I actually said "get out of here" out loud because I put the equation in my phone's calculator and it was exactly the same answer. Technology like this will never cease to amaze me in how complicated yet precise it was! Thank you for this video.
Thank you. I appreciate that. =) I think the part that gets me about these machines is how they show the entire process of the calculation. With a phone you just get the result without further elaboration.
I bet they would be. I've had coworkers who watched a machine like this work and most of them wound up telling me that they suddenly *get* division. Maybe I could make a briefer video showing a division on the machine and explaining the principles behind it. I think it'd be really cool if someone finds it and uses it for class. (if not I'll have fun doing it :) )
I once read a description of a CPU as "a rock we tricked into thinking", which is plenty amazing too. I think the difference is that it's easy to grasp how a mechanical calculator works, so you can appreciate it for what it is, instead of explaining it with "science magic".
Thank you so much for this video. My parents used to have such a machine standing around as decoration. I played around with it a lot as a kid, but never understood what it actually did and no one ever could explain. I finally get it now (30 years later). Greetings from Germany.
That is really cool for me to hear! It was the same story for me. My uncle had this exact machine and nobody knew how they worked. Years down the line I come across one and manage to find a resource on how to use them and here we arre.
Someone nicked your video and retitled it "Unintentional ASMR". It has gotten tens of thousands of views because your voice and the mechanical sounds are very calm and deliberate.
I appreciate the heads-up! =) I noticed that video a while ago. Was pondering a DMCA for a while, but decided to let the fellow keep the video after having had a chat with them. At the end of the day I want to show this stuff off and it seems like that person helped it reach a lot of people it wouldn't have otherwise. I probably wouldn't want to have that keep happening, though, so it was an exception rather than the rule.
I should mention that they DO link their videos to the original source and make a disclaimer that none of it is theirs (Additionally, they will remove any videos they've uploaded upon request).
In their defence, they were tremendously polite about it when I contacted them. That said, it feels very strange to have your work straight up taken, with the burden on you to request it be taken down if you are not OK with it, rather than being asked first. I really enjoy sharing these videos with you all, so I didn't mind as long as I got credited (so I could show you my other stuff if you were interested). It's definitely not a mindset or way of working that I would want to encourage regardless.
1stSpyGuy also keep in mind that people sampling your content draws viewers to your channel. That's how I found you. I love these old machines! Subbed!
You can't control the way your content is used and that becomes even more true when an audience apart from the original is formed. I never would've found these videos without that other channel because I'm just into ASMR. What these reupload channels are selling is context and convenience. Nobody is going to browse hundreds of random videos in hope for something relaxing but that quality still does exist in many videos and will largely go unappreciated without channels like unintentional ASMR. That content wasn't stolen it was brought to people who never would've enjoyed it otherwise
Thank you ! Perfect video, I just picked up and old Original Odhner model 207, cleaned it up, got it working all fluidly, and followed along with you video to get the same answer to test it out. Great job and a great presentation.
Came here after seeing your comment on the Unintentional ASMR video- that stinks that they took it without asking. But this is really cool! I've never seen anything like it. Thanks for posting it.
You can't control the way your content is used and that becomes even more true when an audience apart from the original is formed. I never would've found these videos without that other channel because I'm just into ASMR. What these reupload channels are selling is context and convenience. Nobody is going to browse hundreds of random videos in hope for something relaxing but that quality still does exist in many videos and will largely go unappreciated without channels like unintentional ASMR. That content wasn't stolen it was brought to people who never would've gotten the chance to enjoy it otherwise
monkeyhorserider that's a good point! But it ain't a perfect system. Most people haven't clicked through to this video. There should be a better way to curate these kinds of things that still directs the views and associated benefits to the original creator, or at least involves them and obtains their consent to repost. At least with the videos that aren't under a Creative Commons license.
Great video. (I watched the whole thing, no need to doubt yourself on the outro) it was awesome to see how these actually work, weird seeing how long it takes and how much mechanical technology was used to calculate such sums not so long ago.
Omg I had no idea there were even mechanical calculators, even less so, ones that are so cool, and many types of them. Thank you for sharing your awesome collection it's a lot of fun to see this part of mechanical history and how to use it. You've opened a new world of mechanics to me!
