Amazing Old Calculator (Curta) - Numberphile
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- Опубліковано 20 сер 2024
- Alex's book: amzn.to/1l0yX46
The Curta is a pocket-sized, mechanical, digital calculator!!! It was invented by Curt Herzstark.
More links & stuff in full description below ↓↓↓
Shown here by Alex Bellos, author of Alex's Adventures in Numberland.
More about our contributors, including Alex, at www.numberphile...
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In 1964 or 1965 I was in an electrical engineering class and watched two guys sitting on the front row. Each was using a strange cylindrical calculator.
It was a big class and the students using the calculators were older than the rest of us and we never found out what kind of calculators they were using. I have wondered all these years. I never again saw a calculator like that. Now finally I know.
Thank You!
Oh nice... How old are you now? 😊
@Boco Corwin now 4 years
@flix7280 now 5 years
so does it become a grenade when you divide by zero
l4wl3rbl4d3r You can only add with this device.
Derek Leung wrong you can subtract as well they didn't add that in or they didn't know. You pull the thing you circle around up and it will do subtraction
***** Go learn how this device actually works please. The mechanism inside can only do addition, just like an ALU used by modern computers.
***** Go learn how this device actually works please. The mechanism inside can only do addition, just like an ALU used by modern computers.
Derek Leung lol double post
I want one so bad! Imagine being in a chemistry class and pulling out this bad boy in college to calculate with. Instant awesomeness status.
People who think that a Curta calculator equals "awesomeness" are the kind of people I love the most.
ghuegel Like, the definition of a nerdgasm.
Pulled one of these babies out in my SAT 2 Math test as a joke, but the proctor got mad at me. Proctor for my IBHL Math Exam didn't mind though.
jyk000 Really? You have one of these?
Bought on eBay when this first came out for 500 bucks. Type 2
Now I can't help but wondering about the inner workings of this beautiful device.
type in how the curta works into the search bar, amazing 3d video
Golden Mean Media I know, i shared that video in this commentsection as well. A beautiful video indeed! ^^
Bas Groothedde
Aah. Its only because I had watched that video just before this one I thought it might be of great help to you. I'd say I understood about 75% of it when I watched it. :)
Golden Mean Media I had to re-watch it as well, what a simple yet complicated machine!
+Bas Groothedde there is a vid about it on youtube... sorry for bumbing a year old post
My grandfather gave me one of those - the construction is so incredible and the feel of the gears so solid. Over the years it has been difficult to explain to people exactly how amazing and great those things are.
No, you can do subtraction. You pull up on the handle to put it in subtraction mode. Turning the handle then decrements the turn counter and subtracts the number on the output by the number on the input. You can also do really complicated stuff like cube roots. It's a really powerful tool.
you did not mentioned that it also can perform subtracts, divides, square roots, cubes, factors, and percentages.
It CAN??????
wipi 8055 Can it even make a decimal number for square root?
Technically, it can only add. But with help of moving the decimal point and similar tricks, you can do all of those operations. Algorithmically, it is very similar to what the arithmetic logic unit in every electronic computer does.
That....is disgustingly incredible....what a marvel of engineering!
By pulling the lever, the Curta calculator goes in subtraction mode by reversing gears. It can do it mechanically, not with operation tricks.
I loved hearing the rally reference in this video! I have a friend in the rally community who has one, in fact. How were they used in rally? On a TSD rally (Time-Speed-Distance), you given distances, and the speed you are expected to go. The goal is to arrive at an undisclosed point along your route at exactly the right time. If you know how fast you are supposed to go, you can know how much time should have elapsed for each unit (10th or 100th of a mile) of distance. So the co-driver could give the Curta a crank for each "tick" of the odometer and accumulate the ideal elapsed time. By comparing that to a clock you can tell if you are running ahead (driver needs to slow a little) or behind (driver needs to speed up a little).
My dad used to lay out and participate in those rallies, and he had a Curta. Since he's passed, it's now my brother's, and one of his most prized possessions.
@@adamplace1414 Love seeing that this video is getting fresh views after the Objectivity / Adam Savage video!
after an EMP strike or nuclear war this machine would still work.
that's one reason why you need it.
And it's just cool.
Good thinking.
I agree that it's cool, but you don't really need a machine to do arithmetic multiplication. You can do it with a pencil and paper, or even just a bit of charcoal and a wall. As far as practical devices for doing science or engineering, a slide rule is *way* more powerful.
