I figured as long as the debates are going on, I'd add this one.
I'll need proof. NO speculation. If you can back it up with scripture or something from a collateral (since they have been cited as being part of the new Canon) all the better.
Hey.. if we're going to engage in silly arguments, why not make it entertaining?
Undocumented would be the answer. But since you did not try to speculate on some number as a basis for a claim of content or something I think your OK.
By the way I don't consider any argument to stop the surpression of truthful facts as silly.....
Why? Every time human beings have been documented as seeing angels, they always take the form of a human being. Therefore, you can simply substitute people for angels in this case, and ask how many people can dance on the head of a pin. Since it is not possible, the answer is zero.
Ah but P-Mosh - let's have some fun here. Since, in your words, angels "take the form of a human being" we don't know what their real form is...maybe they appear as human but can balance on a single bit of whatever they are made of - in which case the number could be excessively large...
Just messin' with you for humor's sake - please don't get offended at a comic relief refutation of your premise.
Simple. The answer is zero.
Why? Every time human beings have been documented as seeing angels, they always take the form of a human being. Therefore, you can simply substitute people for angels in this case, and ask how many people can dance on the head of a pin. Since it is not possible, the answer is zero.
Why? Every time human beings have been documented as seeing angels, they always take the form of a human being. Therefore, you can simply substitute people for angels in this case, and ask how many people can dance on the head of a pin. Since it is not possible, the answer is zero.
Not so fast Every time? Really ...I know people that think angels appeared as animals. regardless people or animals what they appear to be is not necessarily what they are. Hense the old saying Things are not what they seem.
Ah but P-Mosh - let's have some fun here. Since, in your words, angels "take the form of a human being" we don't know what their real form is...maybe they appear as human but can balance on a single bit of whatever they are made of - in which case the number could be excessively large...
The thing is, if they are spirits, then their "real form" is not physical and thus non-physical beings can not directly interact with a physical thing like a pin. Therefore, part of my thesis is that angels must take physical form as a prerequisite to performing any dancing.
Additionally, dancing is a human art form, which means that they would be required to take human form to literally be dancing. While we do have animals "dance", they aren't truly dancing, but just moving in a way they have been trained to. They are lacking the emotional aspect that humans have to spontaneously dance and enjoy it. We do say things like, "the Christmas lights are dancing on the tree" as a form of personification, but I also exclude the usage of figures of speech here.
Just messin' with you for humor's sake - please don't get offended at a comic relief refutation of your premise.
Me too. Although I'm possibly coming across as argumentative, I'm just doing this for fun, and not taking it seriously. It's difficult to express a dry sense of humor like mine on the internet.
SANS/NADA, Royal Institute of Technology, Stockholm, Sweden
Abstract
We derive upper bounds for the density of angels dancing on the point of a pin. It is dependent on the assumed mass of the angels, with a maximum number of 8.6766 x 1049 angels at the critical angel mass (3.8807 x 10-34 kg).
Ancient Question, Modern Physics
"How many angels can dance on the head of a pin?" has been a major theological question since the Middle Ages.
According to Thomas Aquinas, it is impossible for two distinct causes to each be the immediate cause of one and the same thing. An angel is a good example of such a cause. Thus two angels cannot occupy the same space. This can be seen as an early statement of the Pauli exclusion principle. (The Pauli exclusion principle is a pillar of modern physics. It was first stated in the twentieth century, by Pauli.)
However, this does not place any upper bound on the density of angels in a small area, because the size r of angels remains undefined and could possibly be arbitrarily small. There have also been theological criticisms of any assumption of angels as complete causes.
Stating the Question Correctly
The basic issue is the maximal density of active angels in a small volume. It should be noted that the original formulation of the problem did not refer to the head of a pin (R¼1 mm) but to the point of the pin. Therefore, the point, not the head, of the pin is the region that will be studied in this paper.
One of the first reported attempts at a quantum gravity treatment of the angel density problem that also included the correct end of the pin was made by Dr. Phil Schewe. He suggested that due to quantum gravity space is likely not infinitely divisible beyond the Planck length scale of 10-35 meters. Hence, assuming the point of the pin to be one Ångström across (the size of a scanning tunnelling microscope tip) this would produce a maximal number of angels on the order of 1050 since they would not have more places to fill.
While this approach does produce an upper bound on the possible density of angels, it is based on the Thomist assumption of non-overlap.
Since angels can be presumed to obey quantum rules when packed at quantum gravity densities, the uncertainty relation will cause their wave functions to overlap significantly even if there is a strong degeneracy pressure. If the non-overlap assumption is relaxed, this approach cannot derive an upper bound.
