Calculator Sticks from the 1600s
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- Опубликовано: 7 фев 2025
- Napier's bones, invented in the 1600s. They multiply a big number times a single digit.
This is episode 8 of my video series about calculating devices.
Chris Staecker webarea: faculty.fairfi...
Page about the bones: faculty.fairfi...
Related videos:
RETORTS! I respond to my favorite comments from this video: ruclips.net/video/VxXq06oDc6Y/видео.html
Numbring Nines Rods- a variation from 1684: ruclips.net/video/FhL8QXJGZMY/видео.html
Genaille Rods- a variation from 1891: ruclips.net/video/JCUPFZ0iH_s/видео.html
Napier's location arithmetic board- a binary multiplier published in the same book as the bones: ruclips.net/video/tVoMdddBQ5k/видео.html
The way he says "the bones" is one of a kind
Came into the comments just to say I like the way he says bones
Doesn't everybody say it like that?
@@ChrisStaecker bawwwwns (no)
Almost like 'Billy bones'
Me say "Booouuuaans"
Small things like this are what medieval/fantasy films are missing.
Yeah, the authenticity ... In avatar, Navis had eight fingers. So their number system was base 8.
I have never seen Napier's bones used in a film. Get on that, Hollywood!
maybe real people were much smarter than movie makers?
Not appropriate for medieval settings at all.
It's largely an Early Modern thing from when there were intellectuals not necessarily part of a clergy, and after getting access to islamic knowledges. Two things not even close to relevant to Middle Ages.
@@edwardmaginot um...mideavil isnt just europe js. Also banks existed since the crusades atleast which this is def a banker kinda thing
You got a real good giggle out of me with the calculator.
Same
Yea that got me too.
Awesome. I never understood how Napier's Bones worked, but this makes it super clear and super obvious. The connection to lattice multiplication is excellent too.
You know what I say? Screw math. Math can suck my clit, my nuts, my nipples, and my ass.
i can't understand a thing, it easier to learn another language, then math for me, it never was my thing you know
Seeing these awakened long-buried memories in me of elementary school. I don't think we had these in particular, but we had similar things. I remember long, flat plastic rods with numbers along the side next to notches in the side that a small string would nest in as you wrapped and weaved it around the rod.
Yes- those are “math wraps”! They don’t calculate for you, but you do a bunch of calculations as you wrap it up and then the string lets you check the answer.
We had those back in the early 2000's in the school I went to here in Sweden :)
I wonder if they're still used nowadays or if they've been replaced by electronics.
@Get on the cross and don’t look back shoo shoo go away shoo
Still used these days in a school near me!
I like that you not only explain this interesting mathematical object but tell us how to use it and that the Home Depot people will get suspicious of you ask for too many free materials
I learned lattice multiplication in school and it’s actually been my preferred method to multiply since third grade, so I recognized it on the bones immediately and felt extremely vindicated when you confirmed it for me later lol
I never learned how and abacus worked until now… it’s actually quite beautiful in its own way.
I actually like that. I wish in history class they would teach us some older stuff like this... "evolution of math", instead of going over the same history we have been and barely adding anything new. Honestly, I can learn more about History on the internet than my High School history class.
Remember, History class is usually a summary of the History of your country. Which society at large feels you should know as a citizen of X country.
But don't worry. You can still learn more at home! I suggest you looking for trust worthy books on various historical subjects. You might even have a few at your school's library. Otherwise, order them at a public library or order them online.
@@cracno1125 School is out of the picture as of now. High school graduate. I am currently working a factory job so any knowledge of history I would have to do online anyways.
@@JustSway Why so?
@@cracno1125 I am trying to control my spending habits and I work at a factory. I also said "as of now", I still have potential of going to a good school.
@@JustSway Ok, that's cool. Remember, it's one's goal to enrich oneself in this life before going unto the next alongside Christ.
