On occasion, I feel so moved to resurrect an old post for the edification of my 'newish' readership. Of course, it has nothing to do with me being a fundamentally lazy arse...... O, no. Anyway, this is one from my 'Blue Period'. A time when I was trying to 'wing it' without the medication. It has always been a dilemma: If I don't take my meds my creativity runs riot and the thoughts tumble through my brain like tumbly (not a real word) things. But on the downside, I sometimes take note of the voices exhorting me to burn stuff- although, not necessarily a bad thing (see link). When medicated, the cacophony in my head is leashed however, my creativity suffers according. But at least the good Burghers of Tipton can sleep secure in their beds at night without getting their bed shirts singed, spontaneous combustion excepted.
How many angels can you fit on the head of a pin? Don't laugh, this was a hot topic for debate amongst Clerics, c1332. This is a surprisingly subtle question and raises further questions about the fundamental nature of our existence. Anyway, if angels are not made of matter and are pure 'spiritual energy', whatever that means, then they are without dimension and form and occupy no space. Having said that however, ultimately all matter can be reduced to waves and therefore solid matter is but an illusion, although a very persistent one. What is perceived as matter is really ‘a whizz’ of wave radiation bound by forces which are poorly understood.
But contemplation of angels as 'energy' is not as simple as envisioning angels as photons. Angels are sentient and therefore their 'energy' is not the energy we are familiar with. Angels are supernatural entities and therefore reside outside the natural world and by extension are not subject to causality. Even if we could persuade a host of angels to gravitate toward the vicinity of a pinhead they would defy measurement. This is but one aspect of the discourse.
This raises the question of how sentient supernatural beings can interact with us at all. In the distant past angels apparently communed with man; tis in the bible- look it up........
According to the Bible, angels can connect with the natural world and therefore, during this interactive interlude, they must be subject to natural law and hence causation. So, let us take a different tack for sophistry's sake.
"The medieval doctors of divinity who did not pretend to settle how many angels could dance on the point of a needle cut a very poor figure as far as romantic credulity is concerned beside the modern physicists who have settled to the billionth of a millimetre every movement and position in the dance of the electrons."
According to Thomas Aquinas, the ultimate Catholic scholar and medieval ‘Angelic Doctor’, no two angels can occupy the same space. This is in accord with quantum physics and abides with the Pauli Exclusion Principle. The next point concerns the size of the pinhead under question: to wit, the size of a standard pinhead. In order to move this argument along it is necessary to make an assumption.
For our purposes, said size will be a sphere of 1Angstrom diameter with an associated mass of 9.5 x 10-29kg. Also, we need to note that space is not infinitely divisible. This limit is denoted as the Planck length, or 1.6 x 10-35 m. Next, we need to decide the information carried by a standard angel. Note: I have made no allusion to mass. In fact, in this simple case, I’m assuming mass-less angels. The introduction of mass into the equation will result in ‘reducto ad absurdum’- which would make the whole argument just silly. So for our purposes, I will assume that angels comprise of ‘one bit’ of information. They cannot be less than this information limit and logically remain within our reality. There is one last concept to be introduced before we begin our calculation. The Bekenstein bound (k) or universal entropy bound is a limit on the entropy that can be contained in a physical system or object with a given size and total energy. It follows: In a system of diameter D and mass M, less than kDM distinguishable bits can exist, where k=2.57686 x 1043 bit/metre kg. From this, we can derive an upper limit of 2.448 x 105 angels on our pinhead.
There are some clever bastards who demand that the angels should be 'a dancing'. This introduces a whole new set of thermodynamic and velocity parameters into our hypothetical situation which will undoubtedly alter the upper limit of angels gyrating on the pinhead- basically, these bastards can fuck off.Makes me want to burn stuff.