Numberaid the American Abacus! Review / HowTo
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- Опубліковано 4 жов 2024
- The Numberaid: The American Abacus created by Andrew Schott in 1957. It's a strange hybrid Russian/Chinese abacus meant to teach kids something about something.
This is episode 74 of my video series about old calculating devices.
Numberaid Guidebook PDF: archive.org/de...
End song inspired by "Hotter than a Molotov" by The Coup.
Chris Staecker webarea: faculty.fairfi...
#america
This is a great video about numbers. Too bad we'll never know the name of its creator.
The ending is perfect. My first thought after hearing "you choose how to represent a 5" was "Freedom!1! ™".
I love it when these things make you all philisophical. Also when you talk about melonheads.
You did it again Chris - always the best and funniest calculating machine videos on UA-cam. What a crazy yet also rather cool calculating machine, and fantastic news, if I have no money in my bank account, I can safely go out and spend lots of money and I'll still have no money - I won't be in debt at all!!!!
"Zero minus any number is zero." There it is, in undeniable print. And now it's on the internet too, so that really proves it. Sorry, that's just how it works!
Well of course naturally not!
This feels like if Videogame Dunkey did obscure maths devices. I love it.
CalculationDunkey
Absolutely top tier video. From the "never knowing her name" joke (which made me audibly produce sound), to a serious philosophical musing on the reality of numbers and then back to freedom, this video has it all.
Great video! I always enjoy this series, and that Inca knot numbers cameo was a great way to visualize the concept you happened to be talking about.
I’ve gotten into the habit of making my own mathematical devices, mostly counting boards and an abacus or two. Your work really inspires me and gets my creative ideas going, so thanks for that!
Cheers ✌️
Your sarcastic tone is not attractive though the video itself is excellent. I was taught math with this exact abacus in 1961 in first grade at St Christopher’s Catholic Elementary School in Metairie, Louisiana. I picked up how to use it in days, I didn’t even know what addition, multiplication or division even was! the teachers were superb. The abacus taught me visually and with tactile input. Flash forward to 1976, I get a BS in Mechanical Engineering at Georgia Tech. Never have had a problem with numbers after first grade. They taught us phonics too, never have had a problem writing or spelling. Very high quality for the time, probably cutting edge.
The Japanese abacus is great. I suck at using it however. The abacus isn't about moving beads one at a time. It is about recognizing a pattern, and knowing what new pattern will be formed when adding some number. For example when adding 7 to 5, the skilled operator adds 1 to the ten's rod and sets the one's rod to 2. In fact, you can use the abacus effectively without being able to add. It's about the pattern. This is one reason skilled Japanese abacus jockeys are insanely fast and accurate. Check youtube for videos.
I think the soroban (Japanese abacus) is way easier to use than the suan pan (Chinese abacus). The ten compliments are a blast to use. It makes life easier.
Beginning: Mathematics
Ending: Poetry
Hallo Mr. Staecker,
I enjoy seeing all of the old maths devices on your videos. Thank you.
I think it would make a very interesting video if you showed how subtraction is done on abaci and counting boards using the "Nines Compliment Method". This illustrates the usefulness of having more beads on each wire and sliding the beads in the other direction for the subtrahend . Computer science students may recognise this method as it is the same way subtraction is done on microprocessors. It would also show how negative numbers are represented on an abacus just like some binary methods.
steps:
1 slide all nine beads up to make 99,999
2 enter the subtrahend by sliding them backwards instead of usual (this is a "9C" negative number)
3 add the minuend as usual
4 carry as usual
5 add one to the sum
No fuss, no borrowing,
Speaking of freedom, I just got back from fishing with my dad; while we were on the river, a bald eagle took flight off a nearby dead tree, and flew above us as we traveled. Pretty wicked sweet.
I could see this being handy for hexadecimal if you called the top bead a 6-bead instead of a 5-bead, or if you added a bead underneath.
On mine, I can easy remove beads since the bottom pops off. So you could count the 2 on top as 8s, plus 8 beads on bottom for a nice hex setup.
@@robertswaine6096 Since there are already 9 beads on the bottom, you could call the top bead a 10-bead and get base30 for free.
As far as other modes of compression, you can think of each stringer of beads as being two stacks, which I'll call yes and no. The beads start in no and are moved into yes to increment the counted value. Reading the beads can then be thought of as asking how many beads are in the yes stack. Moving a bead can be thought of as popping it from one stack and pushing it onto the other. You cannot pop a bead without also pushing it. I can see no means of compressing that process without further operations.
@@ChrisStaecker For true minimalism, I'd pop two beads off to get 8+7 values, plus one more for zero. Kinda like the Japanese abacus with a 5-bead and 4 1-beads. It would be weird to enter 0xFF and have leftover beads underneath for example. Thinking about that with hex checks out pretty nicely!
@@totally_not_a_botAn even more minimalist approach (likely incompatible with this model) might use 3 4-beads and 3 1-beads.
As it is with two top beads and nine bottom beads, it makes a base 30 abacus.