Sarah with pen and paper you can make mistakes and it would take more time when you have 8 digit numbers or so.
And the thing is if such a caltulator would become more popular people will start improving it and more functions would be added.
Wouldn't it fry its cogs?!
I have a calculator that was invented in the 1600s. I think I am also set for the EMP strike/ nuclear world war. YEAH!!!!
Just imagine if this would had been invented 2000 years ago, it would blown everybody's mind
Some genius 2000 years ago may have been able to design something like this, but there's no way they could have built it back then. The engineering is too advanced. They'd need a way to make steel into extremely precise gears and all that for this to work. So yeah, minds would be blown. They'd probably all cry witchcraft.
@@carterwood4197 Yeah, precision is a technology of its own. This device can only be made in the industrialized world.
Ancient Greeks made the antiktera mechanism,which is quite the complicated machine,it's not far-fetched to think that a "Greek Curt" could be out there.
@@Bronze_Age_Sea_Person The components of the Anitkthera are much larger, and also somewhat simpler. It's a very surprising device to be sure, but it doesn't measure up to modern precision engineering.
They did, friend, and even more complex- the Anthikithera device.
it doesnt take much to realize it is indeed a magnificent little mechanical wonder.
I'd love to pull that out on my next exam and see the confused looks
hahahaha LOL
+Alfredo Moreno great input there hahahaha LOL
And then you'll have to calculate sin(π/7) and you'll be screwed. ^^ But I admit that it would be amazing
grenade!!!! everybody on the floor ;)
+Anim' Max by Mojert
If I am expected to use a calculator during an exam and I have forgotten to bring it then I just leave those uncalculated parts in symbolic form. =P
It's the solution steps that are important anyway, and I can always show those steps without making numerical calculations, since variables have nothing to do with specific numbers.
I'm an Electronics Technician and I love collecting vintage calculators, computers, etc.
This calculator (The Curta) is one of the most amazing designs I've ever seen.
Thanks for the video and memories!
This is soo beyond me. I cant even begin to think how someone could take mechanical parts and make a calculator like that. That man must have been some sort of genius!!!
What tha...? that's from the fifties? i thought it was some kind of revival!. Oh boy, one of the coolest things i've ever seen.
SHUT UP AND TAKE MY MONEY!!!!
I was gonna say that :(
you got over $1000
I was a SCCA Professional rallye driver in the early 1970s. My co-driver used a Curta to do all the time/speed/distance calculations. One of the wonderful things about the Curta is that you could, to some extent, set it up by feel (although we had interior lamps (red) for Curta, the Halda odometer, and Heuer timepieces). The Curta was tough, accurate, and easy to use - a work of art and genius.
I so want one of these now.
sadly they are super expensive
My grandfather grew up in Germany following the second world war and stayed there until the late 80s. I'm not sure where he got it from, but he gifted me one of these and every once in a while I like to look and see how much these things cost. I'd never dream of selling it but I always thought it was interesting.
Very cool. These were of course not cheap back in the day either- a friend of mine in high school had one but I couldn't afford it.
I have an Ohdner calculator of about the same vintage. It was invented in 1873 and works similarly, so the idea is an old one. But it's not a pocket device- it's the size of a small loaf of bread. The Curta is a wonder of mechanical elegance.
I remember going to a party at one of my physics professors' houses in college. He had an Odhner calculator and he gave it to us cold and challenged us to figure out how to do long division on it. We got it in 20 or 30 minutes.
Anyone else want to see a Matt Parker unboxing for this?
+Edward Sim Probably give it a 2 for accuracy.
Bear McBear MC Hmm, infinite cred though
Edward Sim you evil
I DO I DO I DO!
living in a digital world, i find a simple elegance in this... i wish that things like this were still made and improved upon.
Thanks to this video, two things have happened:
1) The value of Curta calculators have skyrocketed.
2) I now have a mechanical calculator :)
My late father bought a Curta Type II while living in Austria after WWII, and used it for many years to calculate estimated board feet while walking through his tree farms in Arkansas. I have it now and keep meaning to learn how to use it properly. It is the coolest thing I own, without question.
If you do 0 to the 0, does it generate electricity?
The world implodes.
Primus Productions Yes! Free energy!
+Primus Productions
0 to the power of 0 is just 1, though I'm not sure if the Curta would give the right answer as that's a more extraneous equation.