I have a similar Odhner calculator of my own with a few extra digits made by a Japanese manufacturer during World War II, provided by my late grandfather. This video among others inspired me to take it back out again and figure out more about it. It's now probably my favorite mechanical trinket I own to play with, period. Division is interesting on that thing, especially with how you showed it off, unintentionally showing both division methods at once. I realized that if you wanted to just do quotient-and-remainder division, you aren't required to shift the carriage all the way to carry it out, since you don't need that extra decimal space and can just look in the results register for the remainder. It's only decimal-based division that requires the carriage shift, although for me it took a while to get used to decimal point placement on more advanced problems, particularly those that involve decimals in the dividend and divisor themselves. Overall I think I've found myself more fascinated with this kinda thing than I normally would be, combined with my old fascination for old mechanical and electromechanical pinball tables. Kudos to you, good sir.
It's this kind of story that's really interesting to read. I'm really glad you could get such a treasure from your grandfather and that it can bring joy to this day. Thanks for sharing & stay well!
It is not apparent but the Original Odhner had a quirk in the way that the register mated with the counter and accumulator. Because of this, for numbers with many digits, you may get an additional digit of accuracy in division and square roots by placing the carriage to the 7 position rather than the 8. This is because the 7th digit of the register isn't hanging off the end of the accumulator.
Yeah, they're pretty much all like that. I know the Hamann Manus does it too, while indicating the cut-off point with a little red dot. Good tip on not shifting the entire way, though! I hadn't given that much thought myself.
I love your voice and plus your voice along with the mechanical sounds makes it better you would be awesome at ASMR your videos are so fascinating well wishes from Japan ps If you are any old calculators from Japan you should really try if out though not as beautiful as this one And possibly more simple ( sorry my English is not good)
No. Placing the dividend into the accumulator is the first step. The divisor is then placed into the register and subtracts that from the register as described. The quotient is then displayed in the counter and the accumulator holds the remainder if any.
jedi1357 I think we got a difference of math terms here! The dividend is the end result of a division. If this machine uses RPN then the Quotient enters the Accumulator first, then the Divisor is entered into the Entry register - in that order. I am presuming that is the logic of these machines. The Dividend might be generated in and displayed on the Turn Counter(cyclometer), the Remainder will be what's left in the Accumulator and displayed there. Does that now sound right? Did you read my last comment??
I don't know if things are different where you are or if things are taught different now but even Google says a dividend is a number to be divided and the quotient is the result of a division. Other than that it looks right. I don't think RPN is what I'd cal it though. It's just repeated subtraction and shifting.
jedi1357 Oh yes, I got it backward - - the Quotient is the end result. But still, is not, or can the Quotient be indicated by the Turn-Counter aka Cyclometer??
Yes. The answer/end result is indicated by the turn counter. It is limited by the number of digits available however so it is not always exact. Example: 1/3 gives 0.3333333 in the counter and 0.00000001 in the accumulator. Think of the 1 constantly moving right because 10-(3*3)=1.
How do you determine where along the setting register you initially load the 358 and 32? E.g. Why decide there are 4 'blank' slots to the right of the loaded 32? Sorry for my ignorance. Great videos!
It's about the alignment of the carriage. If you look to the left of the 32 you'll see that those levers are actually off the accumulator register, so they won't have an effect. The aim is to put the dividend (and divisor) into the far left of the counter register.
Hello, I was wondering if you have any information on the Facit Original. I found one at an antique store and aside from identifying it from online pictures have been unable to find anything more about it. Please let me know, thanks!
Do you have or know of a calculating machine, like your Odhner here, that when operated in multiplier mode the number of turns(of the crank) that is needed to achieve the final product is determined solely by the number of (decimal)figures in the machine's entry register times a factor of ten? (Example: 212 * 100 or 100 * 212 will result in 21200 when the machine's crank is turned 30 times)..
I'm not sure what you're asking. In a mechanical calculator a multiplicand is entered into the register. It is then added to the accumulator through multiple additions and shifting until the multiplier appears in the counter. Then the product will be in the accumulator. In the case of 212*100...Enter 212 in the register. Turn 0 times in the one's place. Shift. Turn 0 times in the 10's place. Shift. Turn once in the 100's place. The register still has 212, the counter has 100 and the accumulator has 21200.
jedi1357 In the late 1960's they built a mechanical calculator that could compete with the new desktop electronic machines, and could be operated in a similar way in terms of how data/numbers could be keyed in. But this machine was so big and complex it needed three different kinds of lubricant to keep its components running accurately.
