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| How does a human calculator do it? | How does a human calculator do it? |
| (2 days later) | |
| Root of all easy: Lemaire did this sum in 2004 in less than four seconds | Root of all easy: Lemaire did this sum in 2004 in less than four seconds |
| Alexis Lemaire has broken the record for finding the 13th root of a 200-digit number. It's an incredibly hard calculation so how does the "human calculator" do it? | Alexis Lemaire has broken the record for finding the 13th root of a 200-digit number. It's an incredibly hard calculation so how does the "human calculator" do it? |
| Fancy yourself as a bit of mental arithmetics buff, one of those who relishes totting up the bill after a restaurant meal for 12, one of those who looks down their nose at calculator users? | Fancy yourself as a bit of mental arithmetics buff, one of those who relishes totting up the bill after a restaurant meal for 12, one of those who looks down their nose at calculator users? |
| Well try this for size. | Well try this for size. |
| The task is to find the 13th root of 85,877,066,894,718,045,602,549,144,850,158,599,202,771,247,748,960,878,023,151,390,314,284,284,465,842,798,373,290,242,826,571,823,153,045,030,300,932,591,615,405,929,429,773,640,895,967,991,430,381,763,526,613,357,308,674,592,650,724,521,841,103,664,923,661,204,223. | The task is to find the 13th root of 85,877,066,894,718,045,602,549,144,850,158,599,202,771,247,748,960,878,023,151,390,314,284,284,465,842,798,373,290,242,826,571,823,153,045,030,300,932,591,615,405,929,429,773,640,895,967,991,430,381,763,526,613,357,308,674,592,650,724,521,841,103,664,923,661,204,223. |
| The answer's 2396232838850303. Multiply that by itself 13 times and you get the above. Even with a calculator you wouldn't beat Alexis Lemaire doing the calculation in his head. | The answer's 2396232838850303. Multiply that by itself 13 times and you get the above. Even with a calculator you wouldn't beat Alexis Lemaire doing the calculation in his head. |
| On your marks... Lemaire prepares to break the record at OxfordLast week, at Oxford's Museum of the History of Science Lemaire broke his own record for the task, taking it down to 77.99 seconds. Mental athlete he may be, but he speaks of his hard work in much the same fashion as any other kind of athlete. | On your marks... Lemaire prepares to break the record at OxfordLast week, at Oxford's Museum of the History of Science Lemaire broke his own record for the task, taking it down to 77.99 seconds. Mental athlete he may be, but he speaks of his hard work in much the same fashion as any other kind of athlete. |
| "It is quite difficult. I did a lot of preparation for this. More than four years of work and a lot of training every day. A lot of memorising. I need three things - calculating, memorising and the third on mathematical skills. It is a lot of work and maybe a natural gift." | "It is quite difficult. I did a lot of preparation for this. More than four years of work and a lot of training every day. A lot of memorising. I need three things - calculating, memorising and the third on mathematical skills. It is a lot of work and maybe a natural gift." |
| There is a long-standing fascination with those who can accomplish astounding feats of mental agility. The "ordinary" human wants to know how, but sadly the geniuses and the savants can only offer fragments of insight into how they function, and the scientists who have studied them rarely offer a definitive answer. | There is a long-standing fascination with those who can accomplish astounding feats of mental agility. The "ordinary" human wants to know how, but sadly the geniuses and the savants can only offer fragments of insight into how they function, and the scientists who have studied them rarely offer a definitive answer. |
| Researchers have tried to link problems with the brain either through trauma or malformation to extraordinary mental abilities - one of the theories being that damage to one area prompts compensation in another. Brain scientist Dr Allan Snyder has suggested that everyone may possess such abilities but be unable to access them. | Researchers have tried to link problems with the brain either through trauma or malformation to extraordinary mental abilities - one of the theories being that damage to one area prompts compensation in another. Brain scientist Dr Allan Snyder has suggested that everyone may possess such abilities but be unable to access them. |
| Transforming numbers | Transforming numbers |
| Kim Peek, the inspiration for Dustin Hoffman's character in the movie Rain Man, has a malformed brain and a below average IQ and yet is able to rapidly read books, memorising vast swaths of information. | Kim Peek, the inspiration for Dustin Hoffman's character in the movie Rain Man, has a malformed brain and a below average IQ and yet is able to rapidly read books, memorising vast swaths of information. |
| I have these associations between places and numbers - some places are imaginary, I try to vary so I don't confuse the numbers Alexis Lemaire Lemaire explains that what he does is about transforming raw numbers into other structures so he can "see" the answer to the problem. | I have these associations between places and numbers - some places are imaginary, I try to vary so I don't confuse the numbers Alexis Lemaire Lemaire explains that what he does is about transforming raw numbers into other structures so he can "see" the answer to the problem. |
| "When I think of numbers sometimes I see a movie, sometimes sentences. I can translate the numbers into words. This is very important for me. The art is to convert memory chunks into some kind of structure. | "When I think of numbers sometimes I see a movie, sometimes sentences. I can translate the numbers into words. This is very important for me. The art is to convert memory chunks into some kind of structure. |
