The spectrum of human memory potential: Daniel “Brainman” Tammet beats blackjack and Japanese schoolchildren become human calculators.
Numbers, or digit strings, are considered by many mnemonists and cognitive scientists to be the most difficult data to memorize. If numbers are both abstract and difficult, how did Hideaki Tomoyori of Japan memorize PI to more than 10,000 places? How did my classmate in Tokyo also multiply four-digit numbers in seconds?
The answer is proper encoding, or translation of the abstract to the concrete. Hideaki used what I’ll teach you here, whereas my classmate used a phantom abacus like in the above video.
The average person can only hold seven or fewer numbers in their working memory at any given time, using vocal repetition as an aid. Using proper encoding, trained subjects can memorize all of the area codes in the United States within a 24-hour period… By encoding abstract data first as letters, then as nouns, one can accurately store and recall hundreds of items (images) both forwards and backwards.
This introduction to encoding will provide an overview of the consonant system mnemonic, which encodes numbers as consonants of the English language. In this system of encoding, vowels (a, e, i, o, u) have no value, nor do w, h, or y. Numbers are converted to consonants, which are then converted to nouns and images. Bear with me — the examples make this simple to use.
Here are the encoding pairs that Tomoyori used to recall 10,000 numbers without error. Numbers are encoded as indicated below, and suggestions for remembering the pairings are provided in parentheses:
1 = t (also th) or d (single downstroke)
2 = n (two downstrokes)
3 = m (three downstrokes)
4 = r (the last letter of “four” is “r”)
5 = L (you have five fingers on your Left hand)
6 = j, ch, soft g, sh (“J” is a near mirror-image of “6”) (Ex: Jelly, CHips, garaGe, SHoe)
7 = k, hard g, hard c (“7” side-by-side with a mirror image form a sideways “K”) (Ex: Kite, Goat, Cat)
8 = f, v, ph (“8” is similar to the lower-case cursive “f”) (Ex: Flame, Vest, graPH)
9 = p or b (9 is a mirror-image of “P”)
0 = z, s, soft c (0 signifies “zero”) (Ex: Zipper, Scarf, iCe)
Using the above conversion table, 8209 could equal “fan” (82) and “soap” (02), thus a fan made of soap. If you can then place one such composite image at 20 preselected locations (loci), you will memorize 80 numbers with ease. Numbers are converted to words by the phonetics (sounds), and spelling is unimportant. Thus: 8762 = FKSHN = fikshun = fiction (vowels possess no value). Use whichever vowels you want.
Likewise, repeated letters are represented by a single number unless two separate sounds are made: 3230 = MNMS = Minnie Mouse (“nn” represents the single 2).
The second step is to take each image, made from 2-6 numbers, and place them in a sequence. The loci method uses preselected and familiar locations:
1. Choose a familiar route marked intermittently by outstanding features. Horizontal sequences are easiest to use: streets, hallways, room perimeters, etc.. Using the path from your bed to the shoe rack as an example, the following locations could serve as placeholders for your composite images: bed, bedroom door, staircase, kitchen table, shoe rack.
2. Associate your composite images, in appropriate order, with the predetermined locations. To memorize the number (905) 811-3710, you could follow this sequence:
a. PAISLEY (905 = PSL) sheets on your bed
b. A huge PHOTO (81 = FT) of yourself plastered on your bedroom door
c. Princess DI (1 = D) sitting on your staircase
d. A huge MUG (37 = MG) on the kitchen table
e. TIES (10 = TS) where shoes should be in the shoe rack.
By mentally tracing your loci route, you produce (905) 811-3710. And guess what happens if you trace your route backwards, taking into account the order of letters? 0173-118 (509). This combination of encoding methods automatically permits you to recall digit strings both forwards and backwards!
Encoding, and improved abstract recall, can be used to learn 500 foreign vocabulary words in a single 12-hour session, increase IQ testing results by 20-30 points, or memorize all of the ticker symbols on the NYSE.
Increase your recall capacity by 500% and you can effectively quintuple your lifetime learning capacity. Learn to efficiently encode the abstract and the results can be superhuman.
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63 Replies to “Savant School: How to Memorize 10,000 Numbers and More”
I think that this stuff is great, especially for students. I’ve been getting really interested in it. One site that goes into more detail is http://www.memorizeeverything.com
Oh it’s incredible!