Dear sire, your voice is like an angel's song! It's gifted upon to me relaxation, though I did succumb to slumber while doing homework.😯Create an ASMR channel, won't you dear chap?
I may sound slightly dumb for asking this (have no idea how these machines work, just interested in them) but how do you determine where the numbers go in the settings register? For example, you put the 3 in the 6 spot and the 2 in the 5 spot for 32, why not just any other place? wouldn't it work as long as you set the decimal place right and have the numbers next to each other?
This is about aligning the divisor with the dividend in the accumulator. The 6th position is the leftmost position in the setting register that connects to the carriage when it's shifted to the far right (carriage position 8). This allows us to determine how many times 32 * 10 fits in the number 358. If I had put it in positions 5 and 4 I'd determine how many times 32 fits in 358, which causes some problems. 1) The amount of times I need to turn the crank increases by at least ten 2) This model of machine doesn't support carryover in the counter, so the result would be rather incomprehensible. I hope that explains it! Let me know if something needs to be clearer. =)
I would take 3 years just to learn how to do a single division with this one. Thank God I have paper and pencils, so I can do a division in just one year.
Professor: Alright everyone, we have a Physics exam tomorrow. Don't forget to bring your calculator That one kid: *brings the mechanical calculator* Professor: He's out of line, but he's right
Di står åver alt i Oslo jore på bruktbutikker menn det virker somm noen prøver å fjerne alle bruktbutikker i Oslo så mann ikke finner gamle greier helt sykt
Det är tråkigt att höra. :( Jag har tittat i en del andrahandsbutiker och hittat räknare, men urvalet är dåligt, priserna höga och de flesta är trasiga. Alltid intressant att se vad de har i butikerna, i alla fall.
They can go for quite a fair bit if they can be proven to be in good order / good shape. This machine went for about $150ish, which isn't too bad for what it is. You can get perfect machines in need for a cleaning for much less if you aren't concerned about doing some work yourself. I'd recommend looking on ebay if you're interested in picking one up.
1stSpyGuy Thanks for the explanation. Even though this is not something I'm personally interested in, quite cool stuff. I stumbled across this video on another channel where it was uploaded as ASMR content lol.
I can do it in about 30 seconds with the machine when not demonstrating what to do. Doing numbers by hand is a good way to do it, however in an office setting you'll want some tool to help you math better, if only to avoid fatigue.
“Thank you for watching....if you’re still with me.” I’m still with you dude.
I actually said "get out of here" out loud because I put the equation in my phone's calculator and it was exactly the same answer. Technology like this will never cease to amaze me in how complicated yet precise it was! Thank you for this video.
now you're thinking
Thank you. I appreciate that. =)
I think the part that gets me about these machines is how they show the entire process of the calculation. With a phone you just get the result without further elaboration.
I'm wondering if these old machines wouldn't make good educational tools for showing *what division is* and *how it works*.
I bet they would be. I've had coworkers who watched a machine like this work and most of them wound up telling me that they suddenly *get* division.
Maybe I could make a briefer video showing a division on the machine and explaining the principles behind it. I think it'd be really cool if someone finds it and uses it for class.
(if not I'll have fun doing it :) )
I once read a description of a CPU as "a rock we tricked into thinking", which is plenty amazing too.
I think the difference is that it's easy to grasp how a mechanical calculator works, so you can appreciate it for what it is, instead of explaining it with "science magic".
Somehow, these old relics seem much more magical than their digital equivalent.
I didn't know devices like this existed, thank you.
I'm glad I could show off something new! =)
Starxgamer12 Obviously you were born after 1965
I didn't know videos like this existed
Thank you so much for this video. My parents used to have such a machine standing around as decoration. I played around with it a lot as a kid, but never understood what it actually did and no one ever could explain. I finally get it now (30 years later). Greetings from Germany.
That is really cool for me to hear! It was the same story for me. My uncle had this exact machine and nobody knew how they worked.
Years down the line I come across one and manage to find a resource on how to use them and here we arre.
Someone nicked your video and retitled it "Unintentional ASMR". It has gotten tens of thousands of views because your voice and the mechanical sounds are very calm and deliberate.
