This is lovely. I can't wait to hear the rest of the story.
It gave me lots of bittersweet nostalgia to my early childhood when everyone was excited beyond words about what a genius I allegedly was, and had about three complete timelines of my life scripted out for me, from primary school to grave, only I pissed it all away to become a foul- mouthed loser with a trucker husband and a hog farm.
Feb 2, 2022·edited Feb 2, 2022Liked by Mathew Crawford
Very interesting and it may interest you to know one of the ACT tests had a question on the quadratic expansion process of multiplication. As for memory i have known 2 people in my life with true total recall. In high school at the Donoho Academy (Anniston Academy at the time) we had a fellow student who I got to know pretty well. The first day of school he brought no books to school. We had 7 classes and he and I were in all but one together. I asked where his books were and he said he looked at them the night before and did not need them any more. I said - What??? and he said he remembered them. In disbelief I opened book after book and could flip to any page and as long as I gave him the page number he could recite every word on the page. I tested him will all the books. Throughout the year he never brought the books - even when we took turns reading Hamlet in class - he read his parts verbatim with only a clean sheet of paper in front of him. He was quite remarkable.
The next one was really interesting. I was working in a truck shop changing tires and servicing transfer trucks. I had to get the mileage off of every truck on the yard every day. It could range from 20-100 trucks. The mileage was always 6 digits. I noticed this other guy who worked fueling the trucks every day and he had to get the trucks and pull them over and fuel them and record the mileage and how much fuel he would put in them which would range from 50-150 gallons and oil which could range from none to 3 quarts. The truck numbers were 4 digits. He would fuel 30-50 trucks and never write anything down and then go sit in the break room and write it all down. Since I also had the mileage I tested him to see if he really remembered them. I could go back a year or so and if I gave him the date he knew the numbers - all of them. However he said he had to look at a calendar every day to know when something occurred. That gave him a refernce point. He remembered everything he saw.
For number crunching i had one friend who computed cube roots in his head with great efficiency. I tested him with a calculator and he never missed and could compute decimals as far as I could check him.
Congrats on all your number computation techniques. I have developed several myself that are similar but as you said - if you do not practice it regularly it slips away. I still find it more interesting to spot patterns if possible. I am already looking forward to the next episode:) Thanks again for the enormous amount of work you have done and thanks for sharing it.
One skill I developed in high school was reading upside down and that was quite easy and then about 15 years ago I taught myself to write upside down so that I could sit across the table and work math problems for the students I work with. I worked on cursive but it took a little more effort and once I got to where I could do a little I quit trying to expand it. I can work math problems almost as fast upside down as normal and I can read at the same speed either way.:)
This reminded me a lot of my own high school years, where I memorized entire plays, took all of my notes in mirror handwriting, and derived geometric formulas in the margins of my papers. I was never focused enough on the math part to learn the tricks that you describe, but that's definitely something that would have been within my capacity as an above-average non-genius.
It is sad and frustrating to see how the downstream effects of corruption can be so huge. So much time, money and brainpower wasted on research that is built on a flawed foundation, or on fixing problems that already had a solution, but the solution was quashed due to someone's ego or pocketbook.
I'm always intrigued by memory. I've played a ton of golf, and if I pick up a scorecard, look at the date, and really think about the day, I can remember all the shots from that round. But, I can't remember what I had for dinner 10 days ago.
Fascinating article, Mathew, especially since I used to be a big fan of Daniel Tammet. I *loved* his book, “Born on a Blue Day,” and frequently recommended and gave copies of it as gifts. And then I read “Moonwalking with Einstein,” which exposes the very trickery you describe in this article. Tammet evaded certain tests of his skills by saying he had promised his dead mother he would never be a performing monkey, but then of course he’s perfectly comfortable doing so with tasks he’s prepared for. I was severely disappointed to discover the possibility that he is a fraud, but I still love “Born on a Blue Day” if I think of it as fiction.
I’m so old that I took a “business math” class where we were taught to do calculations in our head. I got my first hand-held calculator—a Sperry, which I still have somewhere in the basement—as a junior. My physics teacher had to take a look. The math skills I learned lasted for years. Likely destroyed when I got a watch with a calculator. Now it’s difficult to add simple digits in my head.
My husband's cousin is one of those language people. She works for the Foreign Service. She speaks English, Spanish, Chinese, Japanese, Portuguese, and Swedish.
I don’t have this, but there is a pretty short fiction book about a girl finding out she has it – both spacial and numbers and colors. It is called A Mango Shaped Space by Wendy Mass.
