I’ve been scratching my head for a while now thinking up a method for encoding (into a mnemonic) maths formulas, but even after an hour of thinking about it I just can’t seem to pin anything concrete down.
So let’s brain storm! Maybe if we try to crowd think about a new technique for memorising formulas we might come up with something.
The formula I’ve been experimenting with is the quadratic one.
To stay on topic let’s all try to encode this formula.
Here’s some food for thought:
You can ignore the "X = " part
Variables can be any letter and you can almost memorise it just by taking out B B A C A and turning that into some sort of story like (a Big Banana Accelerated Toward an Antelope) and fill in the rest of the formula from memory by using this as a refresher of sorts, but it’s not a method that works 100%
I’ve thought of maybe assigning numbers to each maths symbol, for example
→ 10
/ → 11
Variables → 90 or over
Then you can say 90109701195 and use the Major System to store that which would decode as A-B/C.
But there are a couple of problems with this, 1) it can becomes a large number meaning lots of loci space or a long story and 2) I’m not sure what to do about actual numbers which would get lost in there.
Only other method I can think of is assigning a different image to each symbol and constructing a story out of that and placing them into locis but there may be interference from all the repeating images
Can anyone here think of any other methods? Or even just any random idea that pops into your head about this.
I would take a very visual approach, since the formula is already very visual. Off the top of my head, here are some thoughts:
I would encode minus as cold (and plus as hot, but no plus in this equation). The plus minus looks like a cross or old school TV antenna
I would convert the letters to images they resemble (credit here goes to Gary Lanier and his visual alphabet):
b = a leg with a foot, perhaps kicking something in front of it. Could also be a golf club.
4 = butterfly
a = a tadpole
c = a cookie with a bite taken out of it
2 = a guy with a monocle and a pointy nose
The whole thing looks a bit like a house.
So I’d turn it into a visual story using these elements.
It’s a house. On the top floor there’s a deck off the left side of the attic. Beneath is the first floor
On the deck we find a cold person (shivering) kicking the antenna (to try to get better reception I suppose).
In side the attic is another person, his buddy. He’s got a buck tooth (two) sticking out of his mouth (for the exponent 2). He’s kicking a cold (icy) butterfly while a tadpole nibbles at a cookie.
Meanwhile, down on the first floor, a fancy guy with a monocle is sniffing another tadpole.
Kind of crazy, and there’s plenty of room for improvement here. Maybe for the numbers use images derived from number rhymes (2=shoe) or Major system (2=hen) instead of shapes. Then again, I like the idea of it all being visual, so the whole formula can appear in your mind as is.
Just musing, I haven’t tested any of this. Good luck.
I think as long as you can assign images to the symbols, then following normal operations order will allow you to store formulas as a list. If you’re familiar with entering equations in graphing calculators, you’ll be familiar with the order necessary to place the symbols and which sections to put in parentheses. As long as you are consistent in your notation it should be usable in all situations.
Then you’ll have to find a way to associate the formula with its meaning (if it isn’t apparent), so that you can apply the formula in the correct situations.
Maybe peg system? That way you don’t have to deal with loci and you can keep the repeated symbols separate by linking them to their position in the list.
I’m a noob, so I don’t yet have the experience to know how it would work with reusing images or how likely that is to mess things up.
So this morning I was able to remember the formula, but I also saw some room for improvement in my proposed method. The main problem is that I don’t draw an “a” that way. I draw it like the picture below, and I imagine most other people do as well. So instead of a tadpole, perhaps it could be an old fashioned bowler hat.
Or make life easier and use capital letters. As I mentioned in my first post, Gary has already given us images for these which of course everyone is free to tweak. Here’s my second try at this.
B = a bumble bee (both sound and image association on this one)
B squared = a B waving/saluting with its wing
4 = butterfly
A = an artist’s easel
C = a cookie with a bite taken out of it
2 = a guy with a monocle and a pointy nose
So my new translation of the formula would be:
Outside on the deck a cold shivery bee is about to land on the tv antenna.
Inside the attic a warm bee is waving its wing at his buddy trapped outside.
Next to the warm bee is a shivery cold butterfly painting a picture on an artist’s easel of a cookie with a bit taken out.
