Doing theology from below, from below?

The patient's view: doing medical history from below.

Constructing Cardinals from Below

If the initial segment Σ of Ω is a set, then it has a least strict upper bound S(Σ) ∈ Ω. Thus, for numbers α = S(Σ) and β = S(Σ′), α < β iff α ∈ Σ′; α = β iff Σ = Σ′; S(∅) is the least number 0 (although Cantor himself took the least number to be 1); if Σ has a greatest element γ, then α is its successor γ + 1; and if Σ is non-null and has no greatest element, then α is the least upper bound of...

Kuratowski Theorem from below

Proof. Let us assume that G is planar but not free planar. Then there exists an edge xy not belonging to the graph whom adding to the graph it becomes non-planar. Then in G for an arbitrary cycle C through x, y there exists a pair of screening bridges Bx and By x from y with respect to C, i. e. either Bx and By are not placeable on one side against C or they are connected [i.e. not placeable to...

Solitons, from below.

It was 3:15 A.M. on a cold night in Urbana, Illinois about 25 years ago. I had been on my feet since the previous morning, preparing the experiment. Professor Enrico Gratton had instructed me to machine a brass piece to replace a window in the cryostat. I finished the piece on a lathe, drilled a hole in the center, soldered a 1/4-in. copper tube and sealed the end outside the cryostat with a co...

Superstrings:the View from Below

We review the Standard Model in a form conducive to formulating its possible short distance extensions. This depends on the value of the Higgs mass, the only unknown parameter of the model. We suggest methods to reproduce many of the small numbers in the model in terms of scale ratios, applying seesaw like ideas to the breaking of chiral symmetries. We then investigate how the N = 1 Standard Mo...