Please don’t stop reading — I really do. Algebra is the only thing that allows me to design knitting the way I want to.
I suppose you can cast on for a scarf or other simple garment and just start knitting, especially if you listen to Debbie New and follow some of her swatchless knitting techniques, but that is not the way I want to work most of the time. I want to knit things that mold to and follow the ins and outs of the human body (maybe also the dog body, I may make a doggy sweater in the not too distant future). I also want my knitting to be convincingly three dimensional.
Don’t tell me only crochet can do that; it will get my hackles up. Just imagine your reaction if I said that all knitters can crochet, but not all crocheters can knit, and you will get some idea of the force of my feelings on this subject. You just can’t get there without math, unless you are a freeform whiz, which I am afraid I cannot claim to be.
I generally start with a gauge swatch and work out my gauge in stitches and rows to 4 inches[10cm]. I then get out the measuring tape and start measuring everything. At this point I don’t think you can measure too many parts of your body to get an idea of how everything will fit together. Then I multiply the number of inches by the gauge per inch. This gives me an idea of how many stitches should be in each part. Then you need to start working out how many stitches difference there are between each section and how much distance there is for the pattern to increase or decrease enough.
Now there needs to be some understanding of how many stitches are needed to make complete repeats of any patterns you are including and to make the increases and decreases work out.
I follow the instructions I remember from grade 11 physics – assign variables to all the values you need to know and write down all the values you do know and just start deriving variables until you get all the variables you need.
To give you an idea of what I mean, here is my spreadsheet with my calculations for Josephine:
I confess I knit from a spreadsheet and write everything out in a way others can understand it only later. I use formulated cells in Excel in all my calculations too, because I love algebra, not arithmetic.