I appreciate the heads-up! =)
I noticed that video a while ago. Was pondering a DMCA for a while, but decided to let the fellow keep the video after having had a chat with them. At the end of the day I want to show this stuff off and it seems like that person helped it reach a lot of people it wouldn't have otherwise.
I probably wouldn't want to have that keep happening, though, so it was an exception rather than the rule.
I should mention that they DO link their videos to the original source and make a disclaimer that none of it is theirs (Additionally, they will remove any videos they've uploaded upon request).
In their defence, they were tremendously polite about it when I contacted them.
That said, it feels very strange to have your work straight up taken, with the burden on you to request it be taken down if you are not OK with it, rather than being asked first. I really enjoy sharing these videos with you all, so I didn't mind as long as I got credited (so I could show you my other stuff if you were interested).
It's definitely not a mindset or way of working that I would want to encourage regardless.
1stSpyGuy also keep in mind that people sampling your content draws viewers to your channel. That's how I found you. I love these old machines! Subbed!
You can't control the way your content is used and that becomes even more true when an audience apart from the original is formed. I never would've found these videos without that other channel because I'm just into ASMR. What these reupload channels are selling is context and convenience. Nobody is going to browse hundreds of random videos in hope for something relaxing but that quality still does exist in many videos and will largely go unappreciated without channels like unintentional ASMR. That content wasn't stolen it was brought to people who never would've enjoyed it otherwise
Thank you ! Perfect video, I just picked up and old Original Odhner model 207, cleaned it up, got it working all fluidly, and followed along with you video to get the same answer to test it out. Great job and a great presentation.
Thanks! Glad I could help you sort your machine out!
Came here after seeing your comment on the Unintentional ASMR video- that stinks that they took it without asking. But this is really cool! I've never seen anything like it. Thanks for posting it.
You can't control the way your content is used and that becomes even more true when an audience apart from the original is formed. I never would've found these videos without that other channel because I'm just into ASMR. What these reupload channels are selling is context and convenience. Nobody is going to browse hundreds of random videos in hope for something relaxing but that quality still does exist in many videos and will largely go unappreciated without channels like unintentional ASMR. That content wasn't stolen it was brought to people who never would've gotten the chance to enjoy it otherwise
monkeyhorserider that's a good point! But it ain't a perfect system. Most people haven't clicked through to this video. There should be a better way to curate these kinds of things that still directs the views and associated benefits to the original creator, or at least involves them and obtains their consent to repost. At least with the videos that aren't under a Creative Commons license.
It’s funny that there are several channels I’ve found that cover these mechanical calculators, and they’re all pretty ASMR.
Dont worry i was still with you at the end :)
Great video. (I watched the whole thing, no need to doubt yourself on the outro) it was awesome to see how these actually work, weird seeing how long it takes and how much mechanical technology was used to calculate such sums not so long ago.
Omg I had no idea there were even mechanical calculators, even less so, ones that are so cool, and many types of them. Thank you for sharing your awesome collection it's a lot of fun to see this part of mechanical history and how to use it. You've opened a new world of mechanics to me!
You really should make an ASMR channel, your voice is so relaxing. :(
^^^^^ to add to this, the asmr community is HUGE! you would get so many more views and subscribers
I have a similar Odhner calculator of my own with a few extra digits made by a Japanese manufacturer during World War II, provided by my late grandfather. This video among others inspired me to take it back out again and figure out more about it. It's now probably my favorite mechanical trinket I own to play with, period. Division is interesting on that thing, especially with how you showed it off, unintentionally showing both division methods at once. I realized that if you wanted to just do quotient-and-remainder division, you aren't required to shift the carriage all the way to carry it out, since you don't need that extra decimal space and can just look in the results register for the remainder. It's only decimal-based division that requires the carriage shift, although for me it took a while to get used to decimal point placement on more advanced problems, particularly those that involve decimals in the dividend and divisor themselves. Overall I think I've found myself more fascinated with this kinda thing than I normally would be, combined with my old fascination for old mechanical and electromechanical pinball tables. Kudos to you, good sir.
It's this kind of story that's really interesting to read. I'm really glad you could get such a treasure from your grandfather and that it can bring joy to this day.
Thanks for sharing & stay well!
What an amazing machine. Thank you for sharing this.
