Calculating Machine: Newsletter Challenge (01/04/11)

How do you count data entry and operative actions?

Correct to how many decimal places? Fixed number or variable as a proportion.

I skimmed through this in #106, above.

Thanks for the response. Good questions.

I do not have a good answer. I was trying to come up with some kind of test but actually had a little trouble deciding how to evaluate the usefulness of each machine. My first cut ranking system was intended to account for some measure of effort or time required. However, the question is about usefulness and maybe that means something other that time or effort.

I have envisioned a machine with a keyboard containing the digits 0 through 9, a decimal point, and a negative sign that could only do a single operation on two numbers. Numbers to be operated on would be typed in and the solve button pushed. The result would be displayed and could be one of the two numbers used for the next operation. If we are going to do something manually with the result, we would write this number on a piece of paper and use a pencil to keep track of other operations. Maybe the machines are configured differently. I surely did not envision anything programmable or having scanning capabilities. My opinion is that inputting a number, even a multiple digit number, would be a single operation. Pushing the solve button would be a single operation.

Precision of the answers is of course dependent on the use of the answer. Being an engineer from the slide rule age, four significant digits are usually more than adequate for most situations. However, there are clearly situation where more precision is needed. For the test I proposed, I used integers for inputs and five significant digits for the outputs. It is not clear to me what the rounding precision for adding or multiplying using a division machine would be.

I also had an additional thought that the answers need to be decimal fractions and not permit irrational fractions. The machines used or the processes used with them could be irrational (must be some type of pun to put here) but the inputs and output, for this test, need to be common, everyday decimal representations. I also have no concept on how to deal with scientific notation, etc.

I hope that, as group, the rules for this demonstration can be worked out and some results posted.

Thanks,

Jim

113 – 355 = -242

or -(355-113)=-242

I like the subtraction best. The biggest negative is the number of iterations.

I like the division second best: The biggest negative is writing down all of the 1/X values in a complex calculation and then reentering them in the appropriate spot. I enter the wrong number more times than the correct number. if you would allow a memory in the calculator, division would be my favorite.

The addition is third: the biggest negative is the subtraction necessary for the 9s compliment.

I don't like the multiplication. I would love to have someone in favor of it show their justification.

I use to do all of these on my slide rule with, of course, very few significant figures. I must admit that I seldom added or subtracted, but it was possible.

The fourth machine - the one that only divides - is the most useful.

Addition as it can be used to do all the other functions.

The most fundamental addition process of adding 1+1 is actually a multiplication by 2. That is why the binary addition principle forms the basis of all computing platforms. Even the original creator of this Universe used it when HE allowed the basic Cell to duplicate itself by adding one of its own kind or multiplying itself by 2. Subtraction would be the opposite of creation; the destruction of a Cell.

subtraction is similar to a separation of one thing from other/others.

Adding machine with the use of recipocals (Comptometer)

With subtraction you can get to any number from any other number.

With addition, it's a one-way trip, baby. (no, you can't enter signed numbers.)

Subtraction is what you want. No worrying about two's complements, bit widths, ignoring high end digits, and such.

(Incidentally, all the computers in the world can be built from NAND gates, but that's another story)

you can say a-b=c or a=b+c and you can count how many times 1 has to be added to reach a from c, this is b!

That takes b times the circle to reach a!

By subtraction this is only one cycle to subtract, addition is a second cycle to subtract from zero (see before).

The most usful is the Add machine as long as you can use - numbers. ex.- (8+(-9)=8-9

I decided that my answer, while brilliant, didn't answer the question that was asked. I interpret it to ask which machine, if you could have only one machine and it could only be used for its primary purpose and each function is performed an equal number of times, would save the most labor. I think it cannot be answered without further clarification.

For this example, I accept that we do all of the actions on paper and don't "do it in our heads". Using the numbers from another response; 269 & 71

For addition I write both numbers, one above the other. I add 1 to 9 and get 10, write zero and remember a carry 1, or do I write a small 1 as a reminder?

If this is followed for the other functions, they are all finite except the division. Dividing 269 by 71 yields, 3.788732394366...... To how many decimal places should we be correct? I think the sun still shines on the division machine; there are many small calculations in trials of the next digit of the answer.

I decided to also look at just doing it on paper.

cost for the four calcs is 166 using the same criteria. Maybe I should change my vote to "None of the above"

Conceive a small child, just gettiing to grips with numerical manipulation. It goes something like this:

"Eight eights are sixty-four

Multiply by seven

If it's more,

Carry four,

And take away eleven.

Nine nines are eighty-one

Multiply by three

When it's done

Carry one

And then it's time for tea!"

_{- with apologies to A.A. Milne.}