Seeing that you mentioned the abacus at the end, I think the Chinese/Japanese abacuses (?) are also worth talking about. Instead of using rows of 10 beads, they use columns of 5/7 beads separated by a bar in the middle, with the top beads representing a value of 5 and the bottom beads representing 1. A lot of children in Japan still learn to use the abacus, and both the Chinese and Japanese have used it to take mental calculations to the next level (6-digit multiplications in their head).
I featured the Japanese abacus in this video: ruclips.net/video/FetVWSsj77M/видео.html
@@ChrisStaecker Yeah I realised that after going through your videos a bit more. Thanks for taking the time to respond though!
The way he said "They get suspicious" at the end is kind of hilarious when you try and come up with a visual image of a home depot employee thinking what kind of nefarious things are you doing with paint sticks.
my dude had no idea…
Love that "Ah-ha" (eureka) moment when you explained how to do the lattice method! Makes super sense and saves a TON of space. Can't wait to show my 13 year old who loves math as much as I do! Thankyou for sharing this!
I used the lattice method all through school, I couldn't long multiply any other way and I still can't long divide. I always wondered if there was a whole school of thought in math that was like the lattice method. That drawn out grid helped me out so much as a person who is hands-on but I failed at math and nothing else was like the lattice method to me.
Same, lattice is how my primary school teacher taught.
If I don't do the lattice method, I do another method where I split up one of the operands by tens place.
So 1234*1234 becomes 1234*1000 + 1234*200 + 1234*30 + 1234*4
my school did not teach it but I used that method as I found it better
Same. My teachers hated grading my tests and homework when you have to show your work. And I had cubes with numbers and slashes all over my papers. They also work really nicely for decimal point multiplication as well.
@@layleedayne4772 oh yes true, makes it easy
I would like teachers to teach this method when they see a child struggling with the usual way to calculate.
But strange enough most teachers will give you less points on a right answer if the way you got this answer is not exactly the same way they teached!
Isn't this totally wrong?
Every Math teacher needs to refer their students to your videos
The Japanese abacus is awesome. Check out videos of them using it. They are amazing. You can also be very good on the Japanese abacus and not know how to add. It's all about patterns.
Abacus are Awesome as Well.
Maths Teacher : Why did you bring "Ice-Cream Sticks" to the examination hall?
Me : *"My goals are beyond your understanding"*
Мы в школе сдавали экзамены на счетной (логарифмической) линейке.
ruclips.net/video/8MtMZv6Uluc/видео.html
The intro background music made medieval calculators sound as sick as a skateboarding ad.
"Wanna use my calculator?"
Nah, i got the bones
This is a prime example of how techniques/formulas have changed over time.
Each generation seems to have been taught a different way to find the answer to math problems.
A lot of them over complicate it, confusing people and making people, like me, _hate_ math....
This is really neat!
This guy makes me laugh out loud I love it
One of my first comp sci projects in college was making some of these out of cardboard and photographing me using them. What an odd professor, but he got the point across well.
The personality on display here is captivating. That Burroughs calculator bit was a 10/10
I did not realize it at the time, but my 5th-grade teacher taught us lattice multiplication to demonstrate the fun of mathematics.
Your voice is very soothing. We learned about Napier Bones and abacus in history class in middle school. That's when they really taught history.🙂🙂
Me: I would like 50 free paint sticks please.
Home Depot employee: Sure, no problem sir. (Frantically presses the Napier's Bones Alarm under the counter.)
The most chill mathematician
Ha ...... not just the 1600's, I learnt to use them at school in Edinburgh in the 1960's along with slide rules. Mind you, that was just down the road from Merchiston Castle, the family home of the Napiers.
I remember at studying this school text book under computer subject. With just a picture and a paragraph, happy to see after so many years someone showed us this calculator.
if you put the smaller number on the right side you can also put decimals and get pretty accurate percentages. sometimes it can take some guessing to get the right decimal place in your answer.
