Memorizing numbers using fixed PAO

Fixed PAO visualizations are traditionally used to memorize numbers. In the first decade of the 21st century, most memory masters used this methodology for memory competitions. While I recommend using flexible PAO to encode pretty much everything, fixed PAO visualizations for numbers do not get enough attention from me. Here I want to address this subject.

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The initial PAO

For most practical purposes, we do not need PAO of more than 3 digits. This means that we can do quite a lot with one visualization per digit: person, action, and object. Learning to apply just 30 visualizations is not very hard and does not require a lot of practice. Typically the application of such tables becomes automatic and effortless after two weeks of practice.

If you need to remember more digits, just generate several such visualizations. Since each visualization is 3 numbers long, when generating the visualization pad the number by zeros from the left. For example, 1981 becomes 001 981 and is encoded as two very simple PAOs. This is sufficient for many practical scenarios, and possibly I could add my article here. However, we usually open up subjects for more complex investigations.

More precision means more speed

In theory, we could almost triple the visualization speed and stability of memorization by using a visualization per 3 digits. Then every PAO could encode 9 digits. Let us discuss this claim.

More unique PAOs with fewer PAOs per room of a mental palace will increase the accuracy of memorization the next time we revisit the mental palace. A 3-digit number will probably be reused many times, generating more opportunities for mistakes. A 9-digit number is significantly more likely to be unique.

Placing 3 visualizations in a mental palace is slower than putting just one visualization, and also requires more rooms and palaces for long data. Moreover, after some practice large visualization tables become as fast as smaller ones.

However, this approach is purely theoretical. The amount of practice required to remember 3000 visualizations and use them automatically is prohibitive. The practice literally takes years, several hours per day that could be used better than that.

A different consideration is numerical accuracy. We just do not need to remember multi-digit data very fast. I do not have a single use case for this skill. We have digital devices especially constructed for similar tasks.

Numerical accuracy

To be honest, in most engineering tasks we need just three digits: one digit before the decimal point, one digit after the decimal point, and an exponent.

It is useful though to memorize the sign for the number and for the exponent. This means that we can easily learn and benefit from signed visualization: 19 persons and objects between -9 and 9 as well as 10 actions, which we probably already learned when visualizing 3 digits. This is less useful for memory competitions but can help in practical tasks, like estimating the validity of engineering solutions and their cost.

For science, like physics, this accuracy might be not sufficient. Typically we need to extend the visualization, using 2 digits after the decimal point and exponents say between -12 and 12. This requires a large collection of actions, 100 visualizations overall, and an extended collection of objects, say 25 or more for cosmological scale.

The complexity of training such tables is not prohibitive, and usually, within several months, people can memorize huge tables of constants. Typically constants require 4 corners of a mental room. The first visualization encodes the subject, like thermodynamics. The second visualization encodes the name of the constant. The third visualization is a PAO of the number. The fourth visualization is the unit of measurement, e.g. person for nominator like Joules and object for denominator like hours. Clearly, the same physical constant may have many visualizations based on the chosen measurement units, making this exercise fun for several months.

Sparse matrix PAO use case

In some cases, we may want to use many PAO rooms for short term memorization, for example, if we want to compare several executions or versions of processing algorithms

If we want to memorize a pointcloud value of a lidar measurement, we have four PAOs in a room: X, Y, Z, and Value. We are not confined to the corners of the mental room, and can use walls to encode for example, frame number, confidence, and second reflection.

A very different approach would be remembering the horizontal and vertical index of the point on a rectangular grid and its value. The horizontal and vertical index usually run to several hundreds or thousands. The same applies to frame numbers or object categories.

PAOs for accounting

While engineering or scientific PAO visualizations usually deal with floating numbers, accounting usually deals with fixed numbers. For accounting, we usually need a sign and two digits for thousands, three digits for dolars and two digits for cents. If larger numbers are used, the tables do not really change but instead of dollars in a child’s budget, we have millions of dollars in a state’s budget.

It is easier to visualize objects, more complex people and still more complex actions. We can relatively easily get used to three digits in object as dollars and two digits in action as cents.  Regarding the person as thousands, we need also to keep sign, so we can slowly increase the complexity starting with -9 to 9 range, then -99 to 99 range, and beyond.

Regarding the increase in complexity, it takes a couple of years to get proficient, especially using 3-digit objects. But we do not really need this proficiency and can use a different encoding, for example,  encoding every 3 digits as a separate PAO.

How to make fixed PAO incrementally

From this short discussion, it becomes clear that PAO is something we build up incrementally. Moreover, the build-up is not symmetrical. We start with 10 people, actions, and objects. Then we get 20 people, 100 actions, and 20 objects. Once proficient, we can increase the number of objects to a thousand. As the last step, we increase the number of people to 1000.

This means that when we start, we need already be prepared to scale up to 1000-100-1000 setup, even if we do not actually use it. For actions, visualizing more than 100 actions is hard, so we use modulo so that V(N) = V(N%100), e.g. the same visualization for 97, 397, and 897. Then we get essentially to encode 1000 people, actions, and objects. For people and objects, we need to visualize both positive and negative numbers. I  recommend folding the numbers around a thousand e.g. V(-N)=V(1000-N).

While this preparation is hard, it is much easier than practicing the visualizations till they become automatic. So we prepare 10 visualizations for person-action-object and practice them till automatism. Then we will have enough experience to increase our tables to 120 people, actions, and objects e.g. 0 to 99 and -20 to 0 ranges. We can practice with that for several months till this becomes natural. Whether or not we actually want to have 1000-100-1000 visualization range is a big question. A sane person will probably vote against it. If you like the challenge or suffer from insomnia, you can definitely try it.

Choosing the PAO

There is also a question of actually choosing the words for the fixed PAO. The typical solution involves using a Major system or maybe its variation. With the major system, there is a phonetic symbol associated with every digit. Since there are 3 digits in 1000, we get three letters. And then we need to build a word using these three letters. For every set of three letters, we select an object and a person.  For the action, we use just two letters. Notice that every object, action, and person needs to be easily recognizable and uniquely visualized. In the beginning, this can be especially awkward, since we reuse the same 2 letters for 00X. There are not many words with double S, so it makes sense for signs or thousands to use not a letter but a subject selection, e.g. “List of X” on Wikipedia.  There are also plenty of fixed PAO lists online, of single and double-digit variations.


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