Review
Review
Which things were you surprised to learn are metaphors?
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14-7
Tablespoons of butter.
A tablespoon is a unit of volume. Namely, it is one-sixteenth of a cup.
Now, there are two distinct units called “ounces” that are commonly used in the United States. One is the avoirdupois ounce, also know as the United States customary ounce, which is a unit of weight; it is one-sixteenth of a pound. The other is the U.S. customary fluid ounce, which is a unit of volume; it is one-eighth of a cup.
One-sixteenth of a cup is a tablespoon. One-eighth of a cup is an ounce (fluid). One-eighth of one-half of a cup is a tablespoon. These are all measures of volume.
Butter, however, is sold by weight:
The 16-oz. package of butter in the photo above says that it contains four sticks. This is one stick:
The stick is divided into eight “tablespoons”.
But the “tablespoons” of butter depicted above are not one tablespoon each in volume. And there is no such thing as a unit of weight called the “tablespoon”.
So what is this? Well, one stick of butter is 4 ounces in weight. 8 ounces in volume is one cup. By analogy, if we think of 8 ounces in weight as a “cup” in weight (which is not actually a real weight unit!), then one-sixteenth of that weight is a “tablespoon” in weight (by analogy with one-sixteenth of a cup in volume being a tablespoon in volume). Neither cups nor tablespoons are real weight units! But if we call an 8-oz. weight a “cup”, then we can call a 1/2 oz. weight a “tablespoon”.
Sticks of butter are divided into metaphorical tablespoons of butter.
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 the density of butter is 1 oz / 2 fl oz?
4
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.
4
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.
2
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
2
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).
3
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.
4
The density of butter is reasonably close to 1 avoirdupois ounce per 1 fluid ounce, but is definitely not exactly equal:
https://kg-m3.com/material/butter gives the density as 0.95033293516 oz./fl. oz., or 0.911 kg/m^3.
(The link you provide doesn’t give a source; the data at the above link is sourced from the International Network of Food Data Systems (INFOODS).)
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Further commentary:
The density of water (at refrigerator temperatures) is ~1 g/cm^3. 1 oz. = ~28.35 g; 1 fl. oz. = ~ 29.57 cm^3; thus the density of water is (1/28.35) / (1/29.57) = ~1.043 = oz./fl. oz. (This is, of course, equal to 0.95033293516 / 0.911, allowing for rounding and floating point errors.)
Note that the composition of butter varies. In particular, it varies by the ratio of butterfat to water (there are also butter solids, i.e. protein, but those are a very small part of the total mass). American supermarket butter has approx. 80% butterfat; Amish butter, European butters (e.g. Kerrygold), or premium American butters (e.g. Vital Farms brand) have more butterfat (up to 85%). Butterfat is less dense than water (thus the more butterfat is present, the lower the average density of the stick of butter as a whole—although this doesn’t make a very big difference, given the range of variation).
Given the numbers in the paper at the last link, we can calculate the average density (specific gravity) of butter (assuming butterfat content of a cheap American supermarket brand) as 0.8 * 0.9 + 0.2 * 1.0 = 0.92. This approximately matches our 0.911 kg/m^3 number above.
2
Plus, butter is churned, so it is a few percent air by volume when solid.
83
Music pitch (high/low); the metaphor is so embedded in me from pre-memory days that I struggled to accept that it's just a convention. Many other binaries (such as long/short) would work just as well.
Isn't it the case that when you sing a high note, you feel something higher in your mouth/larynx/whatever , and when you sing a low note, you feel something lower? Seems difficult to tell whether I actually do need to do that or I've just conditioned myself to, because of the metaphor.
2
This is at least in part conditioning: singing teachers always teach you to think "down" as you sing higher, because the thing you instinctively do when you think "higher" is wrong.
Also, (or so I've heard) the ancient Greeks used "high" and "low" backwards (at least when writing their music down) because they thought of it in terms of taller and shorter strings on a harp, where the taller strings are lower notes.
-80
The Rumbling.
-5
In relativity, space and time are just different directions in spacetime with a single pseudometric determining separation between events. With this understanding, the time/space distance metaphor is more literal than most people think.
The correspondence isn't exact since it's a pseudometric and not a standard metric, and everyday units of time correspond to much greater than everyday units of distance, but it's still more than just a metaphor.
A classic example is that, at least in English, time is often described using distance metaphors
For me, I knew this was a metaphor, but until I took Mandarin in college I never realized that other languages/cultures/people used different spatial metaphors for time. Is the future in front of you, or behind? Are you moving towards it, or it towards you? This has some practical applications, since apparently even in English people have different intuitions about what it means to push a meeting or event up/out/back/ahead.
And English has it backwards. You can see the past, but not the future. The thing which just happened is most clear. The future comes at us from behind.
Tad James has a fascinating theory called timeline therapy. In it, he explores how different people represent their timelines and his theory about how shifting those representations will change fundamental ways you relate to the world.
I have time-space synesthesia, so I actually picture some times as being literally farther away than others.
I visualize the months of the year in a disc slanted away from me, kind of like a clock with New Years being at 6pm, and visualize years on a number line.
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