The Endless of Sandman

The Endless are merely patterns. The Endless are ideas. The Endless are wave functions. The Endless are repeating motifs. The Endless are echoes of darkness, and nothing more… And even our existences are brief and bounded. None of us will last longer than this version of the Universe.

Destruction of the Endless

The Endless are:

    • Destiny
    • Death
    • Dream
    • Destruction
    • Desire
    • Despair
    • Delirium

Further Reading:




Linear Logic and the Laws of Excluded Middle and Noncontradiction

If LEM is the Law of Excluded Middle and LNC is the Law of Non-contradiction then

  • Classical Logic preserves both LEM and LNC
  • Intuitionistic Logic preserves LNC, but rejects LEM
  • Co-Intuitionistic Logic preserves LEM, but rejects LNC
  • Linear Logic broadly preserves neither, but narrowly preserves and rejects them with its pairs of conjunctive and disjunctive logical operators

Above is shown the four operators of Linear Logic and the statements for their preservation and rejection of LEM and LNC.

Further Reading:

Pete Wolfendale / Essay on Transcendental Realism
(at PhilPapers)





Charles Howard Hinton

Another early author of note about the fourth dimension, Charles Howard Hinton, invented the terms “Ana” and “Kata” to denote the two movements along a fourth-dimensional direction. He was also the inventor of the term “tesseract” for a four-dimensional cube.

Further Reading:






Four-Dimensional Vistas

The Fourth Dimension has been an interest of mine since I was a child. I’m not sure when I first heard about it, but I still have my coverless copy of “Geometry of 4 Dimensions” by Henry Parker Manning that I bought in a used book store. (I wonder why it hasn’t ever been reissued by Dover?) Maybe I heard about the fourth dimension in some science fiction TV movie, or in some mathematical survey book like “Mathematical Snapshots” or “Mathematics and the Imagination”.

Once I tried to explain to my best friend about my newly discovered insight how a hypercube could be folded up in four-dimensional space from its so-called three-dimensional net consisting of eight cubes, just as a regular three-dimensional cube could be folded up from its two-dimensional net of six squares. This 3D net somewhat resembling a cross is famously seen in Dali’s “Crucifixion (Corpus Hypercubus),” although I probably didn’t refer to this painting in my explanation.

I’m not sure who came up with the take-away message from my exposition, but it remains clear in my memory that the “junk in the middle” of the hypercube was a piece of the fourth dimension, just as the faces of a cube enclose a piece of our normal third dimension.

I recently came across Claude Fayette Bragdon, architect, author, draughtsman, stage designer, and mystic. At first I was interested in his drawings found on-line. His book “Four-Dimensional Vistas” started off with a good if overly wordy introduction to the concept of the fourth dimension. But then he suggests that many esoteric concepts such as the meaning of dreams, reincarnation, past-life regression, prognostication, ESP, etc. could possibly be explained by higher dimensional space or even higher dimensional time.

Even though I initially found many of these hypotheses too far-fetched for my tastes, I still found some interesting ideas to mull over in this little book.

Further Reading:

The art of Claude Fayette Bragdon, 1866–1946

Claude Fayette Bragdon / Four-Dimensional Vistas (1930)

Claude Fayette Bragdon / The Beautiful Necessity (1910)

Claude Fayette Bragdon / Architecture and Democracy (1918)

For my gratuitous anime tie-in, Bragdon’s world-view suddenly reminds me of the anime character  Haruhi Suzumiya, who wished for her aliens, time-travelers, and ESPers so much that she willed them into being. If only she had known about the fourth dimension!

[*3.139, *12.121, *13.50]