The Numbers Game

When I first acquired this comptometer from a local thrift store several years ago, I'd noticed the worn keycaps, indicating years of long fingernails on keys (there's even a hint of red fingernail polish on some), but didn't understand at the time why only the 1 through 5 keys showed this wear, nor why the 3 keys seemed especially worn. Now I understand.



Then I located this archived scan of the book How to Use the Calculator and Comptometer, Third Edition, by James R. Meehan, distributed by Gregg Publishing, and finally sat down today to read up on the formal method of comptometer use.

As it turns out, the book teaches a "touch method" whereby the first and second fingers of the right hand are located on the 3 row - the home row - and the fingers are permitted to reach from the 1 to the 5 keys. For addition and subtraction, numbers larger than 5 are entered in a two-step process; for example, 7 is entered by pressing 4, then 3, in rapid succession. It may seem slower than directly entering the 7, but this method enables the user to enter these numbers by feel, keeping one's eyes on the work at hand, and thus ends up being faster in practical use.

This explains the wear on only the 1-5 keys, and the excessive wear on the 3 row. The user(s) of this machine (my sample dates back to ~1915) obviously were schooled in use by the Gregg method, which I find very interesting.

I should also mention that the odd-numbered key caps are dished in, while the even key caps are flat, making it easy to navigate the keyboard by feel.

Okay, but is using this machine any faster than a crank-operated adding machine of its day, or a modern electronic calculator (or computer keyboard) of today? I can say without a doubt yes! The Gregg method requires the use of the first and second fingers of either or both hands, and the entire number is entered in at once, parallel fashion. Emphasis is made on using the correct fingering technique for efficient number entry; the fingers hover over a group of keys to form the number being entered, and they are all pressed down at once. Being a "key operated" adding machine means as soon as the keys are pressed the calculation is performed and the digits in the register dials immediately indicate the result, real-time, as the calculation progresses, by means of the machine's internal planetary gear mechanism. This is the difference between a comptometer and a lever-operated adding machine.

By the way, the lever on the right side of the Burroughs machine is for clearing the machine, not for number entry.

For example, to add three 3-digit numbers, the right hand forms each number in turn and makes three rapid presses of the keys, which takes less than two seconds. I can't do this same sequence of operations (adding three 3-digit numbers), using a conventional electronic calculator or keyboard, nearly as fast. The difference in speed is amazing.

Subtraction uses the smaller sets of numbers on each key, which are the 9-complements of the main numbers, and the technique is to enter the complement number that's 1 less than the actual number being subtracted. For example, to subtract 18, the user simultaneously presses the 8 and 2 keys on the tens and units columns, which corresponds to the 1 and 7 complement numbers (i.e. 1 less than 18). In practice this is entirely intuitive and easy.

I'd already grasped addition and subtraction before I found this manual online, so what I was interested in was discovering how multiplication and division worked. Would they be difficult and time-consuming to learn? Surprisingly, no. Multiplication and division use the entire keyboard; numbers larger than five are entered directly, rather than broken up into smaller numbers like with addition and subtraction. In multiplication the user enters the larger of the two numbers being multiplied (the multiplicand) and, starting at the units column (it can be done in either order) presses the number into the keyboard that number of times corresponding to the units number of the multiplier. Then the user shifts the fingers so the same multiplicand number starts at the tens column and presses it in that number of times corresponding to the tens digit of the multiplier, etc.

For example, in the problem of 357 times 24, the 357 is held over the keyboard starting at the ones column and pressed in 4 times; then the fingers are shifted one column to the left and that same number is pressed in 2 times, for an answer of 8568. In practical use a three digit number times a two digit number can be done in about 3 seconds. I can't do it that fast on a modern calculator, no way.

I won't attempt to describe in words how division works, but suffice it to say that it's quick and easy. I plan on making a video about this soon, if you're interested; but in the meanwhile check the link above to the instruction manual for details.

