Russian Multiplication - Numberphile
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- Опубликовано: 10 июн 2024
- Johnny Ball on Russian and Egyptian Multiplication.
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More on Johnny Ball, including his books and live shows: www.johnnyball.co.uk
Russian multiplication is also known as Ethiopian multiplication.
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Наука
9 × 13
Brady : I want another example
Ok
13 × 9
True, this was the worst example ever of "falsifying the premise" to test the hypothesis! 😂
PopeLando Well, not necessarily. Mathematically, it is necessary to treat 9*13 and 13*9 as separate calculations, and in order for the method to be valid, it is necessary that both calculations have the same output, since we know multiplication is commutative. Hence, we can consider this as a teat of sorts. If the result for calculating 13*9 fails to be equal to the result for calculating 9*13, then the method is invalid - the converse is not true, though, so if this test is passed, more tests are needed to determine sufficiency. However, this is the first step.
@@angelmendez-rivera351 the magic phrase is "necessary but not sufficient"
Outstanding move
@@PopeLando How do you know the operation he performed gives you the same thing for a*b and b*a? The reason you rely on your usual intuition for a*b = b*a is is because multiplication over R is commutative. It may well be that the operations he was performing would result in a*b not being the same as b*a or one of these not being defined altogether.
I could enjoy listening to this man reading a phone book.
True
@שחר א. No entiendo
He sounds happy and he talks in a way that makes it infectious.
What's a phone book?
Gonna take a long time in binary!
I've been told this is the person that got Numberphile's very own James Grime into maths!
Makes me wonder what got Johnny's father's friend into maths.
@@jacksonpercy8044 What makes you think it was his father's friend. Johnny's story took place in a time when adult men could still speak to strange children without anyone being suspicious of their motives. I've always thought it's sad that can't happen anymore.
@@thomasyates3078 He says so.
@@qwertyTRiG No he doesn't. He says he met a fella in a pub.
@@thomasyates3078 At 26 second he says "Mate of me dads".
Just seeing Johnny Ball in a Numberphile video was enough to blow my mind, never mind the maths! One of my childhood heroes, definitely inspired me in my early life. I'm now a software developer of thirty years. Love you, Johnny!
This guy is a 22 year old in the body of a 52 year old, but he’s 82.
Hot damn. He's healthy for 82.
I hates them even numbers.
That doesn't sum up at all ...
he is actually 81 (from wikipedia)
52 year old body LOL
Am I alone, or does anyone else want more Numberphile videos featuring Johnny?!
You‘re not
He's truly a master educator/communicator/story-teller, the perfect combination for this channel.
Just look for 'Think of a number'. Johnny Ball is a hero to many Brits. During the 70's and 80's this is what we all watched (Only 3 tv channels at that time and on at 5pm).
I want MORE Cliff Stoll and Johnny Ball!
More. Much more.
When he was halving it at first, I didn't realise what was going on.
But when he did the doubling on both sides, it dawned on me what was going on because I've actually used this.
You see, old CPUs - like the MOS 6510 in the C64, which was the second computer I ever owned - didn't have multiplication or division instructions. They were cheap and simple 8-bit chips and complex operations like that would have used up too much of the silicon.
And this is exactly how you'd do multiplication on a chip like that, which didn't directly have a multiplication instruction.
Because, in binary, to multiply something by 2, you just shift all the bits over to the left one. Just like how, in decimal, when you multiply anything by 10, all you do is stick a zero at the end - basically shifting all the digits left and dropping a zero in the gap you just created. Same idea works in binary, but shifting it all left and dropping a zero in the gap is multiplying by two, rather than ten, as this is "base 2" and not "base 10".
So multiplying by any power of two is simple, just shift the bits over to the left. Once to multiply by 2. Twice to multiply by 4. Three times to multiply by 8.
But what if you want to multiply by 3? Well, shift the bits over one - that's multiplying by 2 - and then add the original number to it. I.e. 3 x 9 = 2 x 9 + 9.
If you want to multiply by 5 then multiply it by 4 - shift left twice - and add the original number to it. As 5 x 9 = 4 x 9 + 9.
If you want to multiply by 6 then you can multiply by 4 - shift left twice - and multiply by 2 - shift left once - and then just add them together. Because 6 x 9 = 4 x 9 + 2 x 9.
