestled next
to my DigiComp I manual.
>
> CMcF
>
> --- In friendsofdigicomp@yahoogroups.com, "rmelzer" <rmelzer@> wrote:
> >
> > Hello Folks,
> >
> > (Slightly off topic, but related): "Norelco Electronic Educational Kit EE20"
> >
> > Yes, I still have my Digicomp I received as a gift when I was a kid. The
box still has one of those postal stamps dated 1966.
> >
> > But we are cleaning out the garage. I knew I had this electronics kit, but
haven't opened it in decades. It appears to be complete, only 1 missing part
that I can tell. It has the breadboard, wiring diagrams, the instruction book.
> >
> > I put a couple of pictures here:
> >
http://groups.yahoo.com/group/friendsofdigicomp/photos/album/2101722262/pic/list
> >
> > You can build a 3 transistor radio, automatic night light, a light meter, a
Morse code trainer, electronic organ, and whoo-hoo!
> >
> > Couldn't find much on the web, just:
> > http://ee.old.no/20/
> > http://ee.old.no/library/
> >
> > Anyway, I thought some people here in the Digicomp group might be interested
to see this.
> >
> > Roland
> >
>
The Raytheon kit was great. In less than one minute, I could build 3-transistor
AM radio that could pick up 3 or 4 stations. Mind you, this was back in the late
1960's, when AM was popular music while FM hosted "elevator" music.
I would credit my Raytheon Lectron Kit, DigiComp I, and Kohner Easy Adder as the
sparks that influence my future decision to become an Engineering Technician, a
job I loved for 30 years.
cmcf
--- In friendsofdigicomp@yahoogroups.com, awasson2001 <no_reply@...> wrote:
>
> I had the Radio Shack version which was awesome but a buddy of mine had that
Raytheon kit which I thought was top notch. I really liked the block idea. I
haven't seen one of those since then and that was the mid-seventies.
>
> Andrew
>
> --- In friendsofdigicomp@yahoogroups.com, "Courtney" <abcmcfarren@> wrote:
> >
> > Mine was a Raytheon Lectron Series Two kit. Each component was mounted
inside a 1-inch square block with magnetic sides. Each block was capped with a
component symbol marking.
> >
> > To build a project, all you had to do was match the printed symbols on the
blocks with the schematic, and slap the magnetic blocks together. No
breadboarding, clips, springs, or wires needed.
> >
> > Sadly, I had to cannibalize the parts in a deperate attempt to finish a
college project. I still have the instruction manual, which is now nestled next
to my DigiComp I manual.
> >
> > CMcF
> >
> > --- In friendsofdigicomp@yahoogroups.com, "rmelzer" <rmelzer@> wrote:
> > >
> > > Hello Folks,
> > >
> > > (Slightly off topic, but related): "Norelco Electronic Educational Kit
EE20"
> > >
> > > Yes, I still have my Digicomp I received as a gift when I was a kid. The
box still has one of those postal stamps dated 1966.
> > >
> > > But we are cleaning out the garage. I knew I had this electronics kit,
but haven't opened it in decades. It appears to be complete, only 1 missing
part that I can tell. It has the breadboard, wiring diagrams, the instruction
book.
> > >
> > > I put a couple of pictures here:
> > >
http://groups.yahoo.com/group/friendsofdigicomp/photos/album/2101722262/pic/list
> > >
> > > You can build a 3 transistor radio, automatic night light, a light meter,
a Morse code trainer, electronic organ, and whoo-hoo!
> > >
> > > Couldn't find much on the web, just:
> > > http://ee.old.no/20/
> > > http://ee.old.no/library/
> > >
> > > Anyway, I thought some people here in the Digicomp group might be
interested to see this.
> > >
> > > Roland
> > >
> >
>
Oops! I have forgoten to include my coveted Parker Brothers Soma Cube to the
list, a big influence in the logic and (later) algorithm departments.
cmcf
--- In friendsofdigicomp@yahoogroups.com, "Courtney" <abcmcfarren@...> wrote:
>
> The Raytheon kit was great. In less than one minute, I could build
3-transistor AM radio that could pick up 3 or 4 stations. Mind you, this was
back in the late 1960's, when AM was popular music while FM hosted "elevator"
music.
>
> I would credit my Raytheon Lectron Kit, DigiComp I, and Kohner Easy Adder as
the sparks that influence my future decision to become an Engineering
Technician, a job I loved for 30 years.
