At all levels of Mental Calculation (especially elite levels) you can gain speed and accuracy by learning more shortcuts. For example:
- At school we learn our times tables from 2×2 until 12×12
- For quickly calculating square roots it is helpful to know the square numbers from 31² = 961 until 99² = 9801
- For calculating calendar dates it is faster if you know for each year in the century, what the contribution will be in the algorithm (e.g. for me, 19 in 2019 gives +4)
It is maybe the least interesting part of training calculation, but to some extent it is unavoidable!
The same is required in other applications outside of Mental Calculation:
- Memorizing systems for memory competitions
- Learning vocabulary for languages
- Learning properties of medical products for Pharmacology study
- Learning the names of many people very quickly
Luckily there is a powerful shortcut for this – known as spaced repetition. I’ll explain it using the example of learning vocabulary as this is familiar to most people.
Typically at school you will be given vocabulary lists. For example for an English-speaker learning Spanish:
- cat = gato
- dog = perro
- fish = pez
- sheep = oveja
- rhinoceros = rinoceronte
- horse = caballo
- goat = cabra
- ant = hormiga
- spider = araña
- owl = búho
You would practise all of these words until you knew them, and then move onto another vocabulary list. Over time you might worry that you forget some words, so you start to practise old vocabulary lists again.
This is quite effective but inefficient. Maybe for you it is obvious that “cat” = “gato” because it sounds similar, and “dog” = “perro” because you often talk about your pet dog, so it is a waste of time practising this so regularly.
Maybe you find that every time you look at the list you forget the word for “ant” because there isn’t an easy way to remember it, or you forget that “horse” = “caballo” because the word is similar to the Spanish for “hair” and “gentleman”.
Spaced repetition is a solution to this inefficiency. it works as follows:
- Download a spaced repetition mobile app or desktop application
- Add all the words you want to learn (for example starting with the 10 animals above, but usually adding much more)
- Every day the software tests you for a few minutes on the items you’ve added to the dictionary
- You provide feedback on each item to indicate whether it was easy / hard / impossible for you to remember the answer
- The software learns (with powerful algorithms) which of the words were simple / difficult for you to learn
- The software selects every day only the words that it thinks you are about to forget (so it might test you on “cat” in 2 months’ time, but “ant” tomorrow and also the day after)
- You can add new items to the dictionary at any time – or change existing ones.
To illustrate this in more detail, this is how I would use spaced repetition to efficiently learn the squares from 31 ro 99:
Download software: I use Mnemosyne, but the most widely-used is Anki
Make input file: create a plain text file and on each line use the format [question][tab][answer], e.g. “38 1444” Creating this file is also good for learning this information, but you could instead create it in Excel or download an existing file online. Here’s a prepared input file for the squares 31-99.
Import to Mnemosyne: select “File -> Import” to import these cards as a tab-separated text file
Daily practice: every day spend a few minutes using the software. For each item, grade your answer as 0 or 1 if you had to calculate the answer rather than remember it, 2-3 if you could remember it but you were slow, and 4-5 if you could remember it and it was easy
Succeed: After spending 1-5 minutes each day for a few weeks you’ll find that you’ve basically learned all of it and don’t need to continue this training. Your normal calculation training should be enough to keep this information in your memory, but if not, you can always resume the training at any point.
Hopefully this speeds up some of the boring parts of your calculation training, or learning of languages! If you have any other solutions you like for learning raw data more efficiently, please share it with us in the comments.
This is the last update of 2018 – I’m wishing you all a happy and prosperous 2019!