Turing Computer

[SFB]

Why is an abacus not digital? And why is an abacus considered a computer, since all it does is store numbers and does not do any computations?

I dunno. I guess a good definition of computer is in order. At what level of development does a device become a computer? Is a calculator a computer? An abacus multiplies, divides, adds, and subtracts and thus approaches the same functions as a basic electronic calculator. According to this site,

http://www.ee.ryerson.ca:8080/~elf/abacus/intro.html

it can be used to extract square-roots and cubic roots.

http://www.ee.ryerson.ca:8080/~elf/abacus/

So what constitutes a computer?

 

[Skeptoid]

Turing basically defined what it means to compute. If a Turing Machine can do the same thing an abacus can, then an abacus is a computer.

 

[xouper]

SFB: An abacus multiplies, divides, adds, and subtracts and thus approaches the same functions as a basic electronic calculator. According to this site,
http://www.ee.ryerson.ca:8080/~elf/abacus/intro.html

Pardon, but you misquoted that site. That's not what they say. Here is the exact quote (with yellow highlighting added by me):

The standard abacus <span style="background-color: #ffffaa;">can be used</span> to perform addition, subtraction, division and multiplication; the abacus can also be used to extract square-roots and cubic roots.

The operative phrase here is "can be used". Well, so can a pencil and paper. And just like pencil and paper, the abacus itself does not do any computations. Perhaps you missed the other quote at the top of that site:

The abacus is a mechanical aid used for counting; it is not a calculator in the sense we use the word today.

In other words, an abacus does not do any calculating, it simply acts as paper and pencil while the human performs the actual algorithms.

So what constitutes a computer?

That's a good question. Here's one common definition (from webopedia):

A programmable machine. The two principal characteristics of a computer are:

• It responds to a specific set of instructions in a well-defined manner.
• It can execute a prerecorded list of instructions (a program).

A calculator meets that definition. Even the old mechanical calculators that were prevelent before electronic devices. An abacus does not meet that definition, since it does not execute any kind of prerecorded instructions (or algorithm).

Another way to ask the same question is how would a Turing Machine be programmed to model the algorithms performed by an abacus? Answer - it can't since an abacus has no algorithms built into it.

Which brings us back to my original questions to you.

Why is an abacus not digital? And why is an abacus considered a computer, since all it does is store numbers and does not do any computations?

 

[xouper]

Skeptoid: Turing basically defined what it means to compute. If a Turing Machine can do the same thing an abacus can, then an abacus is a computer.

You managed to hit the post button two minutes before I did. But then your answer is a lot shorter than mine was.

I think I know what you were trying to convey, but I would like to quibble with the way you put your answer, however. A Turing Machine can indeed be programmed to do the same thing an abacus can do, but I disagree that means an abacus is a computer. A Turing Machine can also be programmed to do the same thing a pair of dice can do, but are dice considered a computer?

 

[SFB]

Why is an abacus not digital? And why is an abacus considered a computer, since all it does is store numbers and does not do any computations?

Okay, it is not a computer. I agree with what you've posted.

But it is digital in the sense that it's manipulated by digits!

 

[Skeptoid]

xouper wrote:
A Turing Machine can also be programmed to do the same thing a pair of dice can do, but are dice considered a computer?

Is a random number generator a computer? I think so.

I think I see your point though. The human is the computer behind an abacus, which is merely a storage/output device. But then, can't the same thing be said of a hand held calculator or a huge mainframe computer? After all, the input data and an algorithm must be provided by a human in all these cases.

 

[xouper]

Skeptoid: I think I see your point though. The human is the computer behind an abacus, which is merely a storage/output device.

Yes, that's another way of saying what I meant.

But then, can't the same thing be said of a hand held calculator or a huge mainframe computer? After all, the input data and an algorithm must be provided by a human in all these cases.

I can see how that would be an obvious question. The key point here is not how the algorithm got into the device, but whether the device has a way to store and execute the algorithm. Does an abacus perform any preprogrammed algorithms at any time? How about dice? In my opinion, no. A single die, for example, only generates a random number if the human puts it through a proper "algorithm". The dice themselves do not contain the algorithm necessary to generate a random number. To use your own words, "The human is the computer behind the dice, which is merely a storage/output device."

 

[xouper]

SFB: But it is digital in the sense that it's manipulated by digits!

Ya got me there.

What I had in mind was that an abacus uses discrete positioning of the beads for storing data. A bead is interpreted as either up or down on the rod. There is no provision for in-between positioning. This is what makes it digital.

If an abacus was analog instead of digital, then it would use continuously variable positioning of the beads to store data. In other words, the value of a bead would dpend on measuring precisely how far it is along the rod. Clearly this is not done in typical abacus use, so it is not an analog device.

 

[epepke]

Very interesting site DD. Though not digital in nature, the abacus, often considered the first computer, still predates the rope and pulley device.

The abacus was mentioned in a Chinese piece of literature dated 190 CE.

Only people who have never learned how to use an abacus consider it a computer. It's just a register. One might as well say that pebbles in piles were the first computer.

 

[SFB]

Only people who have never learned how to use an abacus consider it a computer. It's just a register. One might as well say that pebbles in piles were the first computer.

epepke,

I conceded as much above in a response to xouper.

I fell into into the commonly expressed idea they are computers, not having given it much thought. And yes, I have never tried to use an abacus.

 

[SFB]

Ya got me there.

What I had in mind was that an abacus uses discrete positioning of the beads for storing data. A bead is interpreted as either up or down on the rod. There is no provision for in-between positioning. This is what makes it digital.

If an abacus was analog instead of digital, then it would use continuously variable positioning of the beads to store data. In other words, the value of a bead would dpend on measuring precisely how far it is along the rod. Clearly this is not done in typical abacus use, so it is not an analog device.

Makes sense to me.