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.
@@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.
@@porkeyminch8044 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.
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.
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).
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!
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.
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.
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!
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. 🙂
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.
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.
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.
@@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
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.
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.
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.
@@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.
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!
@@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.
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!).
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!
It's also called the Egyptian method. It's base 2. (There's the lattice method also called Napier's Bones, Chinese Method, Italian Monk's method. There's also several Indian methods.)
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.
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.
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.
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!
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.
Johnny Ball, one of the best TV presenters ever. Haven't seen him for ages, but he's so great at explaining things so clearly and concisely. My mind is blown by this, as it seems very elegant in a way to do the calculation. Yet for many people in the world this is just normal.
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. :)
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.
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.
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.
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'm self taught when it comes to multiplying tricks, but I use a variant similar to the egyptian one. I see multiplication as collecting boxes. So you can divide any multiplication into smaller subgroups of boxes that are easier to calculate. Then you add them together. You can even subtract a subgroup. Generally how I multiply is 13x9 = 13x10-13x1=130-13=117. Here's a harder one: 589x113 = 589x100+589x10+589x3=58900+5890+1767=63900+890+1767=64790+1767=65790+767=66557 A more advanced variant that is quicker: 589x113 = 600x100+600x13-11x100-11x13=60000+7800-1100-143=67800-1100-143=66700-143=66557
Oh my gawd, Sir Johnny 'Think of a Number' Ball! What a legend. You are spoiling us getting him on the Channel. And on my birthday. Brings me back to my yoof in the early 80s.
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.
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!
@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.
@@terranrepublican5522 I wish it had been taught in my first-year computer science class. I learned about this from the book "The Structure and Interpretation of Computer Programs".
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. 😀
@@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.
I've seen this video before, when it came out. I see it again now. I think this old guy looks vaguely familiar. I didn't see his name. Finally, I realize this guy was on tv when I was a kid. He had a science program. I don't even remember the show, I just remember the name. Johnny Ball probably got more kids interested in maths and science than anyone else - in the UK at least.
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.
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.
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.
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.
Johnny Ball on Numberphile! The circle is complete. I used to adore Think of a Number when I was a kid (many, many years ago). I'm sure it helped spark my love of mathematics, physics and computer science, and now people pay me to turn mathematics into computer programs.
6:01 This process works for any base, not just binary, just use the modulo result of the base instead of odd/even (which is the modulo 2 result). e.g. 47 in base 3 47mod3 = 2 47/3 -> 15mod3 = 0 15/3 -> 5mod3 = 2 5/3 -> 1mod3 = 1 Roll them up to 1202 which is 47 in base 3.
@@garr_inc да понятно, просто слегка обидно узнаквать про такие небольшие но интересные детальки от западных матешников а не от наших. (хотя я всё ещё не совсем разубедился, что в описанном случае в баре рассказчик назвал способ русским только в силу мистчиеской далёкости сего прилагательного для местных)
Stret173 посидите полчаса и сами придумайте удобный для вас метод на основе определения умножения. Я умножаю по-своему, не так, как другие в столбик, ибо carriage разряды и "единичка в уме" не для меня.
The Legend that is Johnny Ball. Probably responsible for more kids getting into maths and science than pretty much anyone I can think of :) He was much watch TV for me growing up
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'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.
@@porkeyminch8044 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".
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!
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!
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.
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!
I have adored Johnny Ball since I was a small child, he was one of the inspirations for my love of maths.
Likewise
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.
I never hear of him before this video
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.
@@TibbsMM In binary it multiplies by two.
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
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
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.
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. 🙂
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.
Suddenly, I'm a kid again. We need more Johnny Ball!
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.
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"
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.
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
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.
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...
If more ad placements had such relaxing music i think i'd sit through it. That was simply pleasant.
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.
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.
One of my childhood heroes, and once again, he reveals all...
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!
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.
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!).
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!
It's also called the Egyptian method. It's base 2. (There's the lattice method also called Napier's Bones, Chinese Method, Italian Monk's method. There's also several Indian methods.)
Was so good to see Johnny Ball again, such a massive influence on my childhood and love of science :)
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.
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.
Bristolian here and as soon as I heard that accent I smashed that like button!
This is the greatest thing I’ve heard today. Love it and want to teach my son this.
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.
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.
Johnny Ball on Numberphile!? I would never have expected this. Also this method is kinda mind boggling.
oh seeing johnny ball just made my day ! loved him as a kid
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!
Gotta love Johnny Ball.
Still teaching me stuff, 35 years after I used to watch him on TV as a kid 🍺
I’ve implemented this multiplication algorithm before in 6502 ASM, and I still didn’t recognize it till he did the Egypt version
Oh, yes, more of Jonny Ball, please… so inspiring, he is a superhero!
Beautifully explained, fascinating to see so many different ways to find the result. Numbers don't lie!
Johnny is a legend.
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.
Why isn’t Johnny Ball still explaining it all on national television?
Johnny Ball, one of the best TV presenters ever. Haven't seen him for ages, but he's so great at explaining things so clearly and concisely. My mind is blown by this, as it seems very elegant in a way to do the calculation. Yet for many people in the world this is just normal.
