Talk:Scott W's Couscous
Is the cheese supposed to be 2 cups before or after you cut it into cubes. There's a big difference in the packing fraction. Maybe specifying the cheese by weight would be better? Scott Nelson 15:18, 23 June 2008 (PDT)
- It is 2 cups of cubes. The item says "2 cups cubed cheddar cheese" so I thought this was clear. It doesn't say 2 cups of cheese cut into cubes, which would be less specific. Weight would probably be better, but until I make the recipe again I won't know how much 2 cups of cubes weighs! :) Feel free to reword the ingredient list if you can make it less ambiguous. Also, I didn't specify the cube size, which makes a difference. I think I used around 1 cm x 1 cm x 1 cm, BUT all this is somewhat irrelevant because the recipe is pretty rough. Scott Webster 16:15, 23 June 2008 (PDT)
- Ok. But I don't see how the cube size affects the packing fraction. Wouldn't the ratio of cheese to empty space be the same regardless of how big the cubes are? Scott Nelson 08:09, 24 June 2008 (PDT)
- This is becoming some sort of interesting geometry problem :) I think you are right actually... my initial thought was that it would matter, because clearly _one_ cube with a volume of 2 cups would be more cheese than 2 cups of smaller cubes with air space included. However, it does seem that for any reasonable cube size that the cheese:air ratio would not necessarily change too much. This is not a rigorous proof :) Scott Webster 10:56, 24 June 2008 (PDT)
- Clearly what is needed is a rigorous proof of the relationship between cube size, volume of cubed product and weight. Then we can put it into a wiki template which takes the dimensions of the cheese chunks, type of cheese and volume of finished loose-packed cheese and spits out the required weight, so anyone can replicate the recipe using different dimensions of cheese chunk... {{cheeseathon|type=cheddar|chunkwidth=1|chunkheight=1.5|chunkdepth=1|volume=400}} --Matthew 11:05, 24 June 2008 (PDT)
- Jeff came up here and drew some plots on my whiteboard. There was a plot of cheese mass vs cube size. Basically the worst case cube orientation scenario is a strangely decreasing function of cube size. Scott Webster 12:19, 24 June 2008 (PDT)
- This is becoming some sort of interesting geometry problem :) I think you are right actually... my initial thought was that it would matter, because clearly _one_ cube with a volume of 2 cups would be more cheese than 2 cups of smaller cubes with air space included. However, it does seem that for any reasonable cube size that the cheese:air ratio would not necessarily change too much. This is not a rigorous proof :) Scott Webster 10:56, 24 June 2008 (PDT)
- Ok. But I don't see how the cube size affects the packing fraction. Wouldn't the ratio of cheese to empty space be the same regardless of how big the cubes are? Scott Nelson 08:09, 24 June 2008 (PDT)