>
> cmcf
>
Anyone heard of this? A kit customer from France emailed me saying, "When I was
a kid I was just totally amazed by this device. I took a long time to understand
how it was working. Furthermore, the documentation was not very friendly for
kids." A search or two reveals it was apparently developed by Bull General
Electric, sold in France by Jouets Rationnels -- no doubt where the "JR" came
from. The box front states it won the "Oscar D'Or du Jouet Français" (in
effect, "French Toy of the Year") award in 1970. Very few of these around, it
seems.
Here are some links:
- http://www.jnorman.com/cgi-bin/hss/39352? [History of Science.com bookshop,
lists one for $750]
- http://phijvmi.chez.com/data/machines/jr01/jr01.htm [useful info page, in
French (Google Translate does a good job)]
- http://dhenin2.free.fr/Algo/Principes_JR01.pdf - [A lengthy treatise on
mathematical logic and its implementation on the JR01. The original kit had two
booklets, and this appears to be one of them. Again, all in French. No doubt
this is the documentation "not very friendly for kids"... but hey, for us
grownup types...]
- Also, an entry on the Worthpoint site notes a 2009 eBay (US) auction for what
appears to be an equivalent item attributed to Honeywell: "Jr. 01 Computer Kit,
made by Electronic Data Controls Corp. in 1972, developed in conjunction with
the Honeywell-Bull Company"
Tim
Minds-On Toys
No, but Radio Shack made a similar machine (I have one). ISTM it's a series of
switches and lights that does simple logic.
http://www.ebay.com/itm/251045325149
Neil
From: Knurly
Anyone heard of this? A kit customer from France emailed me saying, "When I was
a kid I was just totally amazed by this device. I took a long time to understand
how it was working. Furthermore, the documentation was not very friendly for
kids." A search or two reveals it was apparently developed by Bull General
Electric, sold in France by Jouets Rationnels -- no doubt where the "JR" came
from. The box front states it won the "Oscar D'Or du Jouet Français" (in
effect, "French Toy of the Year") award in 1970. Very few of these around, it
seems.
[Non-text portions of this message have been removed]
I've got one!
It's in my storage unit; I'll have to dig it up and take a look at it again -
probably setting next to the Computer Basketball game and the Hasbro Thinkatron
("The Machine that thinks like a Man")
How many other early computer-like semi-educational toys were out there?
certainly there were games, and there were some other items like the "Cardiac."
Would the geniac count, or was that too serious?
--Larry Groebe
I had another similar type sold by Radio Shack in Canada called the Logix Cosmos
SF-5000 (still have it).
http://www.computerhistory.org/collections/accession/102621921
Andrew
--- In friendsofdigicomp@yahoogroups.com, beyondparsley <no_reply@...> wrote:
>
>
> I've got one!
>
> It's in my storage unit; I'll have to dig it up and take a look at it again -
probably setting next to the Computer Basketball game and the Hasbro Thinkatron
("The Machine that thinks like a Man")
>
> How many other early computer-like semi-educational toys were out there?
certainly there were games, and there were some other items like the "Cardiac."
>
> Would the geniac count, or was that too serious?
>
> --Larry Groebe
>
Hi everybody;
This is my first post in the group. I recently became a member, with hopes of
having my own homemade DC1.
Does anybody have a pdf version of the original DC1 Instructions Manual? I am
trying to read the jpg version in "Files" but it is a little difficult for me.
Thanks to all and excuse my bad English,
GCR.
I have done a new scan with better scanner than I had in 2003 and saved as pdf
of the DC 1 instruction manual and posted to files in the group. I optimized
file in Acrobat Pro to get small enough to put all in one file (<5meg)
Dwight Watt, EdD,MCSE,A+,CCP,COI,MCT
http://www.dwightwatt.com
View my Microsoft Certifications
https://www.mcpvirtualbusinesscard.com/VBCServer/dwightwatt/profile
________________________________
From: gc_rios <no_reply@yahoogroups.com>
To: friendsofdigicomp@yahoogroups.com
Sent: Mon, April 30, 2012 3:02:09 PM
Subject: [Friends of DigiComp] DC1 Instructions Manual
Hi everybody;
This is my first post in the group. I recently became a member, with hopes of
having my own homemade DC1.
Does anybody have a pdf version of the original DC1 Instructions Manual? I am
trying to read the jpg version in "Files" but it is a little difficult for me.
Thanks to all and excuse my bad English,
GCR.
