--------------------------------------------- How many angels fit on the tip of a needle? --------------------------------------------- Who first discovered the exclusion principle? Commonly attributed to Pauli, we shall see that its first description is in medieval work by Thomas Aquinas, in a context related to the above question. Anton Zeilinger writes in http://www.ap.univie.ac.at/users/Anton.Zeilinger/philosop.html ''the question whether such a description exists or not was therefore similarly irrelevant as, according to Pauli, the old question how many angels fit onto the tip of a needle.'' This question has become a well-known mfigure of speech for doing irrelevant physics. But how old is this question really? Who were the persons who discussed it seriously? What was their intention? http://web.maths.unsw.edu.au/~jim/headsofpins.html mentions explicitly Chillingworth's ''Religion of Protestants a Safe Way to Salvation'' (1638, reprinted 1972, 12th unnumbered page of the preface) accusing unnamed scholars of debating ''Whether a Million of Angels may not fit upon a needles point?'' It seems that, as here, the question has always been used in a derisive manner only. In the historical essay E.D. Sylla, Swester Katrei and Gregory of Rimini: Angels, God and mathematics in the fourteenth century, pp. 251-270 in: Mathematics and the Divine: A Historical Study (T. Koetsier and L. Bergmans, eds.) Elsevier 2005, http://www.elsevier.com/wps/find/bookdescription.cws_home/704302/description#description Sylla conjectures that the question might have been coined by Thomas Hobbes, who had learnt the scholastic tradition in Oxford between 1603 and 1608. See also http://en.wikipedia.org/wiki/How_many_angels_can_dance_on_the_head_of_a_pin%3F http://www.straightdope.com/columns/read/1008/did-medieval-scholars-argue-over-how-many-angels-could-dance-on-the-head-of-a-pin But similar questions were discussed much earlier. Sylla mentions an anonymous 14th century mystical treatise ''Swester Katrei'' (= Sister Kate or Sister Catherine) referring to ''a thousand souls in heaven sitting on the point of a needle''. Cf. also the paper G.M. Ross, Angels, Philosophy 60 (1985), 495-511. http://www.jstor.org/pss/3750436 http://www.philosophy.leeds.ac.uk/GMR/articles/angels.html and the web site Sister Catherine (Schwester Katrei) http://people.bu.edu/dklepper/RN413/katrei.html See also https://en.wikipedia.org/wiki/How_many_angels_can_dance_on_the_head_of_a_pin Even earlier and most prominent is the discussion of angels in Thomas Aquinas' ''Summa Theologica'', published in 1266. It is surprisingly interesting. It looks as if Aquinas was the first writer anticipating quantum theory and the Pauli exclusion principle. Replace 'angel' by 'electron' and he sounds surprisingly modern; in modern terms, angels are Fermions, according to Thomas Aquinas. An English translation of the ''Summa Theologica'' is available online. Part I (http://www.newadvent.org/summa/1.htm) contains the chapter on angels. The sections 50-53 on their substance relate to their physical properties and hence are of scientific interest. There he discusses the properties of a point particle from a logical point of view. His 'angels' are not the winged creatures we might imagine them to be, but incorruptible, indivisible, extended objects, ''form without matter'', with quite precise properties. Two angels cannot be in the same place, but they have virtual (sic!) positions, and can be in an extended place: ''So the entire body to which he is applied by his power, corresponds as one place to him.'' They may go from one place to another with or without being observable in between: ''But an angel's substance is not subject to place as contained thereby, but is above it as containing it: hence it is under his control to apply himself to a place just as he wills, either through or without the intervening place.'' Their number roughly matches those of the number of electrons: ''Hence it must be said that the angels, even inasmuch as they are immaterial substances, exist in exceeding great number, far beyond all material multitude.'' (With ''angel'' interpreted as ''electron'', ''immaterial'' could thus be interpreted as zero baryon number.) Like early chemists hiding their scientific insights in an alchemist guise, Aquinas might have phrased his scientific speculations in terms of notions acceptable to his clerical collegues... If we attribute to the Greeks the concept of the atom (though they thought of it in - for modern ears bizarre - terms that have little to do with our modern view), we should perhaps be as generous towards Aquinas and attribute to him the exclusion principle. PS. On a more tongue-in-cheek basis, the Annals of Improbable Research published an article A. Sandberg, Quantum Gravity Treatment of the Angel Density Problem, Annals of Improbable Research 7 (Issue 3), (2001), 5-8. http://www.improbable.com/airchives/paperair/volume7/v7i3/angels-7-3.htm