Iirc the extra beads on a Chinese abacus (vs Japanese Soroban) are useful in deferring carries in multiplication, and are particularly useful with borrows for subtraction/division.
You know the American abacus being a plastic and colorful combination of three different, older types of abaci is somehow both poignant and way too on the nose, much like America itself
"...teacher needs a smoke break." Then the final slice of americana, "The American abacus, it's about Freedom!"
I am (was) proficient with Chinese abacus and wish to point out that which could do hexadecimal arithmetics. Though i know nobody use it that way. (Edited for clarity)
You mean use the top beads for 8s? That would work! I didn’t mention it because I’m not sure if it’s intended or mine is broken, but the bottom of the frame easily pops off of mine, which lets me remove beads from the lower portion. So you could take off one of the lower beads and make it a real hex abacus.
Don't this have too many earth beads compared to the suan pan?
@@ChrisStaecker Two top ones weighting 5 each, plus 5 bottom ones weighting 1, making a total of 15 (0xF) per column.
Clarify: I refer to Chinese abacus, not the one in video title.
Ah OK I misunderstood. But now I agree with you- you can express 0-15 so it would work.
Adding in here, most accounting/merchant abacus found throughout the world, not just Chinese, were base-16 (which is what you have). The reason for this is because most systems of unit division for most of history had to be easily divisible by a large number of common ratios. Hence, you see things like 60 minutes in an hour, 24 hours in a day, 12 in a dozen, 16 to a pound. These weird units were chosen because they've got a lot of the common primes, and thus can construct common ratios. So in those situations, your unit conversions would be your rows, so you'd want to have enough bandwidth on the row to put 16 ounces worth on the bar and have it carry to a pound on the next bar. All divisions of measurement are equivalent up to the first exponent; 3 is 3 whether you are in trinary, or centenary. End result, these abacus would be used in a much, much, much more advanced way - each ROW would be in a different base, carrying over to the next unit. So your first row would be in base 3 (or whatever) and the next row is in base 16, then go to base 4, and so on.
There are rare examples of abacus with even more beads, and I have to believe these would be used in much the same way - they did not think about "base 10" like we do today. They used the rows to represent the units with whatever base they came in, and some bases require more beads than others.
In Japan using the abacas, they can add faster than most people using a calculator. Also they can simulate in hand motions, without an abacus and still get it correct.
This truly is the American Abacus, you have the freedom to choose something on a system that's overly-complicated and inefficient!
You could use the extra sliders for negative numbers.
I love the idea, but I don't think it works if you're using one of the top beads to represent a 5 or a 10.
I just stumbled across your counting device videos and am absolutely enthralled. By chance have you heard of or used a CSMP mini-computer? It's a technique for teaching arithmetic in grade school. I'd love to see you do a video covering it!
Very interesting! Never heard of it, but I'll check it out- thanks
We used these in the 1960s in Catholic school, in the early grades. So funny that we pronounced them “noomeraids.” We loved it when the teacher passed them out.
was it st christopher’s catholic elementary School in metairie, louisiana, by any chance?
Great video, as usual!
Fortunately we have Kojima to show us how to represent negative numbers on the abacus!
Also, I’ve dabbled a bit in the 9-bead abacus: ua-cam.com/video/ZhHitcFXKhQ/v-deo.html
Nice! 9 beads makes sense as kind of a soroban-style russian abacus. The Numberaid's 2+9 setup doesn't make any sense at all to me. I'd expect either 2+10 or 1+9. But 2+9? Very strange.
The denial of negative numbers really got me. wow.
great closing sentence
Nice video. I never heard that americans had developed their own (albeit quite confusing and limited) abacus. Here in Brazil we also have a local version called "Soroban Moraes" developed in 1949 by Joaquim Lima de Moraes who had progressive myopia and adapted the japanese abacus to be used by blind people by putting a non slippery material under the beads to keep then in place when being read using the fingers.
By the way, I also have a chinese abacus (suanpan) just quite like yours and I noticed there are two metal rods (on de 3rd and the 9th column) among the bamboo made ones . When I first saw this on my sample I tought It was some kind of impromptu fixing, but after checking similar suanpan on the web and yours, they seem to have some meaning/function.
Do you have any idea?
Maybe just to help you keep track of which column is which. On wide abacuses people would often use the columns to represent more than one number at a time--I could see someone putting the units digits on the metal rods.
Because each column can represent up to 20, it's like leaving that little extra space at the end of those things you're supposed to wear with anonymous partners: potential addition doesn't affect partn -- ahem, columns, later in the ni -- heh, excused me, operation. At least that's what I've heard. I also couldn't help but notice the pdf of the manual was 69 megabytes.
Patent lists Milwaukee, WI… hey that's where I am! neato
Just ordered mine
Is that damn quipu at the end? Good!
I wonder if any of the Chinese dialects/languages use biquinary counting schemes? For instance, are there idioms or words that refer to the number five without calling it five (sort of like the term "baker's dozen" implies the existence of 12)?
