i think the reason why parallel calculations arent popular today for personal arithmetic use is because the cost of each calculation is pretty low but on an old mechanical calculator cranking, that thing takes so much effort so it could make sense to allow for parallel calc even if theres some overhead and nowadays if you wanna do that sorta thing you can just a spreadsheet or a scripting language and on the topic of computers, that kind of parallel math is a very big deal and is a massive part of modern computers and especially in gpus (look up intel mmx if you wanna learn more) so even if the average person doesnt think about them they still use them extensively
parallel calculations are pretty great. A couple years back Excel made it so you could fill in whole arrays using this sort of thing, and I use it a lot. Used to be, to do (for instance) a multiplication table, you'd put =$A2*B$1 into B2 and then fill-drag it in both directions, but now if you have =A2:A11*B1:K1 it'll fill in the whole square without any fuss.
Yes! Come to think of it, that's really the killer feature of the spreadsheet, that you can do parallel formulae that way without even thinking about "programming" in the coder sense. I think it goes back to VisiCalc.
Yes I had another 30 seconds explaining how everybody's parallel calculating needs are fulfilled today by spreadsheets. The spreadsheeet really is a much better general solution, but the Curta is easier if you only want two parallel numbers. (and you're sure they won't overflow into each other)
To be fair there's nothing stopping you from doing 130000190 times 4.7 on your standard electronic calculator. You just wouldn't because an electronic calculator output is usually the exact number you want, whereas the output of attempting 130 times 4.7 on a mechanical calculator already requires some post processing so you're used to that kind of thing.
I think parallel calculation is also the reason that in Japan they like their abaci to be nice and wide. You might not care about 13-digit numbers but you could divide it into two or more "registers" any way you want. With a modern calculator there's usually at least a memory register that can store one number, or you can have multiple variables in programs or multiple stack levels (if it's that kind of calculator), so there's less of a need to stuff two numbers into one register.
Parallel ops might be useful for some of the "target" audience. Curtas were reportedly popular with drivers especially ones on cross country rallies. figuring out what fluids might run out at what times seems like a good use case. Knowing that you're using x fuel and y water per hour you can extrapolate both to know when you might need to pull off for a refill.
Parallel calculations also work on slide rules! Circular slide rules are the easiest since you don’t have to worry about realigning the slide. And obviously the precision is limited, but I can see how the precision is limited on a Curta or an abacus…
I agree and the reading out isn't really clear. There are actual (and past since 1986) handheld calculators where user may type no zero, but may use brackets (or accolades) instead: { 130 190 } 4.7 * display { 611 893 }
@@ChrisStaecker All Texas Instruments graphing calculators since antiquity have that feature. I think TI calls the feature "lists". You can display the input list and the output list beside one another in a table, sort of like Lotus 1-2-3. Also you can take a bus pass or something and drag it across the keypad to make a sound similar to cranking a Curta.
The same with Hewlett-Packard as old RPL calculators HP-28C/S, HP48, HP48SX/GX, HP50g and actual Hp Prime "array"s and "list"s all allow parallel computing. Perhaps CASIO and Ti graphing calculators have this feature before HP-28C/S. Is antiquity past 1986 ?
Love the Curta. Reminds me of a teched-out promptuary. Slide Rules are excellent, and nothing beats a book of tables. Still, with Napier's Bones, you can do a lot of calculations, and you can even get a lot out of an exchequer board, or even tablet of Salamis. If you don't have paper and pencil, you can always bang out division using the galley method vs. the long-division algorithm in the sand. [ It's easier to deal with. ] Great video!
Most electronic calculators have a multiplication shortcut for when you are multiplying several numbers by another. On my iPhone, I type 130x4.7=190= and it displays 611 and then 893.
Very interesting! I must admit I kinda hate these features (there are similar tricks about repeatedly pressing the = button). They are useful, but always seem totally arcane to me- I'm always so unsure of exactly what will happen that I never trust myself to use the feature properly. Similarly on calculators with a C for clearing and an AC for clearing "all". I can never predict the precise behavior of the C, so I always hit the AC. (Usually at least twice.)
@@ChrisStaecker The percent key on a calculator has always been that way for me. Different calculators have percent keys that do slightly different things and I can never remember how to use it, whereas I understand percents and I can remember how to divide or multiply by 100. So I never touch the percent key.
The parallel computing reminds me of array programming languages which equally didn’t take off. Typing “130 190 × 4.7” into an APL repl gives the two answers you’d expect because the multiplication operation dynamically operates however many values are on either side
Didn't take off? More like: They left the planet and only visit from time to time. They're still used, but in niche areas, and you need to be able to cast at least 3rd level spells. That keeps the (coder [not programmer]) riff raff out.
