Psalms 139:1-10 NIV
You have searched me, Lord,
and you know me.
You know when I sit and when I rise;
you perceive my thoughts from afar.
You discern my going out and my lying down;
you are familiar with all my ways.
Before a word is on my tongue
you, Lord, know it completely.
You hem me in behind and before,
and you lay your hand upon me.
Such knowledge is too wonderful for me,
too lofty for me to attain.
Where can I go from your Spirit?
Where can I flee from your presence?
If I go up to the heavens, you are there;
if I make my bed in the depths, you are there.
If I rise on the wings of the dawn,
if I settle on the far side of the sea,
even there your hand will guide me,
your right hand will hold me fast.
On the evening of that first day of the week, when the disciples were together, with the doors locked for fear of the Jewish leaders, Jesus came and stood among them and said, "Peace be with you!"
The dimension of a vector space is a constant which indicates the number of vectors in any basis for the vector space. This number is independent of which basis is selected. The vector space of three-dimensional space has dimension three (surprise, surprise). However, not all vector spaces have a finite dimension. If you think of the vector space consisting of polynomials with real number coefficients, bases have a countably infinite number of elements. It is easy to construct and infinite basis here; the standard basis is the infinite collection of polynomials 1, x, x2, x3, . . . xn, . . .
God also is infinite dimensional, very likely even of uncountable dimension! There is no way to escape God's presence! If we think of God as an infinite-dimensional being, we can extend the concepts from the book Flatland* to understand a little of the nature of Christ's post-resurrection body. In that book, creatures in a higher-dimensional space are able to enter and exit lower-dimensional spaces easily. The image to think about is a sphere crossing a particular fixed plane. If the sphere is outside the plane, it cannot be seen by objects living only in the plane. But if the sphere crosses the plane, it will appear as a point or an expanding/contracting circle. In the same way, if we think of Christ living in a higher dimension, his sudden appearance in a locked room makes a little more sense. Broadening the concept of dimension is certainly helpful in this sense.
*You can read Flatland online at http://www.alcyone.com/max/lit/flatland/