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The Spectral Delay Pëdal Incompleteness Theorem

Writer's picture: Kyle KamrathKyle Kamrath

Kurt Gödel ruined math in the 20th century. 


Until that point, mathematicians were hopeful that a “complete” system of math existed: one where the rules of math and logic could be used to prove any fact, and where new facts could be discovered using math and logic. But mathematicians were running into problems. Across several fields, there seemed to be truths that were inherently unprovable: paradoxes. These paradoxes were thought to be the result of errors—and if we could correct those errors, the pieces of the puzzle would fall into place, revealing a full and complete picture. Two mathematicians (Russell and Whitehead) attempted to do exactly that: rebuild math from the ground up using nothing but logic. It was a two thousand page book full of nearly unreadable glyphs and symbols, and it took ~70 pages to prove “1+1=2”.


But, as Gödel would…prove...math isn't complete. It turns out that no matter what set of ground rules (aka. axioms) that you create in math, it will always produce a contradiction—something that is true and untrue at the same time, like the phrase, “this statement is false.” Gödel showed that there will always be a piece missing from the jigsaw puzzle. 


And so it is with this damn pedal.


Every time we rearrange the circuit, every time we fix an issue, every time we find the last puzzle piece…it seems like some flaw presents itself that prevents us from completing the pedal. Every problem solved is a problem created. Aptly, we are stuck in an endless loop, no closer to finishing than when we started.


Our most recent struggle has been navigating the learning curve of working with SMD suppliers. We made the decision to go SMD because our prototypes were too big to be practical—pedal board real estate is at a premium these days. But not all SMD components are as cheap as their through-hole counterparts, and in some cases are not available at all. No problem, we’ll tweak the circuit to use more available components. Uh-oh, now the bypass switch pops when you step on it. And on it goes.


Gödel’s Incompleteness Theorem proved that there will always be things that math cannot prove, that computers cannot compute, logic cannot explain. Looking for an all-encompassing complete system is the wrong approach—and ultimately limits what math is capable of. 


We’re excited to introduce the Spectral Delay. We have been meticulous—even obsessive—about making it as good as it possibly can. We’ve struck a balance between quality, nice-to-haves, cost, component availability, and a few dozen other variables that keep us up at night. But it won’t be complete. No such thing.

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