deutlich or eindeutig?
Can someone please explain the difference between 'deutlich' and 'eindeutig' to me. Some example sentences would be appreciated.
That is not really easy.
deutlich is something pretty clear, like letters on a sign (Die Schrift ist deutlich), pronunciation (Die Aussprache ist deutlich); if you can understand or see or hear etc something very well, but another person could think otherwise, you'd say: Es ist deutlich.
eindeutig is stronger, like the proof of a fact could be free of doubt (Der Beweis ist eindeutig), or you may have a clear position on something (Deine Position ist eindeutig); if there would be no degrees possible, but only 0 or 1, you'd say: Es ist eindeutig.
Grammatikalisch zwar richtig, aber man wuerde eher sagen: Jetzt ist es mir klar / Jetzt verstehe ich es :)
I wouldn't say eindeutig is stronger; it's just different: deutlich means clear-cut, eindeutig means unambiguous.
So, is deutig used more with continuous things (on a sliding scale with no clear cut off point) and endeutig more with discrete (it is or it isn't, for or against and no middle ground)? So, whether a colour is green or blue could be deutlich, but whether it is green or orange is eindeutig?
It's more that the words carry connotations that come from their earlier, more concrete meanings. Deutlich and eindeutig are both derived from deuten, roughly to indicate, to explain. (This in turn may be related to deutsch, so deuten would be to explain something in German.)
Deut-lich originally means something that can be gedeutet, i.e. explained.
Ein-deutig means something that can be explained in only one way.
To apply the words to colours:
A colour is deutlich if it's not washed, if there is enough light available to see it etc. It may still be a weird hue somewhere between green, blue and grey that we would have trouble naming.
A colour is eindeutig if there can be no doubt about how to name it, e.g. ultramarine blue. This may be the case even under circumstances that are not favourable at all to determining colours in general.
So would the difference be something like the use of "clear" and "clearly" in following English sentence? The color is clear (visible, deutlich) to me now, it is clearly (obviously, eindeutig) red.
The difference between clear and clearly is that the former is an adjective and the latter the corresponding adverb. This is a little misleading for "deutlich" and "eindeutig" as both words can be both adjective and adverb. Your example still works well, though.
It is good to go back to the verb deuten (interpret, indicate, explain).
deutlich - means unambiguously interpretable/indicated/explained
Ich habe es dir deutlich gesagt. (adverbial) I've told you clearly.
Ich hoffe, das war jetzt deutlich. (attributive adjective) I hope, this has been clear.
eindeutig - means having only one possible interpretation/explanation (often used with proven facts).
Es ist eindeutig über Rot gefahren. (adverbial) He has unambiguously run a red light.
Die Ergebnisse sind eindeutig. (attributive adjective) The results are clear/unambiguous/leave only one possible interpretation.
Both words are interchangeable in the above examples but I the nuances would shift. Deutlich is closer to clear and eindeutig is closer to unambiguous.
Er schläft deutlich zu lange. (adverbial) He sleeps clearly too long.
Er schläft eindeutig zu lange. (adverbial) He sleeps too long without (possible) doubt.
There are some variations that may either confuse or make the concept clearer. Let's risk it ;)
zweideutig - ambiguous, allowing two conflicting interpretations (often used with innuendos)
Lass diese zweideutigen Bemerkungen. Stop these sexual innuendos. (ambiguous remarks)
Sie gab mir zweideutige Blicke. She gave me flirtatious glances. (that could mean something more, but not necessarily)
Mathematicians invented a crazy word:
meaning that each element of one group can unambiguously be referred to exactly one element of a second group and vice versa.
Both deutlich and eindeutig are turned into their opposites with un-.
Er spricht undeutlich. He speaks unclearly./He mumbles.
Die Ergebnisse sind uneindeutig. The results are ambiguous. (can not be interpreted in one way only)
There even is unzweideutig. Meaning that there has been an effort to remove all ambiguity.
Folglich muss das Mittel der grafischen Darstellung unzweideutig und objektiv sein. Consequently, the means of graphic representation must be unequivocal and objective.