John Napier: *invents extensive multiplication tools*
Me, a distant relative: *traumatic war flashbacks of memorizing multiplication facts in 3rd grade*
I watched a lot of your videos, amazing stuff. Napier was the man
I began a career i8n surveying in the early 1960's, several years before electronic calculators were available. Each field crew had at least one Curta mechanical calculator. If you can put your hands on one, I think many of your viewers would find it interesting.
Never seen or heard of this before. I thoroughly enjoyed this... Well done!
One: you accent is awesome! Two: the bones...brilliant. I am just so glad the electronic calculator was invented by the time I came around....
John Napier was my ancestor. Everyone in my family has a gift for math.
Thats pretty Special
except Kate. (She replied here too)
I came here after watching the retorts. Very interesting! You make math fun and creative. I am going to try the lattice method.
Whoever you are, thank you for giving me something to do with my kid that's fun and pedagogic at the same time.
I love how the bones are just the times tables for each number
Wow, I spent a few years learning the Chinese abacus in my youth, got really quite fast at it, then never used it again and up until your demonstration, I had quite literally forgotten how it even worked. Kid me seemed like magic for most of my adult life.
How happy you were with your big calculator made me happy.
I have often used the lattice method since I learned it in elementary school, but after elementary school and I got a bit older, I used it in my scratch paper that I had to turn in for proof that I did the work, and the teacher was like “what is this?” And I got points counted off for it. I tried telling them what it was and they said they’d never heard of it. Smartphones weren’t common at the time, so I couldn’t just Google it and show them. Then I started asking other people and they had no idea what I was talking about, even when I wrote it down and showed them. For years I started thinking I was just crazy and had made it up in my head or something, but I kept using it because it worked. Now I know I’m not crazy, those other people were just dumb or forgot about it.
This channel is really cool. Definitely deserves more subs... and hoagies.
Thanks! ... meatball for me.
True bro you are very good
I learned so many methods of calculation today thanks to you. Much obliged.
interestingly, in elementary school they taught us both the traditional method of multiplication and the lattice method - i had completely forgotten about it tho until you showed it
I don't care about the content. I just listen to him talk and relax.
You'll love this guy: ruclips.net/video/Nw6TYp_EgG0/видео.html
My uncle did business with Chinese people in the mid-'30s and he told us how they used abacus in a very expert and quick way. Never had a problem.
Great. Just great. I'm randomly suggested this video. Now I have to watch more.
Real great.
In all seriousness those are really cool.
Imagine if kids were taught how to use those before learning how to do math with a pencil. I feel like they would expand the mind.
Okay not for nothing but these bones would have been so fun to make in 4 grade art class, and useful too
I didn't recognize the formula until he draw the box, I was stunned I was using it the whole time.
Sometimes I want to pick all ytubers and time travel them back to when I was a kid, this makes sooo much more sense
When I was in high school in the 1960s they still taught how to use a sliderule for the advanced students. In my first job in the 1970s I used the old manual calculator that had rows of numbers to punch.
Napier's Bones are a great teaching tool. I used them in the classroom many years ago.
I think a teacher would be impressed if you used this in highschool
That music at the start got me thinking "why does this sound familiar?" And i saw a minecraft lego ad in my recommended and it was this same music it used.
Thank you for this detailed video!
This video is as though ripped from the internet of my childhood and brought here to the internet of my sad late 20's.
I've never seen this page, but I like it based off of this video. Especially The calculator part.
Lol new to your channel. Loved how gitty you were over that calculator
In my school system we actually learn multiplication using the lattice method! We get taught the older method and the lattice so we could use what works best for us
this video has such a charm
The form of multiplication was used in the 1202 Liber Abaci and 800 AD Islamic
mathematics and known under the name of lattice multiplication. "Crest of the
Peacock", by G.G, Joseph, suggests that Napier learned the details of this method
from "Treviso Arithmetic", written in 1478.
Yes I mentioned lattice multiplication around 2:50.
This is a perfect youtube video. Perfection.