Yes genius is enjoying something so much you come to fundamentally understand its very nature. Once you have this knowledge you can manipulate it to make it look like magic.
I myself have had problems during lfe, since child, by never meating anybody, in schools, university, including teachers, and other places, that among knews as much as I concerning, mathematick (400 books), history, engines, Universe, and much more, but now i Stive Kirch there I meet persons who also knows much about Covid-19, virusses (maybe 600 or 700 books).
But concerning mathematick, while reading the artickel I remembered Ramanujan, from India, only interesting in Mathematic, and who came to Hardy and Littlewood in London before the 1 War, after they had read his letter (no anser from 2 letter to other professors). By self study, Ramanujan had needed to invent mathematical signs, and Hardy and Littlewood had to speculate. Hardy later said that he himself only had the number 60 in mathematic while Ramanujan was 100. He died only 33 years old, way back in India. But in parallel to concerning numbers only divisible by themselfe and 1, then when Hardy one day visited Ramanujan in a hospital and told that he came in a taxy with the number 1729. Then Ramujan answered back "A special number as this is the lowes number which 2 times has the sum of 2 third exponent numbers the 1^3 + 12^3 and 9^3 + 10^3. And it took half a year before it was prowed.
Fabulous article. Your skills are fascinating. Brings back memories of returning home from high school only to do math homework immediately afterwards. More, please.
I was interested in math as a young person, and I wish I had had a teacher like you, because I think I might have enjoyed learning to do the kinds of computations you described above. To be sure, as an adult, I have thought very little about math and forgot a lot of what I learned as a child. But I do have a tiny parlor trick that impressed my husband when we were first dating. I grew up in Mexico, where we used the decimal system. When my husband and I would go out to eat, he would struggle to calculate the 15% tip. Because I was familiar with the decimal system, I could calculate it in seconds, by moving over the decimal point so I had 10%, dividing that by 2 then adding half for 15%. It’s easy to calculate any percentages this way. It seemed impressive to him, but it’s really just a trick. And now my decidedly non-math inclined husband can do it too with very little thought. This is a way less complicated example of the principle you illustrate in your essay, but it helped me to extrapolate the principle to the calculations you were explaining, given the ease that I have with percentages, when I’m really not very good with numbers or math at this point in my life. And it’s only because of my understanding of the relationship between the decimal system and percentages. Great essay and fun read! Thank you.
The film Rain Man was an interesting one and with the right acters. But concerning memori some children are born with ability only one time to hear or see something fore storing in memori, now a days we connected to the autism have seen som cases, but often only concerning one topic. We have seen a person who after just one time oround in Londen, then at home draw a detailed 3 dimenional drawing of af big center part of London, as drawn while sitting in an airplaine. And parallel to Mozart, as we se in films, after just one time hearing another persons complete music number, then himself played it, and corrected it. And parallel to a family, I think it was in London, with their son to a concert, and after this asked for a copy of the notebook, but denied, Then at home, the son jost wroute it down! And concerning mathematical and numbers - or the famous words "Don't disturb me in my Circles", and then was killed, 82 years old - we for excample had Poul Erdoes, about whom I 16 years ago wroute the book Paul Hoffman: "The Man Who Loved Only Numbers". But when it comes to brain and remembering something which not should know by the actual person, then we had the strange case with Edgar Cayce. He, never educated, in trance could tell recept for curing sick persons. In some cases, of his brain came out old discoveries by doctors, but which had been firgotten. Is this telepathy? One person wroute that a cousin knew 6 languages, and parallel to this we had a Polish mathematic person, who talked 32 anguage. Before a left side skull fracture, I talked 4 languages, but after 12 days again waking up from being in another World, with normal communication to my friens, I have been told, then monday the 27th of May years ago, I had lost all languages, and only bad relearned 2, but can't relearn the beatifull French language.
The language alone makes me expect so much more, but these tricks only entertain those that lack education or interest in math. This is why virology is claimed to have saved lives, even though it just made up reasons for existing disease, but never really cured them.
I'm a certified dumbass, and I have never been able to memorize my wife's phone number (which is 6 digits, not 7 because we don't live in the USA) even though I see it on my screen every day. Therefore, I cannot speak to memorizing numbers or calculating tricks.
What I can talk about is the kid learning languages (I saw the documentary years ago). Icelandic isn't particularly complex, but it is rather grammatically dense in that it uses noun cases as WELL AS all the other things many European languages have such as grammatical genders (often more than just two) and stricter rules on verb tenses.
