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The motivation for this question came from this Software (C#) question

"Why is it faster to check if dictionary contains the key, rather than catch the exception in case it doesn't?"

and answer:

"On the one hand, throwing exceptions is inherently expensive, because the stack has to be unwound etc. On the other hand, accessing a value in a dictionary by its key is cheap, because it's a fast, O(1) operation. ..."

Well, on one hand, the hands illustrate different points, (but/however) on the other hand they are both supportive of the original question "why is it faster..."

I thought the idiom "on the other hand" can be replaced with "but" or "however".

But for this case that appears not to be true and the idiom would need to be replaced with something like "additionally."

http://idioms.thefreedictionary.com/on+the+one+hand http://idioms.thefreedictionary.com/on+the+other+hand

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Of course they can both support the main issue. For instance:

The Holocaust is one of the best documented events in human history, supported on the one hand by numerous eyewitness testimonies of survivors and liberators, and on the other by German records, written and photographic. —Nicholls, Christian Antisemitism, 1993, p. 391

And consider this description of Pickett's charge at Gettysburg, where the same metaphor has literal force:

General Pickett's division of 5,000 men. with their commander at the head. and supported on the right by Wilcox with 5,000 men, and on the left by Pettigrew with 5,000, moved steadily forward in three columns. —Nelson’s ... Encyclopedia, 1909,s.v. ‘Gettysburg, Battle of’

As you say, it is not only the conjunction, but the entire context which determines whether the two hands are collaborating or opposed.

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    Noting that, in both these examples, the use of "and" carries the weight of defining the relationship to the main issue. The example within the question begins the sentence with "On the other hand..." Maybe that's where the confusion stems for me at least. – crokusek Nov 20 '14 at 19:24
  • @crokusek It's not the conjunction but the context which determines whether this hand and that are working in the same direction or opposite directions. "We have a dilemma: OT1H X, OTOH Y" vs "Our way is clear: OT1H X, OTOH Y". – StoneyB Nov 20 '14 at 20:55
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    Agree that an optional leading phrase can forecast dissent or agreement. However the conjunction is key when the leading context lacks a definitive forecast or does not exist: "I should go to bed because OT1H it is nighttime and OTOH I'm sleepy." vs. "I should go to bed because OT1H it is nighttime but OTOH I had too much coffee." A no context example: "OT1H it is nighttime but OTOH I'm wide awake." – crokusek Nov 21 '14 at 6:14
  • @crokusek People don't speak in isolated sentences. Context may be discerned beyond the sentence boundaries, in the larger context of which the sentence is a part. – StoneyB Nov 21 '14 at 23:03
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    "OT1H sugar is sweet (and|but) OTOH it creates farts." Here the conjunction carries the entire assent vs. dissent bias. Either the author enjoys farting ("and") or he doesn't ("but"--no pun intended!). Perhaps in your first comment, you could have written "Its not just the conjunction but the entire context..." That statement I could have agreed with. – crokusek Nov 22 '14 at 0:12
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Both your links seem to support your assessment (and mine) that it doesn't make sense to use the two to support the same thing.

On the other hand = however.

On the other handfurthermore.

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