And if you keep following this logic, then you realise that you can - by arrangements of shifting left and adding it together (where adding on the original number can be seen as being "shift left zero times" - that is, 3 x 9 = 2 x 9 + 1 x 9).
Then you realise the combination of what you need to shift left and add together is given to you by the binary of the number you're multiplying by. 5 in binary is 1001 = 4 x 9 + 1 x 9. 6 in binary is 1010 = 4 x 9 + 1 x 9.
So you can write a subroutine to multiply two numbers together that shifts right one of the numbers and tests if there's a 1 bit shifted out. If there is then shift the other number left by as many times as you've shifted the other number right. Add this to a running total. Repeat until you've shifted all the original bits out of the "shift right" number.
Done. The running total will now be the result of multiplying those numbers together. Multiplication using only bit shifting and addition. Using only halving and doubling, and adding up.
(And, truth is, though modern CPUs do include multiplication and division instructions directly, doing it manually on those older CPUs tells you exactly how the hardware is doing it. It just automates the whole procedure into a single circuit for you.)
Oh, and the other thing to note is that you need double the number of bits to store the result. If you're multiplying x and y together and they're both 8-bits, then you want 16-bits to store the result. Because 8 bits times 8 bits cannot produce a result more than double the size - so 16-bits. Or 32-bits by 32-bits, you need a 64-bit register for the result. As long as the result is double the size of the longest number in those you're multiplying, the result can't overflow.
Thank you for explaining
That's the missing part of the epilogue 😄 It's all clear now! Thank you!
I thought it was the 6502 processor.
The video was great, just like this response. Nice things to learn.
Very interesting, particularly the bit shifting. Thanks!
The egyptian method also shows how computers multiply numbers together - if you shift a number left by one position, you've doubled it, and the first factor is already in binary.
Plus the egyption method is basically the same as the standard decimal way of multiplying most kids learn, except in binary.
@@Carewolf о
I would like but your comment's at 64 likes
What? Shifting a number left means youve multiplied it by 10.
@@tibbsgaming7460 In binary it multiplies by two.
I have adored Johnny Ball since I was a small child, he was one of the inspirations for my love of maths.
Likewise
My son and I both have our own copies of his "Think of a Number" book. Bought for each of us 35 years apart by my mother. The cover is different, but inside it's the same. The latest textbook I wrote has a section on phyllotaxis, which I remember first learning from that book. He is such a legend. And such an inspiration for our whole generation.
Me too, he was inspirational then and still is now
Ditto!
Me too...I loved him on TV in the 80's and I still have 'Think of a Number' on my bookshelves.
love his accent
he knows story telling
When I saw the 1, 2, 4, 8, 16 in a column my eyes widened. The ancient Egyptians were using binary and had no clue they were doing it. This is blowing my mind.
to be fair, the only thing they didn't know was that a future civilization will call them "binary numbers" ^^
I think they did not even have positional notation for numbers - neither binary nor decimal! I am now wondering if they had influenced the invention "Arabic" numerals, or if Indian people came to them independently.
the egyptians probably knew it very well and were super advanced beyond what you know. think about what would happen if the internet disappeared along with all your ebooks. future civilizations would not know about your technological prowess
@@icyuranus404 There's evidence of Egyptians urinating near anthills to diagnose diabetes. I really don't think they were very advanced beyond what we do actually know of their advancements.
@@hypsin0 it is more environmentally friendly to pee on an anthill than to concoct a test that is administered by a debt laden college student wearing sterile gloves produced by dinosaur turds. they used binary because they knew what they were doing and we use it too and one day when civilization falls, there will be no youtube to convince the world that we ever used binary to interface with video drivers and it will only be found in egyptian and russian caves. maybe they had it all together and knew they were going to pass on so they encoded binary into our ancestoral knowledge which gave us the ability to use binary to make computers and share in their technological prowess. maybe they were so woke that they understood that you can still keep some things simple
Oh Jeez! I absolutely LOVED Johnny Ball’s TV when I was a kid, and ever since. I’m SO glad he’s still passionate about maths. PLEASE do as many videos with him as he feels able to do.
My wife and I met Brian Cant in Poole after a show there, told him what a difference he’d made to us growing up and introduced our own kids to him. He seemed genuinely touched. Would love to meet Johnny too some day!