+PokemonTom09 numberphile has a video linked to 0^0, and its not 1
PokemonTom09 'twas a joke.
I saw an ad for this in American Scientific back when I was a Jr High School. I wanted one. Had no idea it would become a cult classic!
To me, this is more impressive than any electronic device that will ever be created. It's all mechanical. It "fits" in your pocket. And it multiplies faster than my computer starts up.
I'm sold.
These were very popular with land surveyors, my old boss had one, which he utterly treasured.
I loved this video and the Curta so much that I went out on eBay and bought one! Cost me $500. I hope it was worth it.
Really amazing! We need some company to do replicas of this engineering masterpiece.
Wouldn't that be something!
A relative of mine had one, I played with it as a child and when he died they offered it to me, but I wasn't interested at the time, still kicking myself every day for that ...
I know this video is two years old, but I'm over here nerd-gasming. I collect antiques, especially devises that display amazing mechanical engineering like this one. I'm on the prowl for one now, thanks!
I wish someone would make these. I would buy one.
i could sell one for you but if you check the price in ebay its pretty expensive
+Renner just search curta calculator from ebay mine is bot for sale yet
You'll be able to print one up for yourself in a few years.
+Chrstphre Campbell
Hmm... we just need someone to design it in SolidWorks or AutoCAD, I guess. (Would 3dsMax, Maya, or Blender work?)
Maybe I'll do it one day if nobody else has.
ua-cam.com/video/zh2Z11miQ0w/v-deo.html
Never mind. It's been done.
Too bad the only 3D printer I would be able to get access to is almost certainly incapable of handling the size or precision of those parts.
Sometimes I feel digitalization has been negative to the human race when you see these analog devices.
The Curta is digital technology! A slide rule is analog, but the Curta uses exact values represented as digits--decimal rather than binary as an electronic calculator would use.
"Effortful"
Not only does this channel provide us with amazing maths knowledge, we get an English lesson! Cheers.
A friend of mine had one in the late 1960s. Truly a beautiful machine
Divide by zero and it becomes a hand grenade.
I would be tempted to open it up. They should make a clear one
I am simply blown away by the ingenuity and engineering required to build a device like that which is so user friend
I wish they would produce them again. I think that this would be an interesting way to help children learn multiplication. With turning the crank of the calculator it makes it a physical action which would probably help in memorization and it would certainly keep their attention.
That amazing object is the epitome of form and function
This video is going to cost me $700 cause I definitely need one of these.
Found the manual online. For everyone wondering about division it's done the same way as multiplication, except looking for the correct output instead of the correct multiplier. So, 42/7 is calculated by setting the input to 7 and keep adding 7 to the output until 42 it reached the multiplier (white) is the answer. The manual also explains things like division with decimals, etc. And with addition, and multiplication all kinds of things are possible including square root, sine and cosine. =)
Such an astounding contraption! Beautiful look, love the little noises it makes.
That blew my mind. I want one.
amazing!. had to go into ebay and look, but the prices are a bit too high for me :-)
The design of it is timeless, it looks really ace!
When I first saw it I thought it was a modern revision. Truly timeless.
This thing honestly inspires more awe than your average 5 dollar calculator but the fact that something as complex as this calculator can be miniaturized into something as big as your thumb thanks to electronics is very much insane
My best friend in the 60's-80's (sadly died in '86) was a champion rally navigator, and, indeed, had a Curta, and made special odometers, with precision gear trains, to get exact distances from a front wheel(in rear-drive cars) speedometer drive cable...even had 3 or more odometer sections for keeping track of section totals, upcoming turns, and all of that 'navigating stuff'...
A steampunk hipster's dream
And very soon the quantum computers shall be old dust .
I might not be the biggest math guy, but being a retro-tech man and a machinist... I have always wanted one of these since my grandfather tried to teach me math with slide rules and had me work with a telex. It's on my top 10 list of things to have in my possession by death and one of the top three to pass down to my children. Thanks for doing the light puff piece on it, it's difficult to explain the concept of a mechanical computer to newer generations with out a working example.
The statement is not an oxymoron. Mechanical means that it physically moves stuff with force, while digital means that it deals with discontinious numbers.
Put 999999999 x 999999999 into it.
+JJ Warner I did 99999999x999999999 (the turns counter only has 8 digits and I didn't want to count 90 extra turns for nothing) and the answer has overflowed (obviously) so the result register reads 999998900000001 which is accurate for the digits it can actually represent. The full answer is 99999998900000001 (I'll save everyone the trouble the Curta overflows the leftmost 2 9s)
MrRtkwe You must be fun at parties.
