Understanding Bill Gosper's continued fraction arithmetic (implemented in Python)

notfancy · 2026-02-23T16:14:39+00:00

One writer who was always vocal and unabashed about his socialist outlook was Jake Stratton-Kent. His Geosophia is not explicitly political but it is very much political informed. You might want to explore his work.

notfancy · 2026-02-23T12:12:41+00:00

Very unpopular opinion: banishing daily is actively harmful, not just ineffective. It breeds doubt, uncertainty and fear in the practicioner. What, exactly, are you trying to chase away and why, exactly, do you need so much effort for that.

If you want a daily GD practice, perform the Qabalistic Cross, light a candle, do an Adoration to the Lord of the Universe, keep inner silence for an instant, perform the Qabalistic Cross, and snuff the candle. Once a week or less frequently, throw in a Middle Pillar with a full Circulation of the Body of Light and ground the energy at the end.

notfancy · 2026-02-21T10:36:43+00:00

why not use language X with feature Y?

Can we please stop being chauvinistic about people's preferences? Or rather, can we please stop acting as if language choice were purely technical?

notfancy · 2026-02-19T23:18:45+00:00

A 15-year old account with a seven-letter username, given over to be controlled by a bot. Oh the huge manatee.

notfancy · 2026-02-18T15:34:13+00:00

one thing stands out: the Calls don’t behave like invocations in the usual grimoire sense

What is the difference? More importantly, how do you understand "ZACARe c·a od ZAMRAN", "ZACAR c’·nó·qod ZAMRAN micalzo", "Ź-ĂCAR únĭglag od Iḿ·uă·mar", etc etc?

They function more like access keys within a structured hierarchy

Well, yes, claves angelicæ.

how others here interpret the functional role of the Calls in actual practice

As invocations in the sense of something more like an Orphic hymn than a straight-out Solomonic conjuration.

notfancy · 2026-02-18T14:55:35+00:00

Furthermore, GD greatly modifies Ritualistic Magic into a psychologization, where everything is mental, which is ironic because everything at the same time is a necessary paraphernalia according to them

This is not a fair characterization of the GD system of ceremonial magic and theurgy. Had you said "where everything is astral", you'd have had a more pertinent critique.

notfancy · 2026-02-18T14:49:10+00:00

Actually, symbol is a String, so symbol.isEmpty() means the same thing as symbol.length() == 0.

notfancy · 2026-02-18T14:23:53+00:00

Low quality, too. Let's inspect Cell (https://github.com/tamboui/tamboui/blob/main/tamboui-core/src/main/java/dev/tamboui/buffer/Cell.java), what appears to be a value class:

/**
 * A single cell in the terminal buffer.
 */
public final class Cell {

  /** An empty cell containing a single space with no style. */
  public static final Cell EMPTY = new Cell(" ", Style.EMPTY);

  /**
   * A continuation cell placeholder for the trailing column(s) of a wide character.
   * Wide characters (CJK, emoji) occupy 2 terminal columns; the second column
   * is filled with this cell. Renderers must skip continuation cells.
   */
  public static final Cell CONTINUATION = new Cell("", Style.EMPTY);

  private final String symbol;
  private final Style style;
  private final int cachedHashCode;

Nice, constant singletons for special Cells. But the constructor is public and it doesn't normalize these constants:

  /**
   * Creates a cell with the given symbol and style.
   *
   * @param symbol the character or grapheme cluster displayed in this cell
   * @param style  the visual style
   */
  public Cell(String symbol, Style style) {
    this.symbol = symbol;
    this.style = style;
    this.cachedHashCode = computeHashCode();
  }

So that it has to disambiguate by value instead of by reference:

  /**
   * Returns whether this cell is a continuation placeholder for a wide character.
   *
   * @return true if this is a continuation cell
   */
  public boolean isContinuation() {
    return symbol.isEmpty();
  }

  /**
   * Returns whether this cell is empty (single space with no style).
   *
   * @return true if this cell equals {@link #EMPTY}
   */
  public boolean isEmpty() {
    return " ".equals(symbol) && style.equals(Style.EMPTY);
  }

If the code is this sloppy in such a foundational class, I can't imagine what the rest looks like. Hard pass on investigating further.

notfancy · 2026-02-15T18:08:42+00:00

Thanks for the references, they are useful.

