Does Exodus 3:14 explain who God is to everyone regardless of time and culture? Exodus 3:14 states:


  God said to Moses, “I am who I am. This is what you are to say to the Israelites: ‘I am has sent me to you.’


This seems appropriate in regard to the Israelites since they have had knowledge of God beforehand, but what about in terms of today and other cultures? Can this as a stand-alone passage be used to describe who God is to a people other than the Israelites and possibly in this present time?

For example, I also read Hebrews 8:10:


  "For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts."


It seems to apply to the Israelites or "His people", that they should know "I Am" to be the author of these laws which are in their hearts. However, can this be sufficient to those who are not God's people or not Israelites? This passage causes a lot of confusion for those who  live in a culture steeped with traditions of "multiple-gods".

EDIT: Consequently, when Jesus proclaims himself as God, does that only explain who he is based on previous knowledge of who the Father is?
I think that the best answer to this question is "Yes...and no."

Yes

God does not say "I have always been" or "I will always be" or "I am coming". He says "I am." This verse is often used as part of the common Christian understanding that God exists above and outside of the human understanding of time. 

This verse as a summary of God's universal, achronological reality is applicable to all people regardless of time and culture. God's existence applies identically to all people. No matter your original culture, no matter what era you live in, it is an aspect of Christianity to regard God as a single, powerful, timeless entity*.

No

Personally, I do not favor attempts to fine stand-alone verses to explain concepts, especially important theological points. While verses in isolation can still carry very important messages, local context (nearby verses) and absolute context (whole Bible) are critical.

The nature of God is a very fundamental piece of Christianity (and most religions, for that matter). While I think that Exodus 3:14 is a very good member of the list of verses that help describe God, I do not consider it sufficient as a stand-alone verse. It does not address:


God's desire for justice
God's desire for mercy
God's triune nature
God's relationship with mankind.
God's role as Creator.


As a person raised in the church, it's difficult to guess at other perspectives, but I think that hearing Exodus 3:14 without any other introduction to God would confuse me more than it educated me.

Note

I still think it's a very important verse, I think it's valuable to include in an exposition into who God is. But if it were sufficient on its own, the Bible would be a lot shorter.



*I hope that was phrased loosely enough to account for most majors Christian views, I know there are differences on the specifics of this point, please correct me if I am wrong.