JJ Warner Didn't take long just 72 crank turns. It's a fast little machine.
+MrRtkwe Im pretty sure that isnt the right answer.
Matthew Bolan You'll have to be more specific. Which number there's many in my post? The first one definitely isn't right it overflowed but the digits that were there are right. And the second is direct from google. Also notice I didn't do the exact number OP asked for because it's more than the turn counter will hold.
But does it run Tetris?
Truly a thing of beauty.
I think I just found the world's best fidget toy ever.
Very beautiful...but looks like a granade!
I am so glad i am not the only who thought that!
If you pulled that out in school you'd be kicked out
It's sometimes referred to as the math grenade.
Pepper mill. Would you like some cracked numbers on your salad?
There was one on pawn stars
I believe many models of this type of calculator also had a switch to make a single turn subtract, so you could divide by clearing, adding the numerator, and then subtract the denominator until the total is less than the denominator.
The value in the total display is the remainder and the value in the white count (number of turns) display is the quotient + 1 (because the initial addition added an extra turn).
Wow, I wish these were still in production.
what happens if you exeed the maximum number it can calculate? Does it go back down to zero?
It overflows--the most significant digit is lost.
Display: 6
Functionality: 1 (can only do multiplication)
Accuracy: 4 (no decimals)
Ergonomics: 7 (fits quite snugly in the hand)
Cred: 11
Durability: ???
I see that you are also a big fan of matt parker's calculator reviews
Only 11 cred?! It's easily 20 or 30!
7,8/10 too much calculations
ihathtelekinesis no, you can definitely do more than just multiplication
ihathtelekinesis it can do all kind of division, substraction, multiply, square root, add, and factorize
It looks like the kind of stuff that my grandfather would have in his house. Love you :3
Yes it is . For substraction you rotate the opposite way, and division is multiple substraction:
24/3: Insert 24 into the top register, the accumulator, (this involves zeroing it and adding 24), then set the input register to 3 and start substracting it from 24 by rotating the handle "the wrong way". When the accumulator reaches 0, read the amount of turns in the counter register. That's the result.
You shift the whole thing when dividing a large number.
No, so subtract you pull the handle up. You always rotate to the same direction.
I would love to have one BUT $1,600 ON AMAZON!!!!????
I just bought one for €900 on eBay. Gotta be patient and you can usually get better prices on the smaller local markets.
When he states "digital" folks he doesn't mean "electronic" LOL.Digital as in numerals.
Square root of n, one method:
Successively subtract the odd numbers from n starting with 1. Every time the odd number can be subtracted without going negative you add 1 to a counter. That will eventually give you the square root, rounded down to the nearest integer. If you want more precision just put an even number of zeros after n and move the decimal point left in the answer 1/2 of the number of zeros you put after n.
that is even more amazing than a digital calculator that can make curves and solve functions. This is grand.
Made in Liechtenstein, I wonder what else has been made there in the 20th century. Doubt much is being made there now.
Neutrik is making great plugs ther for stage-use
Hilti (hammer drills and other professional construction tools) is baed in Liechtenstein
anyone has a link where i can buy like a rip off?
Rip offs dont exist unfortunately
Before electronic calculators you could use this machine to do any arithmetic. You would only need the standard tables for the trig and logarithmic functions, which were around long before this machine was invented. The mathematicians, physicists, chemists, etc., could use calculus, statistics, etc., to derive equations, then use this machine to calculate results in the application of the equations. This was a huge leap beyond the slide rule, partly because it enabled more precise results.
You didn't mention the fact that it subtracts by adding!
The way that this subtracts is so ingenious that modern computers still use the same method.
Neat!
But... how do you divide numbers?
Guan Huang Subtract until you get to zero, and see how many times was that. :)
-_-
Guan Huang That's how computers divide, btw.
msolec2000 most computers have up and down shifters which can double or half binary values a more efficient way is to shift first then subtract making the calculation faster but using more memory like to times by 10 you shift x three times save to memory then shift x 2 times save to memory and add both of these together so unless a computer doesn't have shifters or maybe it has a barrel shifter allowing it to shift more than once at a time allowing it to do division even faster and no matter how high the number is in the same amount of time so there's no repeat until 0 otherwise large numbers would be slow and small numbers would be fast
Well, that shifter is in the Curta too, the top carriage. It just multiplies by 10 instead of 2.
