Folks, no need to argue about colorful alternative mathematical theories - the thorny problem of division by zero was solved for good over 100 years ago by the rigorous development of infinitesimal calculus. Which says: division of a positive non-zero constant by something that tends to zero, tends to infinity [added note: dividing "zero by zero", or more exactly, two things that tend towards zero, is more complicated: it can give zero, infinity, or anything in-between, but that's for another time...]. So the calculator sort of gives the right answer, using almost the correct method: trying to fit an infinitesimally small number into a big one, and finding it fits so many times it goes to infinity. I would put it in the category of happy mechanical accidents.
@@banana1231234 Or whose math knowledge is derived from a Google of Wikipedia... People in the comments are just mixing up stuff hopelessly. Although it is true that for the purpose of pure mathematical logic dividing by zero is not allowed, that's not what matters in practical computer calculus. Dividing by zero can be a programming error, but in most cases it is the result of an underflow in a valid calculation, when the divisor got vanishingly small, and got rounded off to zero. This is why a correctly implemented IEEE compliant computer math library will return Inf (for infinity) if you divide by zero, and not NaN (not a number). However, it will return NaN if you try to divide 0 by 0, because there is no way to know what the result should be (see my top post). Both are the correct and standardized results for modern machine computation. So you could say the Friden calculator does a fair job of being IEEE compliant way ahead of its time...
I wouldn't even call this a mechanical accident. This result is actually logically consistent, and it correctly models the math that computability theory is based on. It's more of a mechanical consistency! That said, for practical purposes, you would want to program a failsafe or an exception in this case because infinite recursion is not useful for anything.
There was another "dangerous" phenomenon on this or a very similar Friden machine: The instructions warned against holding down the multiply button. At age 12 or so, around 1963, I could not resist the temptation to challenge this rule. The machine would make terrible noises and then jam up so badly that the service person had to come fix it!
What really fascinates me is that they implemented this division algorithm *fully mechanically*. It would be just a couple of lines in any programming language, but with springs and rods... Wow. Hats off to the designers!
The actual electronic logic gates behind dividers inside coding languages are probably the exact same if not similar to what this mechanical calculator does
@@enderkoregameing8090 yes, they are, only base is 2 instead of 10. I find this machine impressive too, but compared to amount of smartness put in electronics and software it's just piece of cake.
I had an older professor for linear algebra and he once told our class about what he and his classmates would do when they got bored in their physics labs. He said they had a mechanical calculator around and they’d divide by zero on it and the calculator would start chugging without end. I didn’t get why that would be pleasing to do until today. Truth be told, I’d do the same as well
When I was an intern, we got a new one of these in the engineering department. I hesitate to disclose the year. I was young and now I am old. Who else but a college intern would try dividing by zero on the first day of its use? Off the Friden went to the unstoppable quotient races. After a couple of minutes, I realized there was no way provided to stop it. No "div-stop' key on our early model. I had to pull the plug. No one else could stop it, despite repeated attempts. It had cost so much, all were afraid to break it. We had to call for Friden service to reset the machine. He explained that it was a good thing I unplugged it because the internal motor was only rated for 'intermittant duty.' No, it probably would not have caught fire, but it would have overheated, likely damaging the motor windings. Expect smoke! Epilogue: We later got the first Friden model that could do square route. I swear you could have sold tickets to watch that machine work. Basically, it did square route the same way we would do it on paper, a sort of trial-by-square. The carriage did this amusing dance, but sure enough, it worked. Square route was rather "like a dog walking on its hind legs; it didn't do it well, but was amazing it did it at all." And it achieved the correct answer.
@@jimshaw899 Heh. We all make mistakes. I wasn't sure if it was a dialect thing or something, but I was pretty sure "root" was universal math language 🤔
By the time I went to school, they no longer taught that square-root method that the Friden used, so I never learned it. I tried learning it and doing it by hand just recently, tried to see if I could approximate the square root of 2 and, wow, it's fine for small numbers of output digits but it gets harder rapidly as it goes on. (What I *did* learn, outside of school actually, was the other method where you take your first guess, divide it into the number, average your guess with the result and get a closer guess, then repeat. That actually is more efficient at least for large numbers, since it converges pretty fast; it's equivalent to Newton's method for finding the positive real root of x^2-c=0; but it was harder to automate with a mechanical calculator, since you'd need to store and recall intermediate results while you do whole long divisions.)
There were several ways you could get those machines into an infinite or else very long calculation; the div stop button was handy for aborting most any calculation if you realized that you had fat-fingered the inputs before it was finished thinking. This is also what happened with early computers that didn't have a check for divide by zero. They would just "lock up" in an infinite loop until someone hit the reset key. They didn't blow up, or go insane, or any of those things that newspapermen and authors and Hollywood screen writers claimed they did.
It's probably still how it's done, except the 'stop div' is automatic and it just happens in fractions of a millisecond, now. Things don't work on magic. Computers are still just essentially very fancy calculators.
If someone was dumb enough to accidentally put a mechanical calculator like this into a loop, get distracted and walk away for a coffee break, it might damage the machine. The electric motor is probably not designed to dissipate the heat caused by continuous non-stop operation. So the motor could burn out, releasing a puff of smoke and the smell of burning insulation. Not as dramatic as flames shooting out, but it is a realistic scenario.
My mother had (likely still has) a cell counting “calculator” that was used to manually count blood cells in the field while staring into a microscope, touch-type-style. It didn’t have a motor, but it sure did clink-clunk, and it even had a bell. There was a little crank on the side used to reset counts to zero. It was “portable” - it’d fit into an oversized purse, turning into a first-class bludgeoning weapon. The case was made from bent heavy sheet steel.
genericwhitemale both actually, I love the mechanical sound. The sound it makes when he presses the keys reminds me those old white keyboards from way back. I love the noise it makes counting too.
My father had one of these at work. I did this same experiment. I freaked out when the calculator started smoking. I don't remember what I did to make it stop. I was sure I was going to get in trouble.