For a native English speaker, these are some pretty tough concepts to get your head around. A sentence like "a man rides a horse" and "the horse is ridden by a man" use two different forms of the word "man" and "horse," for instance.
Did this kid Daniel know any other languages beforehand? Did he memorize a grammar book or read a text outlining basic Icelandic sentence structure? We don't know. All we see is him chatting by a geyser with the audio muted and glancing at a book in the library.
But I will say this - if you know ONE language with noun cases (and grammatical genders, et al), it's a whole lot easier to learn a second one.
However, what clearly set this kid apart is that he is doing an EXCELLENT job of pronouncing Icelandic, regardless of how good his grammar, sentence structure, fluency, et al, is. It's fucking phenomenal, actually. And there's no book in the world that'll teach you how to "hear" a language well enough to mimic it, even if it doesn't have any new sounds.
I mention this because - again, I am definitely not a genius. I am learning my fifth language (Russian) at the moment. Just the other day, a lovely woman at the pharmacy told me I speak it "excellently," which I certainly do not.
What I AM good at, however, is a combination of a) pronouncing it well and b) using memorized stock phrases and grammatically simple sentences. And the reason I'm even halfway good at is that I've been learning foreign languages since I was a kid, including one with noun cases (Russian has 7 of them).
In other words, if you dolled me up and said I was a genius, I could go on a Russian TV show and "dazzle" them with my Russian, even though I can't even read a children's book without help. On the other hand, just the other day, I saw a report from an American who lives in Donbass, and his Russian was far superior, except that he spoke it with an atrocious "foreign accent" that would be described as "thick" if it were in English.
People can do all kinds of things that seem whizbang cool. Doesn't mean they're geniuses. Pretty sure Einstein was the one who said it's 99% perspiration, not "inborn talent gifted by God."
This is lovely. I can't wait to hear the rest of the story.
It gave me lots of bittersweet nostalgia to my early childhood when everyone was excited beyond words about what a genius I allegedly was, and had about three complete timelines of my life scripted out for me, from primary school to grave, only I pissed it all away to become a foul- mouthed loser with a trucker husband and a hog farm.
Very interesting and it may interest you to know one of the ACT tests had a question on the quadratic expansion process of multiplication. As for memory i have known 2 people in my life with true total recall. In high school at the Donoho Academy (Anniston Academy at the time) we had a fellow student who I got to know pretty well. The first day of school he brought no books to school. We had 7 classes and he and I were in all but one together. I asked where his books were and he said he looked at them the night before and did not need them any more. I said - What??? and he said he remembered them. In disbelief I opened book after book and could flip to any page and as long as I gave him the page number he could recite every word on the page. I tested him will all the books. Throughout the year he never brought the books - even when we took turns reading Hamlet in class - he read his parts verbatim with only a clean sheet of paper in front of him. He was quite remarkable.
The next one was really interesting. I was working in a truck shop changing tires and servicing transfer trucks. I had to get the mileage off of every truck on the yard every day. It could range from 20-100 trucks. The mileage was always 6 digits. I noticed this other guy who worked fueling the trucks every day and he had to get the trucks and pull them over and fuel them and record the mileage and how much fuel he would put in them which would range from 50-150 gallons and oil which could range from none to 3 quarts. The truck numbers were 4 digits. He would fuel 30-50 trucks and never write anything down and then go sit in the break room and write it all down. Since I also had the mileage I tested him to see if he really remembered them. I could go back a year or so and if I gave him the date he knew the numbers - all of them. However he said he had to look at a calendar every day to know when something occurred. That gave him a refernce point. He remembered everything he saw.
For number crunching i had one friend who computed cube roots in his head with great efficiency. I tested him with a calculator and he never missed and could compute decimals as far as I could check him.
Congrats on all your number computation techniques. I have developed several myself that are similar but as you said - if you do not practice it regularly it slips away. I still find it more interesting to spot patterns if possible. I am already looking forward to the next episode:) Thanks again for the enormous amount of work you have done and thanks for sharing it.
One skill I developed in high school was reading upside down and that was quite easy and then about 15 years ago I taught myself to write upside down so that I could sit across the table and work math problems for the students I work with. I worked on cursive but it took a little more effort and once I got to where I could do a little I quit trying to expand it. I can work math problems almost as fast upside down as normal and I can read at the same speed either way.:)
This reminded me a lot of my own high school years, where I memorized entire plays, took all of my notes in mirror handwriting, and derived geometric formulas in the margins of my papers. I was never focused enough on the math part to learn the tricks that you describe, but that's definitely something that would have been within my capacity as an above-average non-genius.