What would happen if you put 999,999,999 (all 9's possible) times x (any number).
I know, engineering speaking there is a limit, but what would Curta do/show? Numberphile
Javier Reyna it would overflow to zero then continue the calculation
It overflows--the most significant digits of the result are lost; the rest of the digits are correct.
I loved the interesting bit of trivia at 4:25 about the Curta's utilization among rally drivers and their co-drivers!!! I love when the worlds of automobiles and motorsport collide with the art of science and mathematics. This kind of innovation is truly what set the automobile apart from horse-drawn carts and wagons. NOW I MUST SAVE UP FOR A CURTA CALCULATOR!!!! (Thanks, Numberphile!! Lol)
This is a beautiful machine and works so smoothly and elegantly.
How do you divide using that calculator?
The switch on the side changes the crank from adding to subtracting. With the switch in the subtraction position, it counts the cranks needed to drive the top register to zero. (You have to look at the register to see when you pass zero.)
David Fink I figured there HAD to be a way. Antique mechanical adding machines can also subtract and divide. Even though they're called "adding" machines, they did a lot of other operations by entering in "complimentary numbers" and using other tricks. It's amazing what these mechanical devices were capable of doing once you learn how to use them.
I have a Curta --used it for surveying calculations in the field.
I didn't even know that this thing existed. Thanks, numberphile.
I don't know what this says about me, but that is probably the coolest thing I have seen in recent memory.
Wow, this is an absolutely beautiful machine.
So elegant and functional at the same time. Truly a marvel of Austrian engineering.
Want. So. Badly.
Electricity doesn't randomly stop working after an EMP, it just frys all electronics more advanced than a vacuum tube. As for reactors, most of them have a manual physical arrest device or a chemical process that arrests the process when the reactor breaches a certain temperature. Provided that the rest of the reactor doesn't melt or break in half during the apocalyptic earthquake soon to go.
Must get one.
This is genius. Good work Sir Curta.
The Curta crank can only be turned in one direction. Normally the counter will only count up as it is turned. If you want the counter to decrement for subtraction or division, you slide that switch. It reverses the movement of the counter.
I'm amazed of how this things even looks :O
holy. shit. That is amazing. No electricity, all mechanical. Unbelievable genius of engineering.
I stand corrected, in this model, to substract , you pull up the handle and rotate the right way.
For the record, there were many kinds of desk calculating machines that did the same thing at that time and much earlier. This was probably the most compact one though.
Holly genius that man, how is even possible to imagine something like this. Amazing!
What's amazing is how up-to-date the design of this calculator is. It's design is so modern it looks like it could have been recently manufactured.
What a beautiful little thing.
Tip: If you want something like this to play with but can't afford to pay 1000 € or more (this seems to be the lower limit on German eBay right now), you can look for a desktop calculator based on the same principle. With a bit of luck you can get e.g. a Brunsviga or a Schubert for 50 € or less.
It can do basic addition, you just have to change 534 to 495 during the first time you turn it round and the second time. And if you want to use decimals just change 0,7 *3,6 to 7*36 and divide by 100 in your head.
What a cute little machine. Truly a stroke of genius.
The Curta has built-in 'functions' to speed up multiplication. Also you can use tables of logs to speed up multiplication, the 13th root of 1 million etc.
Anyone designing the next generation of 3d printers could use this as an ultimate test. Imagine trying to print a 3d working model in one solid peice and having it work.
What a beautiful little thing. I'm astonished by all mechanized things, and this was pretty, clean and it was working really good! Great work on that machine seriously!.
After watching this video and Adam Savage's, I just had to had one. Managed to pick one up for a fair price and I gotta say it looks even more amazing in real life and feels great to use. No regrets (though I doubt I'll be using it for any real calculations ;))
Imagine using one of those in a rally car.. "how much farther until we have to refuel?" *Cranks Furiously*
Division is possible because you can multiply decimals the way you described.
For example:
To find 10/2 you would find 0.5 multiplied by 10.
Or a more complex example 73/8 would be 0.125 multiplied by 73.
You could even use the device to find the value of say 1/8. If you inputted 8 and turned 125 times you would get a value of 1000, meaning 1/8 = 125/1000 = 0.125
Much simpler division methods could be done through subtraction, mechanical subtraction can be made in the same way as addition