Quantum Gravitational Treatment
A stricter bound based on information physics can be derived that is not based on overlap assumptions, but merely the localisation of angelic information.
Assuming that each angel contains at least one bit of information (fallen / not fallen), and that the point of the pin is a sphere of diameter of an Ångström (R=10exp-10 m) and has a total mass of M=9.5 x 10-29 kilograms (equivalent to that of one iron atom), we can use the Bekenstein bound on information to calculate an upper bound on the angel density. In a system of diameter D and mass M, less than kDM distinguishable bits can exist, where k=2.57686*1043 bits/meter kg. This gives us a bound of just 2.448*105 angels, far below the Schewe bound.
Note that this does not take the mass of angels into account. A finite angel mass-energy would increase the possible information density significantly. If each angel has a mass m, then the Bekenstein bound gives us N<kD(M+Nm). Beyond mcrit>1/kD ¼3.8807*10-34 kg this produces an unbounded maximal angel density as each angel contributes enough mass-energy to allow the information of an extra angel to move in, and so on.
However, if angels have mass, then the point of the pin will collapse into a black hole if c2R/2G< Nm (here I ignore the mass of the iron atom at the tip).4 For angels of human weight (80 kg), we get a limit of 4.2089*10 14 angels. The maximal mass of any angel amenable to dance on the pin is 3.3671*10 16 kg; at this point there is only room for a single angel.
The picture that emerges is that, for low angel masses, the number is bounded by the Bekenstein bound, and increases hyperbolically as mcrit is approached. However, the black hole bound decreases and the two bounds cross at mmax=1/(4GkM/cexp2+kD), very slightly below mcrit. This corresponds to the maximal angel density of Nmax=8.6766*10exp49 angels (see figure).
Dance Dynamics
If the angels dance very quickly and in the same direction, then the angular momentum could lead to a situation like the extremal Kerr metric, where no event horizon forms (this could also be achieved by charging the angels). Hence the number of dancing angels that can crowd together is likely much higher than the number of stationary angels.
However, at these speeds the friction caused by their interaction with the pin is likely to vaporise it or at least break it apart. Even for a modest speed of 1 m/s the total kinetic energy of Nmax angels of mass mcrit would be 1.682*1016 J. In the case of charged angels at relativistic densities, pair-creation in their vicinity would likely cause the charge to dissipate over time,6 and charge transfer to the pin would also likely induce electromechanical forces beyond any material tolerances.
The uncertainty relation also imposes a limitation on the dance. Since the uncertainty in position of the angels by assumption is less than the size of the point Ðx�R we find that the uncertainty in momentum must be ÐpŽhbar/R, and this leads to a velocity uncertainty Ðv>hbar/Rm. If m= mcrit we get Ðv>> 8.6766*10exp59 m/s (>> c), which shows that:
(1) the angels must dance with speeds near the velocity of light in order to obey quantum mechanics;
(2) a full relativistic treatment is necessary; and
(3) that the precision of the dance must break down due to quantum effects.
This can be used to rule out certain types of dance due to their high precision requirements.
Discussion---
We have derived quantum gravity bounds on the number of angels that can dance on the tip of a needle as a function of the mass of the angels. The maximal number of angels -- 8.6766*1049 -- is achieved near the critical mass mcrit>1/kD ¼3.8807*10[sup-34 [/sup]kg, corresponding to the transition from the information-limited to the mass-limited regime. It is interesting to note that this is of the same order of magnitude as the Schewe bound.
Angel physics has until now mainly employed theological methods, but as this paper shows, modern information physics, quantum gravity and relativity theory provide powerful tools for exploring the dynamics and statics of angels.
These bounds are only upper bounds, and do not take into account the effects of a finite number of available angels, degeneracy pressures if angels obey the Pauli exclusion principle as suggested by Aquinas, or the theo-psychology of the angels themselves. The exact dance dynamics also clearly play a major role. A full relativistic treatment of the dance appears as a promising avenue for further tightening of the bounds.
Maximum number of angels for a given mass. The allowed region is bounded from above by the line c2R/2G=Nm (gravitational collapse) and the curve N=kD(M+Nm) (information density) which has an asymptote for mcrit, and from below by N=0. The maximal number of angels occurs at the intersection of the gravitational bound and the asymptote at mcrit
...................
Thats one mans opinion, of course I tend to doubt it, if I were an angel I'd be doing other things than attempting to dance on a damn pointy thing especially an incredibly crowded one... If that were the case wouldnt the the question have to become just how stupid are a multitude of angels and why do they dance around on pins anyway?
