Since it’s weekend and I’d a bit of time, i wondered if there is some good “theory of mnemonic systems”… What I’d thought about, is some theoretical approach to optimize Systems like Major, PAO or others. Today I did a bit of math, and tried to overview how complex and or useful some systems are.
The main idea is (which is not really my own), to use combinatorics and it’s effects to reduce the amount of necessary images to learn for a maximum amount of encoded numbers (for example, i will stick to numbers here).
Since faculty grows faster than exponentials (in principle) we see, that it could be beneficial to use what i call a “Permutation-System” to enlarge our space of numbers covered by our images. But for now, I’d no really practial realizable idea how to do this…
For analyzing the quality of a (combinatorical) system or appraoch i used a definition which i called the “Benefit” of a System. The benefit b is just the amount of Signs or Numbers which can be adressed or encoded by the system, diveded by the number of Images used to realize this. You could also use it’s reciprocal.
So what I did first, ist compute the general Benefit of Systems like PAO an then computed the real ones for some examples. The first thing is, that, since in a PAO -like System, the number of Attributes (definition later) is constant for the System definition, and the variable which could be increased, is if we use one, two, or three digits for each person. So if we have 10, 100 oder 1000 Persons (and Actions / Objects).
I call the individual parts like Persons, Actions and Objects the “Attributes” of the system. For example i made a PAO(M) for me with only 10 digits, but an additional Attribute which is material. etc.
So the interesting thing is, that the benefit of a such a system grows polynomial. The degree of the polynomial is more or less depending on the amount of attributes in our system and there is a linear factor in front of the simple polynomial. Naively I’d hought, it would grow exponentially but this is really not the case.
So now we know that, the question arise, how we could use Permutations to increase our benefits. One example which i developed could function. But I don’t think, that this is practicable.
Example:
I thought of a PAO like System which I call PCS (for Person-Clothes-systems). It has 7 attributes, which could also be increased. They are: A Person and Clothes for: Head, Face, upper Body, Arms / Hands, lower Body / Legs and Foots. The benefit of this system grows with n**6 (with linear factor 1/7), where n is the amount of numbers / digits / signs we use generally.
At first glance, I defined a hart coded sequence from head to foot, which should ensure, that i do remember the clothings for myself (like a route or body method). But since dressing oneself is not a priori somethin which is needed to do in a particular order, we could use the permutations resp. the sequence of the clothes, when taking on, to encode additional information. Mathematically, this would lead to a linear prefactor, depending on the amount of Attributes in our system. In fact, using the permutations in this example would lead to a factor of 720 without really using more images. Just with differentiating between sequences of clothes. But the prefactor would be somethin like k!, where k is the number of attributes, but constant. So we’d had the faculty “involved”.
So what problem would occur, if the would do this. And would this be practically realizable?
- The Problem ist, that our Numbers-List in the System is already complete (complete not as math. term here).So in some “simple” case, we’d need to construct a special function, which maps each single of those numbers into a linear sequence of new numbers which are also complete and correctly organized So we would need to map our “normal number” for every permutation of the image of the number, into a sequence of new numbers to encode more numbers due to use of permutations. At least, I do not know such a function by heart, and more: Would it really be realistic that I / we encode such information with computing the real number which is stored. And when decoding it, we would need to do the reverse route.
In Fact, I think permutation could have some advantages. But I’m not sure, if this would be realizeable. Especially when it would be necessary to remember a bunch of permutations by their own. Also, I’m not sure, if it’s worth this, for only a linear factor. Adding one more attribute to the system would lead to one by one larger degree of the polynomial. But since adding an attribute would also lead to a bigger faculty within the linear factor, perhaps we should think about it?
(using permutations of the numbers itslef, would not lead to a benefit, since we cover all numbers till x already)
I would really like to speak about such considerations with you. What do you think about such things? And do you or do you not think, if acutal systems could be math. optimized?
And i really wonder if there is somethin like a “Theory of Mnemonic Systems”?
So lets talk.
And I hope the post was not too long.
