3

I was thinking of bounds for functions yesterday and it occurred to me that a bound from above is an "upper bound" (not "higher"), whereas a bound from below is a "lower bound".

Is there any etymological reason why we say "upper bound" but not "downer bound", or "lower bound" but not "higher bound"?

  • As Brian suggests, "upper" and "lower" have long been regarded as opposites, as in "upper and lower bunks". – Hot Licks Oct 25 '15 at 11:27
2

Because "higher" is scalable (high, higher, highest). So is "low" (low, lower, lowest").

"up" and "down" are not scalable. The suffix "er" on "upper" and "downer" does not make them comparatives. In the case of the drug slang "upper" and "downer", it's an agentive suffix. Something that brings you up or brings you down.

"Upper" as an adjective means above or on top. "Lower" as an adjective means below or on the bottom. Consider bunk beds. There is a lower bunk (the one on the bottom) and an upper bunk (the one on the top). Likewise, the 1st and 2nd storeys of a house are the lower floor and the upper floor respectively. And we have lower and upper teeth. In other words, when there are only two choices, rather than degrees of "upness" or "downness", the two choices are called lower and upper.

An aside:

There is not always symmetry in word usage. Our up-and-down words present other counterexamples: Consider lower the bridge. Now, if you put it up again, what did you do? You raised it—you didn't "higher" (or "upper") it. And back to drug slang: you get high but you don't "get low"—you come down.

Anyway, I agree it's peculiar. But that's how English goes. I'm not an etymologist, so I'll leave it at that.

  • Are you a relative of Alfred's :)? – MickG Oct 25 '15 at 11:03
1

The term downer has been associateted more with a physical/phsychological state from the 60's when the term became popular, (see Ngram) probably from its earlier usage (Down: sense of "depressed mentally" is attested from c. 1600.):

(n.) Slang

  • A depressant or sedative drug, such as a barbiturate or tranquilizer.
  • One that depresses, such as an experience or person.

(adj.)

  • Unable to stand because of disease or sometimes injury. Used of livestock.

(AHD)

Downer:

  • 1966 in sense of "barbiturate;" 1970 in sense of "depressing person;" agent noun from down (v.).

(Etymonline)

  • 1
    The drug references are about 100 years too late to have influenced the terms "upper bound" and "lower bound." I suspect that the choice has something to do with the translations of the work of mathematicians Bolzano and Weierstrass, who wrote in German. Alas, my German isn't good enough to check their work in the original. Mostly because my German isn't good enough for anything. – deadrat Oct 7 '15 at 7:17
  • @deadrat - I can't confirm or reject what you are assuming,but the fact that the term use actually spiked up from the 60's appear to support the idea of a new trend in its usage. – user66974 Oct 7 '15 at 7:23
  • @deadrat: well, "upper" is also used as the opposite of "lower" in place names, which seem unlikely to have all been influenced by German. For example: "Upper India", "Upper and Lower California", "Upper and Lower Egypt" – herisson Oct 7 '15 at 7:40
  • 1
    If by "the term," you mean downer, then you're surely correct. But the question is why downer bound isn't the opposite of upper bound when down is the opposite of up. And that decision was made long before Valley of the Dolls. – deadrat Oct 7 '15 at 7:42
  • 1
    I'm sorry, but I'm not following you. In drug slang, the opposite of a downer (barbiturate) is indeed an upper (amphetamine). The slang term downer isn't old enough to have influenced the choice of "lower bound" in function theory. What am I missing? – deadrat Oct 7 '15 at 7:52
0

The ending -er is generally applied to adjectives. And down is not an adjective.

You might say "Up isn't an adjective either!", but apparently up was actually used as an adjective at one point. The OED entry for the adjective upper says

Comparative of up adj., and signifying ‘higher’, ‘over’, ‘loftier’, ‘top’ (in contrast to lower, nether, under).

That said, the linked OED entry for up as an adjective doesn't seem to have many example quotations, so I'm not sure exactly what went on with the word upper.

In some cases, higher is in fact used as the opposite of lower, as in "higher and lower faculties" or apparently "Higher and lower orders".

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.