[Non-text portions of this message have been removed]
I loaded the manual last night, but it does not show in Files this morning. I
will reload tonight
Dwight Watt, EdD,MCSE,A+,CCP,COI,MCT
http://www.dwightwatt.com
View my Microsoft Certifications
https://www.mcpvirtualbusinesscard.com/VBCServer/dwightwatt/profile
________________________________
From: Dwight Watt <dwight-watt@...>
To: friendsofdigicomp@yahoogroups.com
Sent: Mon, April 30, 2012 10:08:14 PM
Subject: Re: [Friends of DigiComp] DC1 Instructions Manual
I have done a new scan with better scanner than I had in 2003 and saved as pdf
of the DC 1 instruction manual and posted to files in the group. I optimized
file in Acrobat Pro to get small enough to put all in one file (<5meg)
Dwight Watt, EdD,MCSE,A+,CCP,COI,MCT
http://www.dwightwatt.com
View my Microsoft Certifications
https://www.mcpvirtualbusinesscard.com/VBCServer/dwightwatt/profile
________________________________
From: gc_rios <no_reply@yahoogroups.com>
To: friendsofdigicomp@yahoogroups.com
Sent: Mon, April 30, 2012 3:02:09 PM
Subject: [Friends of DigiComp] DC1 Instructions Manual
Hi everybody;
This is my first post in the group. I recently became a member, with hopes of
having my own homemade DC1.
Does anybody have a pdf version of the original DC1 Instructions Manual? I am
trying to read the jpg version in "Files" but it is a little difficult for me.
Thanks to all and excuse my bad English,
GCR.
[Non-text portions of this message have been removed]
[Non-text portions of this message have been removed]
Thanks Dwight.
I cannot find the pdf version in "Files", I can only see the 2007 jpg archives.
I've also read some old posts of discussion on legal issues on copyright.
Anyway, that's OK.
GCR.
--- In friendsofdigicomp@yahoogroups.com, Dwight Watt <dwight-watt@...> wrote:
>
> I have done a new scan with better scanner than I had in 2003 and saved as pdf
> of the DC 1 instruction manual and posted to files in the group. I optimized
> file in Acrobat Pro to get small enough to put all in one file (<5meg)
> Dwight Watt, EdD,MCSE,A+,CCP,COI,MCT
>
> http://www.dwightwatt.com
>
> View my Microsoft Certifications
> https://www.mcpvirtualbusinesscard.com/VBCServer/dwightwatt/profile
>
>
>
>
>
> ________________________________
> From: gc_rios <no_reply@yahoogroups.com>
> To: friendsofdigicomp@yahoogroups.com
> Sent: Mon, April 30, 2012 3:02:09 PM
> Subject: [Friends of DigiComp] DC1 Instructions Manual
>
>
> Hi everybody;
> This is my first post in the group. I recently became a member, with hopes of
> having my own homemade DC1.
> Does anybody have a pdf version of the original DC1 Instructions Manual? I am
> trying to read the jpg version in "Files" but it is a little difficult for me.
> Thanks to all and excuse my bad English,
> GCR.
>
>
>
>
> [Non-text portions of this message have been removed]
>
Now I can see it. Looks wonderful! Thanks Dwight.
GCR.
--- In friendsofdigicomp@yahoogroups.com, Dwight Watt <dwight-watt@...> wrote:
>
> I loaded the manual last night, but it does not show in Files this morning.
I
> will reload tonight
> Dwight Watt, EdD,MCSE,A+,CCP,COI,MCT
>
> http://www.dwightwatt.com
>
> View my Microsoft Certifications
> https://www.mcpvirtualbusinesscard.com/VBCServer/dwightwatt/profile
>
>
>
>
>
> ________________________________
> From: Dwight Watt <dwight-watt@...>
> To: friendsofdigicomp@yahoogroups.com
> Sent: Mon, April 30, 2012 10:08:14 PM
> Subject: Re: [Friends of DigiComp] DC1 Instructions Manual
>
>
> I have done a new scan with better scanner than I had in 2003 and saved as pdf
> of the DC 1 instruction manual and posted to files in the group. I optimized
> file in Acrobat Pro to get small enough to put all in one file (<5meg)
> Dwight Watt, EdD,MCSE,A+,CCP,COI,MCT
>
> http://www.dwightwatt.com
>
> View my Microsoft Certifications
> https://www.mcpvirtualbusinesscard.com/VBCServer/dwightwatt/profile
>
> ________________________________
> From: gc_rios <no_reply@yahoogroups.com>
> To: friendsofdigicomp@yahoogroups.com
> Sent: Mon, April 30, 2012 3:02:09 PM
> Subject: [Friends of DigiComp] DC1 Instructions Manual
>
>
> Hi everybody;
> This is my first post in the group. I recently became a member, with hopes of
> having my own homemade DC1.
> Does anybody have a pdf version of the original DC1 Instructions Manual? I am
> trying to read the jpg version in "Files" but it is a little difficult for me.
