TETRAMETHYLENECYCLOBUTANE

1,2,3,4-tetramethylenecyclobutane is a molecule with a HOMO-LUMO gap, in which the HOMO is doubly occupied but the LUMO is unoccupied. It is a stabilized singlet molecule. You can rearrange the squaroexocyclobutadieneite pattern into an alternative pattern comprised of tetramethylenecyclobutane substructures. Just by rotating around, at a right angle, the 1,3-dimethylenecyclobutane units in the "squaro" lattice. I am not sure if the rest of the single C-C bonds form a stable lattice, but I think they might. It might be an especially stable alternative pattern to the "squaro" version because of the relative stability of the tetramethylenecyclobutane substructures.

UNIFIED REPRESENTATION

One way of describing, or accounting for, the Eddington ratios, in their mathematical approximant forms, would be to construct a 5th-order polynomial equation, in which the 5 roots of such an equation would just correspond to the 5 mathematical approximants, with powers of 10 truncated off of them. Such a 5th-order polynomial equation, in a factored form, would be: (x - a)(x - b)(x - c)(x - d)(x - e) = 0...where a, b, c, d, e are the corresponding Eddington constants alpha, beta, gamma, delta, epsilon. The factored form, thus, could be multiplied out to its 5th-order form, and it could thus be plotted in the Cartesian x-y plane for clarity and illustration and for further mathematical analysis. It also is to be noted that there may be Eddington ratios of: (a) mass(x)time over mass(x)time (b) force(x)time over force(x)time (c) force(x)mass over force(x)mass...to accompany (i) length(x)time over length(x)time...which is alpha, and (ii) force(x)length over force(x)length...which is epsilon...MJB

FUTURE of PHYSICS

There should be a 6th Eddington ratio...a ratio of mass(x)time over mass(x)time...Do the Eddington numbers somehow correspond to the number of fundamental forces or the number of spatial + temporal dimensions? I do not know. The approximants are also equally mysterious, and the eventual mathematical solution to these conundrums should yield, profitably, new insight on the origins and potential scope of physical theory, in terms of the infinite in time and space. Equations or relations that describe the origin of these approximants, will yield new forms of fundamental physics including potentially new fundamental force laws or a new understanding of the structure of space-time in terms of additional dimensions of time or space...MJB

NATURAL PRODUCTS

The March, 2020 issue of the Journal of Natural Products honored Jon Clardy. It is an American Chemical Society (ACS) journal. I read the opening editorial biographical piece about Professor Clardy. I might add to this that Jon Clardy taught me in a graduate crystallography course. I used what I learned in this course in my work as a theoretical chemist. Clardy taught the course with graduate level applied mathematics in a way that I could understand...with a competency to explain the concepts and mathematics in a way that was accessible to me. He was also very supportive of me when I tried to teach at a 2- or 4-year college level. I am very lucky to have met him in life. The Journal of Natural Products editorial piece did a nice summary of some of Professor Clardy's accomplishments up to now.

NETWORK DISCOVERY

The 3-,4-connected networks of C were all derived from a building block strategy I used in this work. The Jubilite network was derived from transforming atomic sites in 1 lattice (Waserite) with diatomic sites in another lattice (Jubilite) by "stretching" the atomic sites in to diatomic sites thus. The Moravia network was derived from an Andreini space filling of octahedra and cubooctahedra. The other 3D patterns I just "saw" them...Wells had well over 100 networks published...maybe over half of these were 3-,4-connected networks...I have done about 15 networks...O'Keeffe and his people have derived over 1000 networks I believe...O'Keeffe's networks are spread over all coordination types and polygonal circuit types. My strategies for the 15 networks I have done could be extended to derive many more networks probably. The (1) exocyclobutadiene and (2) cyclohexadiene and (3) barrelene building block motifs are indeed rich sources of 3D organic patterns waiting to be enumerated. The Andreini polyhedral space fillings are the basis for perhaps many potential inorganic and MOF networks. The replacement of atomic sites for diatomic sites could be extended to other inorganic and organic networks thus. O'Keeffe RCSR database, at more than 3500 entries, probably has covered more than 95% of all the possible networks in the Universe, I believe, at this point. Proserpio's SACADA database has over 500 potential C allotrope patterns in it, and probably thus has over 95% of the possible C allotropes in the Universe in this database.