Because Division by 0 approaches infinity. What a beautiful mechanical way of expressing that. Note: dividing by 0 does not =infinity because infinity is not a number. Dividing by 0 _approaches_ infinity. If this was not so all math would be broken.
no you can "approach it" without hitting it. Approaching something means you are going towards it which doesn't mean you have to be any close. It isn't "close"to infinity but APPROACHING. The terminology is correct
@@JohnSmith-eo5sp They were expensive at first, though. I was just reading up on the HP 9100, the first really successful scientific calculator (with trig and hyperbolic functions, etc.; it was also fully programmable though there had been a few successful programmables already) from 1968, and realized it cost twice as much as a new car.
Grandpa had one of these at the company... he could get it to play a drum cadence... some certain numbers, not sure if div or mult, played a nice cadence! Enjoyed the video, thanks for posting!
It's called the Friden March. I think I found how to recreate it. Need to make video of it. [Edit: I did, here: ua-cam.com/video/-MLQ0yI1BrQ/v-deo.html ]
When I was a 10 years old child, my father gave me a strange old digital calculator, wich had that strange function to hide the floating point until you press a button to show the fractions. When I divided some number by zero, it did not showed "E" or something like that.. just stucked on zero...but imagine what I discovered that when you pressed the floating point option. It was just like you evidenced in this mechanical calculator. Amazing! It took to me 35 years to find another machine that explained to me what was really happening, since not even my math professors could do it. Thanks a lot!!!!
@mario mario Black metal double pedal double bass literally sounds like a machine gun. Just look up "Laser Cannon Deth Sentence" by Dethklok to see what I mean.
I remember using a hand cranked Ohdner machine at school some 45 years ago. Division was exactly the process your machine went through, except all movements had to be done by hand. I nearly broke my wrist when I tried dividing by zero.
Once, I was writing a program for a PLC -5, there was a division. Shortly after I compiled and went back to run mode, the PLC faulted shutting the whole plant down. Upon investigation, I found that the denominator sometimes would go to zero, which caused the fault. I solved the problem by restricting the range of the denominator to >1.
Quite accurate. Dividing by a big number results in a very small result. The opposite aplys, where dividing by a very small number gives a very bug result. Zero is a very, very, very small number, so you get a very, very, very big number, thus infinity
Two great things regarding this video. Firstly this is one of the best videos I’ve ever seen on UA-cam and secondly this machine is one of the coolest and most beautiful things on earth!!!!!!!!!!!!!
Hey, this brings back memories. Back about 1963 they had a whole room full of these at the computer center in our college (used for classes, I guess). Some of us were in there once and one of us (it wasn't me) suggested we see what happened if you divided by zero. As you see in the video (spoiler alert!) it starts cranking and cranking. After a couple of minutes we got nervous and unplugged it before it could catch fire. Probably when it was plugged back in, it would keep cranking... I just hope whoever was in charge of these knew about the zero-divide escape button!
Brings back fond memories. My grandfather had two of these of which I inherited both of them slightly different models. That was 40 years ago I was a teenager and I spent many hours playing with these machines not fully understanding what they are doing. I don’t ever know what become of the two that I had. But I sure miss playing with them.
*machine implodes and creates a black hole* That is a beautiful machine, btw. The engineering that must have taken to build that is undoubtedly staggering. I know even micro processors are still machines with moving parts, but with this bulky, heavy machine, it's much more satisfying to watch.
Nice demo!! The distinctive noise of these machines is, I believe, the source of the phrase, "crunching the numbers." BTW, what you're calling "overflow," I would call an "underflow," because it results from a subtraction that takes the accumulator "below" 0. Addition that gives a result that takes the accumulator "above" all 9's, would be an overflow. But the distinction is somewhat moot because, in practice, the machine produces leading "9"s, as though it's a very large number, even though that really means a negative number. Fred
Stack overflow is the correct terminology. Rolling under is considered expanding beyond the bounds. This is a common glitched function in videogames; sending a variable outside of its dimensions resulting in a binary rollover. Whether the game is tricked into subtracting without stopping at zero, or adding after there are no leading bits left, it's the same core computational error. I liked the term 'stack underflow' at one point myself, but you struck the point of the lack of difference in the distinction.
@@TheJacklikesvideos The use of the term stack overflow is used to mean to overflow the stack, a specific type of memory. If you had 255 overflowing to 0 after an increment, that would be an integer overflow. -128 going to 127 from a decrement would be an integer underflow.
@@TheJacklikesvideos This has nothing to do with stack. We are talking about integer underflow or overflow here. Stack overflow is about accessing memory that doesn't belong to stack, it has nothing to do with arithmetics.
I worked for Friden Inc inc 1972 in Houston Texas. I repaired the rotary calculator among their other products. Friden made a Nixie tube electronic calculator in 72 and the mechanicals were slowly being phased out. The electronic calculator was $1500. in 1972 and that was very expensive.
Hello Marc. I have a small challenge for you: can you find out what numbers Jack Lemmon entered on the Friden to get that exact drum beat, when the carriage moves to the left 1, 2, 1-2-3, 1, 2, 1-2-3 spaces ? Being a drummer, I'm curious what those numbers were... The Friden could make a primitive "programmable" mechanical drum machine ! lol
[Edit: Friden March video here: ua-cam.com/video/-MLQ0yI1BrQ/v-deo.html ] @AlainHubert: Great catch! I had not noticed the rhythm on the video, but that's indeed what makes that scene work so well. I'd just put in something like 5551155511 and divide by 1. It will do 6 trials until overflow when on the 5's and just 2 trials for the 1, as explained in the video. That should give you the rhythm you are looking for! [Edit: I just tried it, works great, it's hilarious. It must be what was called the "Friden March". I need to make a video of it!]
In the 70s I owned a hand-held, battery-operated calculator (Texas Instruments?) that would count from 1 on up if I divided by zero. Like a stopwatch. Always fascinated me. This is the first concrete info I've ever run across that explains why. Thank you!
I remember going to my Dad's place of work and watching him use this machine. He was very experienced in using it, so all you heard was the clackity clack noise in the office. I miss my Dad.
This is brilliant machine, brilliantly explained. Naturally it's not a "simple machine" but I do like early technology. I sailed on a WWII Victory ship (1944). We could make turns on the propeller without one Candlelight of power available.