I was using “Super Memory Numbers” Android app ( http://goo.gl/gynrm ) to increase my photo memory but this is a different way to increade my large Time memory.
You can also try my iPhone/Android App “The 4 Most Powerful Memory Techniques” which will give you further memory techniques. Do let me know how it goes. Thanks.
Composite imaging is good stuff, very helpful with names as well!
That’s some cool stuff. Keep the updates flowing, Tim.
Just started subscribing, Tim. Great stuff. I really appreciate your perspective, as well as all the sweet tips.
Unfortunately my day job requires a tie each day. Thanks to you, though, I’m now a windsor knot guy. Peace.
Can one apply this mnemonic technique to perhaps memorizing an entire deck of cards, removing one, then determing which one has been removed by going through the entire deck?
Killer post Tim. Coincidentally I’ve spent the past week digging into this searching for methods to boost my learning retention and memory chops. So far the best book I’ve come across has been titled Mind Performance Hacks by Ron Hale-Evans. The whole concept of mind palaces and the various number encoding systems out there is fascinating.
741 ! (GReaT) !
Has anyone else read Daniel Tammet’s book, “Born on a Blue Day”? Daniel has a form of autism/Asperger’s syndrome, and his book is an interesting taste of how that kind of mind approaches the world. It’s odd, but worth reading, especially if anyone you know is somewhere on the autism/Asperger’s spectrum.
As usual an interesting post Tim. The technique you have used seems to have originated from Harry Lorayne’s book by the name ‘How to have a super power memory’ which I remember reading as a kid. This technique you have described is called the Peg technique.
To remember a list of thousands of objects in sequence you can use another technique called the link technique, where you make ridiculous associations between the sequence of objects. Eg: Phone, Book, Comb, Fish…
1. Imagine yourself talking into a huge Book instead of a phone.
2. Imagine yourself studying for an exam reading a massive comb
3. You are fishing at a lake, and you pull out combs instead of fish
and so on…
This “peg” technique — often referred to as the “loci” technique — actually originated in Greece, from what I’ve read, where Socratic-era orators would use it to remember speech points, as written notes were forbidden. Harry is a smart man, though, to be sure.
You could be right about the greek origins. Btw, using these techniques to remember speech points is an excellent application of this method. Thanks for mentioning that. I wonder if world leaders use these techniques in their seemingly fluent and long speeches.
I’m actually too lazy to memorize a bunch of random stuff. It is easier to remember where to look up the information should I need it….wait, I guess that is a kind of memorization too…hmmm
so 500 foreign vocab words in 12 hours (and all the other amazing stats) what would your error rate be when tested? 85%? and retention period? THANKS DAN for the url… any other good (as in simple/easy) sites to pick this up?
If followed with a repeat session of about 1 hour on the slower items the following day, I’ve generally seen an 80-90% retention rate after 24 hours. The forgetting curve is typical Ebbinghaus after that.
For the VA questions, I’d recommend you hit the resources I recommend in 4HWW, especially http://www.elance.com, but you can also try http://www.odesk.com, which has good tools. Just post your criteria on each marketplace you choose.
Derren Brown has a book called Tricks of the Mind that includes some cool memory tricks plus some magic tricks as well. But you’ll have to order it from the UK Amazon to get a hold of it.
Someone once asked Einstein how many feet were in a mile. “I have no idea,” he said. “Why should I fill my mind with useless facts that can be found in any reference book?”
The mind is better used for *thinking* than for storing endless facts. Yes, being able to remember Pi to 10,000 places is interesting….
…Wouldn’t it be far more efficient to use the ancient reference method “pencil and paper” and then go spend the rest of your time doing something *fun*? 😉
Memory is a key component to thinking. For example, if you spend some mental effort memorizing numbers, memorizing numbers becomes easier and easier. You are developing a new capacity in your brain which actually expands thinking rather than impeding it. The brain does not get “filled up,” it grows.
Got a source for that Albert quote? If true, imagine what he’d have accomplished if he did care.
I recently talked to a competitive digit-memorizer (mnemonist?), and according to him, the standard technique among memorizers is something a bit more complicated. Basically, you associate a character, an action, and an object with each two-digit number. That lets you chunk each six-digit number into an image: Maybe 425661 is Bruce Lee (42) sweet-talking (56) a pile of rubies (61). You can then use the method of loci as Tim described. (Interestingly, this leads to odd errors with perceptual explanations — if Bruce Lee is 42 and Jackie Chan is 98, you might insert 98 where you were supposed to have 42 if you didn’t cement the image in your mind firmly enough.)