Based on your video, it seems that this product could have used some field tests with various iterations of the instructions. While it is pretty cool that there are multiple ways to calculate something, a neophyte user wants to know the most straightforward way. Did this guy publish any academic papers were he reported results from field testing? I know for the literature on path dependence, reports on the efficiency of the DVORAK keyboard compared to the QWERTY keyboard were important rhetorical tools for claiming or debunking which system was better.
Awesome.
3:32 *MORE BEADS!*
I heard it in Jack Black's voice in The Fatties (Fart 2).
The version of the Numberaid that I have uses beads that are only half round (and thus don't slide as well as they should), but the instruction book has the lines that are missing at 6:12 in the video.
Yes I’ve seen pictures of the half-bead version. I think that was a later revision? Glad to see they fixed the book-
@@ChrisStaecker I'm guessing it's later based on the book being fixed. There are sellers on Etsy and EBay selling prints (And t-shirts and coffee mugs) of the patent drawing for the half-bead version. I don't know if there are 2 patents, or if the design was changed before the patent was submitted.
the one thing i like about so many extra beads-beside it allowing experts to work in either the Russian or the Chinese/Japanese style-is that by letting every column go to 19, you can hold off on carrying numbers until AFTER you’ve otherwise added them. Great for learners or others bad at keeping track of things. But yeah, it’s very clear the maker of this had some…”interesting”ideas about math…
Yes I would say “deferred carry” is the killer feature. This is a big obstacle to me trying to use an abacus- moving the beads correctly and also carrying at the same time is a lot for me to keep track of.
Do you have the Original Odhner 227?
Sadly no
Great video! Too bad we'll probably never know the name of the creator...
obviously it's designed for a base 30 number system. Each top bead is 10, and each bottom bead is 1
Are you sure it’s not about finding something you could patent
Yes! I didn’t mention it but the patent is silly- it’s obviously just an abacus. He had other patents which were more interesting.
3 "original"s in one video! My cup runneth over
The chinese abacus can handle hexadecimal stuff. Now they do have hexadecimal measures.
The freest abacus is freefloating apricot pits. MURICA
Ooooh, the American one gives ya freedom to use it how you want. Get it? FREEDOM !! ‘Murica !
I'm just trying to wrap my head around the base 30 abacus.
You seam like you might know how to fix a Remington Rand adding machine display model... Kinda having some issues with mine.
Actually I've had bad luck repairing big metal machines. Often lubrication is all it needs, but it's hard to get in there and grease up the parts that really need it. Good luck!
@@ChrisStaecker ya i took it apart and now wish i just added some oil and used a can of air to blow it out. It was extremely dirty but at least the carage worked correctly, now it kinda needs manual assistance every time you push a button and it has occasional errors, so ya supper happy lol
The multiple representations of numbers remind me, in Takashi Kojima's Advanced Abacus, an early section on the history of the abacus mentions an earlier system of reckoning blocks used in China and Japan. I can't find a single other source describing their operation. Google just sends me back to various copies of that book. Do you know anything about this old system?
I don’t but it sounds interesting! I’ll check it out
@@ChrisStaecker Okay, so after further bingeing I found out that you did actually mention these things in passing, but they're called counting rods! The Abacus book must have just chosen an odd translation. Thanks!
@@glarynth ok yes I am aware of counting rods- planning on covering them some day! Some decent basic info at Wikipedia.
I want a quinbinary abacus oh wait you can just turn the biquinary upside down
Imagine only being able to count to AAAAAAA4AAA. Is it easier somehow than 999999994999?
2:42 i think you said it backwards
Sure, there are different ways to represent the same number - but should there be different ways *within the same system*? That's just a recipe for confusion. The soroban beats this hands down. I felt as if you were building up to calling Schott a nincompoop, Prof. Staecker, and I wish you had.
To me it’s a trade off between flexibility and confusion. I’d guess that some students would really thrive with the flexibility, but probably most would be confused.
(Also probably you know but even the Arabic number system has nonunique representations as in 1.0 vs .999… But this in practice never leads to confusion, at least not the type you’re talking about.)
@@ChrisStaecker It leads to big arguments on the Internet
Funny, I have a Chinese abacus (suan pan) that I use using the Japanese abacus (soroban) way. The soroban way is way easier to use for me. 😂😂
how did this get a patent? what's original about it?
It's pretty weak- the patent I showed is a "design patent", which is different from an ordinary patent. A usual patent is supposed to be for a new invention, but a design patent is just to protect a new design of an existing invention. I don't understand why he felt it necessary to patent this thing- maybe just so he could say so on the box.
I'd bet a nickel that not one person ever read the entire "guidebook for parents" before you. (But don't you want the Guide for Classrooms"?)
Yes I do!
“0 minus any number is 0”😭
If this man was trying to save American education I reckon he missed the mark
That zero logic is causing crippling national debt, or is it?
Volume need to be higher I cant hear you at all even at 100 %
Sounds good to me
I can also hear him perfectly
CC
Jajajaja, Muh'rican abacus? Is there anything gringos wont try to take credit for? Lmao
Frankly, looks ugly, totally lacking effort in design. Order a pile of inexpensive real hand-made Chinese abacus-es. Might as well use something attractive while learning math.
Awesome.