Salad Entropy
Opened this issue · 4 comments
i just disagree with the salad entropy theory
I think the number of unique ingredients should be in the logarithm because that way a food item consititing of one ingredient will always result in a salad entropy of 0
therefore a food item consiting of a single ingredient is always not a salad
i would postulate that 30 french fries is not a salad
but simply 30 friend fries
i would also consider that spices are not ingredients when pertaining to salad entropy
because i would say that 1 french frie with a grain of salt is not a salad with 2 unique inedients
neither is salt water a salad
salt in water is one homogenious solution
therefore 1 ingredient
so for the purpose of our reading i would consider the salad entropy equation to be something along the lines of ln(x) where x is the number of unique ingredients
i would say that the total number of ingredients does not matter, only the number of unique ingredients
if you wanted to refine the formula further you could perhaps add some statistical theory to outrule ingredients with a statstically significantly low constitution to the total volume of the salad
i had considered mass instead of volume, but that would easily rule out low mass contitutents like lettuce quickly, even tho lettuce may be the primary visual component of the salad
so i would think volume would matter more, considering volume is generally what gives you the immediate feeling of "fullness" when you eat
regarding what log base to use, I have not considered this thoroughly. It would make sense, if we stick with the idea that a salad entropy of 1 is a true salad, to make a standard salad, as considered by the general populace, to have as close to a entropy of 1 as possible, however then a "statistically generic" salad idea must be agreed upon
this is a reasonable take. I think the number of non-unique ingredients should still increase entropy, but it's quite reasonable to say that the number of unique ingredients is more salient.
that is why I say that a glass of water with ice is a salad, but only barely
One issue that I have is that increasing the number of the same ingredient doesn't decrease the entropy. I would argue that a salad consisting of one piece of lettuce and one cashew has a lot higher ingredient entropy than a salad consisting of 1000 pieces of lettuce and one cashew. In the former, both ingredients are very noticeable, in the latter, either only a single bite will have the cashew or the cashew will be spread among so many bites that it is not noticeable at all.
I like the idea of going by volume rather than an amount but regardless, I would present that the total ingredient entropy is the sum of the entropy contribution of each unique ingredient. The entropy contribution being the proportion (i.e proportion of the amount or proportion of the volume) of the ingredient compared to the entire salad multiplied by one minus the proportion of the ingredient compared to the entire salad.
For a single ingredient salad, no mater how many items you have, the entropy will always be 0 because 1*(1-1)=0. As you add more ingredients of equal proportions, the entropy will get closer and closer to 1. A theoretical salad consisting of infinite distinct ingredients would have an entropy of 1. It seems reasonable that the first few ingredients that you add to a low-entropy salad would have a much larger contribution than adding a new ingredient to a salad with 20 other distinct ingredients.
If you add only a very small amount of an ingredient compared to the total of the salad, it will only increase the entropy by a small amount. As you increase the amount closer to that of other ingredients, the entropy will increase until it starts to dominate the salad which then decreases the entropy again.
Since this would change the range of the ingredient entropy to be from 0 to 1, a new minimum entropy would need to be established. Perhaps 0.5 which would be two equally proportioned ingredients.
You make good points; if there's a particular formula you have in mind, I'd be happy to include it as an alternate measure.
that is why I say that a glass of water with ice is a salad, but only barely
earlier you argued temperature should not matter, so why now?