It sounds like 1⁄2 cup of butter (8 tbps) weighs 4 oz, so shouldn’t this actually work out so each of those sections actually is 1 tbsp in volume, and it’s just a coincidence (or not) that 2 fl oz of butter weighs 1 oz?
This is almost true. Fat is less dense than water, so a tablespoon of butter weighs something like 10% less than a half ounce. Not enough to matter in practice for most cooking. Your toast and your average chocolate chip cookie don’t care. But, many approximations like this exist, and are collectively important enough that professionals use weight not volume in most recipes. And enough that the difference in fat content between butters (as low as 80% in the US but more often 85+% in European or otherwise “premium” butters) can matter in more sensitive recipes, like pie crust and drop biscuits. I used to add 1-2 Tbsp of shortening to my pie crust. I stopped when I switched to Kerrygold butter—no longer needed.
Edit to add: I think almost every concept we use in life is part metaphor, part not, and the difference is one of degree and not kind. I was definitely surprised to learn this, or at least to learn how deep the rabbit hole goes.
All of the sources I can find give the density as exactly 4 oz = 1⁄2 cup, although maybe this is just an approximation that’s infecting other data sources?
No, you’re misunderstanding. There is no 1⁄2 cup of butter anywhere in the above scenario. One stick of butter is 4 oz. of butter (weight), but not 1⁄2 cup of butter (volume).
It sounds like 1⁄2 cup of butter (8 tbps) weighs 4 oz, so shouldn’t this actually work out so each of those sections actually is 1 tbsp in volume, and it’s just a coincidence (or not) that 2 fl oz of butter weighs 1 oz?
This is almost true. Fat is less dense than water, so a tablespoon of butter weighs something like 10% less than a half ounce. Not enough to matter in practice for most cooking. Your toast and your average chocolate chip cookie don’t care. But, many approximations like this exist, and are collectively important enough that professionals use weight not volume in most recipes. And enough that the difference in fat content between butters (as low as 80% in the US but more often 85+% in European or otherwise “premium” butters) can matter in more sensitive recipes, like pie crust and drop biscuits. I used to add 1-2 Tbsp of shortening to my pie crust. I stopped when I switched to Kerrygold butter—no longer needed.
Edit to add: I think almost every concept we use in life is part metaphor, part not, and the difference is one of degree and not kind. I was definitely surprised to learn this, or at least to learn how deep the rabbit hole goes.
Almost all human thinking is part metaphor.
Words have uses not meanings. Definitions are abstractions.
In otherwise, everything is (in part) a metaphor.
All of the sources I can find give the density as exactly 4 oz = 1⁄2 cup, although maybe this is just an approximation that’s infecting other data sources?
https://www.wolframalpha.com/input?i=density+of+butter+*+(1%2F2+cup)+in+ounces
No, you’re misunderstanding. There is no 1⁄2 cup of butter anywhere in the above scenario. One stick of butter is 4 oz. of butter (weight), but not 1⁄2 cup of butter (volume).
But 1⁄2 cup of butter weighs 4 ounces according to every source I can find: https://www.wolframalpha.com/input?i=density+of+butter+*+(1%2F2+cup)+in+ounces
Which means a 4 ounce stick of butter is 1⁄2 cup by volume.