> Thanks to all and excuse my bad English,
> GCR.
>
> [Non-text portions of this message have been removed]
>
>
>
>
> [Non-text portions of this message have been removed]
>
It is there now as digi-comp1-manual-c-s.pdf
Dwight Watt, EdD,MCSE,A+,CCP,COI,MCT
http://www.dwightwatt.com
View my Microsoft Certifications
https://www.mcpvirtualbusinesscard.com/VBCServer/dwightwatt/profile
________________________________
From: gc_rios <no_reply@yahoogroups.com>
To: friendsofdigicomp@yahoogroups.com
Sent: Tue, May 1, 2012 9:13:02 AM
Subject: Re: [Friends of DigiComp] DC1 Instructions Manual
Thanks Dwight.
I cannot find the pdf version in "Files", I can only see the 2007 jpg archives.
I've also read some old posts of discussion on legal issues on copyright.
Anyway, that's OK.
GCR.
--- In friendsofdigicomp@yahoogroups.com, Dwight Watt <dwight-watt@...> wrote:
>
> I have done a new scan with better scanner than I had in 2003 and saved as pdf
> of the DC 1 instruction manual and posted to files in the group. I optimized
> file in Acrobat Pro to get small enough to put all in one file (<5meg)
> Â Dwight Watt, EdD,MCSE,A+,CCP,COI,MCT
>
> http://www.dwightwatt.com
>
> View my Microsoft Certifications
> https://www.mcpvirtualbusinesscard.com/VBCServer/dwightwatt/profile
>
>
>
>
>
> ________________________________
> From: gc_rios <no_reply@yahoogroups.com>
> To: friendsofdigicomp@yahoogroups.com
> Sent: Mon, April 30, 2012 3:02:09 PM
> Subject: [Friends of DigiComp] DC1 Instructions Manual
>
> Â
> Hi everybody;
> This is my first post in the group. I recently became a member, with hopes of
> having my own homemade DC1.
> Does anybody have a pdf version of the original DC1 Instructions Manual? I am
> trying to read the jpg version in "Files" but it is a little difficult for me.
> Thanks to all and excuse my bad English,
> GCR.
>
>
>
>
> [Non-text portions of this message have been removed]
>
[Non-text portions of this message have been removed]
I bid $41. Yeah, right. That'll do it.
Neil
1965 Digi-Comp II ESR Model 601 Digital Computer mechanical
http://www.ebay.com/itm/251051272822
Item condition: Used
Ended: May 02, 201218:35:35 PDT
Winning bid: US $511.01 [ 12 bids ]
Shipping: $16.20 USPS First Class Package
[Non-text portions of this message have been removed]
On May 2, 2012, at 6:39 PM, Neil Morrison wrote:
> I bid $41. Yeah, right. That'll do it.
Well... I *really wanted an original.* (We have several working copies, now.)
http://www.ebay.com/itm/160789242920
The US recession is officially over!
Neil
From: Paul Westenkirchner
I went all the way up to 84. It seems like the last one went for over 500
too.
[Non-text portions of this message have been removed]
It certainly wouldn't be difficult to finance a working time machine.
On 5/2/2012 6:39 PM, Neil Morrison wrote:
> I bid $41. Yeah, right. That'll do it.
>
> Neil
>
> 1965 Digi-Comp II ESR Model 601 Digital Computer mechanical
>
> http://www.ebay.com/itm/251051272822
>
> Item condition: Used
>
> Ended: May 02, 201218:35:35 PDT
>
> Winning bid: US $511.01 [ 12 bids ]
>
> Shipping: $16.20 USPS First Class Package
>
I had a DC II until a basement flood trashed it. It required a lot of modifying
to make it work right, most of the time. I would offer $10 for it, tops.
Bill Kustes
My new game book, MORE FUN with DIGI COMP I, Final Edition, is still
available. All of the 31 original activities, with corrections, are still in
it,including Rock Paper Scissors (a magic trick), Thirty-one (a dice game),
Grundy's Game (a pebble game), and Tic-Tac-Toe. Plus 10 new activities as
well(total 41 activities). Send an e-mail for complete information and to see
the Table of Contents.
Bill Kustes
DigiComp expert
Thank you for the link Paul. The devices appear to be relays with complex
contacts moved by electrostatic force instead of electromagnetic.
Bob S.
Project MECHL started 11/11/11.
On Jun 12, 2012, at 3:34 AM, "pmwestenkirchner" <paul.westenkirchner@...>
wrote:
>
> A nice article on some current mechanical computing research:
>
Send Email