I will say this: I've kept my Burroughs comptometer stored away to protect it from dust and because of its size, as it takes up a sizable footprint on my desk. But also, up till now I'd only known how to add and subtract, whereas I frequently have need for multiplication. Now I can see the possibility of using it for more practical purposes in my daily life, and that's exciting.



I've just received this book today and haven't yet delved into it, but there are lots of fun party tricks a person can do with the humble pocket calculator. I was inspired to get this book by a fond memory, from back in the 1970s, of a book called Games Calculators Play; back when these were new gadgets and I'd begun to amass a small calculator collection.



I'm really enjoying my Voss Modell 50 typewriter (used to type this piece), now that the imprint smudging and ribbon issues have been resolved. The smudging was caused by the carriage tripping right as the character was being printed, and required an adjustment to the escapement timing. These Voss typers have more adjustments than I've seen on many other machines, making it easy to resolve these kinds of problems. Also, the keyboard is a bit wider than many other medium sized portables, and there's ample clearance between the "A" key and the shift lock; touch-typing is therefore a breeze.

I was also enjoying typing on this vintage, slightly yellowed, notebook paper, which lends an immediate aged look to the piece. I need to find more of this old paper.

Stay well and do something creative!

It's a Done Deal

Post-Script: I did the final typing of the story on Adobe Rose, the Royal QDL, seen above. Though it had a partly used silk ribbon, I ended up swapping out the ribbon mid-story for the fresh ribbon Bill Wahl had installed in my Hermes Rocket. Also, the type alignment of the Royal isn't perfect, though it hasn't bothered me in the past; but for some reason I felt self-conscious about it, thinking the imprint needs to be as "professional" as possible. And then I was reminded by John Lewis, my local typewriter repairman, whom I visited this morning, that it's a manual typewriter after all - it's not supposed to look perfect! I like John's fresh perspective on things.

I suppose if I knew for certain that the story was top-notch, I'd be less worried about the aesthetics of its typewritten appearance. Oh well.

Today I placed a visit to Rust is Gold Coffee, to touch base and remind them that our ABQwerty Type Writer Society will be meeting there this coming Sunday, at 12:00 noon. I brought my Triumph Norm 6, upon which to type a few notes, and they loved the machine, especially considering they are a motorcycle-themed coffee shop, and there's a connection between the German Triumph typewriter firm and the British Triumph auto/motorcycle company. I permitted Sara to take some photos of the machine, for use in marketing their coffee shop. She's the gal I'd sold one of my Royal Mercury machines to, and I'm happy to announce that she's been doing lots of typing on it, even taking up virtually permanent space on her kitchen table. She loves typing on it, says there's something about a manual typewriter that brings out the creativity in her. I'm pleased that she's finding good use for the machine.

This typecast was done via iPhone 6s, instead of my flatbed scanner. I've used an iPod Touch previously, usually while on vacation, away from my scanner, and the results have been marginal. But I like what the iPhone produces, at least under my bright video table lights. Gives me less reason to rely on the scanner.

I'd used a backing sheet of paper while typing this piece in the Olivetti Underwood 21, and I noticed afterward that I could see the imprint rather distinctly in the backing sheet. So I took a no.2 pencil and did a rubbing, to reveal the imprint thusly:



I've boosted the contrast of the image a bit, but in person the rubbing is very readable, which gives me pause to consider that, in the event typewriter ribbons become scarce in the future, a charcoal rubbing might suffice. Not exactly steganography, since you can easily see the imprint with adequate side-lighting, but an interesting effect. I need to try this again with just one sheet of paper in the stencil mode, and rub with a real charcoal pencil.

I was reminded yesterday that I'm now in two cassette tape letter exchanges. I need to remember to bring a recorder with me when running errands, so as to take advantage of location sounds that make such taped letters so much more interesting.