It's very interesting, most calculators say error, but it should really just check if it's divided by 0, if so, say infinite. Because 1) we do use infinity for limits and summations for convergence of sequences. And 2) If you do 1/0.01, you get 100, if you do 1/0.001, you get 1000, so as you get closer to 0, your number gets higher (which logically would be written as infinity). So it's reasonable this machine would do an infinite loop.
Dear god, my father brought one of these home when his office upgraded! I used to do the divide by zero thing, he must have shown me. I haven’t thought about this in years. Cheers.
I watched the whole video because you risked such a valuable antique piece of equipment for our entertainment! Edit: That's an incredible piece of machinery. It sounds beautifully mechanical, like a steampunk factory. :)
when I was a little kid my father had one in his office.. I would push all the 9s then multiply and then all the 9s again... how long would that take to complete???? and was there a way to stop it????
Learned to use a Friden in high school (1964) business machines class. Mr. Pichel was very protective of this expensive piece of equipment. The standard was. “You jam my machine and you clean the mimeograph machine for a month. A very dirty job, for those of you who are old enough to know what a mimeograph is. LOL
When I first saw this, I never expected I'd have one, but the other day on the way to school I saw two at an antique shop just sitting on the asphalt. Turned out to both be ST10's that were left outside. After school, I rode my bike over there bought both for a total of only $30 and I'm now trying to restore them. Will definitely do this exactly once I finish.
Ngl this has to be to the coolest thing I’ve ever seen. Something that we never get to see being done by our modern electronic calculators. I’d love to have one, purely for when I forget what 2+2 is
This is probably more complicated than the modern electronic calculator. Loved the noise so much, imaging sitting in an exam and using this to do calculations.
My dad got a surplus one of these for our home office when his company was upgrading in the 1960's. For the longest time if touched it, I got 'one around the ears'. However, I'd play with it when they weren't home. Even dividing by 7 was scary. Yours is a newer version than we had. Mom must have divided by zero by accident. He un plugged it and that seemed to stop it. Later, we weren't allowed to use it for our math homework as he wanted us to be good at mental math. Thanks for the memories.
Great video and explanation! The game Human Resource Machine gave me an intuitive feel for iterating simple operations to form a complex process, and it was great to see the real thing here.
Honestly the proper division and the noise it makes as it repeatedly underflows and reverses one step is more fascinating than dividing by zero. I've seen mechanical counters going up before.
I used these things at UCLA prior to the introduction of digital computers -- they were then installing the two huge IBM 360 Model 95 mainframe computers between the Engineering and Math Buildings in a new three-story building.
As Air Force orbital analysts in the mid-'60's, we used Friden calculators ... When we performed a certain calculation -- I believe it was a zero division -- the model we used would go into a cadence we called the "Friden March" ...
Many years ago, I worked with a really weird Friden "system" which consisted of 3 or 4 of these in series(?) inside a cabinet next to a standard Flexowriter keyboard/paper punch. I believe it was called a "computator" and it did all sorts of things: billing, general ledger, inventory etc. It was a royal PITA, but it got the job done. I wish I could find some info, such as programing etc, but it doesn't seem to exist any longer.
I grew up down the street from the Friden plant that made that machine. We thought it would be a 'lifetime' job to work there. They were said to treat their employees VERY well. Then came Silicon Valley and the end was quick and merciless.
A mechanical calculator like that is more impressive than modern electronic calculators because of the amount of engineering that went into constructing something like that.
Do you realize there's more engineering in digital electronics than these? It's just more hidden in electronics... It's probably just because you think it sounds cool, but you might wanna reword it
@@floppaquest4916 and how do you think the lines of code are executed behind the scenes? Every computer is still to today an electromechanical wonder.... (not wanting to say that the pure mechanical isn't top notch - typing this on an old style mechanical keyboard ...
@@floppaquest4916 a CPU which run those code lines are far more impressive than this mechanical machine Heck, the language behind those code lines are just as complex as this machinery Your comparison is not apple-to-apple
right, i commented too early, i saw that later on... I saw another mechanical calc vid, and I guess what's happening is that it's trying to subtract zero from the first number, but can't, so it infinity loops. (i forgot if you said that in your video or not, then again, that might not be how your model works)
This video brings back some memories. Around 1970 I was going to a Junior College and one of the courses I took was course on learning to use the Friden Mechanical calculator. The calculator in this video might not be the same model that the Junior College had, but it sure looks the same. These calculators made plenty of noise when doing calculations. This was the time before electronic calculators were developed. I suspect that now about the only place one of these Friden Mechanical calculators can be seen is in a museum. Maybe a few of these calculators have been restored to running condition.
Your job skill wouldn't have lasted long. Just 4 years later my college course was on operating a computer. IBM had a big manufacturing plant for their 360 and 370 machines at the time, right next to SUNY Binghamton. THE computer existed in THE Computer Building, attended by the high lords of senior programmers. I learned how to use punch cards the cutting edge real time remote time-sharing on fan-fold paper. Quite a gap in 4 years, although I'm sure there was a transition period before small companies could cover to computers. But my skills wouldn't have lasted much longer, punch cards were on their way out. The basic programming concepts would have lasted, but I never pursued that field.
@@donjones4719 The junior college was the first and the last place I saw these Friden Mechanical Calculators. This junior college was the first and last place I also learned to program an IBM1620 computer. I ended working 34 years at the Los Angeles Department of Water and Power in Generating Stations operating the large power plant equipment.
What’s important is that the engineers that made this machine understood how to divide by zero, and were able to implement that into a device. This machine’s soul purpose is to show us what happens when you divide by zero.
UA-cam algorithm went crazy to recommend this video to me :-D What I really take with me from this video is that Pi is 355 diveded by 113! Great knowledge :-D
@@8180634 they work the same really. Decimal gates instead of binary gates. Its like a processor gate translated to mechanical movement, rather than electricity passing through silicone.
@@alexandrutereify Indeed I get how it's mechanically possible, but having to figure it all out on paper, design all the parts on paper, make the parts all fit together perfectly as a package on paper, etc.. you can't simulate it but it's got to work, that's a whole lot of memorization and work!