I need these as a peak into our ancestors' strange, sideways ingenuity. It's stuff like this - not just swords, battles, and politics - that I love from history
You have just changed my math grades…. Thank you
Really good going to try to remember these techniques for my kids. The grid will really help. But only negative is the music is louder than the vocals and makes it a little hard to hear
3:27 you're missing a 3rd way of doing it ... it's cross between the two method (the way I learnt it) 3x5 = 15 you keep the 5, then put the 1 (or any digits after the first) up in the corner, then 3x2 = 6 then you add the corner number written to the 6 for 7
So cool to see a demonstration of these! Btw, the sound level for the VO was a little low and the music a little high. Overall, another great video. Keep it up!
“Let me use my calculator”
Dame I laugh so much I didn’t expect that 😂 thx bro nice touch
When I was younger I could never figure out multiplication and only knew lattice, so it's interesting to see that other people used I'd more frequently for more applications
I remember that my 3rd grade teacher taught my class how to make these: I completely forgot how, until now.
You could also use jetons on an exchequer table, or even calculi on a sand table or Salamis-styled board.
These are cruel a napier is killed to make these
I wondered why he didn't start with multiples of 1 when figuring out which numbers to put on the bones until I realized multiplying anything by 1 wouldn't require a device
I'm related to John Napier and I think this is the first time I've learned anything about him besides from family
Let me just say, I wish you had been my math teacher when I was in grade school.
I learned the abacus as a child, this thing is faster in operation speed but it needs time to setup. Plus, it can be arbitrary length - abacus is kinda limited and really unwieldy.
Good abacus operator can calculate really fast and with enough practice, it's muscle memory.
I wonder how fast can the calculation be if people practice using this enough.
New life goal: Have my DM run a "you are transported into ancient times" game and trade the knowledge of napier's bones, thus gaining the favor of the merchant's and draftsman's guild in my coup attempt against the king
My brain died in the abacus demonstration
this was so much fun to watch. thank you.
Hahahah first video I see from this RUclipsr and pulls out the calculator joke 🤣 Subscribed and liked real quick.
Certified B O N E S moments
0:02
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1:32
3:47
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4:00
4:05
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5:36 U SE T H E B O 0 N E S
If I was a teacher I wouldn’t even bother confiscating these from a student.
I subbed bcuz I love, used and understand the Napier Bones. We made small ones from popsicle sticks, just for fun in middle school. I loved the clicks of the Abacus.🙂🙂🙂
I was actually taught lattice multiplication in middle school and it was so much easier that I had a hard time grasping regular multiplication for years
Thanks man just found another way to multiply big numbers
The first time I watched this video I burst out laughing cuz my science teacher’s name is “Mr. Napier”
I love how his horrible handwriting is almost as bad as mine! You got yourself a sub. The calculator is cool ig.
YT Algorithm: Wanna see a Stick Calculator from 1600s??
Me, watching in a sunday: WHY NOT?!
"ok what is 7,777,777 x 7?"
"sorry each digit can only be used once I need to go get a few more sets of bones!" 🤣
Cool invention thanks for sharing! 😃
When the abicus was used by our saleswoman in the school cafeteria, we couldn't even see her fingers
I learned the lattice method in elementary school in the 2000s! I found it easier to learn than the method compared to the usual way today. My mom always said the lattice method was some weird new age multiplication lollll
This is really amazing, Napier had to have been a genius
Не зря его именем (Neper) назван один из параметров звука.
that's a pretty cool way to calculate things
this video was awesome as someone who like numbers its cool to see a old way of computation that works the way my brain dose math
man how did he get my bones
Those are my bones!
You could do multi digit with multi digit using the bones by writing out the rows on a different paper and doing lattice on them.
Pretty sick.
Also first time I ever saw someone explain the abacus
The bones were about 2 to 2½ inches long, and ¼ of an inch on a side. A set of 30 took up very little space. You could also use them to compute square and cube roots. With three or four sets, you could get some serious precision. Want to see fancier, look at the promptuary.
Ok, you had me at the calculator. Liked, commented, and subscribed!
"Let me check it on my calculator"... hilarious 🤣🤣🤣