The way we get into Mathematics is not always an easy decision, however every minute after that, we get to appreciate our decision more and more.
Until stats
@@briangeer1024 or when numbers no longer arranged linearly, and ancient letters show up
I just dont get it... psi.
I love this comment.
@@briangeer1024 Stats is the best bit.
I could listen to this man for hours. His enthusiasm for the field of mathemaics is apparent & astonishing!
Nobody beats the enthusiasm of Prof. Klein Bottles
Johnny Ball is such a legend! He made that so simple for somebody as maths illiterate as me. Never knew he grew up in my home town of Bristol either. 🙂
For clarity:
Division by two then rounding down is equivalent to removing the last digit in the number's binary representation.
All even numbers end in 0 and all odd numbers end in 1.
This process is the very definition of the binary representation.
Thank you, I was wondering why this crucial step was left out. Without it the "connection" between the methods is incomplete.
1st Column: Shift Left (automatically rounds down) until equal to 1.
2nd Column: Shift Right the same number of times as the above line.
Check each number in the 1st column to see if the 1s bit is a 0. If so, remove the same entries in both columns.
Add together what's left.
Edit: thanks for the correction, @theblinkingbrownie4654, also because of your first correction I found another mistake.
@@legendgames128you confused your lefts and rights
@@theblinkingbrownie4654 Thanks.
Suddenly, I'm a kid again. We need more Johnny Ball!
I can't believe you got Johnny Ball. He was like the Brady Haran of kids' TV in the UK in the 1980s. He made maths & science fun for a whole generation.
The fascinating part is finding out how/why it works. He said that he learnt this from someone who was taught around in the 19th century. Thank you Numberphile.
I can guarantee you that every 6502 programmer knows this egyptian method. The 6502 processor did not have a multiply instruction so If you wanted to multiply you could do it with a series of Add and "Shift Left" instructions (shift left will double a binary number!).
I'm russian and i never heard of something like that.
Same lol
But it might have been used a long time ago (I’ve heard of that from a 1910s book)
Maybe it's just called "russian" because of the "purging" part.
Абсолютно аналогично.
@@FriedrichHerschel I don't think it's related to that, it was a joke. As far as I know, it is named "Russian peasant multiplication" which explains a lot lol
( Хорошие книги по истории математики у Ван дер Вардена {Van der Waerden}) "Science awakening"
The arithmetic you describe definitely appears in the Rhind Mathematical Papyrus ca. 1550 B.C. This is not from ancient Egypt (where it was likely preserved in Alexandria) but in fact from ancient Sumer. These sections in Book 3 (as in all the sections) used units and common denominators to work out difficult fractions. One problem to look at is 79. Although the solution to problem 79 suggests an arithmetical fact which is not true in general, it clearly shows an intimate understanding of arithmetic in its working out in this specific case.
Problem 79 of Rhind Mathematical Papyrus? Where do I find a copy of that?
i see...
Beautifully explained, fascinating to see so many different ways to find the result. Numbers don't lie!
Johnny was teaching me as a child with his TV show (and the audio cassette that came with my Salter Science chemistry set... And now is teaching me something new as an adult...
Hats off to Johnny, what a fantastic influence he has been for so many of us.
That Bristol geezer voice is priceless. :D
Pretty damn accurate, gotta say (as a Bristolian).
Arr kid does a proper job with maths proper like
@@ubertoaster99 seeing as he's *from* Bristol, not particularly surprising ;-)
@@PhilBoswell Yeah, but he moved north when he was young. His normal accent is slightly northern.
Initially, I was like “Meh, I know this one”. Then the binary connection and... boom. :)
Definition of a pleasing explainer: he begins at 0:40, I fully understand the video at 0:47, I still watch it until 5:10.
There's still an interesting bit hidden starting at 5:57 where he explins how this can be used to almost effortlessly convert from base 10 into binary.
That cheeky little wink at the end, I love it.
One of my childhood heroes, and once again, he reveals all...
Do we have more videos with this man? I need all of them.
Plenty outside of Numberphile, just search RUclips for Johnny Ball.
I search that and just get videos in climate change denial
@@xera5196 search YT for Johnny Ball think of a number, then play a few and click like a few. Algorithm will correct itself.
