One night I dreamt I was in a place best described as the Sixth Circle of Hell.

Dark Cistern
Dark Cistern - Credit: Pikist

I was in a stone room that seemed like a combination dungeon/cistern with iron gates over glowing red. In the center of the room was a large stone table.

There sat a man dressed darkly and seemed ancient, almost vampiric in his appearance and demeanor, not too different from Rasputin. He wanted to teach me what at first seemed to be a game but turned out to be much more.

When I sat he threatened to kill me if I damaged the pieces as they were each hand made by him in memory of someone.

The pieces were what appeared to be well-worn wooden blocks of ebony and ivory color approximately a half inch each. These blocks could be attached to one another via some invisible means and strung together and articulated into what seemed to be arbitrary three dimensional shapes. Not too dissimilar from a snake-cube puzzle but far more complex.

Unsolved Snake Cube
Unsolved Snake Cube - Credit: Wikipedia

These constructed shapes (polycubes) were placed upon an old parchment with the outlines of what appeared to be polyominos which acted as constraints.

Pentacube Puzzle
Pentacube puzzle - Credit: Wikipedia

The ebony color he called “Bas” and the ivory color “Ga”. Perhaps meaning Soul and Motion?1 Regardless of the meaning I felt there was some sense of duality here that was key. At this point I no longer thought of this as some game but instead as some form of divination through programming these structures.

On the parchment in one of the polyomino shapes there was a marking upon which the “start” of polycube was placed and constrained. My “teacher” referred to this with the letter “I” (or roman numeral 1?) and said it had no name and that it was “unrepresentable”, though the purpose to me seemed clear.

Pentomino Identity

I suggested the term “Identity” and upon hearing this his demeanor changed. He was satisfied and wished for me to write my name upon the parchment so that he could remember me and that he would show me how to perform arithmetic next time we met and other things. At that moment I had a flash in my mind of symbols and expressions in what appeared to be some combination of Stack effect diagram and Fitch’s notation.

I wrote the name “Dreamer” and awakened.

Instead of waiting in hope of another dream I can take this as inspiration and attempt to realize this mysterious construct.

While I have little to go on, there was still plenty of information I think to develop a model of computation. I’ll fiddle with this idea and in a future post try to formalize this. In the mean time, here is a note dump of possibly related ideas.

  • The Piet language
  • The Piet++
  • What is the significance of the starting/identity block? Entry point?
  • Can the blocks self organize like some type of 3d cellular automata? Should they?
  • Does Liquid Intelligence apply where each block acts as a fixed Perceptron? Statistical physics of liquid brains
  • Why the constraint on the board? Does the constraint apply above the base? Can overhangs exist?
  • How does the user get feedback from the system? Symbolic?
  • If a power source is contained within each block, what would that look like? Perhaps a diamond battery”?
    • The power source could then drive the unseen force holding the blocks together.

# Footnotes

  1. I’m guessing to the meaning of these words based on the feeling I had in the dream. Maybe off the mark. 


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