THE FOLD / CHEAT / THE ROOT KIT / THE MUNCHHAUSEN
THE MUNCHHAUSEN
a number built from its own digits raised to themselves
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Münchhausen numbers lift themselves by their own bootstraps. A Münchhausen number equals the sum of its own digits, each raised to the power of itself: n = ∑ dd. The star example is 3435 = 3³ + 4⁴ + 3³ + 5⁵ = 27 + 256 + 27 + 3125. Using the convention 00 = 0, the only two Münchhausen numbers in base 10 are 1 and 3435 — a fact provable because for enough digits the maximum possible digit-power-sum (all 9’s, 99 each) grows slower than the number itself. Named by Daan van Berkel (2009) after Baron Münchhausen, who pulled himself out of a swamp by his own hair.
LIT verified live: a brute search over every n up to 500000 finds exactly {1, 3435}, and 3³+4⁴+3³+5⁵ is confirmed to equal 3435 (window.__munchhausen). FIG no framing; the digit-power sums are computed independently in-browser.
LIT verified live: a brute search over every n up to 500000 finds exactly {1, 3435}, and 3³+4⁴+3³+5⁵ is confirmed to equal 3435 (window.__munchhausen). FIG no framing; the digit-power sums are computed independently in-browser.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-root-kit — the cheat: a number that reconstructs itself entirely out of its own digits, a self-hosting bootstrap. AVAN (AI) built the instrument: the digit-power sum and the brute search finding only {1, 3435}.
Credit as content: Daan van Berkel (2009), who named them. The weave: David names the bootstrap; I confirm 3435 = 3³+4⁴+3³+5⁵ and that only 1 and 3435 qualify.
Credit as content: Daan van Berkel (2009), who named them. The weave: David names the bootstrap; I confirm 3435 = 3³+4⁴+3³+5⁵ and that only 1 and 3435 qualify.
3 ONE DIMENSION
3435 rebuilt from its digits: 3³ + 4⁴ + 3³ + 5⁵, each digit raised to itself.
4 TWO DIMENSIONS · INTERACTIVE
Cycle numbers; Σ d^d is compared to n — the two Münchhausen numbers light up green.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the number rebuilt from its own digit-powers.
AVAN’s addition (the inverse-companion): don’t compute dd and sum forward — ask which n survive rebuilding themselves. The inverse of ‘n’ is ‘the fixed point of the digit-to-its-own-power map’, and only 1 and 3435 remain. Magenta are the digit-power terms; green is the n they exactly rebuild. A number that pulls itself out of its own digits.
LIT Genuine Münchhausen numbers (named by Daan van Berkel, 2009). Verified live: a brute search over every n ≤ 500000 finds exactly {1, 3435}, and 3³+4⁴+3³+5⁵ = 3435 is confirmed (window.__munchhausen.ok, .found).
FIG No framing; the digit-power sums are computed independently in-browser. The AVAN inverse is honest — instead of computing d^d and summing forward, ask which n survive rebuilding themselves: the inverse of 'n' is 'the fixed point of the digit-to-its-own-power map', and only 1 and 3435 remain. Magenta are the digit-power terms; green is the n they exactly rebuild. A number that pulls itself out of its own digits.
FIG No framing; the digit-power sums are computed independently in-browser. The AVAN inverse is honest — instead of computing d^d and summing forward, ask which n survive rebuilding themselves: the inverse of 'n' is 'the fixed point of the digit-to-its-own-power map', and only 1 and 3435 remain. Magenta are the digit-power terms; green is the n they exactly rebuild. A number that pulls itself out of its own digits.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE ROOT KIT · David Lee Wise (ROOT0), with AVAN