Initially, I was like “Meh, I know this one”. Then the binary connection and... boom. :)
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 cheeky little wink at the end, I love it.
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.
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. :)
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 Ball on Numberphile! Never have I clicked so fast!
Johnny Ball.... I absolutely love this man. He was a major factor in my childhood. Lovely to see him. Thanks, Brady.
Wow, truly brilliant techniques from what must be an original "learning by doing" pattern.
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.
The OG still reveals all
I'm self taught when it comes to multiplying tricks, but I use a variant similar to the egyptian one. I see multiplication as collecting boxes. So you can divide any multiplication into smaller subgroups of boxes that are easier to calculate. Then you add them together. You can even subtract a subgroup.
Generally how I multiply is 13x9 = 13x10-13x1=130-13=117.
Here's a harder one:
589x113 = 589x100+589x10+589x3=58900+5890+1767=63900+890+1767=64790+1767=65790+767=66557
A more advanced variant that is quicker:
589x113 = 600x100+600x13-11x100-11x13=60000+7800-1100-143=67800-1100-143=66700-143=66557
this was fascinating information compacted in 5 short minutes, mind blowing
Oh my gawd, Sir Johnny 'Think of a Number' Ball!
What a legend. You are spoiling us getting him on the Channel. And on my birthday. Brings me back to my yoof in the early 80s.
That's pretty darned brilliant if you ask me...or even if you don't ask me, it's still pretty darned brilliant.
I never thought I would have Johnny Ball astound me ever again, thanks Numberphile.
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.
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!
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
This man's ability to describe and tell a story is brilliant! Such an enjoyable, pleasant character.
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
This guy johnny ball came to my school St Anselms, what a W guy
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.
@@terranrepublican5522 I wish it had been taught in my first-year computer science class. I learned about this from the book "The Structure and Interpretation of Computer Programs".
So happy to see Johnny ball again. Just brought my childhood flooding back!
Oh my! They're converting it to base 2 and multiplying in base 2!
Tentoes Yes
It would have been a great addition to the video if he mentioned that doubling an integer in binary is shifting the bits to the left.
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's grandchildren will listen math stories at night with his utterly simple and elegant narration skill. Love it😘
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.
Great to see Johnny here, used to love his TV programme Think of a Number back in the day.
Johnny Ball: legend!
I've seen this video before, when it came out. I see it again now. I think this old guy looks vaguely familiar. I didn't see his name.
Finally, I realize this guy was on tv when I was a kid. He had a science program. I don't even remember the show, I just remember the name.
Johnny Ball probably got more kids interested in maths and science than anyone else - in the UK at least.
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.
You can hear his accent shift when he goes from story to math at 3:00 "they did it a slightly diffent way" and it's amazing
This is how I imagine Samwise Gamgee's gaffer sounds like.
Johnny's math book got me through school because my brain couldn't handle the teachers way, but his method made sense to me. Thanks Johnny!
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.
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.
Anyone else want a series of "Think of a Numberphile"?! 😎😃
Yes please!!!!
Please redo every single numberphile video with Johnny Ball. Puleeeeeze.
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.
Johnny Ball on Numberphile! The circle is complete. I used to adore Think of a Number when I was a kid (many, many years ago). I'm sure it helped spark my love of mathematics, physics and computer science, and now people pay me to turn mathematics into computer programs.
As a Russian I could say for sure this is the first time I see this method in my life! Am I even Russian after all? 😨
нет
We want more Johnny!! His voice and energy is so lovable and enjoyable!
That just sounds like binary numbers with extra steps.
Not rly. It's just binary representation for N ary system, where N is the multiplicator (2 in binary)
6:01
This process works for any base, not just binary, just use the modulo result of the base instead of odd/even (which is the modulo 2 result).
e.g. 47 in base 3
47mod3 = 2
47/3 -> 15mod3 = 0
15/3 -> 5mod3 = 2
5/3 -> 1mod3 = 1
Roll them up to 1202 which is 47 in base 3.
как обычно у нас в россии про русское умножение слышат впервые
Потому что отчаянно давно так делали. Сейчас это никому не интересно, всех учат в столбик.
Garr_Inc потому что столбиком можно объяснить любому (почти) ученику. Это интуитивно понятная методика 😁
@@garr_inc да понятно, просто слегка обидно узнаквать про такие небольшие но интересные детальки от западных матешников а не от наших. (хотя я всё ещё не совсем разубедился, что в описанном случае в баре рассказчик назвал способ русским только в силу мистчиеской далёкости сего прилагательного для местных)
@@Stret173 Абсолютно справедливо.
Stret173 посидите полчаса и сами придумайте удобный для вас метод на основе определения умножения. Я умножаю по-своему, не так, как другие в столбик, ибо carriage разряды и "единичка в уме" не для меня.
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!
"That's Numberwang"
The Legend that is Johnny Ball. Probably responsible for more kids getting into maths and science than pretty much anyone I can think of :) He was much watch TV for me growing up