The limitation of this system relative to Tim’s/Tomoyori’s is the up-front time commitment. A ten-number system probably takes much less time to master than a 100-number system, especially where each number maps to three different things. However, it’s much more determinate — instead of making choices about how to shoehorn the number-sounds into words, you’ve got a fixed image for every location — and more efficient (6 digits per image instead of 1-3 in Tim’s example).
In theory, you don’t have to limit yourself to two-digit numbers; obviously a three-digit system would be more efficient, since each image would be worth nine digits instead of six, and so on. But apparently almost no competitors have had success with three-digit systems — I’m guessing it’s just too hard to come up with 1000 people, actions, and objects that are so distinct that you won’t confuse them with one another. However, I think there’s at least one guy who’s used a three-digit system extremely successfully.
Sorry to be so hand-wavy about all this — I’ve gotten it only from conversation, so I don’t have any references for any of it. But the guy I was talking to did definitely memorize 120 decimal digits in 2 minutes, and describe the images and the route he used, so I’m confident that he knows what he was talking about.
Nice hack Tim! Speaking of hacking things, do you happen to have a copy of your audiobook “How I Beat the Ivy League” available? I would love to hear that as I’m planning to go to business school. Or perhaps you can make a post about it?
Thanks and keep up the good work!
Well described. Two systems: numbers=letters (and vice versa) item locations. Both work wonders but I find ‘item locations’ more practical. Lecturers in ancient Greece studied art of memory, to dramatic effect. In the day, it was common to see students wandering slowly, deliberately around Athenian buildings–memorizing features as mental reference for “storing” objects of recall. I recommend storing objects in a mental representation of your clearest “house” memory. For example, I know my childhood home in extreme detail so that’s my virtual database. When I want to remember a series of objects, I mentally drop off each object in myriad room locations. Each position has a special, emotional meaning to which I may associate with the object I’m leaving there. When I want to recall all the objects, it is quite easy: I walk around the house in a standard path and collect all the objects from the standard positions. It’s tedious mental work, but completely doable to memorize the entire menu at a restaurant this way. To add more layers of information, I am free to add the numbers trick. Net, if I drop off a Caesar salad at the front door to my house, and the salad costs $6.31, I think J M N which I’m free to translate as “Cumin,” so I dump an absurd amount of Cumin on a Roman looking doorman who is lunching on salad. These pictures are difficult to forget, hence the detail one can remember is remarkable.
The loci method isn’t so great because you’re limited by how many items you can remember in your house/whatever to begin with.
The peg system that mbm was referring to in an earlier comment is actually the link system where you link one item to another until the end of your list.
As I understand it, the peg system is great unless your peg system isn’t based on phonetic mnemonics. For instance if you just randomly pick words to associate with the numbers 1-10 in order to memorize a separate list of ten items, you’ll do fine but what if you have to remember 100 items or more? How are you going to remember what number stood for what item? That’s where the phonetic mnemonic system comes in … and you covered it in your post, sort of.
Each number has a sound, so if you ever forget any number, you can sound it out with the phonetics and that will remind you of the object associated with that number. This is unlike a random list of objects associated with numbers.
Example: 1 can’t be ball because it has the ‘t’ sound. But one can be tie! The sound of the number (phonetic mnemonic) will remind you of the associated word!
Making phonetic mnemonics from 1-100 even 1-1000 etc, or using someone else’s pre-made list will prepare you to use the link method (and drop the loci method) with a great advantage over the loci guys.
For instance, you could memorize PI to as many digits as you’d like by just linking your image for the first three numbers to your image for the next three. Then linking your image for those three numbers to the next, etc.
Of course, as mjw has said, learning those initial 1000 or 100 numbers might be sort of a [short] time commitment, but it could be worth it for some people.
If you can memorize the first 100 peg words, or whatever you’d like to call them, the next 900 will be a breeze! How? All you do is take your image for the number 1 and set it on fire to mean 101 or put it in ice to mean 201 or smother it in jelly to mean 301, etc.
The system is pretty easily expandable. Lets say you don’t even want to go that far. Lets say you just want to memorize 100 items. Ok, just memorize the first 10. Your image for 1 might be “t”ie, and your image for 2 might be “n”oah. Don’t link these, because you want 100 separate items. Now what would the image for 12 be? It could be a frozen noah! And 11 could be a frozen tie? 22 could be a burning noah, and 21 could be a burning tie! Etc.