Ноль, целковый, полушка, четвертушка, осьмушка, пудовичок, медячок, серебрячок, золотничок, осьмичок, девятичок, десятичок.
Так считали наши предки.
Партия и сюда добралась
Does that translate into english? Google Translate just made me more curious.
@@keithstathem872 lol go study languages
@@PersimmonHurmo I've tried several times, and the differences in grammar are very interesting, but I have such a hard time remembering vocabulary that I've never been able to get very far.
Great to see Johnny again. He was a hero of mine when I was younger. I've got a signed copy of one of his books that had this method in it.
My uni professor taught us this method when we were studying binary, oct and hex, haha. Pretty interesting!
I understood binary, but how does it work with base 8 and base 16 numbers?
@@SpiacyLos uh, it was more like a fun fact that had some relation to binary numbers. Not sure if it works with octal and hexadecimal tbh...
@@SpiacyLos , base 8 and base 16 are just compressed binary representations. Hex is specially perfect for human readability because it divides all power of two variable sizes to whole sections.
not sure what I said before made sense, but halfing and doubling seem to apply to any base systemI think:
in deci (convert it)
9x13
in octal (start doubling and halfing)
11x15
4 32 (remember halfing 11 in octal is half of 8+1, i.e. 4&half, etc.)
2 64
1 150
15+150=165
165 octal is 117 in deci.
@@GreenIllness , Correct. Base doesn't matter.
Odd bases are harder because you can't make even or odd check as easily as in even bases. But basic algorithm doesn't care about base as long as you can do even or odd check.
oh seeing johnny ball just made my day ! loved him as a kid
Was so good to see Johnny Ball again, such a massive influence on my childhood and love of science :)
Such a treat to see and hear Jonny Ball after so many years. I remember him being a fixture on the telly back in the early 80s! Very happy to see he's still going string, and as enthralling as ever.
This may be my favorite fact about maths practices, at least for now. Thank you for sharing this, including the history and the binary reasoning behind it. Makes so much intuitive sense with the doubling and halving, especially with this fantastic presenter. Grazie to both of you!
This is the greatest thing I’ve heard today. Love it and want to teach my son this.
Yep, I was one of them kids that sat glued to Think of a Number on the telly back in the 80s! 40 years later and Johnny still showing us maths in a fun and entertaining way! Brilliant!
I love Johnny Ball! One of my earliest school memories was watching him forty years ago! This video took me back. He has all the energy and love of numbers he always used to. Great to see him on one of your videos.
I've been using the Egyptian method in programming, and I didn't know where it came from! I thought for sure that was a computer-era invention, or at least not older than binary.
They used this method for engineering calculations when designing pyramids.
The aliens had very fancy computers so it indeed was computer-era invention.
I'm not sure why you would need this method when every programming language has a * operator, except for some low-level old 8-bit chips. And to figure out what a number is in binary, the bitwise and and shift are generally more handy.
@@fghsgh Yep, it's on a low-level 16-bit chip! The SNES to be exact. It does have multiplication registers, but multiplying by powers of two and adding is probably more efficient there.
@@mebamme Is doing it manually really faster? Maybe check the instruction set. I don't know the SNES CPU though. I do mostly Z80.
Why isn’t Johnny Ball still explaining it all on national television?
Wow! This is my favorite Numberphile yet. Maybe because I actually understand it. Really, this is something I've never heard of before and is so mind warping-ly simple yet at the same time perfectly illustrates the complexities and symmetry of math. Thanks for making these Brady (and Objectivity!). You and your comrades make, imho, the perfect videos: Fun, smart, thoughtful, and positive. Your vids are full of exuberance and there is no negativity, which is refreshing in today's world. You made my day!
I can probably thank Johnny Ball for getting me hooked on maths & science when I was a kid, he's great. Loved his TV shows!
Didn't know about this approach for multiplication.
Great anecdote & history to go with the great explanation. Many thanks.
Johnny is a legend.
Gotta love Johnny Ball.
Still teaching me stuff, 35 years after I used to watch him on TV as a kid 🍺
Johnny Ball on Numberphile!? I would never have expected this. Also this method is kinda mind boggling.
This is my favourite numberphile video in years. Johnny Ball is amazing, thank you so much!