| "I see images, phrases, actions. It's very tactile, sensitive. I have these associations between places and numbers. Some places are imaginary, I try to vary so I don't confuse the numbers. It's important to memorise. I have to be precise." | "I see images, phrases, actions. It's very tactile, sensitive. I have these associations between places and numbers. Some places are imaginary, I try to vary so I don't confuse the numbers. It's important to memorise. I have to be precise." |
| Lemaire's explanation is similar to that of British savant Daniel Tammet. Tammet set the world record for reciting pi at more than 22,000 digits at the museum in 2004. | Lemaire's explanation is similar to that of British savant Daniel Tammet. Tammet set the world record for reciting pi at more than 22,000 digits at the museum in 2004. |
| To him, each number has a distinct colour and appearance, some beautiful, some not, with each complex calculation making up a landscape. | To him, each number has a distinct colour and appearance, some beautiful, some not, with each complex calculation making up a landscape. |
| Icelandic in a week | Icelandic in a week |
| But his skills also stretch to words, with Tammet having reportedly learned Icelandic in a week after a challenge. | But his skills also stretch to words, with Tammet having reportedly learned Icelandic in a week after a challenge. |
| It's safe to assume that Lemaire's brain processes don't involve the words "carry one". But there is an explanation for some of what he does. The memorisation he talks about is a series of algorithms, such as a set to tackle the first five digits of the 200-digit number. | It's safe to assume that Lemaire's brain processes don't involve the words "carry one". But there is an explanation for some of what he does. The memorisation he talks about is a series of algorithms, such as a set to tackle the first five digits of the 200-digit number. |
| He has refined these processes to mind-boggling lengths. For the much simpler calculation the 13th root of a 100-digit number, the first record was set at 23 minutes in 1970. Now Lemaire can manage the calculation in under four seconds. | He has refined these processes to mind-boggling lengths. For the much simpler calculation the 13th root of a 100-digit number, the first record was set at 23 minutes in 1970. Now Lemaire can manage the calculation in under four seconds. |
| And whatever the mental processes that lead him to the answer, the fact that he can do this in seconds and without pen or paper remains awesome to the "ordinary" brain. | And whatever the mental processes that lead him to the answer, the fact that he can do this in seconds and without pen or paper remains awesome to the "ordinary" brain. |
A | Below is a selection of your comments. |
| Remarkable talent and he is unique within his generation, but he is also very lucky; most savants can hardly tie their own shoe laces never mind hold a fluent conversation and the high level savants find friendships and social interactions difficult at best. Curse or talent I'm not sure which. Frank Kerrigan, Glasgow | Remarkable talent and he is unique within his generation, but he is also very lucky; most savants can hardly tie their own shoe laces never mind hold a fluent conversation and the high level savants find friendships and social interactions difficult at best. Curse or talent I'm not sure which. Frank Kerrigan, Glasgow |
| Read "The Man Who Mistook His Wife for a Hat" for insight into amazing mental feats and quirky malfunctions. One chapter on the two brothers who are idio-savants pulling 12 digit prime numbers out of thin air is amazing. They can also tell a person what day a date occurred on, up to 50,000 years ago. Donovan Rittenbach, Oakland US | Read "The Man Who Mistook His Wife for a Hat" for insight into amazing mental feats and quirky malfunctions. One chapter on the two brothers who are idio-savants pulling 12 digit prime numbers out of thin air is amazing. They can also tell a person what day a date occurred on, up to 50,000 years ago. Donovan Rittenbach, Oakland US |
| The mathematics software Mathematica worked this 13th root out in well under 1/1000 of a second on my rather old machine. Hmmmm... William Shaw, London | The mathematics software Mathematica worked this 13th root out in well under 1/1000 of a second on my rather old machine. Hmmmm... William Shaw, London |
| Very impressive, but what actually is the point? Learning a language has an obvious benefit, as does the ability to complete basic mental calculations, but given the time and training involved in this feat, one has to wonder if there aren't more productive means of employing intelligence.Jenny, London | Very impressive, but what actually is the point? Learning a language has an obvious benefit, as does the ability to complete basic mental calculations, but given the time and training involved in this feat, one has to wonder if there aren't more productive means of employing intelligence.Jenny, London |
| How is he at factoring large prime numbers? If he can get that down below a few hundred years he could un-make most of the world of e-commerce! (The difficulty of factoring large prime numbers is one of the important bits of maths that supports internet security)Ben, London | How is he at factoring large prime numbers? If he can get that down below a few hundred years he could un-make most of the world of e-commerce! (The difficulty of factoring large prime numbers is one of the important bits of maths that supports internet security)Ben, London |