Downstairs the fancy monocle guy is having a hard time finding inspiration for his painting, and stares off to the left while the blank canvas sits on the easel to his right.
In looking back on this, I’d really like to replace the hot/cold plus/minus thing. Any ideas there?
No loci. The formula/house is the loci.
If I were learning more than one formula, however, I would place them along a memory journey or in a memory palace so I could review them and make sure I wasn’t skipping any. So in this case, since all my journeys begin at the front door of a house, there would be a doll house sitting in the doorway, and that doll house would be this formula.
As for the plus/minus thing, some more possibilities
tall/short
healthy/sick
right side up / upside down
sunny/rainy
The hot/cold thing worked for remembering over night, but it isn’t particularly “sticky” for me. I think it needs to be something more visual. I considered dedicated characters (upbeat Richard Simmons type for plus, Droopy dog for minus) but they’re likely to show up very often and that just creates a mess. I considered colors (red/blue), but this really doesn’t stick for me. I also considered dedicated objects, sort of like what I did with the plus/minus being an antenna. But again, they would show up too often.
I had an idea for a sort of PAO method for basic formulas today that may be tenable. The variables or constants would be people or objects, while the operations would be actions. I haven’t had time to put much thought into it, but it may work. Maybe constants could be objects and variables could be people. I’ll have to think more about the structure of functions and how best to represent the components.
A simple example, if ‘a’ is an apple and ‘b’ is a butterfly and ‘+’ is throwing, then a+b could be an apple throwing a butterfly. You guys think this would work well.
One thing I’ve been thinking about with this is recognizing the formulas and recalling them. If I wanted to memorize a BIG TABLE OF INTEGRALS, would using a mnemonic system like this help to recognize an instance of a certain integral type? I believe that a sequential mnemonic system would work for recalling the output on the right side of the =, but would be worthless for recognizing an integral that fits a certain format on the left side in order to apply the formula.
loki, i could be wrong but if you learn that 1/x=lnx you know it backward too like how you can go through a journey backwards .also you don’t need to use mnemonics for all of these you just need a reminder for some like 1/(1+x)^2 is = to the same thing but minus and without the power when you integrate.
if you when over you mnemonic enough time it would be i your long term memory memory.also you know that if the number or letters change it’s still the same thing like 3/(5+x)^2dx = -3/(5+x)
what formula do you mean it’s just 1/(x)^2dx= -1/x .i sorry i don’t really know what u mean that’s all but i don’t think i’ll ever memorize all that. there is a lot there i don’t know integration very well.
sorry if i seem rude i’m crap at maths it make me a little annoyed hahaha
I’m trying to work out a PAO system too, it seems like an improvement on just images. Don’t forget PAO really means 3 pegs for each symbol, a person an action and an object.
So far I think this is it, PAO for formulas is probably the best system, just need to do more experiments with it now, will report any progress.
Algebra is not my thing at all, so don’t laugh at my take on the QUADRATIC FORMULA.
Here’s a long way around but may be fun to try.
Rather than visualize the actual formula, write in MATH TALK (18 words or less) what the Q Formula is. As you read your MATH TALK version, follow your own instructions and write out the equation. Once this works, go to step two.
Tangitize (make visible) every word in your MATH TALK version.
Now, instead of using the Visual Alphabet as part of the visual Q Formula, use it as a series of pegs that are made up of the word QUADRATIC.
Hang 2 words on each letter from your MATH TALK version (as in step 2) of the Q Formula. You might peg one and link the other.
Now, starting with the the visual letter Q, go through the letters QUADRATIC, and follow your MATH TALK instructions.
That’s it!
For me, using the word QUADRATIC in the process helps me stay focused, plus it makes for a great memory file.
This may not be what you’re looking for, but if you want to commit the Q Formula to memory, I can say that it worked really easy for me.
I can post my MATH TALK version and procedure, if you like, but I don’t think it would help that much. It’s kinda like Andi Bell’s visual number system. Some of the images make absolutely no sense to me, but look at what he’s done with them.
