How many angels can dance on the head of a pin - or can we not count that high?

Question

Just curious, since it was the subject of debate and controversy in the Middle Ages.

And with all the developments in mathematics prior to and since that time, I thought that we might be able to count and calculate.

But a recent response on Y!A has thrown all that into question.

This article might provide some insight:

http://uncyclopedia.org/wiki/Angels_on_the_head_of_a_pin

Answer 1

I would have answered billions, but thankfully there are smarter YEC creationists here to remind me that a billion is not a valid number because it's too high to count.


*snicker*

Answer 2

6

Answer 3

"Countable" means that it has the same cardinality as the integers, meaning you can create a one-to-one mapping from the angels to the integers (or some subset thereof, since we're dealing with fintely many angels, not a coutably infinite number).

Theorem 1: Uncountably many angels, or a set of angels with cardinality c (same as the reals), would be unthinkable for angels of radius greater than 0, since they would fill up the universe before you could get that many. Proof: Take the minimum neighborhood that can fit inside an angel such that B(x,k) is that neighborhood centered at x with radius k. You can easily cover the universe with these (by Lemma 1), and since the universe is closed and totally bounded (and a subset of R^n), it is compact by Heine-Borel, and thus it admits a finite subcovering. Thus, you can only fit finitely many nonoverlapping angels into the universe.

Thus the number of angels is countable.

Lemma 1: You can make a covering of the universe U using a collection of B(x,k). Proof: Since d = inf{k:B(x,k) fits inside and angel} exists, there exists an M such that we can partition the universe into dyadic cubes of side length 2^(-M) so that each cube has measure b < a, where a is the Lebesgue measure of B(x,k) for k = d. There are only finitely man of these, and these can by covered by B(x,d), where each x is inside one dyadic cube.

Answer 4

I dunno.

here is a insight......

ATHEISTS:
What does God call them? Preach love to them? Lets see what God says, to do with them.

You have unbeliever's, Chaff, Scoffers.

An Atheist is a "scoffer". The WORD of God, clearly tells, ATHEISTS are filhty rags they are, and to stay away

from them, and avoid them. We are NOT to plant seeds. God knows it is useless and that is why he tells us,

"You stand firm against them" ( Jer.17:8 14:1 Iah 44:4) You disassociate them completely. Any Believer that

does not abide in God's own Word, does not know God, according to God Himself.
Atheists are "chaff" A simile of the wretchedness of the wicked. Chaff is carried away by the lightest wind, and

it's removal brings about cleansing by extracting what is utterly useless. (Ruth 1:22). They will NOT stand in the

judgment. They will NOT be able to withstand God's wrath when He judges.( Pslams 76:7 Exra 9:15). This is

not my opinion, this is God's very own Words, in the Bible. You know, the BIble? The same Bible atheist scholars

quote. There is a reason God, said this. Psalms.1.1-3 Jer. 17:8 14:1 12. 1-2 18:9-10 Prov1.10-19 (vs 5)

scoffers:(atheists) those who ridicule God and definatley reject His Law. Prov 1.:22 Ruth 1:22 Jer 18:7 (pull

down-destroy) 1:10 (evil-calamity) 18:11

Pslams 1:
godly wisdom here, declare the final outcome of the two "ways". The paths of "sinners" (unbelievers) and the

"way of the righteous. he speaks progressively of assoociation with the ungodly and participation in they're

ungodly ways.

God said it. End of Story. Jesus Himself said "Let the dead bury they're dead".

Use all the Internet and Dictionaries they want to and call themselves anything they wish. God "defined" what

they are by His own Holy Word.

They can hang a dog tag* around they're neck in the pits if hell itself and separate each other by name

categorically.

God's Word said it. By God's definition. They are nothing but filthy rags. There is NO opinion.

Hate? Where do you get hate? If God's TRUTH is hate too you, then, so be it. You and God, can and will discuss

the means of your scriptural interpretation, consisting with a man-made defacto on a motion of plea bargin I

guess. I dunno.

I W I L L . P R A Y . F O R . A L L . A T H E I S T S. :)

Answer 5

I think you're probably right. Nobody can count high enough to figure that out. Especially as the angels are now zooming towards us from distant space at the speed of light...

Answer 6

If angels are corporeal, a finite number.

If angels are incorporeal, either zero or infinity depending on whether you think a noncorporeal being can dance.

Answer 7

At the same time or one at a time. One at a time all of them is the right response.

Answer 8

contrary to popular belief, angels aren't really good dancers.

besides they would just get all tangled up in each others' wings...

so they generally steer clear of this activity.

it's an urban myth.

Answer 9

Seems like a pain full habit, why would any sensible person want to do that?

Answer 10

Hmm, good call, but consider this: God is infinite. No one can count to infinity, therefore god doesn't exist.