1:57 Lots of foresight. Thats great!!! I remember working for this old guy he was 72 some 23 years ago when I was 14 and he talk about using one of these machines glad to see on in use.
As a young engineer in the 1970s I was asked to make some enhancements to a FORTRAN program I had inherited from a brilliant colleague. Everything done with punch cards of course - submit the deck and wait for the printout. The colleague had not read Dijkstra's paper and had created some serious go-to spaghetti with packed bit fields adding to the headaches. The thing would often crash and create an octal memory dump. One of my officemates dug an octal desk calculator out of storage - I think it was an SCM Marchant. A lot easier to accidentally cause division by zero than with the Friden, and no DIV STOP key, and it would start smoking in 15 or so seconds. I luckily discovered that keying any number into the keypad while it was running would change the divisor and cause it to stop. My officemates were not amused, but I did eventually get the program working.
Folks, no need to argue about colorful alternative mathematical theories - the thorny problem of division by zero was solved for good over 100 years ago by the rigorous development of infinitesimal calculus. Which says: division of a positive non-zero constant by something that tends to zero, tends to infinity [added note: dividing "zero by zero", or more exactly, two things that tend towards zero, is more complicated: it can give zero, infinity, or anything in-between, but that's for another time...]. So the calculator sort of gives the right answer, using almost the correct method: trying to fit an infinitesimally small number into a big one, and finding it fits so many times it goes to infinity. I would put it in the category of happy mechanical accidents.
People who never took a calc course in college sound off
CuriousMarc, Isn’t this the kind of thing that summons Great Cuthulu?
@@banana1231234 Or whose math knowledge is derived from a Google of Wikipedia... People in the comments are just mixing up stuff hopelessly. Although it is true that for the purpose of pure mathematical logic dividing by zero is not allowed, that's not what matters in practical computer calculus. Dividing by zero can be a programming error, but in most cases it is the result of an underflow in a valid calculation, when the divisor got vanishingly small, and got rounded off to zero. This is why a correctly implemented IEEE compliant computer math library will return Inf (for infinity) if you divide by zero, and not NaN (not a number). However, it will return NaN if you try to divide 0 by 0, because there is no way to know what the result should be (see my top post). Both are the correct and standardized results for modern machine computation. So you could say the Friden calculator does a fair job of being IEEE compliant way ahead of its time...
I wouldn't even call this a mechanical accident. This result is actually logically consistent, and it correctly models the math that computability theory is based on. It's more of a mechanical consistency! That said, for practical purposes, you would want to program a failsafe or an exception in this case because infinite recursion is not useful for anything.
@@davidgrover5996 Nah, only the smaller one attends to these matters
Teacher, "You are allowed a basic 4 function calculator for this exam."
*Walks in with this.
Half of the other attending students will bless you, the other one curse you :)
...In the middle of the exam, everything is quite....
*CLONK CLONK CLONK CLONK CLONK BLING*
*CLONK CLONK CLONK CLONK CLONK BLING*
*CLONK CLONK CLONK CLONK CLONK BLING*
@@vladen14 hello fellow thinkers who were searching for this comment
Everyone would kill you if your brought this into a class
Imagine someone trying to cheat
The Div /0 command allows you to oil the mechanicals and then you can cancel the command once oiling is complete.
who knew, huh.
Breaking math to fix the math machine.
Wow
@@vaskedagame880 want to do some breaking math?
@@vaskedagame880 oiling is not fixing.
There was another "dangerous" phenomenon on this or a very similar Friden machine:
The instructions warned against holding down the multiply button.
At age 12 or so, around 1963, I could not resist the temptation to challenge this rule.
The machine would make terrible noises and then jam up so badly that the service person had to come fix it!
Ohhh, the things we do at 12...
@@sophiacristina Getting in shouting matches with strangers on BO2
@@AverageAlien Haha, in my case it would be Quake 1... :)
whitest name I've ever heard
critical error occurred.. XD
So the inventors added an extra Anti-Idiot-Button. Clever XD
The problem is there will always be a better idiot.. Can other infinite loops be found within the calc's capability?
AlfonsoB probably not with the basic functions.
AlfonsoB exactly, always remember, "if you design something idiot proof, nature will create a better idiot"
true XD
AlfonsoB idiot.*
What really fascinates me is that they implemented this division algorithm *fully mechanically*. It would be just a couple of lines in any programming language, but with springs and rods... Wow. Hats off to the designers!
This is only truly possible an a programming language with lazy evaluation.
well, yeah, that would be impressive if we could totally forget thousands of people who designed modern computers and all the programming languages...
The actual electronic logic gates behind dividers inside coding languages are probably the exact same if not similar to what this mechanical calculator does
@@enderkoregameing8090 yes, they are, only base is 2 instead of 10. I find this machine impressive too, but compared to amount of smartness put in electronics and software it's just piece of cake.
hardware and software aren't that different ;)
I had an older professor for linear algebra and he once told our class about what he and his classmates would do when they got bored in their physics labs. He said they had a mechanical calculator around and they’d divide by zero on it and the calculator would start chugging without end. I didn’t get why that would be pleasing to do until today. Truth be told, I’d do the same as well
When I was an intern, we got a new one of these in the engineering department. I hesitate to disclose the year. I was young and now I am old.
Who else but a college intern would try dividing by zero on the first day of its use? Off the Friden went to the unstoppable quotient races. After a couple of minutes, I realized there was no way provided to stop it. No "div-stop' key on our early model. I had to pull the plug. No one else could stop it, despite repeated attempts. It had cost so much, all were afraid to break it.
We had to call for Friden service to reset the machine. He explained that it was a good thing I unplugged it because the internal motor was only rated for 'intermittant duty.' No, it probably would not have caught fire, but it would have overheated, likely damaging the motor windings. Expect smoke!
Epilogue: We later got the first Friden model that could do square route. I swear you could have sold tickets to watch that machine work. Basically, it did square route the same way we would do it on paper, a sort of trial-by-square. The carriage did this amusing dance, but sure enough, it worked.
Square route was rather "like a dog walking on its hind legs; it didn't do it well, but was amazing it did it at all." And it achieved the correct answer.
