Do we know better than angels?

To us, angels are supernatural beings, spiritual beings. They are supposed to be more powerful than us. Yet, they are also creatures, though higher class creatures than us humans. Since they are spiritual, I suppose they are imperishable and will live forever. Put it in another way, while we humans live in a 3-D space, they exist in higher dimensions. Our freedom of movement is limited within 3 dimensions. Angels are free in more dimensions, probably including time. Therefore, they exist outside time. They are, like God, timeless.
In Mathematics, we study infinity. In order to study (compare, operate etc.) sets of infinite elements, mathematicians develop the procedure of one-one correspondence to handle the concept of equality. Two infinite sets are equal if we are able to establish a one-one relationship between the elements in the two sets. Infinity has some very counter-intuitive properties. For example, there are infinite number of natural numbers which are made up of odd integers and even integers. The number of elements in the set of odd integers is the same as that in the set of even integers. Fair enough and this is very intuitive. But if mathematicians prove to you that the number of natural numbers is equal to the number of even integers, that will be mind-boggling! Doesn't natural numbers include even integers? Aren't there some natural numbers not found in even integers? But this is true, though counter-intuitive, because we can establish a one-one correspondence between natural numbers and even integers. [For every x in the set of natural numbers, we can find a y in the set of even integers such that y = 2x. Therefore, the two sets are equal in size.]
That is not the end of the story of infinity. There are infinite fractions even between 0 and 1. Moreover, there are infinite such natural numbers 2, 3, 4 etc. Yet, mathematicians have proved that the set of natural numbers has the same size as that of the set of fractions!!
If you suspect that all infinite quantity are the same, you are wrong. Mathematicians have shown that it is impossible to establish a one-one correspondence between natural numbers and decimal numbers of which there are infinite. Therefore, the infinity of decimal numbers is of a different, a higher class of infinity.
Why did I talk about these different kinds of infinities. God and angels are infinite beings. We are not. Of course, we cannot hope to compare with even angels. However, just as there are different classes of infinity, therefore, the infinite God is of a different class from that of the infinite angels. For us, the power of angels is probably infinite. Yet, compared with God, their infinite power is of a lower order than that of God.
St. Paul mentions 5 types of heavenly beings. In the epistle to the Colossians, we have the following:
for in him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or principalities or authorities--all things were created through him and for him. (Colossians 1:16).
He disarmed the principalities and powers and made a public example of them, triumphing over them in him (Colossians 2:15).
So, there are 5 types of heavenly beings: thrones, dominions, principalities, authorities and powers. I speculate that each of them represents a different class of infinity. If we put archangels and angels below the powers, and cherubim and seraphim above the thrones, we will have 9 classes of angels. This is the traditional teaching of the Catholic church.
Though we humans are lower creatures, it seems that we know something which even angels did not know. That is what St. Paul told us in Ephesians.
that through the church the manifold wisdom of God might now be made known to the principalities and powers in the heavenly places (Ephesians 3:10).
I think Paul meant the mystery of incarnation. In order to redeem the world, God decided to take up the form of a human, slightly below the angels, to die on the cross. This wisdom of God was not revealed even to the angels. Some Church Fathers thought that since some angels, out of pride and arrogance, refused to pay homage to the incarnated Word of God, they became devils. This is indeed our honour and glory, that the Son of God would become one of us.
My dear Advocate, Your wisdom is manifold and infinite. We pray that we will not ignore Yahweh and worship other gods. I pray for the Golden Jubilee of STC. Pray that the organization of celebration will proceed smoothly up to the last minute. Amen.