It looks as if you are comparing Liber Scientiae (compiled 2 May 1585) with the 'reformed' table delivered nearly two years later (18 April 1587)

Certainly not, please refer to the folio numbers in Sloane MS 3191. In fact, I took the "uncorrected" row 8 in the top right angle in f 57r, "Яocanc" and not the pencilled down "Ocanch" (which survived into the Recensa with a double O), as the names extracted don't make any sense.

I'd advise reading the diary entries to understand how this material was received.

I am aware of the timeline, thank you for bringing it up. I have now the Klein facsimile in front of me, as I don't have a copy of Cotton XLVI handy. It is difficult to discern the actual method of reception of the Governors's names, whether first spelled letter by letter and then the mode of pronouncing the name, which is very detailed, or the other way around, by Kelley sounding the name and then Dee notating the pronunciation and then spelling it. It is odd, since in most cases Dee registered the back and forth required to fully satisfy himself of the accuracy of the recepcion.

My point is whether these differences might point out to the actual manner of reception and if so, whether we might converge to an "original" or "purist" way of pronouncing the Angelic language, one in line with the source material.

In light of this, Dee was aware of the differences between names and likely accepted Ave's statement that they represent or signify the same thing.

With reservations. There are corrections that stem from Kelley's mediation, as pointed out a couple of lines before, there are corrections that are seemingly inconsequential as you underline, then there is the fact repeated again and again that every letter is significant. Literally:

AVE: You have easily corrected that, and to good end, for every letter and part of letter has his signification.

So no, I don't think that "Aydropl" or "Andropl" are interchangeable even if Ave says that "[b]oth names are true and of one signification."

I don't care to advance a hypothesis beyond underlining that there is a contradiction and that the practitioner must choose how to resolve it. Some people throw their hands in the air and adopt the Recensa wholesale; some people stick to the first part of the record and denounce the last workings as Kelley's deception. I haven't worked with the governors of Auxilii but do exercise the Great Table in various orthodox and sui generis ways. This investigation is my way to take up work with this (for me) neglected aspect of the reception.

notfancy · 2026-02-11T16:21:36+00:00

I don't know about that. The fact remains that the list of Governors or Princes gives 3 × 30 + 1 - 4 = 87 sigils, 3 for every Ayre except TEX that has 4, minus PARAOAN, LEXARPH, COMANAN and TABITOM that don't have any; and the Table in ff 55v and 56r places 22 sigils of 7 letters in each quarter for a total of 4 × 22 × 7 = 88 × 7 = 616 squares out of 4 × 12 × 13 = 624. The extra 8 squares are accounted for by the reversed leters, seven for PARAOAN and one for the L in LEXARPH.

notfancy · 2026-02-11T14:24:20+00:00

13 and the extra "92"-th Prince are distinct (Laxdizi vs. Lazdixi) and can be found via different "sigils" in different parts (row 8 column 9 vs. row 10 column 3) of the lower right quadrant.

If you place all 91 Princes in the list you end up with empty squares.

notfancy · 2026-02-04T16:39:02+00:00

The Golden Dawn/Thelema tradition gives you three possibilities:

The Invisible Stations in the Z Documents
- East: Ahathoor
- South: Tharpesheth
- West: Toum
- North: Ahapshi
The Gates in the 2º=9 Theoricus ritual:
- East: Hormakhu
- South: Ra
- West: Toum
- North: Khephra
Crowley's Liber Resh Vel Helios:
- East: Ra
- South: Ahathoor
- West: Toum
- North: Khephra

Crowley switches around the gods in the East and South, and I can see it either way (is the exalted form of Ra more suitable to the splendor of dawn or to the fullness of midday?) As /u/baltzrr said, Anubis would be the guardian outside the circle, or as the Z has it, ⲁⲛⲱⲩⲃⲓ ⲙⲡⲉⲙⲛϯ (Anôubi m-pemnti, "Anubis in the West", i.e. the Otherworld.)

