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God flat-out tells us that we will never understand. How could we?

Soooo very true, dear Spruce.

Indeed, we cannot say that particles or fields which have no measurable direct or indirect affects therefore do not exist. Likewise, we cannot presume to know the total number of, and types of, dimensions based on our ability to measure their direct or indirect affects.

That logic applies in our assurance that God's keeps His promises. Every. Single. One. For instance,

But this [shall be] the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people. And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.

Thus saith the LORD, which giveth the sun for a light by day, [and] the ordinances of the moon and of the stars for a light by night, which divideth the sea when the waves thereof roar; The LORD of hosts [is] his name: If those ordinances depart from before me, saith the LORD, [then] the seed of Israel also shall cease from being a nation before me for ever.

Thus saith the LORD; If heaven above can be measured, and the foundations of the earth searched out beneath, I will also cast off all the seed of Israel for all that they have done, saith the LORD. - Jer 31:33-37

Since the total number and types of dimensions are both unknown and unknowable - we are confident that God will never "cast off the seed of Israel for all that they have done."

We do not need a logical reason for the blessed assurance that God keeps all of His promises and yet He provides that comfort.

As another example, God is Truth. When He says a thing, it is. It is because He says it. For instance,

And God said, Let there be light: and there was light. - Genesis 1:3

And the cosmic microwave background radiation confirms, i.e. it records the sound waves at the moment light formed and went its way. To listen, click here.

In the same thought, neither time nor space are properties of the Creator of them. In Scripture, the word "light" is used to describe His glory. And the metaphor is perfect as quantum mechanics confirms, i.e. the photon travels a "null path" - which is to say for the photon as observer, no time elapses at all.

Sheepherders thousands of years ago - to whom the academics love to attribute authorship for ancient Scripture - would have had no concept of quantum mechanics.

Even now, as science learns more and more, the creation itself confirms the words of the Creator, e.g. “In the beginning, God created …” (Gen 1:1)

Truly, the most theological statement to ever come out of modern science is that there was a real beginning of space and time. (Jastrow)

God's Name is I AM.