Who could give such a nice guy any kind of hate? The internet shall never cease to amaze me for all the wrong reasons
This is the first thing related to maths I’ve been interested in
I didn't care for math until I took physics. Then it suddenly became real and useful in my mind.
I have never seen one of these machines in operation. Very cool!
Helped me a lot with the decimal setting on my Triumphator. Thank you
It is not apparent but the Original Odhner had a quirk in the way that the register mated with the counter and accumulator. Because of this, for numbers with many digits, you may get an additional digit of accuracy in division and square roots by placing the carriage to the 7 position rather than the 8. This is because the 7th digit of the register isn't hanging off the end of the accumulator.
Yeah, they're pretty much all like that. I know the Hamann Manus does it too, while indicating the cut-off point with a little red dot.
Good tip on not shifting the entire way, though! I hadn't given that much thought myself.
jedi1357 Whoa!
I love your voice and plus your voice along with the mechanical sounds makes it better you would be awesome at ASMR your videos are so fascinating well wishes from Japan ps If you are any old calculators from Japan you should really try if out though not as beautiful as this one And possibly more simple ( sorry my English is not good)
I'm really bad at division. But maybe with this machine I could learn something. Btw nice video. I like your voice it's relaxing ;)
I think division is the hardest kind of arithmetic to do in your head, so it's understandable. Glad you enjoyed the video!
So let me get this straight, the dividend of this calculator's division operation is displayed/indicated by the the turn-counter (cyclometer)?
No. Placing the dividend into the accumulator is the first step. The divisor is then placed into the register and subtracts that from the register as described. The quotient is then displayed in the counter and the accumulator holds the remainder if any.
jedi1357 I think we got a difference of math terms here! The dividend is the end result of a division. If this machine uses RPN then the Quotient enters the Accumulator first, then the Divisor is entered into the Entry register - in that order.
I am presuming that is the logic of these machines.
The Dividend might be generated in and displayed on the Turn Counter(cyclometer), the Remainder will be what's left in the Accumulator and displayed there.
Does that now sound right?
Did you read my last comment??
I don't know if things are different where you are or if things are taught different now but even Google says a dividend is a number to be divided and the quotient is the result of a division. Other than that it looks right. I don't think RPN is what I'd cal it though. It's just repeated subtraction and shifting.
jedi1357 Oh yes, I got it backward - - the Quotient is the end result.
But still, is not, or can the Quotient be indicated by the Turn-Counter aka Cyclometer??
Yes. The answer/end result is indicated by the turn counter. It is limited by the number of digits available however so it is not always exact. Example: 1/3 gives 0.3333333 in the counter and 0.00000001 in the accumulator. Think of the 1 constantly moving right because 10-(3*3)=1.
Hi my friend I Just found an Original Odhner but I locked it… can you help me to unlock it please ?
How do you determine where along the setting register you initially load the 358 and 32? E.g. Why decide there are 4 'blank' slots to the right of the loaded 32?
Sorry for my ignorance. Great videos!
It's about the alignment of the carriage. If you look to the left of the 32 you'll see that those levers are actually off the accumulator register, so they won't have an effect.
The aim is to put the dividend (and divisor) into the far left of the counter register.
Nicely done. I have a much newer Odhner, but it works the same way.
Hello, I was wondering if you have any information on the Facit Original. I found one at an antique store and aside from identifying it from online pictures have been unable to find anything more about it. Please let me know, thanks!
Do you have or know of a calculating machine, like your Odhner here, that when operated in multiplier mode the number of turns(of the crank) that is needed to achieve the final product is determined solely by the number of (decimal)figures in the machine's entry register times a factor of ten?
(Example: 212 * 100 or 100 * 212 will result in 21200 when the machine's crank is turned 30 times)..
I'm not sure what you're asking. In a mechanical calculator a multiplicand is entered into the register. It is then added to the accumulator through multiple additions and shifting until the multiplier appears in the counter. Then the product will be in the accumulator.
In the case of 212*100...Enter 212 in the register. Turn 0 times in the one's place. Shift. Turn 0 times in the 10's place. Shift. Turn once in the 100's place. The register still has 212, the counter has 100 and the accumulator has 21200.
jedi1357
In the late 1960's they built a mechanical calculator that could compete with the new desktop electronic machines, and could be operated in a similar way in terms of how data/numbers could be keyed in.
But this machine was so big and complex it needed three different kinds of lubricant to keep its components running accurately.
