A POLL: How Many Angels Can Dance On The Head Of A Pin? [View All]

[Itsthetruth]

This is a tough one to answer with precision. I did discover an attempt to answer this question in a "scientific" paper devoted to this most important matter:

"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*10exp49 angels at the critical angel mass (3.8807*10exp-34 kg).

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 10exp-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.<1>

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*10exp-29 kilograms (equivalent to that of one iron atom), we can use the Bekenstein bound<3> 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*10exp43 bits/meter kg.<7> This gives us a bound of just 2.448*10exp5 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*10exp-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.

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).<4> Hence the number of dancing angels that can crowd together is likely much higher than the number of stationary angels.

Anyone understand this aaahhhhh .... scientific explanation?

How many angels have you observed dancing on the head of a pin or other object? Information you can provide would be greatly appreciated.