I don't think I've ever met an engineer that calls it a "square route"
@@AureliusR Good grief! Did I write that? My face feels hot. I'll blame it on Grammarly. I should surrender my PE licenses in OH and FL.
@@jimshaw899 Heh. We all make mistakes. I wasn't sure if it was a dialect thing or something, but I was pretty sure "root" was universal math language 🤔
By the time I went to school, they no longer taught that square-root method that the Friden used, so I never learned it. I tried learning it and doing it by hand just recently, tried to see if I could approximate the square root of 2 and, wow, it's fine for small numbers of output digits but it gets harder rapidly as it goes on.
(What I *did* learn, outside of school actually, was the other method where you take your first guess, divide it into the number, average your guess with the result and get a closer guess, then repeat. That actually is more efficient at least for large numbers, since it converges pretty fast; it's equivalent to Newton's method for finding the positive real root of x^2-c=0; but it was harder to automate with a mechanical calculator, since you'd need to store and recall intermediate results while you do whole long divisions.)
355 / 113 = PIE? And this whole time I have been using an oven ...
It's an approximation. It is not actually the pie as pie is an irrational number which means you can't give its value in a division form.
My first thought: Why have you been using an oven?? What even does that mean... My second thought: I'm so dumb...
Csaba Kocsis by definition Pi is the circumference of any circle divided by its diameter.
TheMangoMangoMango you are right. Let me correct myself. Cant be given in of form of division between two integers.
Haze Anderson Pi, and no... It's approximate to pi bit it is not pi
EDIT: Oops, I didn't read the whole comment
There were several ways you could get those machines into an infinite or else very long calculation; the div stop button was handy for aborting most any calculation if you realized that you had fat-fingered the inputs before it was finished thinking.
This is also what happened with early computers that didn't have a check for divide by zero. They would just "lock up" in an infinite loop until someone hit the reset key. They didn't blow up, or go insane, or any of those things that newspapermen and authors and Hollywood screen writers claimed they did.
Wait a second. What 'early computer' had a hardware divider?
Siana Gearz : This could happen with software algorithms, not just hardware implementations.
Siana Gearz well, you recently watched a video about such a device....
It's probably still how it's done, except the 'stop div' is automatic and it just happens in fractions of a millisecond, now. Things don't work on magic. Computers are still just essentially very fancy calculators.
If someone was dumb enough to accidentally put a mechanical calculator like this into a loop, get distracted and walk away for a coffee break, it might damage the machine. The electric motor is probably not designed to dissipate the heat caused by continuous non-stop operation. So the motor could burn out, releasing a puff of smoke and the smell of burning insulation. Not as dramatic as flames shooting out, but it is a realistic scenario.
My mother had (likely still has) a cell counting “calculator” that was used to manually count blood cells in the field while staring into a microscope, touch-type-style. It didn’t have a motor, but it sure did clink-clunk, and it even had a bell. There was a little crank on the side used to reset counts to zero. It was “portable” - it’d fit into an oversized purse, turning into a first-class bludgeoning weapon. The case was made from bent heavy sheet steel.
Smart weapon
It could be used to analyze the blood samples of victims who were beaten to death with it!
we still use clickers for manual blood and cell counting sometimes
You genius you have cracked perpetual motion!
It’s plugged in
@@SpicyWingsTV but how can we know
@@SpicyWingsTV wow you missed the joke
@@kjl3080 f u
That's incredible that they foresaw the whole information revolution and popularity of youtube etc.
I wonder if anyone has actually blamed Satan or another mythological creature for given infinite feat lololol
I won't believe it until I see the Like, Subscribe and Comment buttons.
Lmao at this. Made the video.
And all they did with that priceless information was make a button on a mechanical calculator for it, rather than become billionaires.
Clearly dividing by zero does NOT catch machines on fire. It gives you the ability to glimpse the future
Is it me or does anyone else find this incredibly satisfying to listen to?
It’s just because that sound is very similar to one which you can hear when the ATM counts the money you will get )
Роберт Шаманский pretty sure hes talking about when he presses the keys lol
genericwhitemale both actually, I love the mechanical sound. The sound it makes when he presses the keys reminds me those old white keyboards from way back. I love the noise it makes counting too.
Kind of reminds me a bit of the computer sounds in the first alien movie … it sounds so retro-futuristic! I love that
ua-cam.com/video/2ywWFvjE-yU/v-deo.html
You have a strange piano
A jewish piano
It's a flute
*its a iphones operating system*
It's a guitar
It’s obviously a noise silencer
My father had one of these at work. I did this same experiment. I freaked out when the calculator started smoking. I don't remember what I did to make it stop. I was sure I was going to get in trouble.
Because Division by 0 approaches infinity. What a beautiful mechanical way of expressing that.
Note: dividing by 0 does not =infinity because infinity is not a number. Dividing by 0 _approaches_ infinity. If this was not so all math would be broken.
Schner1 yup
What if we were to create a new variable, calling it N, that is equal to the number of numbers in aleph null? Would that equal infinity?
Dividing by 0 also could approach negative infinity.
You can’t approach infinity has it is infinite, approaching something that has no end not beginning is impossible
no you can "approach it" without hitting it. Approaching something means you are going towards it which doesn't mean you have to be any close. It isn't "close"to infinity but APPROACHING.
The terminology is correct
now people know when electronic calculators came out in the early 70's they were considered so amazing.
Desktop digital electronic calculators came out in the mid late 1960s
@@JohnSmith-eo5sp They were expensive at first, though. I was just reading up on the HP 9100, the first really successful scientific calculator (with trig and hyperbolic functions, etc.; it was also fully programmable though there had been a few successful programmables already) from 1968, and realized it cost twice as much as a new car.
Nice to see one in action, we had one in my parents’ office when I was a kid. The sound of it working and the decimal slider brings back memories.
0 divided by 0
Calculator:
*MINIGUN NOISE*
A wonder of technology, even in this day
I know exactly how regular calculators work... but this thing is a fucking blackbox for me WTF
@@BenevolentPasserby yeah so true
This thing is certainly more interesting than a boring regular calculator
Grandpa had one of these at the company... he could get it to play a drum cadence... some certain numbers, not sure if div or mult, played a nice cadence! Enjoyed the video, thanks for posting!