I like this channel mate
Really glad to hear it!
Dear sire, your voice is like an angel's song! It's gifted upon to me relaxation, though I did succumb to slumber while doing homework.😯Create an ASMR channel, won't you dear chap?
Can I buy one of these. If do how much and where from. Thus is sincerely one of the most interesting videos on TH-cam I've ever watched.
Please could you let me know which model this is, I'm guessing a 27?
Jag var med dig until the end : ) Häftigt!
I may sound slightly dumb for asking this (have no idea how these machines work, just interested in them) but how do you determine where the numbers go in the settings register? For example, you put the 3 in the 6 spot and the 2 in the 5 spot for 32, why not just any other place? wouldn't it work as long as you set the decimal place right and have the numbers next to each other?
This is about aligning the divisor with the dividend in the accumulator. The 6th position is the leftmost position in the setting register that connects to the carriage when it's shifted to the far right (carriage position 8).
This allows us to determine how many times 32 * 10 fits in the number 358.
If I had put it in positions 5 and 4 I'd determine how many times 32 fits in 358, which causes some problems.
1) The amount of times I need to turn the crank increases by at least ten
2) This model of machine doesn't support carryover in the counter, so the result would be rather incomprehensible.
I hope that explains it! Let me know if something needs to be clearer. =)
This is interesting.
Where did you get all these machines?
I would take 3 years just to learn how to do a single division with this one. Thank God I have paper and pencils, so I can do a division in just one year.
Professor: Alright everyone, we have a Physics exam tomorrow. Don't forget to bring your calculator
That one kid: *brings the mechanical calculator*
Professor: He's out of line, but he's right
I have no idea how your videos end... :l
P.S. ASMR fan here
I’d love to break one of these open and spend a day trying to figure out how the hell it works
Di står åver alt i Oslo jore på bruktbutikker menn det virker somm noen prøver å fjerne alle bruktbutikker i Oslo så mann ikke finner gamle greier helt sykt
Det är tråkigt att höra. :( Jag har tittat i en del andrahandsbutiker och hittat räknare, men urvalet är dåligt, priserna höga och de flesta är trasiga.
Alltid intressant att se vad de har i butikerna, i alla fall.
These things must be worth a fkn fortune if original...
They can go for quite a fair bit if they can be proven to be in good order / good shape. This machine went for about $150ish, which isn't too bad for what it is.
You can get perfect machines in need for a cleaning for much less if you aren't concerned about doing some work yourself. I'd recommend looking on ebay if you're interested in picking one up.
1stSpyGuy Thanks for the explanation. Even though this is not something I'm personally interested in, quite cool stuff. I stumbled across this video on another channel where it was uploaded as ASMR content lol.
I love you bro im from russia 🇷🇺 and yeah your videos are great even tho im not smart lol
I hope you don't mind the reuploaders because I probably wouldn't have found/enjoyed this place without them.
Unintentional Asmr
Kan du gö en tutorial video på svenska
Inte riktigt tutorial kanske, men nära inpå:
th-cam.com/video/qc1RcQU4O7E/w-d-xo.html
We still here
I'm happy to hear it!
I'm currently giving my all to a java development project for uni. I hope to get some time for videos in the near future.
Iron Felix :)
You sound like you could use a cup of strong coffee.
You sound like baron Zemo from captain America civil war
M A D E I N S W E D E N . . .
Det är ganska kul att veta de första räknesnurrorna är svenskutvecklade. Något att vara nöjd med, kan jag tycka!
hook it to a chainsaw engine = supercomputer
Wholly guacamole that's takes forever. !!!!
i found it!
Cory tower
Vert borti sån kalkulator
are you being held hostage why are you so quiet
50% of comments:
"That's an interesting calculator."
The other 50%:
"LOL LOL UR CHANIL IZZ LIK ASMR LOL LMAOOOOOOOOOOOOO!!!!!!!!!!!!!!!!!!!!!!!!!!!"
...wouldn’t it be easier...just to solve it yourself...why was this invented lol super cool though
This is ai
Could have done it w/ pen and paper in 1-2 minutes.
I can do it in about 30 seconds with the machine when not demonstrating what to do.
Doing numbers by hand is a good way to do it, however in an office setting you'll want some tool to help you math better, if only to avoid fatigue.