Anyways, I hope I helped spread some … memory love.
I’ve always found this stuff interesting. My question is – how does it relate to aptitudes/differences in thought processes. IE: Visual vs. Spatial etc.? While I know that the same techniques can be made to work for all types – is anyone familiar with research specifically that takes this into account?
Hey Tim! Chino here from the Philippines. Amazon just delivered my copy of 4HWW, and it is amazing. I started reading your blog when I saw the post about Scoble reading 622 RSS feeds on Google Reader, and haven’t stopped since. I’ve read the first 3 chapters so far, and I’m finally getting the courage to change my life to do what I want. Thanks and congratulations for getting a spot on the NYTimes Bestseller list!
I have always had trouble with memorization. This guys blow my mind. Dates especially have always been difficult.
I actually think these are excellent examples of why we should *not* use our brains this way. Think about it: These tricks wouldn’t be so impressive if they were easy/natural. That means our brains aren’t adapted for this kind of memorization. It wouldn’t be a problem except memory is a bit of a zero sum thing: Taking up room with a bunch of low-level stuff (such as a billion-digit number, mental todo lists, etc.) chews up brainpower that’s better used on the higher-level stuff: Thinking, coming up with new product ideas, solving problems, etc…
Mr. Cornell, while you do have a point in saying that the brain is awesome when used to develop “higher-level stuff” like coming up with new ideas and solving problems, memory is still a useful tool! Einstein also thought memorizing things was kind of silly when you have reference books and what not. But you and Einstein are forgetting something.
In our school systems (in the US) today, classes require students to memorize junk. Here are some examples:
Elementary: memorize the pledge of allegiance
Middle School: memorize all the presidents
High school: memorize the periodic table
College: memorize all kinds of units
Med School: oh the agony!
So while the brain is a great tool for coming up with new ideas and such, it’s great at memorizing too, and we definitely have no choice but to memorize stuff in this day and age … until the robots take over. 0.o
Just because some people don’t have brains that aren’t doing these memory tricks naturally doesn’t mean that these “tricks” are crap. They’re still good methods for memorizing a bunch of stuff real fast. Plus most of what we humans do nowadays are stuff that we learned from others – i.e learned habits.
Anyways. I still believe genius can be learned, along with everything else … including a photographic memory and whatnot.
i think you made a mistake in this post:
“…Using the above conversion table, 8209 could equal â€œfanâ€? (82) and â€œsoapâ€? (02)…”
shouldn’t 02 here be 09?
Oops! Good catch! Corrected… Thank you.
You never fail to keep posting about interesting and unrelated topics. Great blog Tim.
What technique or combination of techniques was used to memorize 500 foreign vocabulary words? It seems like all the techniques you listed start with numbers, not words.
This is exactly the technique I followed when trying to memorize Kanji while in Japan, using a book called ‘Remembering the Kanji’. It worked great for a while, but the more of them I memorized (I got to ~1500) the images started getting jumbled, and it became more of a hinderance than a help.
I’m wondering if there’s some aspect of the technique that I missed, that helps more for the long-term memorization? In my case, the more hokey the image I used (and it recommended that), the more difficult I found it to isolate the key parts of the image later.
I just took a workshop with Jim Wiltens (JimWiltens.com) called Secrets of a Super Memory. He says we really have an extraordinary capacity for memory, but our retrieval system is really lousy and can be trained. We may think we have a bad memory, but the ability is there, and lots of memories are in there that we just have no way to recall. We learned 3 or 4 memory techniques in the class, applying them to things such as learning names and foreign languages, and immediately saw results.
Jim has written a book called Memory Smart, which was actually written to help parents and teachers teach kids how to memorize things. He reminded us of some mnemonics we used to learn things as kids–like the year 1492(Columbus sailed…) and the ABC song to the tune of Twinkle Twinkle Little Star…There are many of them, and the fact that we still remember them today attests to their ability to work.
Jim describes 9 different techniques, applying visual, audio, and sensory inputs, and applies them to the various things kids are required to memorize in school, such as multiplication tables, states and capitals, atmospheric layers, etc. (Many of the techniques use the silly but very memorable pictures someone described above. These are linked somehow to the actual subject, or name, or word as in a foreign language, to keep the images from being confused.) He even goes beyond the basics to show techniques for learning the consonant code for memorizing numbers, how to memorize a whole book, and how to become a â€œMemory Black Belt.â€? Like a Martial Art, the memory techniques must be practiced regularly to work. And like a martial art, much of the benefit is not in the actual practice, but where it spills over into your life.