It's called the Friden March. I think I found how to recreate it. Need to make video of it. [Edit: I did, here: ua-cam.com/video/-MLQ0yI1BrQ/v-deo.html ]
I should subscribe for this one I guess
CuriousMarc My parents told me about the Frieden March from their Air Force days
CuriousMarc sooo?
LEFT... LEFT... LEFT.
When I was a 10 years old child, my father gave me a strange old digital calculator, wich had that strange function to hide the floating point until you press a button to show the fractions. When I divided some number by zero, it did not showed "E" or something like that.. just stucked on zero...but imagine what I discovered that when you pressed the floating point option. It was just like you evidenced in this mechanical calculator. Amazing! It took to me 35 years to find another machine that explained to me what was really happening, since not even my math professors could do it. Thanks a lot!!!!
What a delightful machine ... my dad used to fix devices like this for a living.
This would make a sick drum track for a black metal song.
grindcore
Swedish crustpunk
Sounds more like a machine gun soundtrack to me lol
🤘
@mario mario
Black metal double pedal double bass literally sounds like a machine gun. Just look up "Laser Cannon Deth Sentence" by Dethklok to see what I mean.
I remember using a hand cranked Ohdner machine at school some 45 years ago. Division was exactly the process your machine went through, except all movements had to be done by hand. I nearly broke my wrist when I tried dividing by zero.
Except you didn't have a stop button, and to this day you are still cranking.
Once, I was writing a program for a PLC -5, there was a division. Shortly after I compiled and went back to run mode, the PLC faulted shutting the whole plant down. Upon investigation, I found that the denominator sometimes would go to zero, which caused the fault. I solved the problem by restricting the range of the denominator to >1.
Quite accurate. Dividing by a big number results in a very small result. The opposite aplys, where dividing by a very small number gives a very bug result. Zero is a very, very, very small number, so you get a very, very, very big number, thus infinity
"made specially for idiots making UA-cam videos" LOL
"They had lots of foresight."
And makes a youtube video himself.
TheDavo10001 and you have 355 likes in your comment.
@@ritikjain4256 Oh God you are the biggest r/woooosh I ever saw
the inventor of this machine even could foretell the users in the future
What a truly beautiful piece of engineering!
Machine-gun mathematics.
Imagine showing up to your first day of Algebra class and you whip this big boy out
Two great things regarding this video. Firstly this is one of the best videos I’ve ever seen on UA-cam and secondly this machine is one of the coolest and most beautiful things on earth!!!!!!!!!!!!!
It's even idiot proof
I laughed at this comment a bit too much.
Get yours now!
It makes calculating a pice of cake! A child could do it!
Comes in 5 diffrent colours and is even *idiot proof!*
lmao
Hey, this brings back memories. Back about 1963 they had a whole room full of these at the computer center in our college (used for classes, I guess). Some of us were in there once and one of us (it wasn't me) suggested we see what happened if you divided by zero. As you see in the video (spoiler alert!) it starts cranking and cranking. After a couple of minutes we got nervous and unplugged it before it could catch fire. Probably when it was plugged back in, it would keep cranking... I just hope whoever was in charge of these knew about the zero-divide escape button!
I have no idea why an infinite loop in a mechanical device like this is so satisfying but my goodness I love it.
Brings back fond memories. My grandfather had two of these of which I inherited both of them slightly different models. That was 40 years ago I was a teenager and I spent many hours playing with these machines not fully understanding what they are doing. I don’t ever know what become of the two that I had. But I sure miss playing with them.
*machine implodes and creates a black hole*
That is a beautiful machine, btw. The engineering that must have taken to build that is undoubtedly staggering. I know even micro processors are still machines with moving parts, but with this bulky, heavy machine, it's much more satisfying to watch.
Moving parts in processors? huh?
Bero256 yes the electrons create physical wear
MibMoot Electrons
@@dragonvarine7553 By that definition then the wires in your walls are mechanical and have moving parts.
They are@@shawnpitman876
Nice demo!! The distinctive noise of these machines is, I believe, the source of the phrase, "crunching the numbers."
BTW, what you're calling "overflow," I would call an "underflow," because it results from a subtraction that takes the accumulator "below" 0.
Addition that gives a result that takes the accumulator "above" all 9's, would be an overflow.
But the distinction is somewhat moot because, in practice, the machine produces leading "9"s, as though it's a very large number, even though that really means a negative number.
Fred
Stack overflow is the correct terminology. Rolling under is considered expanding beyond the bounds. This is a common glitched function in videogames; sending a variable outside of its dimensions resulting in a binary rollover. Whether the game is tricked into subtracting without stopping at zero, or adding after there are no leading bits left, it's the same core computational error. I liked the term 'stack underflow' at one point myself, but you struck the point of the lack of difference in the distinction.
@@TheJacklikesvideos The use of the term stack overflow is used to mean to overflow the stack, a specific type of memory. If you had 255 overflowing to 0 after an increment, that would be an integer overflow. -128 going to 127 from a decrement would be an integer underflow.
@@TheJacklikesvideos This has nothing to do with stack. We are talking about integer underflow or overflow here. Stack overflow is about accessing memory that doesn't belong to stack, it has nothing to do with arithmetics.
@@TheJacklikesvideos somebody doesn't know what he/she/they are talking about
I worked for Friden Inc inc 1972 in Houston Texas. I repaired the rotary calculator among their other products. Friden made a Nixie tube electronic calculator in 72 and the mechanicals were slowly being phased out. The electronic calculator was $1500. in 1972 and that was very expensive.
Thankful to this channel we get to see such incredible machines which otherwise is beyond reach for majority of the people.