Recommended Posts
WhiteDove
Undocumented would be the answer. But since you did not try to speculate on some number as a basis for a claim of content or something I think your OK.
By the way I don't consider any argument to stop the surpression of truthful facts as silly.....
Edited by WhiteDoveLink to comment
Share on other sites
Mister P-Mosh
Simple. The answer is zero.
Why? Every time human beings have been documented as seeing angels, they always take the form of a human being. Therefore, you can simply substitute people for angels in this case, and ask how many people can dance on the head of a pin. Since it is not possible, the answer is zero.
Link to comment
Share on other sites
RumRunner
Ah but P-Mosh - let's have some fun here. Since, in your words, angels "take the form of a human being" we don't know what their real form is...maybe they appear as human but can balance on a single bit of whatever they are made of - in which case the number could be excessively large...
Just messin' with you for humor's sake - please don't get offended at a comic relief refutation of your premise.
Link to comment
Share on other sites
WhiteDove
Not so fast Every time? Really ...I know people that think angels appeared as animals. regardless people or animals what they appear to be is not necessarily what they are. Hense the old saying Things are not what they seem.
Edited by WhiteDoveLink to comment
Share on other sites
George Aar
Well, the real answer is 17.
Trust me, I know...
Link to comment
Share on other sites
waysider
Fox-Trot or Polka?
Link to comment
Share on other sites
leafytwiglet
I think there are really teenee tiny angels who look out for fleas so One maybe two, if they squish real close together. ;)
Link to comment
Share on other sites
Bolshevik
no, it's 47.
Link to comment
Share on other sites
doojable
Now what about if those angels are still in their non-corporeal form? Couldn't there be an infinite amount of angels all doing the bunny hop?
Edited by doojableLink to comment
Share on other sites
GarthP2000
... and why is it that they would do the bunny hop, ehhh?
What? Disco ain't good enough for them?
Link to comment
Share on other sites
doojable
The Bunny Hop was only suggested so that they could dance in a circle (much like the reasoning around here lately.)
But any line dance would work... :D
Link to comment
Share on other sites
leafytwiglet
Link to comment
Share on other sites
Mister P-Mosh
The thing is, if they are spirits, then their "real form" is not physical and thus non-physical beings can not directly interact with a physical thing like a pin. Therefore, part of my thesis is that angels must take physical form as a prerequisite to performing any dancing.
Additionally, dancing is a human art form, which means that they would be required to take human form to literally be dancing. While we do have animals "dance", they aren't truly dancing, but just moving in a way they have been trained to. They are lacking the emotional aspect that humans have to spontaneously dance and enjoy it. We do say things like, "the Christmas lights are dancing on the tree" as a form of personification, but I also exclude the usage of figures of speech here.
Me too. Although I'm possibly coming across as argumentative, I'm just doing this for fun, and not taking it seriously. It's difficult to express a dry sense of humor like mine on the internet.
Link to comment
Share on other sites
mstar1
Quantum Gravity Treatment of the Angel Density Problem
by Anders Sandberg
SANS/NADA, Royal Institute of Technology, Stockholm, Sweden
Maximum number of angels for a given mass. The allowed region is bounded from above by the line c2R/2G=Nm (gravitational collapse) and the curve N=kD(M+Nm) (information density) which has an asymptote for mcrit, and from below by N=0. The maximal number of angels occurs at the intersection of the gravitational bound and the asymptote at mcrit
...................
Thats one mans opinion, of course I tend to doubt it, if I were an angel I'd be doing other things than attempting to dance on a damn pointy thing especially an incredibly crowded one... If that were the case wouldnt the the question have to become just how stupid are a multitude of angels and why do they dance around on pins anyway?
Edited by mstar1Link to comment
Share on other sites
doojable
Hey! If this thread could find some legs, surely angels could find a way to get some dancing feet.
Link to comment
Share on other sites
leafytwiglet
And you all thought you would never use that algebra and physics you learned in COllege and High school.
LOLOL
Link to comment
Share on other sites
waysider
Link to comment
Share on other sites
leafytwiglet
Snicker
Link to comment
Share on other sites
GeorgeStGeorge
I find no scriptural evidence for angels dancing.
George
Link to comment
Share on other sites
sirguessalot
all of em
Link to comment
Share on other sites
Twinky
While they were singing, of course, George.
Anyway, I agree with Bolshevik. 47.
Ah, wait, isn't that that answer to the universe or something?
I just looked where I keep my pins but there are no angels in there.
Link to comment
Share on other sites
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.