## X is the same as Y

It’s been several months since I’ve posted anything, mostly because I’ve been busy with coursework, research, TAing, etc. But I have been keeping some squib notes. Here is one.

In formal methods class one day, my prof. wrote on the board two sets:

$X = \{a,b,c\}$
$Y = \{1,2,3,4\}$

After a few seconds, he realized something was wrong, and said, “Actually, $X$ is the same as $Y$.”

My initial reaction was to think, “Ah, then $X=\{1,2,3,4\}$,” or maybe “OK, then $X=\{a,b,c,d\}$, where $a=1, b=2, c=3, d=4$.” In other words, add an element to $X$ to be like $Y$.

Turns out that what the prof. meant was that $Y=\{1,2,3\}$, where $a=1, b=2, c=3$. In other words, subtract an element from $Y$ to be like $X$.

It made me wonder whether, given any generic sentence like “X is the same as Y”, one could tell whether (one’s conception of) X ought to change to conform to (one’s conception of) Y, or vice versa. For me, I think X is the one to change, not Y.

For example, let’s say you think that John is 5’6” tall, and Sue is 5’8”. If I tell you, “Actually, John is the same height as Sue”, can you tell how tall they are? If I were to actually utter that sentence, I think it would be to convey that John is 5’8”, i.e., (your conception of) Sue’s height. Likewise, to convey that Sue is 5’6”, I’d say, “Actually, Sue is the same height as John.” In other words, the subject of the sentence is the one whose height needs adjusting.

Same goes for lots of other scenarios: “John is as old as Sue” to me means, basically, “However old (you think) Sue is, that’s how old John is, too” and not “However old (you think) John is, that’s how old Sue is.” It holds for comparatives, as well: “John is older than Sue” means “However old (you think) Sue is, John is older than that” (i.e., adjust/raise John’s age to exceed Sue’s; don’t adjust/lower Sue’s age to be less than John’s).

The generalization, I think, is that if I want to correct someone’s conception of X to conform to Y, I say, “X is (the same as/as [adj] as/more [adj] than/…) Y”, and not “Y is (the same as/as [adj] as/more [adj] than/…) X”.

Of course, it’s only a generalization—perhaps a pragmatic, conventional one, which can be flouted. If I’m a landscaper and you hire me to make your front yard as pretty as or prettier than your neighbor’s, and I go and dig holes in your neighbor’s yard and dump trash all over it, you’ll probably say, “That’s not exactly what I had in mind”, but I could probably argue that I successfully completed the task.