It is sad and frustrating to see how the downstream effects of corruption can be so huge. So much time, money and brainpower wasted on research that is built on a flawed foundation, or on fixing problems that already had a solution, but the solution was quashed due to someone's ego or pocketbook.
I'm always intrigued by memory. I've played a ton of golf, and if I pick up a scorecard, look at the date, and really think about the day, I can remember all the shots from that round. But, I can't remember what I had for dinner 10 days ago.
Interesting read.
Great piece. <3 It actually reminds me of something my late husband wrote years ago. It's an enjoyable read and I think you will be able to identify with this. :) https://robbservations.blogspot.com/2010/10/re-wiring-brain.html
Fascinating article, Mathew, especially since I used to be a big fan of Daniel Tammet. I *loved* his book, “Born on a Blue Day,” and frequently recommended and gave copies of it as gifts. And then I read “Moonwalking with Einstein,” which exposes the very trickery you describe in this article. Tammet evaded certain tests of his skills by saying he had promised his dead mother he would never be a performing monkey, but then of course he’s perfectly comfortable doing so with tasks he’s prepared for. I was severely disappointed to discover the possibility that he is a fraud, but I still love “Born on a Blue Day” if I think of it as fiction.
I’m so old that I took a “business math” class where we were taught to do calculations in our head. I got my first hand-held calculator—a Sperry, which I still have somewhere in the basement—as a junior. My physics teacher had to take a look. The math skills I learned lasted for years. Likely destroyed when I got a watch with a calculator. Now it’s difficult to add simple digits in my head.
Response from a language arts lady:
What cult? Tell me more. And sorry. A cult?
My husband's cousin is one of those language people. She works for the Foreign Service. She speaks English, Spanish, Chinese, Japanese, Portuguese, and Swedish.
What a fascinating read. Thank you.
http://www.synesthesiatest.org/
I follow this blogger. The comments are interesting.
https://www.thefrugalgirl.com/spatial-sequence-synesthesia/
ex:
Rachel
October 28, 2014 at 11:53 AM
I don’t have this, but there is a pretty short fiction book about a girl finding out she has it – both spacial and numbers and colors. It is called A Mango Shaped Space by Wendy Mass.
Yes genius is enjoying something so much you come to fundamentally understand its very nature. Once you have this knowledge you can manipulate it to make it look like magic.
I myself have had problems during lfe, since child, by never meating anybody, in schools, university, including teachers, and other places, that among knews as much as I concerning, mathematick (400 books), history, engines, Universe, and much more, but now i Stive Kirch there I meet persons who also knows much about Covid-19, virusses (maybe 600 or 700 books).
But concerning mathematick, while reading the artickel I remembered Ramanujan, from India, only interesting in Mathematic, and who came to Hardy and Littlewood in London before the 1 War, after they had read his letter (no anser from 2 letter to other professors). By self study, Ramanujan had needed to invent mathematical signs, and Hardy and Littlewood had to speculate. Hardy later said that he himself only had the number 60 in mathematic while Ramanujan was 100. He died only 33 years old, way back in India. But in parallel to concerning numbers only divisible by themselfe and 1, then when Hardy one day visited Ramanujan in a hospital and told that he came in a taxy with the number 1729. Then Ramujan answered back "A special number as this is the lowes number which 2 times has the sum of 2 third exponent numbers the 1^3 + 12^3 and 9^3 + 10^3. And it took half a year before it was prowed.
Fabulous article. Your skills are fascinating. Brings back memories of returning home from high school only to do math homework immediately afterwards. More, please.
I was interested in math as a young person, and I wish I had had a teacher like you, because I think I might have enjoyed learning to do the kinds of computations you described above. To be sure, as an adult, I have thought very little about math and forgot a lot of what I learned as a child. But I do have a tiny parlor trick that impressed my husband when we were first dating. I grew up in Mexico, where we used the decimal system. When my husband and I would go out to eat, he would struggle to calculate the 15% tip. Because I was familiar with the decimal system, I could calculate it in seconds, by moving over the decimal point so I had 10%, dividing that by 2 then adding half for 15%. It’s easy to calculate any percentages this way. It seemed impressive to him, but it’s really just a trick. And now my decidedly non-math inclined husband can do it too with very little thought. This is a way less complicated example of the principle you illustrate in your essay, but it helped me to extrapolate the principle to the calculations you were explaining, given the ease that I have with percentages, when I’m really not very good with numbers or math at this point in my life. And it’s only because of my understanding of the relationship between the decimal system and percentages. Great essay and fun read! Thank you.