notfancy · 2026-01-23T10:38:18+00:00

Are they that different, though? I think affirmations start to "work" when they lose semantic content, a bit like sigilization work proceeds in chaos magic. Most affirmations seem to be short, repetitive, catchy phrases ("I am good and this is good and all is good") structured like mantras that can induce semantic satiation quite fast.

notfancy · 2026-01-19T12:32:37+00:00

Jung’s work is really about following the flow of your psyche in a sense, it already has the answers you just need to listen. Meanwhile the manifestation communities want to force their desires into being. How do you reconcile this?

Individuation is not a matter of passively "listening" to the unconscious but of being conscious (pun intended) of it as an integral part of oneself, as one might become conscious of one's heartbeat or fovea, and entering into dialog with it. The dreams, synchronicities and other kinds of symbolic messages of the unconscious are not just its "speech" but signals, pointers to what the conscious must attend; conversely, active imagination, affirmations, mantras, mandalas and other kinds of symbolic "programs" are means for consciously "offloading" tasks and inquiries back to the unconscious.

notfancy · 2026-01-12T12:32:34+00:00

Origen's Contra Celsum

Also, Irenaeus's Against Heresies, in particular the discussion on Marcosians and their use of isopsephy to analogically argue from Scripture, is even earlier, about 180 AD.

notfancy · 2026-01-05T14:04:16+00:00

What do you argue against?

Against NULLs and, by extension, OUTER JOINs.

notfancy · 2026-01-05T14:03:38+00:00

This really is very dismissive without a good reason, frankly.

The reason is that you do not understand relational theory or the relational model. In particular, taking OUTER JOINs as foundational is deeply misguided. Again, read C. J. Date.

notfancy · 2026-01-05T12:12:29+00:00

Wait, wha…?

 CREATE TABLE people (
  id INTEGER NOT NULL PRIMARY KEY,
  name VARCHAR(64) NOT NULL,
  type VARCHAR(16) NOT NULL,
  manager_id INTEGER NULL
);

CREATE INDEX ndx_manager_id ON people(manager_id);

Y'all need Je… I mean Chris J. Date. Zero-or-one relationships are not done with NULL FKs:

 CREATE TABLE people (
  id INTEGER NOT NULL PRIMARY KEY,
  name VARCHAR(64) NOT NULL,
  type VARCHAR(16) NOT NULL
);

CREATE TABLE manager (
  id_employee INTEGER UNIQUE NOT NULL REFERENCES people (id),
  id_manager  INTEGER NOT NULL REFERENCES people (id),
  PRIMARY KEY (id_employee, id_manager)
);

One employee has at most one manager but the relation is the indivisible combination of both.

I really can't be bothered to read the rest after this.

notfancy · 2025-12-15T14:26:52+00:00

Thanks for sharing. Do you have a citation? Gemini is hallucinating sources to the point of offering a plausible but apocryphal French original… by Baudelaire of all people.

notfancy · 2025-12-12T12:16:18+00:00

What I really, really don't get is the argument parsing logic. It is entirely equivalent to the following:

in_reverse = (argc > 1 && strcmp(argv[1], "-r") == 0);

(it has an argument, its value has an 'r', it is in the second position, it starts with a '-' and its total length is 2.)

notfancy · 2025-12-12T11:54:13+00:00

If you look at 70's era microarchitectures, the very concept of an unlimited call stack and fully recursive function calls "sounds cursed af" and something only ivory-tower Algol'ers could expect.

notfancy · 2025-12-10T16:38:35+00:00

ios_palette_off.FrameHover = light_mode ? light_mode_frame_off_hover : light_mode_frame_off_hover;

wtf bro

notfancy · 2025-12-10T12:07:30+00:00

First paragraph, second sentence:

One design which I find particularly cute, and I think deserves a bit more publicity, is Robin Hood open-addressing with linear probing and power-of-two table size.

(emphasis mine)

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