Laying out the numbers on a rectangular grid: methods 1-3

This is the next part of my rewrite of my instructions for turning words into knitting charts (or charts for other crafts). Once the letters have been turned into numbers, they need to be charted on a grid. These are three ways of making rectangular grids with the numbers; I’ll post a fourth way in a couple of weeks.

I have four basic methods for charting the numbers onto grids (the name I use for the digital version of blocks of graph paper). The first three are related; the fourth works on a different principle. I tried coming up with descriptive names, but I never did work out something logical and concise that distinguishes between the four. Therefore, I’ve resorted to numbering the methods.

The first three methods all rely on a basic method of graphing. The fourth uses a layout that’s more like writing or knitting.

Methods 1 and 4 are the ones that can most truly be called secret code, as they are the ones that could reasonably be deciphered. Method 3 could possibly be deciphered, but there’s an extra layer of complication that I think introduces ambiguity. Method 2 isn’t really a cipher at all. (Here’s a post about whether these techniques can really be considered to be secret code.)

For all of these, I will again make use of peace, turned into numbers using base 6: 24 05 01 03 05. There are 10 digits to be encoded.

Method 1

This is the simplest method to chart. There should be a column for each digit, and as many rows as the number of the base. So there are 10 columns and 6 rows.

peace method 1

I have numbered the rows from 0-5, as these are the digits in Base 6. I’ve numbered each column from right to left (as if knitting) with the digits to be marked: 24 05 01 03 05. So in the first column, marked 2, I marked the square in the row numbered 2. In the second column, I marked the square in the row numbered 4, and so on.

Method 2

This method needs as many columns as there are letters and as many rows as the base: so, 5 columns and 6 rows.

peace method 2

I start on the right side as before, and chart 2 4 0 5 0 from right to left; these are the black squares. Then the direction changes, bouncing off the left edge of the grid. I chart 1 0 3 0 5 from left to right. These are the grey squares. I don’t usually use a separate color for this, but I thought it might help illustrate what’s happening here.

The numbers are shuffled up enough with this method of charting that I don’t see how the result could be considered to be a proper cipher – there doesn’t seem to be a reasonable way to know which numbers go with which letters. In this case, resulting stitch patterns are based on words, but aren’t a code.

Method 3

This method also needs as many columns as there are letters and as many rows as the base: in this case, 5 columns and 6 rows. The difference is that both digits for a given letter are charted in the same column.

peace method 3

Again, I start on the right side. P is 24, so I mark the square in row 2 and the square in row 4. E is 05, so I mark 0 and 5, and so on. If any of the letters had been 11 or 22 or 33, then only one square would be marked in that column. If I were using this as actual code, it would be understood that a single square in a column would indicate a repeated digit.

If I were trying to decipher the grid produced by this method without having the numbers provided to me, I’d have to allow for the possibility that each column is one of two letters. For instance, the rightmost column might be 24 or 42. There is the limitation that base 6 has no letters that go higher than 42. For this particular grid, therefore, the columns might be read as (P or Z), E, (A or F), (C or R), E.  It’s not too difficult to work out that the only English word possible is peace. (Not real words: zefre, zeace, zefce, pefce, pefre.) However, there are possible combinations of squares that could indicate any of two or more words. Even so, the “code” is probably decipherable in most cases.

(Method 4 is different enough that I’ll make it the entire next blog post for the rewrite.)

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