The Span of God's Love
Spanning Set
Repeated Samples of Character
Central Limit Theorem
For this reason I kneel before the Father, from whom every family in heaven and on earth derives its name. I pray that out of his glorious riches he may strengthen you with power through his Spirit in your inner being, so that Christ may dwell in your hearts through faith. And I pray that you, being rooted and established in love, may have power, together with all the Lord's holy people, to grasp how wide and long and high and deep is the love of Christ, and to know this love that surpasses knowledge—that you may be filled to the measure of all the fullness of God. Now to him who is able to do immeasurably more than all we ask or imagine, according to his power that is at work within us, to him be glory in the church and in Christ Jesus throughout all generations, for ever and ever! Amen.
The span of a collection of vectors is defined to be the set of all possible linear combinations of the vectors with scalars selected from some set (a field--usually the real numbers). For example, if you select vectors i = <1, 0> and j = <0, 1>, the collection of linear combinations ai + bj (for a, b real numbers) is every vector in the two-dimensional coordinate plane. Creating something so large using something so small is surprising but at the same time expected because of previous experience with vectors, say in Calculus.
Now let's think about something whose words are very simple, say the love of God, and meditate on what the span of God's love might be. We read in Paul's letters to the Ephesians that he prays that they might "have the power. . . to grasp how wide and long and high and deep is the love of Christ." So the span of God's love is really really big! Is this surprising? YES! Just think about our rebellion and sin--so it is a surprise that God should love us! Is this expected? Again, yes! We have models in our families and friends that demonstrate how broad a father's love for his children can be.
"Now to him who is able to do immeasurably more that all we ask or imagine. . . be glory . . throughout all generations, for ever and ever!"