I always lose my calculator at work, I need one of these.
www.amazon.co.uk/GIANT-DISPLAY-BUTTON-DESKTOP-CALCULATOR/dp/B004SGOD3W
Approx size: 8inch X 12inch
@@boring7823 you're the hero everybody needs
Hello Marc. I have a small challenge for you: can you find out what numbers Jack Lemmon entered on the Friden to get that exact drum beat, when the carriage moves to the left 1, 2, 1-2-3, 1, 2, 1-2-3 spaces ? Being a drummer, I'm curious what those numbers were... The Friden could make a primitive "programmable" mechanical drum machine ! lol
[Edit: Friden March video here: ua-cam.com/video/-MLQ0yI1BrQ/v-deo.html ]
@AlainHubert: Great catch! I had not noticed the rhythm on the video, but that's indeed what makes that scene work so well. I'd just put in something like 5551155511 and divide by 1. It will do 6 trials until overflow when on the 5's and just 2 trials for the 1, as explained in the video. That should give you the rhythm you are looking for! [Edit: I just tried it, works great, it's hilarious. It must be what was called the "Friden March". I need to make a video of it!]
@@CuriousMarc dude where's the video
My Dad used to repair those back in the 60s and 70s! If I show him this video he will cry with excitement!
In the 70s I owned a hand-held, battery-operated calculator (Texas Instruments?) that would count from 1 on up if I divided by zero. Like a stopwatch. Always fascinated me. This is the first concrete info I've ever run across that explains why. Thank you!
I'd like to take that with me to take a test.
I want to take the BC Calc exam with this hunk of metal
Just a totally silent test room,"dadadadaddadadadadadadaDINGdaddadadadadadadadada"
This is wonderful! I had no idea a mechanical calculator even existed, but now I'm fascinated! Thanks for a great video!
I remember going to my Dad's place of work and watching him use this machine. He was very experienced in using it, so all you heard was the clackity clack noise in the office. I miss my Dad.
This is brilliant machine, brilliantly explained. Naturally it's not a "simple machine" but I do like early technology. I sailed on a WWII Victory ship (1944). We could make turns on the propeller without one Candlelight of power available.
It would have been hilarious if you have edited the video with the calculator catching on fire after dividing 😁
Erik Lönnrot damn what did vaporwave do to you??
Remi It made him F E E L
Erik Lönnrot you cant game on a Mac
you can, There are so many games on Macintosh Plus you could play.
Vapor Wave - sama that is whay happened to old gas machines. they caught fire when the gas prices went to 4$ a gallon
haha, great! :D excellent stupidity-to-entertainment ratio ;)
Matt Siegel ignorance*
It's very interesting, most calculators say error, but it should really just check if it's divided by 0, if so, say infinite. Because 1) we do use infinity for limits and summations for convergence of sequences. And 2) If you do 1/0.01, you get 100, if you do 1/0.001, you get 1000, so as you get closer to 0, your number gets higher (which logically would be written as infinity). So it's reasonable this machine would do an infinite loop.
Dear god, my father brought one of these home when his office upgraded! I used to do the divide by zero thing, he must have shown me.
I haven’t thought about this in years. Cheers.
I watched the whole video because you risked such a valuable antique piece of equipment for our entertainment!
Edit: That's an incredible piece of machinery. It sounds beautifully mechanical, like a steampunk factory. :)
when I was a little kid my father had one in his office.. I would push all the 9s then multiply and then all the 9s again... how long would that take to complete???? and was there a way to stop it????
Yes there is a way to stop it, use the anti-idiot button
I obviously didn't care when I was little, but I am glad I didn't break it anyway :-)
I'm glad that I wasn't in your place when you're still a kid because I would break it for the sake of curiosity 😂
Learned to use a Friden in high school (1964) business machines class. Mr. Pichel was very protective of this expensive piece of equipment. The standard was. “You jam my machine and you clean the mimeograph machine for a month. A very dirty job, for those of you who are old enough to know what a mimeograph is. LOL
When I first saw this, I never expected I'd have one, but the other day on the way to school I saw two at an antique shop just sitting on the asphalt. Turned out to both be ST10's that were left outside. After school, I rode my bike over there bought both for a total of only $30 and I'm now trying to restore them. Will definitely do this exactly once I finish.
Good luck!
dang! would love to use one in schools today, just to get everybodys nerves wrecked haha
It's not technically disallowed for the SATs...
CODMarioWarfare this needs to happen now
CODMarioWarfare jusssst need to buy one
CODMarioWarfare I’m broke
I kept saying "you're gonna break it you're gonna break it" but you had an emergency stop dont do that you scared me
Ngl this has to be to the coolest thing I’ve ever seen. Something that we never get to see being done by our modern electronic calculators. I’d love to have one, purely for when I forget what 2+2 is
It's 5, duh
This is probably more complicated than the modern electronic calculator. Loved the noise so much, imaging sitting in an exam and using this to do calculations.
Did anyone else get recommended this after watching the LinusTech Tips video on this calculator?
This is so cool. Way better than the calculator I had in school.
Somehow more amazed by a mechanical calculator than the literal computer in my hands.
My dad got a surplus one of these for our home office when his company was upgrading in the 1960's. For the longest time if touched it, I got 'one around the ears'. However, I'd play with it when they weren't home. Even dividing by 7 was scary. Yours is a newer version than we had. Mom must have divided by zero by accident. He un plugged it and that seemed to stop it.
Later, we weren't allowed to use it for our math homework as he wanted us to be good at mental math. Thanks for the memories.
Great video and explanation! The game Human Resource Machine gave me an intuitive feel for iterating simple operations to form a complex process, and it was great to see the real thing here.
Cool. My father had one at home when I was a child in the 1970s.
Honestly the proper division and the noise it makes as it repeatedly underflows and reverses one step is more fascinating than dividing by zero. I've seen mechanical counters going up before.
I used these things at UCLA prior to the introduction of digital computers -- they were then installing the two huge IBM 360 Model 95 mainframe computers between the Engineering and Math Buildings in a new three-story building.
In slowmo it sounds like ambiance from a Silent Hill game
Jack Lemmon seems utterly mesmerized by his STW10 as it calculates 355/133.
355/113
As Air Force orbital analysts in the mid-'60's, we used Friden calculators ... When we performed a certain calculation -- I believe it was a zero division -- the model we used would go into a cadence we called the "Friden March" ...