I figured out a way to distinguish between the different integral patterns, but I am building an all acrostic system. I used the letters f-k and q-s and w to do it. If you don’t understand what you are seeing, look at this. https://ankiweb.net/shared/decks/math “algebra acrostic dictionary”
Why do you think that you would need lots of locis? I mean, what I try to do is just make a chain, a short story. Do you think that creating apart from the story, the loci would enhance the memory? With the loci you encode the number in a list, but in a formula, it is really not needed (if you treat factors for instance that multiply separately, you can switch them).
I use Google Images obsessively to try to understand and memorize whatever it is I need to get into my head. Many times, even with formulas, there will be a schematic or some other visual which makes it easier to understand the relationship of the variables and why when X goes up, Y goes down.
1). Use Action words for symbols / Characters.
example : two chopsticks trying (to find) the light because they are in a dark place. to find :means: the equal sign =, they kind of look like chop sticks.
So Quadratic (from your math memory palace or loci) may be a bright white graph paper with X and Y Lines looking like very serious red ray , and blue ray very confidently look at each other going in there respective directions. this would represent your quadratic formula.
write your formulas down with the mnemonic counter part next to it while doing your problems!
I like to keep my math mnemonics as close to what they are but with a lot of action in the movie in my mind…
enjoy. Hope this helps…
i don’t think it’s helpful to memorize math identities as if they were arbitrary collections of symbols, like phone numbers .
Math identities express a relationship between ideas. The parts are held together by a tight web of logic. If you take the trouble to understand that, which usually means learning how the identity is actually derived, most of your memorization will be done and your math chops will go up several levels…
In this case, the quadratic formula is an abstraction of a method known as “Completing the Square”.
For every single element you might encounter, generate an image (code) of sorts that should be fixed and used only for that element. For example, use a “snake” to represent an “integral.” Do the same for everything else. This might take some time when you first come up with the images, but you only have to do this once. Then, any time you encounter a formula containing an “integral,” you automatically have the specific snake to use for it.
Use the method of loci to anchor the formula. Why? Because you can generate an infinite number of loci, i.e., you have an infinite amount of space to place your images. This also allows you to use the same code (e.g., snake for integral) an infinite number of times without the risk of confusing formulas, since the key to generating and remembering the information is not the code but the loci.For example, you might place the snake for formula 1 in location A and the snake for formula 2 in location B. Thus, when you see location A in your mind, you automatically see the snake but in the context of formula 1, since formula 1 is determined by the context of location A. This means that you do not risk confusing formulas, because they are entirely dictated by the loci and not by the codes (e.g., the snake) themselves.Another reason for using the method of loci is that we need some spatial arrangement of elements in order to remember and understand them. Think about it: whenever you remember something, you instinctively arrange the elements relative to one another in some way or another. In your example of the quadratic formula, even if you did not use any memorization trick, after enough repetition you will see the elements in a relative positioning in your mind—for example, the numerator sitting above the denominator. By using loci, you automatically take care of this relative positioning in a more imaginative, and therefore more memorable, manner.
After enough repetition (by recalling the formula without external help), you will internalize the formula to such an extent (i.e., there will be strong and extensive neural connections related to the formula in your brain) that you will no longer need the images. The formula will simply pop up in your head, much like the words you use when you speak.
Do not try to memorize every formula—only those you find hard to remember. For example, I do not need any mnemonics to remember sin^2(x) + cos^2(x) = 1 or the quadratic formula, since they are so frequently used that they become automatically internalized. However, there are formulas like \int_a^b \lfloor x \rfloor dx + \int_a^b\lfloor -x \rfloor dx = a - b,which are not used as often and are therefore at risk of being forgotten over time. For such formulas, it is a great idea to use mnemonics until they become second nature.
Proving and understanding formulas is good—yes—but inefficient when you need to solve problems quickly. As a matter of fact, I have proved every formula I work with (probably thousands of them), and still I cannot afford to derive them every time I need them, because their derivation may take more time than solving the actual problem. For example, using the “completing the square” method, even though it is relatively easy, might take a couple of minutes. By remembering the formula instead, you can use those minutes to solve the problem itself.As such, you should aim to prove mathematical facts in order to understand them, but also memorize them afterward for a more efficient workflow. You do not have to “reinvent the wheel” every time you need one—just use it as given.