Love this series so far! It’s also interesting to see parallels with the Comptometer that had a bunch of niceties and features that helped with similar use cases! For example splitting the big number into multiple numbers was also possible, and there were even small buttons next to each result digit you could hold to prevent a carry from traveling too far to the left and “contaminating” the other number that was there.
3:16 there is no better tool than a sliderule for this kind of job. Just slide the squares scales by (let's say) 4.7 so you don't have overflows and you have a lookup table for any number of ingredients. It's good that you can also guestimate the closest values for hard to divide things like eggs etc (and maybe adjust the factor around those values) Also a good thing that you can read the values directly and don't have to extract your hands from the dough to fiddle w/ mechanical parts. Gosh I love sliderules. /tangent
The parallel calculation was excellent, but that was when you would have had to do it manually or by cranking a handle. Today, it's easier to type it in as two different calculations or use Excel.
Parallel calculations are a niche tool for sure, but modern CPUs are capable of doing them! In two ways, even. There's the obvious way; a processor has several cores that all operate independently. But there's also a class of instructions called SIMD instructions -- short for Single Instruction Multiple Data. You can queue up a handful of numbers (as opposed to just single numbers at a time), then run the same operation on all of them at the same time in just one instruction. A good software engineer can use SIMD instructions to greatly speed up some algorithms. (Now if only the truly good software engineers weren't in such short supply...)
I gained some knurledge.
i think the reason why parallel calculations arent popular today for personal arithmetic use is because the cost of each calculation is pretty low
but on an old mechanical calculator cranking, that thing takes so much effort so it could make sense to allow for parallel calc even if theres some overhead
and nowadays if you wanna do that sorta thing you can just a spreadsheet or a scripting language
and on the topic of computers, that kind of parallel math is a very big deal and is a massive part of modern computers and especially in gpus (look up intel mmx if you wanna learn more) so even if the average person doesnt think about them they still use them extensively
parallel calculations are pretty great. A couple years back Excel made it so you could fill in whole arrays using this sort of thing, and I use it a lot.
Used to be, to do (for instance) a multiplication table, you'd put =$A2*B$1 into B2 and then fill-drag it in both directions, but now if you have =A2:A11*B1:K1 it'll fill in the whole square without any fuss.
Yes! Come to think of it, that's really the killer feature of the spreadsheet, that you can do parallel formulae that way without even thinking about "programming" in the coder sense. I think it goes back to VisiCalc.
Yes I had another 30 seconds explaining how everybody's parallel calculating needs are fulfilled today by spreadsheets. The spreadsheeet really is a much better general solution, but the Curta is easier if you only want two parallel numbers. (and you're sure they won't overflow into each other)
To be fair there's nothing stopping you from doing 130000190 times 4.7 on your standard electronic calculator. You just wouldn't because an electronic calculator output is usually the exact number you want, whereas the output of attempting 130 times 4.7 on a mechanical calculator already requires some post processing so you're used to that kind of thing.
Chris feelin' those perfectly machined knurls tho
I think parallel calculation is also the reason that in Japan they like their abaci to be nice and wide. You might not care about 13-digit numbers but you could divide it into two or more "registers" any way you want. With a modern calculator there's usually at least a memory register that can store one number, or you can have multiple variables in programs or multiple stack levels (if it's that kind of calculator), so there's less of a need to stuff two numbers into one register.
Parallel ops might be useful for some of the "target" audience. Curtas were reportedly popular with drivers especially ones on cross country rallies. figuring out what fluids might run out at what times seems like a good use case. Knowing that you're using x fuel and y water per hour you can extrapolate both to know when you might need to pull off for a refill.
Parallel calculations also work on slide rules! Circular slide rules are the easiest since you don’t have to worry about realigning the slide. And obviously the precision is limited, but I can see how the precision is limited on a Curta or an abacus…
Knurled! And I love the photo of “Steve Jobs”!
I am a simple man, I see explanations from this channels and I like. I would like twice with the curta, but youtube doesn't allow me.
One thing that amazes me is the great condition of the curta. They sure made things to last.
Hang on... Modern calculators *can* do parallel multiplication in the same way as the Curta! e.g. 13000190 X 4.7 = 61100893.
yes but it feels different if you gotta type in those zeros
I agree and the reading out isn't really clear.