The film Rain Man was an interesting one and with the right acters. But concerning memori some children are born with ability only one time to hear or see something fore storing in memori, now a days we connected to the autism have seen som cases, but often only concerning one topic. We have seen a person who after just one time oround in Londen, then at home draw a detailed 3 dimenional drawing of af big center part of London, as drawn while sitting in an airplaine. And parallel to Mozart, as we se in films, after just one time hearing another persons complete music number, then himself played it, and corrected it. And parallel to a family, I think it was in London, with their son to a concert, and after this asked for a copy of the notebook, but denied, Then at home, the son jost wroute it down! And concerning mathematical and numbers - or the famous words "Don't disturb me in my Circles", and then was killed, 82 years old - we for excample had Poul Erdoes, about whom I 16 years ago wroute the book Paul Hoffman: "The Man Who Loved Only Numbers". But when it comes to brain and remembering something which not should know by the actual person, then we had the strange case with Edgar Cayce. He, never educated, in trance could tell recept for curing sick persons. In some cases, of his brain came out old discoveries by doctors, but which had been firgotten. Is this telepathy? One person wroute that a cousin knew 6 languages, and parallel to this we had a Polish mathematic person, who talked 32 anguage. Before a left side skull fracture, I talked 4 languages, but after 12 days again waking up from being in another World, with normal communication to my friens, I have been told, then monday the 27th of May years ago, I had lost all languages, and only bad relearned 2, but can't relearn the beatifull French language.
I find these "superhuman" grifts boring.
The language alone makes me expect so much more, but these tricks only entertain those that lack education or interest in math. This is why virology is claimed to have saved lives, even though it just made up reasons for existing disease, but never really cured them.
Also quantum theory is https://youtube.com/channel/UCcSIkt24P3WzN1n07l2C97Q
I'm a certified dumbass, and I have never been able to memorize my wife's phone number (which is 6 digits, not 7 because we don't live in the USA) even though I see it on my screen every day. Therefore, I cannot speak to memorizing numbers or calculating tricks.
What I can talk about is the kid learning languages (I saw the documentary years ago). Icelandic isn't particularly complex, but it is rather grammatically dense in that it uses noun cases as WELL AS all the other things many European languages have such as grammatical genders (often more than just two) and stricter rules on verb tenses.
For a native English speaker, these are some pretty tough concepts to get your head around. A sentence like "a man rides a horse" and "the horse is ridden by a man" use two different forms of the word "man" and "horse," for instance.
Did this kid Daniel know any other languages beforehand? Did he memorize a grammar book or read a text outlining basic Icelandic sentence structure? We don't know. All we see is him chatting by a geyser with the audio muted and glancing at a book in the library.
But I will say this - if you know ONE language with noun cases (and grammatical genders, et al), it's a whole lot easier to learn a second one.
However, what clearly set this kid apart is that he is doing an EXCELLENT job of pronouncing Icelandic, regardless of how good his grammar, sentence structure, fluency, et al, is. It's fucking phenomenal, actually. And there's no book in the world that'll teach you how to "hear" a language well enough to mimic it, even if it doesn't have any new sounds.
I mention this because - again, I am definitely not a genius. I am learning my fifth language (Russian) at the moment. Just the other day, a lovely woman at the pharmacy told me I speak it "excellently," which I certainly do not.
What I AM good at, however, is a combination of a) pronouncing it well and b) using memorized stock phrases and grammatically simple sentences. And the reason I'm even halfway good at is that I've been learning foreign languages since I was a kid, including one with noun cases (Russian has 7 of them).
In other words, if you dolled me up and said I was a genius, I could go on a Russian TV show and "dazzle" them with my Russian, even though I can't even read a children's book without help. On the other hand, just the other day, I saw a report from an American who lives in Donbass, and his Russian was far superior, except that he spoke it with an atrocious "foreign accent" that would be described as "thick" if it were in English.
People can do all kinds of things that seem whizbang cool. Doesn't mean they're geniuses. Pretty sure Einstein was the one who said it's 99% perspiration, not "inborn talent gifted by God."
Fascinating, I cannot keep up with the math, but I am captured by the post and the comments !