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by SnowHill9902 1359 days ago
It’s called abuse of notation as it’s useful in practice but not strictly a percentage.

https://en.wikipedia.org/wiki/Abuse_of_notation

3 comments

It's a percentage of a base unit. i.e. the amount of flour used is 100% of the base unit amount.

Sounds like you want the total percentage which is just as easy to find. Given their example, the total is 170%. The proportion of flour to the total is 100%/170% = ~59%.

Think of it as a "separation of concerns". Using a base unit allows you to measure without regard for the other ingredients. Expressing it in percent allows you to scale a recipe without regard for the literal amounts. It's a good system.

Ever write CSS with "rem" units? It's the same idea.

Doesn't it all depend on the implied subject of the percentage? If you're thinking in percentage of total ingredients in the bread, then yes maybe it's an abuse of the notation. But I believe the intent in this case is to express each non-flour ingredient as a percentage of the weight of the flour. In that case it's a genuine percentage relationship.
What’s the abuse here? This seems like ‘math’ to me.
Abuse of notation is incredibly common in mathematics, there’s no conflict there.

The abuse would be if you think that percentages should always refer to portions of the whole. Not sure that’s correct, though.

I don't know that I'd use the term abuse, but the basic idea is that there are things called odds ratios (Bayes' theorem looks especially convenient with them!) as distinct from things called probabilities... The distinction is precisely this one, that probabilities are implicitly normalized to 100% total while odds you're supposed to sum everything together and divide.

And then the point is just that we typically condition people to treat percentages as probabilities rather than odds. So you would have said something like 50:33:1:0.3 in “odds speak” for flour:water:salt:yeast in the dough mixture discussed in OP. But bakers instead communicate “:66:2:0.6” with the first number always implicitly being 100 (great), and they then use the % symbol (slightly confusing).

Because they never say “flour: 100%” an unsuspecting novice might think that a 60% hydration dough is ~40% flour by mass, mix this together to form a 150%-hydration mixture, and wonder why the only thing that they can make with it is some sort of pancakes.

Probabilities? Why do you need to bring those in?

Percentages are just a way of writing rational numbers. Bread recipes are expressed effectively as 1 part flour to n parts of each ingredient. But since n in that formulation is usually a value less than 1, expressing that number as a percentage is convenient. Percentage notation seems completely appropriate for this usecase.

So 60% hydration means 1 part flour to 60% of 1 part water, i.e. to .6 parts water.

As in it goes against the designed usage (where total is 100%), but it still works.

The total ingredients being 170% can be found confusing initially. I'm glad the author provided more context and the example of a 500g flour recipe.

Why does the total have to be 100%?

Do all fractions have to add to 1?