With the help of one of my YouTube viewers I've found a solution to the problem of why I couldn't post comments to blogs hosted on Blogger, on my Mac computer. The reason had to do with a setting in Safari browser dealing with cross-site tracking. Yesterday I did a typewriter blog comment blitz, catching up on many blogs I've wanted to comment but couldn't.

Earlier in this post I mentioned placing a visit to John Lewis's shop. He has a pristine, fully restored Underwood No.5 for sale. The black paint shines, all the decals are virtually new, the nickel/chrome trim is immaculate, the key top legends are fully redone - and the platen is freshly recovered. I took it for a test typing, and boy was I impressed, I can truly touch-type on it with ease, and the spacing of the keys is ideal for my hands. If it sounds like I'd like to buy it, you're correct. But he's asking a pretty penny for it, considering all the work he's put into it, and that it's been professionally restored. Still, what a temptation. One obstacle for me is where to put it, since, unlike portables, these don't have cases. I'd have to find a permanent writing location. Or, like I've done with my Burroughs Comptometer, that's too large to store permanently on my desk, I found a high-quality plastic box with a gasket-sealed lid. I lined the box with foam rubber, secured the calculating machine in a plastic bag and secured it inside the dust-proof box via the gasket-sealed lid, so it can be stored in less than ideal conditions when not in use. I'd have to find a similar solution for the Underwood, were I to acquire it. There's also the little matter of explaining all this to my better half. But, at least she's been bitten by the typewriter bug, with her claiming ownership of the Olympia SM3, so perhaps there's less convincing needed than I think. Do I really need another typewriter? No. Do I need this Underwood 5? Yes!

PPS: Be sure to check out this typewriter-themed blog, Madam Mayo. There's a link to her older blog that goes all the way back to 2006. Nice to find more typewriter bloggers.

Collecting Calculators

Post-Script: I've ordered a copy of a Burroughs key-operated adding machine manual, dated from 1939, so when I receive it and have time to review it, I'll post again on any findings I glean, especially in regard to more efficient methods of operation.

The little ad hoc speed test I conducted between a 10-key electronic calculator and this Burroughs "comptometer" yielded unexpected results. I'd expected to be able to enter the ten 3-digit numbers into the Burroughs in parallel fashion, using three fingers and/or both hands, thus decreasing the time to nearly a third of what one might do on a conventional calculator keyboard, where each individual digit has to be entered one-at-a-time, in serial order. But the efficiency of finger placement on the ten-key pad made up for any advantage gained from parallel digit entry - and, as a matter of fact, I wasn't able to achieve true parallel digit entry on the Burroughs, due to a combination of factors, most notably because of my poor finger placement. The height of each row of nine keys on the Burroughs machine is a wider span than what I can comfortably manage, plus they are arranged in vertical columns, meaning I'd have to use some odd hand placement where my elbows are splayed out sideways and my fingers are parallel to the columns of keys.

I did some Internet research and found an old bulletin board discussion thread from circa 2003 concerning these machines. It seems experienced operators were able to deftly conform the position of their fingers to that required for each number grouping, and then quickly stab their hand down upon the keyboard, thereby simultaneously hitting all the keys of a number at once. Were I able to do that, I'm certain the results of my speed test would have been different.

This does in large measure remind me of the training and practice required to be a proficient abacus operator. And also reminds me that, although I've never been truly proficient at the Japanese soroban, it's one of those skills requiring constant practice, like a musical instrument, as an analogy. And thus there is the expectation that I could, in due time, put in the necessary practice time to actually use the Burroughs machine to its intended purpose. Which, if I do so, will require at least another blog article and accompanying video.

One aspect of the Burroughs machine that I failed to expand upon in last week's video was the fact of it having octagonal keys. These are very elegant in appearance, also reminding me of the old Oliver 5-series typewriters. I'm also reminded, on a personal level, of my maternal grandfather who, back in the 1930s, built an octagonal farm house in Florida, at a time when such configurations were considered especially daring and innovative.