There are actual (and past since 1986) handheld calculators where user may type no zero, but may use brackets (or accolades) instead:
{ 130 190 } 4.7 * display { 611 893 }
@@cret859 interesting- I've never seen a calculator with this feature
@@ChrisStaecker
All Texas Instruments graphing calculators since antiquity have that feature. I think TI calls the feature "lists". You can display the input list and the output list beside one another in a table, sort of like Lotus 1-2-3. Also you can take a bus pass or something and drag it across the keypad to make a sound similar to cranking a Curta.
The same with Hewlett-Packard as old RPL calculators HP-28C/S, HP48, HP48SX/GX, HP50g and actual Hp Prime "array"s and "list"s all allow parallel computing. Perhaps CASIO and Ti graphing calculators have this feature before HP-28C/S. Is antiquity past 1986 ?
Love the Curta. Reminds me of a teched-out promptuary. Slide Rules are excellent, and nothing beats a book of tables. Still, with Napier's Bones, you can do a lot of calculations, and you can even get a lot out of an exchequer board, or even tablet of Salamis. If you don't have paper and pencil, you can always bang out division using the galley method vs. the long-division algorithm in the sand. [ It's easier to deal with. ]
Great video!
the trick here is the use of 10s complement numbers. it's really wonderful how that simplifies complex calcuations
Most electronic calculators have a multiplication shortcut for when you are multiplying several numbers by another. On my iPhone, I type 130x4.7=190= and it displays 611 and then 893.
Very interesting! I must admit I kinda hate these features (there are similar tricks about repeatedly pressing the = button). They are useful, but always seem totally arcane to me- I'm always so unsure of exactly what will happen that I never trust myself to use the feature properly. Similarly on calculators with a C for clearing and an AC for clearing "all". I can never predict the precise behavior of the C, so I always hit the AC. (Usually at least twice.)
@@ChrisStaecker The percent key on a calculator has always been that way for me. Different calculators have percent keys that do slightly different things and I can never remember how to use it, whereas I understand percents and I can remember how to divide or multiply by 100. So I never touch the percent key.
@@MattMcIrvin Yes! I agree 100%
i can't believe curt goedel had time to invent this machine after upending math
The Kürta™
BYW, I just finished cleaning up my Marchant XL-A pinwheel calculator, I’ll post a video soon. Thank you for the inspiration!
The parallel computing reminds me of array programming languages which equally didn’t take off. Typing “130 190 × 4.7” into an APL repl gives the two answers you’d expect because the multiplication operation dynamically operates however many values are on either side
Didn't take off? More like: They left the planet and only visit from time to time. They're still used, but in niche areas, and you need to be able to cast at least 3rd level spells. That keeps the (coder [not programmer]) riff raff out.
Love this series so far!
It’s also interesting to see parallels with the Comptometer that had a bunch of niceties and features that helped with similar use cases! For example splitting the big number into multiple numbers was also possible, and there were even small buttons next to each result digit you could hold to prevent a carry from traveling too far to the left and “contaminating” the other number that was there.
“Success is a lousy teacher. It seduces smart people into thinking they can’t lose.” - Steve Jobs
3:16 there is no better tool than a sliderule for this kind of job. Just slide the squares scales by (let's say) 4.7 so you don't have overflows and you have a lookup table for any number of ingredients. It's good that you can also guestimate the closest values for hard to divide things like eggs etc (and maybe adjust the factor around those values)
Also a good thing that you can read the values directly and don't have to extract your hands from the dough to fiddle w/ mechanical parts. Gosh I love sliderules.
/tangent
Curta
LOL That wasn't Steve Jobs!
Nice machine! I want one now. I thought I had everything I wanted. I was so wrong.
For the algorithm.
The parallel calculation was excellent, but that was when you would have had to do it manually or by cranking a handle. Today, it's easier to type it in as two different calculations or use Excel.
Parallel calculations are a niche tool for sure, but modern CPUs are capable of doing them! In two ways, even. There's the obvious way; a processor has several cores that all operate independently. But there's also a class of instructions called SIMD instructions -- short for Single Instruction Multiple Data. You can queue up a handful of numbers (as opposed to just single numbers at a time), then run the same operation on all of them at the same time in just one instruction. A good software engineer can use SIMD instructions to greatly speed up some algorithms. (Now if only the truly good software engineers weren't in such short supply...)
I DO want a Curta though.
noice
actually, parallel calculations are the new hot topic in computing these days. everybody is like, yo lets do data parallelism for our deep learning
Yes, but parallelism on hand-held calculators? Maybe I should attempt to execute deep learning algorithms with the Curta...
@@ChrisStaecker you could buy two calculators
I dunno, that flatbread yarn seems pretty far-fetched to me...
I believe I was very clear on that point
You had someone over who was 14.7 years old? You guys take the legal flatbread age way too seriously.