Pattern Matching & Systematic Reduction: How I Learn New Ideas Efficiently

Throughout my life I have always searched for patterns. I can’t explain why, but I’ve found it’s been the way I’ve learned most efficiently. One example of this is my recent fascination with Braille. I had the chance to play Scrabble recently with someone who is fully blind.

It was, no pun intended, an eye-opening experience. Not just because I was soundly defeated (I don’t play Scrabble much), but because this person was able to feel their way around the board, their letters, and come up with high-scoring words.

At first I tried to feel my way around the letters and see if I could figure out what they were feeling. I couldn’t find the pattern by touch. It seemed indecipherable.

Earlier this morning I found myself on yet another Wikipedia Learning Adventure. I ended up on the Braille page (after searching for ergonomic keyboards). Curious I decided to read up on it.

From Wikipedia: The 64 braille patterns are arranged into decades based on the numerical order of those patterns.

Oof. That’s a lot of patterns. Sixty-four symbols to memorize is quite a bit. The article goes on: The first decade are the numerals 1 through 0, which utilize only the top and mid row of the cell; the 2nd through 4th decades are derived from the first by adding dots to the bottom row; the 5th decade is created by shifting the first decade downwards. In addition, for each decade there are two additional mirror-image patterns, and finally there are three patterns that utilize only the bottom row of the cell.

Okay. There’s a lot of information to parse out. At first my eyes glazed over when I read this paragraph. To help, let’s look at the chart of Braille cells.

Again, lots of cells to memorize. If you were dedicated, you could try to memorize this entire chart to learn Braille.

What if I could show you how I learned it efficiently?

First, I parsed out that big paragraph. Let’s look at it again.

The first decade are the numerals 1 through 0, which utilize only the top and mid row of the cell;

Cool. For the first set of 10 Braille characters, we can ignore the bottom two dots.

…the 2nd through 4th decades are derived from the first by adding dots to the bottom row;

Sweet. If we memorize the first 10 characters, all we need to do to memorize the 2nd and 3rd is to know when to add a dot.

…the 5th decade is created by shifting the first decade downwards.

Great. The 5th decade is just a shift downward.

In addition, for each decade there are two additional mirror-image patterns, and finally there are three patterns that utilize only the bottom row of the cell.

At this point, we’ve reduced the amount of information we need to memorize. We started with 64 cells. Hypothetically we only need to memorize the first 10 cells, then the transformation rules. But could we reduce that memorization set further?

Let’s look at the first row.

Even those ten patterns look a little daunting. Certainly much more doable than 64. But are there patterns we can find to reduce this set? Yes there are. In fact you could develop rules that reduce your pattern memorization to six. See if you can find them.

Did you find them? Here’s what I came up with.

• 1/a is 1 dot (⠁)
• 2/b is 2 dots (⠃), and 3/c is 2 flipped. (⠉)
• 4/d and 6/f are mirrored ⠙|⠋
• 5/e and 9/i are mirrored ⠑|⠊
• 7/g is filled in (⠛)
• 8/h and 0/j are mirrored ⠓|⠚

Cool! We can reduce our work to memorize 6 cells and apply rules to get the remaining 4. In fact we could reduce this further.

• Apply a 90 degree rotation from 4/d (⠙) to get 0/j (⠚), 8/h (⠓), and 6/f (⠋), or
• Apply a -90 degree rotation from 0/j (⠚) to get 4, 6, and 8 (Sequence: 0, 4, 6, 8)

Our new reduction rule is:

• 0/j creates 4/d, 6/f, and 8/h ⠚|⠙|⠋|⠓
• 1/a is 1 dot (⠁)
• 2/b is 2 dots (⠃), and 3/c is 2 flipped. (⠉)
• 5/e and 9/i are mirrored ⠑|⠊
• 7/g is filled in (⠛)

What about the remainder of that chart? Well, there’s a shortcut for decade 2. Can you see it?

The pattern is simple: decade 2 has a dot in row 3, column 1. Always. With that rule you’ve added 10 symbols to your alphabet.

Decade 3 has two dots in the bottom row, and decade 4 has one dot in the bottom-right row.

Decade 5 is the first decade shifted down by 1 row. Finally, decade 6 is shifted down one more row!

“But Elias, we’ve only memorized 52 symbols? What about the other 10?”

Turns out there’s another rule we can apply. Each decade has two additional symbols. How are they formed? Shift the first two rows right.

My general rule for learning something new is this: I look for patterns that allow me to form rules in order to reduce the amount of stuff I need to memorize. I can more easily remember mnemonics than try to memorize symbols.

Next time we’ll look at how I use this thinking to avoid memorizing the multiplication tables. Stay tuned!