Very interesting.
Very very interesting to read some of the points of view here.
Not sure I agree with all of them or even strongly disagree but maybe the following will give newcomers to memory studies and even newcomers to maths some ideas.
My own interest in the subject is that I use Memory Systems to comprehend the applied mathematics I use (and very often have to create myself) in my work and occasionally (usually because something is bugging me) for pure mathematics for recreation. Learning new maths is like entering a dark mansion and exploring each room, you bump into furniture and trip over things and then eventually you light a candle and see roughly how things are then - usually quite suddenly - you find the light switch and it’s all clear. Then you move to the next room. That’s how the guy who “solved” Fermat’s Last Theorum described how he works. Can’t recall his name..
Anyway my interest for work is primarily using analysis (calculus) with a very heavy emphasis on exponential functions and this cruises over into my memory work - how to develop mental representations of learning and forgetting curves - lots of Sigmoid functions, half and other life calculations and (lots of variations) on logistic functions with partial derivatives.
Like most people who work with mathematics. I work with letters both Greek and abcdefg etc, symbols and operators, ±/°^✓∆÷×|~ dx/dt, e^-kt, π, i, phi, Ω, sigma etc.
The point I’m trying to make is that starting with arithmetic and then basic algebra (up to and including logarithms to different bases) then the two main parts of calculus - every one of these standard functions and their inverses (addition, subtraction, multiplication, division, roots, logarithms, derivatives, integrals, growth, decay,) every one has an operator symbol and usually more than one. And you need to know them. To the point you’re not consciously having to think about them. The symbols represent what you do. + Isn’t the same as ÷.
I encoded the concept by the symbol. Because I understand the concept. The fundamentals.
I don’t personally encode the symbol by the concept. That’s just learning by rote or parrot fashion and with maths the beauty for me comes from the understanding.
So I’d share that for maths I’ve got a whole national park full of experiments and examples encoded by visual scenes where the characters I use build visual representations of stuff that is fundamental.
To visualise steady rate, versus constant acceleration, versus exponential growth and their inverses) I encoded that using imagined drone races (a bit like Robot Wars) where each team (yes I had teams) has to have their drone travel exactly the same distance in the same time - then visually I could compare the differences of the paths.
The use of geometrical representations helps. Well it helped me, especially for visualising
E.g I’ve got Sister Wendy (a nun who used to present TV documentaries about art) getting pushed off a 1km high platform (by Richard Feynman - I’m not aware he had anything against nuns but if he did I wouldn’t mind) he pushes the nun off the 1000m high platform over Loch Lomond, she can slide along a wire. The wire is sometimes straight sometimes curved, where the poor woman screaming her head off accelerates (under G or with a rocket pack striped to get back) towards her target - Newton’s platform which is half way to the water below, the tilt can be varied and Gallileo times it using of numbers, Leibnitz works out her area under her path, Archimedes calculates her distance by infinite series Newton works out the force… Lots of mathematicians all known (to me) to be THE specialist of that little part of the overall impression.
Integrals and partial derivatives can be (I say) visualised by comparison of variables in different runs of the same mind experiment. I’ve got a forest full of experiments…
Here’s one directly to do with memory:
Rate needed to complete a task. Like memorising one hundred numbers. With no system
Change in time needed when you use the peg system.
Change in time when you introduce a journey..
Change observed in results when you introduce the major system.
Change observed when you introduce a PAO… Or a PAOS
Change observed using a different type of memory palace.
These variations are all visualisable in visual mathematical language using symbols and stories and memory palaces but (I argue) that you need to know the meaning of the symbols - what a change in one field will make to the overall result. Plus of course the investment in mental work to develop these systems.
Very useful is Newton’s notation which is used still by physicist where a s with a dot above (or any letter) gives the first derivative and with two dots represents the second derivative. S-dot is the name and s-double dot. The second derivative.
All of which I am really familiar with.
Thing about mathematics is:. Rule 1 - You work ON PAPER.
Rule 2 - DON’T FORGET RULE ONE.
Once you know what you are talking about - encode it into a memory palace. But DON’T THROW AWAY THE PAPER! YOU WILL FORGET.
IN SHORT:
Where memory techniques (for me) come in is AFTER I understand every function or procedure or branch of mathematics I’m using in great detail - only then will I once it’s easy to put onto paper - would I put it into a memory system usually as a story with characters and (if necessary) numbers.
The point that zvuv made in his first post above about the absence of operators - I would STRONGLY recommend from my own experience that know your operators and functions as visualise stories.
The major system is useful. There are other approaches that you might find both simpler and quicker… If you’re trying to get better at maths.
Mm
The pic is supposed to be Katherine Johnson…