The book is geared toward kids, but the techniques are the same. Just for fun I decided to revisit my childhood and re-memorize some of this stuff, and the techniques really work. It’s been less than 2 weeks since the class and I’ve already memorized many things, including half of the 100 numbers of the consonant system. What I have found is that my mind is becoming sharper–I’m much more attuned to paying attention to things. It seems that it is really good exercise for the mind, and from what I understand, like the body, it’s use it or lose it. And it’s fun. So for those who say they can just look things up, I agree, there are references for when you need them, and it may be pointless to memorize long strings of numbers. But life could be much richer if you can spend a minimum amount of time to develop memorization skills and a few facts so you have a better foundation on which to hang new insights and observations, and a better chance at retention…
Jim Wiltens works with faculty at Stanford University on Memory skills. He is a great speaker if you can get him. The technique he recommends for learning languages can be found at 200words-a-day.com We used this in the class â€“it was fun and it worked very wellâ€¦.
By the way, Jim runs what looks like a great wilderness summer camp for kids, called Deer Crossing Camp– check his website. (JimWiltens.com)
i wanted to know where i can learn japanese. i am in california (SF) and want to become fluent. any recommendations. i read your book and really liked it! but i cannot find a recommendation on where to study a language (to learn it in 6 months)
FREAKY COINCIDENCE (Had to share.)
To practice, I picked 4 numbers at random:
At first, I couldn’t come up with a word, until I tried:
CVNT = Savant!
Then I remembered the 7 is supposed to be soft c, but you can bet I’ll remember the number either way!
I want just to remember my phone list. I think this technic is difficult.
Hello there Im having a hard time learning United States Code statutes. Theres like 60 of them do you know and easy way of remember these. Please help .Thanks, Adrian
Great explanation. I believe it is also important to mention that tools exist to convert numbers into words using the consonant system mnemonic that you explained, because this can get quite difficult. The most known online tool is http://www.rememberg.com
Interesting post! I too am agree that Numbers, or digit strings, are considered to be the most difficult data to memorize. However I would like to say some secret memorization tips to easily remember numbers.
Visualizing the numbers is however very difficult for the brain, as you have to remember the many shapes of each number. One way to deal with this, is to assign an object to each number, (e.g. number 2 is a swan) simply because it is easier for our brain to remember real world objects. For instance I had a PIN code for my AMEX card that I rarely used. It was 8012. I normally always forget my PIN code after not using it for a while, but for this number, I just remembered a shark with a wide open mouth. Never forgot the number again!
It is important to realize that some individuals do not need encoding, phonetics, or any special “method” for memorizing. I have an eidetic memory that allows recreation of images very vividly, and I’m fortunate to have an extremely high capacity for numbers.
I was the first person to memorize over 10,000 numbers, recalling 10,625 decimal places of pi on April 1, 1979 (see pi world ranking list website). Hideaki successfully broke my record later the same year, but I have taken great pride in my accomplishment even all these years later. But I depend purely on recall, with no supplemental tricks or additional strategies. And I know many others with similar abilities. Best of luck to those attempting to expand their minds.
Thank you for commenting! It’s great to have you here. I envy you greatly. Have you found any downside to having an eidetic memory?
Very interesting post!
But is it just me or aren’t all sentences displayed properly?
I see things like:
4 = r (the last letter of â€œfourâ€? is â€œrâ€?)
5 = L (you have five fingers on your Left hand)
6 = j, ch, soft g, sh (â€?Jâ€? is a near mirror-image of â€œ6â€³) (Ex: Jelly, CHips, garaGe, SHoe)
Ah, dang. I’ll try and fix that. Thanks!
Hi, I have recently memorized the Yellow Pages phone book. Here is how I did it.
To cure my bad memory I created a list of 1099 pegs for the Major System and used it for a few years (999=baby powder, 099=soap box).
However, one major drawback of the system caused me to quit it. Verbal decoding is impossible.
If a colleague asks you for a phone number, rather than being able to simply announce 303-906-5245, you have to decode and write down the number on a piece of paper or dial it yourself.
You can announce the phrase “MuSeuM PaSsaGe LiNeR eeL”, but you cannot announce the number!