Oh, yes, more of Jonny Ball, please… so inspiring, he is a superhero!
I never saw that connection before... it does get a little unruly with larger numbers pretty quick tho
yeah, although I don't suppose that would have been much of an issue for most of the people making use of this method centuries or millennia ago in their everyday lives
True if done by hand, but I can see how doubling and adding can be computationally less expensive than multiplying in certain programming environments or on certain processor architectures.
@@chaosme1ster This basically reduces multiplication to bit shifting, comparison and addition.
@@chaosme1ster, a question is why the multiplication wouldn't just be implemented like this.
I think it's even to convoluted for 9×13. The way I have learned it school seems more straightforward and wastes less ink and paper too. :)
Wow, what a great presentation! Love the way it tied together at the end
Absolutely brilliant episode! What a wonderful connection.
Johnny Ball on Numberphile! Never have I clicked so fast!
this was fascinating information compacted in 5 short minutes, mind blowing
We want more Johnny!! His voice and energy is so lovable and enjoyable!
So great to see Johnny Ball on this channel. More please please please.
Wow, truly brilliant techniques from what must be an original "learning by doing" pattern.
fantastic video. this is the spirit of numberphile
Johnny Ball is such a wonderful personality from my childhood.
Despite my rocky relationship with maths I find numbers so fascinating I'm going to give subscribing to this channel another try for 2020. Cheers from Australia!
This is one of the greatest things I've ever watched on this channel and I've watched nearly every video. I love these "tricks" that also tie into modern concepts.
The OG still reveals all
While watching this video, I ran into my sister's room to show her the ancient Egyptian multiplication halfway through putting my socks on because I thought it was so cool.
Wow! It's good to see Johnny Ball, I remember watching him on Think of a Number as a teenager, and always loved the way he explained maths in such a simple and easy to understand way. I would like to see more videos with him in.
Thank you for the new horizon and beauty.
That's pretty darned brilliant if you ask me...or even if you don't ask me, it's still pretty darned brilliant.
This is how I imagine Samwise Gamgee's gaffer sounds like.
This is what numberphile is about! The math doesn't have to be complicated - it's all about the storytelling and the fantastic presentation of an interesting subject.
What a great video!
Love this guy! Amazing story teller. I’d love to see more math history episodes.
Johnny Ball: legend!
Oh my! They're converting it to base 2 and multiplying in base 2!
Tentoes Yes
This is insanely cool. Thank you for showing it to us! Спасибо большое!
every single time Numberphile shows up in my recommended, I go, ehhh, okay, I'll watch and then everytime I'm like no effing way!!! Ty for not having click bait titles where i get to be pleasantly shocked and awed each time.
*Johnny is still on the ball!*
now purge any words briefer than four characters or containing a narrow vowel
Brilliant is really helpful
I learned a lot in 6 months
lol nice bot comment
Jolly Joy I’m not a bot
Check my channel
If more ad placements had such relaxing music i think i'd sit through it. That was simply pleasant.
Great to see Johnny here, used to love his TV programme Think of a Number back in the day.
Cliff Stoll, Johnny Ball, -Matt Parker- ,these people should never ever die atleast not before me
Is there some inside humor about Matt Parker I'm not aware of for his name to be crossed out?
@@JohnMichaelson Parker Square
I was shown this by my math teacher like 12 years ago and I've never remembered it since but now I do and know why it works
@Nhật Nam Trần Because of the binary representation. The Egyption method makes it obvious. The original method is a round about way to get the same pattern as the binary presentation on the left hand side.
@Nhật Nam Trần No, that is exactly how it works. The division by 2 and looking at whether or not something is even or odd, is the same as looking at every bit in the binary representation in turn. Every division by 2 moves on to the next binary bit, and looking at whether or not the result is odd or not, it looking at if that bit is set.
@Nhật Nam Trần Yes, but not in format this short. The only short proof is to show it is equivalent to binary and use the known properties of that format.
Nhật Nam Trần It is basically equivalent to **binary multiplication:**
=== Algorithm ===
1. Initialize sum
Johnny Ball! What an absolute joy to see him continuing to be enthusiastic about maths.
I remember his explanation of cycloids with a rolling cycloid log keeping a plank level.