I made a video of the Friden March here: ua-cam.com/video/-MLQ0yI1BrQ/v-deo.html
Modern calculators: noooo you can't divide by zero
Mechanical calculators: *cracks knuckles*
got this on random feed and now i want it for the sake of having it
My teather told us a story, that someone broke an arothmometer by dividing by zero. He told as that as a reason to read documentation first.
Luck So in other words, RTFM? Lol
Many years ago, I worked with a really weird Friden "system" which consisted of 3 or 4 of these in series(?) inside a cabinet next to a standard Flexowriter keyboard/paper punch. I believe it was called a "computator" and it did all sorts of things: billing, general ledger, inventory etc. It was a royal PITA, but it got the job done. I wish I could find some info, such as programing etc, but it doesn't seem to exist any longer.
This is better than anything that I expected. Thank you my recommended list for bringing me here while I wait for avengers 4 trailer..
Who else is here after Linus Tech Tips disappointed us by not showing a demo?
It's amazing how purely mechanical mechanisms can reliably calculate complex maths.
Beautiful machine, I had no idea these existed. Great video!
I grew up down the street from the Friden plant that made that machine. We thought it would be a 'lifetime' job to work there. They were said to treat their employees VERY well. Then came Silicon Valley and the end was quick and merciless.
A mechanical calculator like that is more impressive than modern electronic calculators because of the amount of engineering that went into constructing something like that.
Do you realize there's more engineering in digital electronics than these? It's just more hidden in electronics...
It's probably just because you think it sounds cool, but you might wanna reword it
@@lightlysal Making a complex mechanical device is more impressive than coding some lines.
@@floppaquest4916 and how do you think the lines of code are executed behind the scenes? Every computer is still to today an electromechanical wonder.... (not wanting to say that the pure mechanical isn't top notch - typing this on an old style mechanical keyboard ...
@@floppaquest4916 a CPU which run those code lines are far more impressive than this mechanical machine
Heck, the language behind those code lines are just as complex as this machinery
Your comparison is not apple-to-apple
Div stop stops the machine in case of repeating decimals, pretty sure it's not solely to stop the division of zero.
The machine stops on its own even with repeating decimals.
right, i commented too early, i saw that later on...
I saw another mechanical calc vid, and I guess what's happening is that it's trying to subtract zero from the first number, but can't, so it infinity loops. (i forgot if you said that in your video or not, then again, that might not be how your model works)
CuriousMarc Just curious how it handles 1/3 like 0.33333333333 repeating how does it calculate can you do one about this?
Alabamian Alien It just runs out of decimal places to calculate.
This is a beautiful piece of machinery
Your enthusiasm for everything nerdy is utterly unbelievably fantastic
That's one beautiful piece of engineering. I'd love to have that just to listen to it whir and do its thing.
Very nice. As a side lesson, I also learn that 355/113 is pretty near PI() considering a simple division of two integers.
your voice was one of the things that kept me watching
This video brings back some memories. Around 1970 I was going to a Junior College and one of the courses I took was course on learning to use the Friden Mechanical calculator. The calculator in this video might not be the same model that the Junior College had, but it sure looks the same. These calculators made plenty of noise when doing calculations. This was the time before electronic calculators were developed. I suspect that now about the only place one of these Friden Mechanical calculators can be seen is in a museum. Maybe a few of these calculators have been restored to running condition.
Your job skill wouldn't have lasted long. Just 4 years later my college course was on operating a computer. IBM had a big manufacturing plant for their 360 and 370 machines at the time, right next to SUNY Binghamton. THE computer existed in THE Computer Building, attended by the high lords of senior programmers. I learned how to use punch cards the cutting edge real time remote time-sharing on fan-fold paper. Quite a gap in 4 years, although I'm sure there was a transition period before small companies could cover to computers. But my skills wouldn't have lasted much longer, punch cards were on their way out. The basic programming concepts would have lasted, but I never pursued that field.
@@donjones4719 The junior college was the first and the last place I saw these Friden Mechanical Calculators. This junior college was the first and last place I also learned to program an IBM1620 computer. I ended working 34 years at the Los Angeles Department of Water and Power in Generating Stations operating the large power plant equipment.
What’s important is that the engineers that made this machine understood how to divide by zero, and were able to implement that into a device. This machine’s soul purpose is to show us what happens when you divide by zero.
It a electro-mechanical calculculator... as you don't have to operate it via a crank...
ShazamMafia the concept is the same.
Thanks for clearing that up...
UA-cam algorithm went crazy to recommend this video to me :-D What I really take with me from this video is that Pi is 355 diveded by 113! Great knowledge :-D
These things absolutely fascinate me with how they work
Now; Let it loop outside Without stopping.
The engineering that went into this seems more impressive than microchips to me.
@Keshuel probably, I'm a computer engineer not mechanical. But consider this thing was designed by hand on paper, super impressive.
@@8180634 they work the same really. Decimal gates instead of binary gates. Its like a processor gate translated to mechanical movement, rather than electricity passing through silicone.
@@alexandrutereify Indeed I get how it's mechanically possible, but having to figure it all out on paper, design all the parts on paper, make the parts all fit together perfectly as a package on paper, etc.. you can't simulate it but it's got to work, that's a whole lot of memorization and work!
1:57 Lots of foresight. Thats great!!! I remember working for this old guy he was 72 some 23 years ago when I was 14 and he talk about using one of these machines glad to see on in use.
What an awesome calculator!
this machine would probably help with the US budget
Great video mate! Love the clunking sounds!
As a young engineer in the 1970s I was asked to make some enhancements to a FORTRAN program I had inherited from a brilliant colleague. Everything done with punch cards of course - submit the deck and wait for the printout. The colleague had not read Dijkstra's paper and had created some serious go-to spaghetti with packed bit fields adding to the headaches. The thing would often crash and create an octal memory dump. One of my officemates dug an octal desk calculator out of storage - I think it was an SCM Marchant. A lot easier to accidentally cause division by zero than with the Friden, and no DIV STOP key, and it would start smoking in 15 or so seconds. I luckily discovered that keying any number into the keypad while it was running would change the divisor and cause it to stop. My officemates were not amused, but I did eventually get the program working.
This calculator looks like it came from a Steampunk universe.