Time for us to develop an improvement! Here’s an an idea I though of:
> Instead of 2=N, how about 2=T
> instead of 5=L, how about 5=F
> Instead of 9=P, how about 9=N
259 would now be DiVaN, not uNLaBelled.
So, when you slowly announce “Di Va N”,your colleague can respond: “My you have a funny accent. Did you just say “Ti Fa N-” or Two Five Nine?
With a bit of practice you can pronounce Di Va N as Two Five Nine yourself. You could never have done that with uNLaBelled.
Does anyone reading this have any other ideas? Let’s get together and modify the Major System.
Hey, you used to write magnificent, but the last few posts have been kinda boring… I miss your great writings. Past few posts are just a little bit out of track! come on!
I memorized the 1st 86 Fibonacci numbers for fun, no system or gimmicks.
I love the Fibonacci sequence! My favorite number is 89. I memorized the first 60 digits of pi without a system.
The Fibonacci Series has amazing mathematical consistencies built in.
I have now memorized the first 93, but the going gets tougher with longer numbers (20 integers).
If you know the series, you can have fun saying things such as: If X-squared plus Y-squared = 12,200,160,415,121,876,738, then X = 1,836,311,903 and Y = 2,971,215,073, or vice-versa.
Of course you don’t have many friends, but it’s still fun.
I’m 13 and I’ve memorized 60 digits of pi. I didn’t really use a specific technique. I guess I just sort of grouped the numbers together.
I have been reading the book Ageless Memory by Harry Loraine and have learned the peg system for remembering list as well as the phonetic alphabet. I have been applying it to remembering a shuffled deck of cards. I just got into using it to try and remember numbers. I really get stuck trying to make words out of three digit numbers and it really messes with me when I get two or three of the same numbers in a row. Any pointers. Thanks.
Could you give an example as to how one would use encoding to learn a foreign vocabulary faster? Great post, the topic intrigues me.
I have no special abilities or techniques regarding memory, but I have memorized and can recite fluently the first 101 Fibonacci Series numbers.
That is over 900 integers, which is more than I would have thought I could do.
Going through them in my head once a day maintains them. It is a hobby, but I
also find that it helps my overall memory, especially for numbers.
My name is brandon gill i can remember random m
No.s by the hundreds i dont no why but what
Does that mean i oblivious to the reason why
I can memorize number after number and dont
If you want to learn to do something, learn by doing.
I have memorized the first 103 Fibonacci numbers, so far, and that has made memorizing other numbers much easier and more automatic. Numbers become like familiar friends with identities and relationships which attach to your memory more readily. The mental calisthenics of memorizing are important mind strengtheners. I use no special techniques other than thinking through the series once a day.
I wonder how to apply this encoding concept to other things. Like math for example.
I often see even the ultra-educated professors at my university mess up simple calculations and I think with proper encoding this error can be reduce to near 0.
Like, in the movie Stand and Deliver, the math teacher tells his students that a negative number is like a hole in the sand on the beach.
“Come on… -2 +2, you can do it. Fill the hole.”
I would like to know how to apply this to math. It is difficult though because I have always tried to connect my math to something visual before thinking this up but it has never really gotten anywhere.
I also wanted to add that it would be interesting to find out how to make math processing as accurate as verbal processing.
Like, if somone messed up the semantics of their speech when they asked someone to “put that book on the table” they would be more likely to say something like “put that book on the chair” rather than “put that book on the cable”. If someone made the mistake of communicating that they wanted to book on put on table they would be more likely to say chair because of their resemblance than cable, a word which is different from table by only one letter.
If someone confused the word table and cable others would feel as if they are a really stupid person. However, in math these types of erros are very common. The accidental mistakes that are common in math such as forgetting to write the negative sign or divide by something reveal the difference in encoding people have with math as compared to verbal communication. I think if people imagined negative numbers in terms of “filling in the hole” and values as something associated with the senses then math comprehension would go up significantly.
I wish I knew what way to properly encode my maths. As I said before it has been something I’ve been doing for a while but haven’t acheived results in.
One can memorize by the sound of numbers; just say the number in your head a few times and remember what it sounded like. That is the old-fashioned way, but you soon get sharper in retaining the memory of the sounds, thereby improving memory. I have used that approach to memorize the first one hundred and eleven Fibonacci numbers (ending with 70,492,524,767,089,125,814,114). I am no mental whiz or savant; anyone can do it if he or she has time to spend on it.