Very cool! Thanks for the vid Brady
Omg that blew my mind
He taught me to count in Sumerian (12s) and months and seconds and minutes on my hands when I was young.
You count the 3 sections of the 4 fingers on your hand with your thumb. When you have counted 12 sections of one hand you close 1 finger on your other hand. When it makes a fist you have 60.
Counting the twelve sections of both hands gives you the 24 (hours) in a day.
Here's another way to count:
Your finger has 3 sections and 2 bends, that's 5 points to touch. You can touch the front or the side of the finger, doubling the points you can touch to 10.
Each finger on one hand can point to a point on one finger on the other hand. You then have 4 sets of a finger pointing at a point on another finger.
Now you have a 4 digit base-10 abacus.
You can actually count up 1024 on your fingers.
@@MichaelPohoreski, 9999>1024
@@JNCressey Yup, you can use different bases but sadly most people aren't familiar with base 2 or base 60.
@@MichaelPohoreski, then it's serendipitous that my method is in base 10.
His explanation is like a suspense novel: intensely captivating. I wish there were more teachers who excel at storytelling. It makes learning so much more interesting and effective. :)
That was absolutely fantastic! I've seen this about 10 years ago but it was great to see it again.
okay now THIS should be taught in all schools all over the world!!
Not practical for large numbers, complicated to multiply fractions. The method taught always works and is over-all he most efficient.
it's taught in the second week of the first semester at my uni, computer science
Doubling isn't that easy to do in your head with larger numbers.
Last time I was this early, the Tsar was still alive.
Do you mean.. Tsar Bomba?
Last time I was still alive, Russia was called Kievski Rus
OMG it's Johnny Ball! I haven't seen him since I was a kid. Brilliant to see and hear him again. Thanks Numberphile, and thanks Brady!
This was both enlightening and charming. I am delighted.
"That's Numberwang"
Well i’am from Russia and I haven’t heard about this method 😄
But I admit it’s stunning!
It's on several books I have as the "Russian peasant multiplication method"
Lol the comment section is full of people from Russia who have never heard of this method. I guess “Russian” is just the name the Brits have for it. Like French kiss.
Also, Russians must be very fond of mathematics if there’s so many who follow this channel. 😀
next we'll find out brazil nuts actually come from Spain
Нихера не понятно, но очень интересно))
@@pansepot1490 This method was widely used by Russian peasants. This is indicated by the mathematics historian Wiktor Wiktorowitsch Bobynin (1849-1919). But since 1917 in Soviet times he was not taught.
Johnny Ball.... I absolutely love this man. He was a major factor in my childhood. Lovely to see him. Thanks, Brady.
Thank you for this. I first learned about this method some years ago in a Math for Educators course (the professor called it “The Russian Peasant Method of Multiplication”). I couldn’t remember quite how it worked, and was never able to find an explanation of it. You just made my day.
Anyone else want a series of "Think of a Numberphile"?! 😎😃
Yes please!!!!
It is a rare and beautiful moment when I see a new (to me) piece of math like this.
I just want to grab it like a toy and start playing with it. Figure out how it works.
It works the same as the usual method, only slower.
@@tudormontescu6275 But why does it work? That's what's intriguing.
So happy to see Johnny ball again. Just brought my childhood flooding back!
So great to see Johnny Ball again. Thanks Brady.
and we keep wondering how they built pyramids.... well they probably didn't have the tech but for sure they were very inteligent so they knew how to use the limited things they have. very nice stuff. we can use our brain to multiply 2 digit numbers and sometimes 3 digits.. but when it comes to big numbers and you dont have a calculator, this egiptian/russian method and also the indian method are golden.
I'm from Russia and I've heard about this for the first time. REALLY!
Ice_Cream dont worry about it. The French never played French cricket, and the Chinese didnt invent Chinese burns.
hopefully you've heard about how much Russians hate fractions and love purges?
Also the French don't use the words "French kiss" or "French fries".
Btw, in Portuguese we call a "roller coaster" as "Russian mountain". But the Russians call it "American mountain" 😅
The Russia connection is a joke. It's just some story an old guy told a kid in a pub. It's designed to help the kid remember the procedure.
More of this!!! This was amazing.
I never thought I would have Johnny Ball astound me ever again, thanks Numberphile.