| Alexis is well known on the mental calculation circuit but not well-loved! He only ever seems to compete in obscure events in which hardly anyone else is interested, and the rules for which are dependent on him. There are many finer mental calculators out there but they lack one thing, Alexis' flair for publicityCharlie, London | Alexis is well known on the mental calculation circuit but not well-loved! He only ever seems to compete in obscure events in which hardly anyone else is interested, and the rules for which are dependent on him. There are many finer mental calculators out there but they lack one thing, Alexis' flair for publicityCharlie, London |
| Alexis Lemaire says, "I have these associations between places and numbers - some places are imaginary". In her book, 'The Art of Memory', Professor Frances A. Yates tells how the likes of the Ancient Greeks devised astonishingly powerful mnemonic systems based on precisely this activity of creating vast and elaborate landscapes and building like structures wherein memory elements were stored and manipulated. However, he also says, "When I think of numbers sometimes I see a movie, sometimes sentences." Therein may lay a clue to how such memorization works: in all ancients languages like Arabic, Chinese, Greek, Hebrew, Sanskrit, etc., there was originally no such artificial division between numbers and letters: numbers WERE letters, letters WERE numbers. A Borkwood, Liverpool | Alexis Lemaire says, "I have these associations between places and numbers - some places are imaginary". In her book, 'The Art of Memory', Professor Frances A. Yates tells how the likes of the Ancient Greeks devised astonishingly powerful mnemonic systems based on precisely this activity of creating vast and elaborate landscapes and building like structures wherein memory elements were stored and manipulated. However, he also says, "When I think of numbers sometimes I see a movie, sometimes sentences." Therein may lay a clue to how such memorization works: in all ancients languages like Arabic, Chinese, Greek, Hebrew, Sanskrit, etc., there was originally no such artificial division between numbers and letters: numbers WERE letters, letters WERE numbers. A Borkwood, Liverpool |
| Can you invite Jeff from Reading to the BBC and let him show you how easy this task is? Joe, Brussels | Can you invite Jeff from Reading to the BBC and let him show you how easy this task is? Joe, Brussels |
| Jeff in Reading, there is indeed only a certain set of numbers which result in a 200 digit number when raised to the power of 13. However, from a couple of quick calculations, I think that there is around 400 trillion numbers in the set!David, Glasgow | Jeff in Reading, there is indeed only a certain set of numbers which result in a 200 digit number when raised to the power of 13. However, from a couple of quick calculations, I think that there is around 400 trillion numbers in the set!David, Glasgow |
| Jeff, Reading says "only a certain set of numbers" ... well yes. But it's a set of several hundred trillion numbers. It doesn't "sound" complex, it "is" complex. Carol Vorderman is averagely good at arithmetic, but this is an entirely different league.Sam, Cambridge | Jeff, Reading says "only a certain set of numbers" ... well yes. But it's a set of several hundred trillion numbers. It doesn't "sound" complex, it "is" complex. Carol Vorderman is averagely good at arithmetic, but this is an entirely different league.Sam, Cambridge |
| There are "only" 9,541,334 possible numbers, very simple maths will get rid of a large number in a short amount of time (is it odd/even etc) not too hard to memorise if you have four years, I'm interested to know who funded this "training" I wonder how much I could be paid do accomplish one VERY specific job in 43 years? Yes it's "clever" but surely someone of this "genius" could do something a bit more useful? I just found the answer on a calculator in less than a second :)Hywel, Cardiff | There are "only" 9,541,334 possible numbers, very simple maths will get rid of a large number in a short amount of time (is it odd/even etc) not too hard to memorise if you have four years, I'm interested to know who funded this "training" I wonder how much I could be paid do accomplish one VERY specific job in 43 years? Yes it's "clever" but surely someone of this "genius" could do something a bit more useful? I just found the answer on a calculator in less than a second :)Hywel, Cardiff |
| It is amazing that someone is able to calculate that fast to that level of accuracy (I am of course assuming someone has checked his answer ;) He should be given some kind of reward, similar to how good Olympic athletes are given a medal. Now he just needs spend another four years working out (very) long division ;)Oliver, Wivenhoe | It is amazing that someone is able to calculate that fast to that level of accuracy (I am of course assuming someone has checked his answer ;) He should be given some kind of reward, similar to how good Olympic athletes are given a medal. Now he just needs spend another four years working out (very) long division ;)Oliver, Wivenhoe |
| That's amazing. I couldn't even read the question in under four seconds!Callum Brown, Biggleswade, Bedfordshire | That's amazing. I couldn't even read the question in under four seconds!Callum Brown, Biggleswade, Bedfordshire |
| Oh please! This is actually not that difficult. There are only a certain set of numbers which when multiplied by themselves 13 times equate to a 200 digit number. Lemaire has perfected these techniques for sure, but it sounds lot more complex than it is. I bet Carol Vorderman would give him a run for his money...Jeff, Reading | Oh please! This is actually not that difficult. There are only a certain set of numbers which when multiplied by themselves 13 times equate to a 200 digit number. Lemaire has perfected these techniques for sure, but it sounds lot more complex than it is. I bet Carol Vorderman would give him a run for his money...Jeff, Reading |