URB #442 — The TRALSE Number: Dissolving the Real/Imaginary Binary in Mathematics

The distinction between "real" and "imaginary" numbers is not an ontological fact — it is a historical accident embedded in a pejorative label. Descartes coined "imaginary" in 1637 as a put-down: numbers he could not physically interpret but which appeared in his equations. The label stuck. For nearly four centuries, mathematics has officially named one axis of the complex plane "real" (implying genuine existence) and the orthogonal axis "imaginary" (implying non-existence or fiction). TI Sigma identifies this as a category error with consequences for both mathematics and physics: it treats the content dimension of experience as ontologically privileged over the phase dimension, when TI Sigma's central claim is precisely the opposite — that all of reality is held in consciousness, consciousness is irreducibly complex-valued (content AND phase), and therefore all quantities describing reality are inherently complex. The real/imaginary binary is a TRALSE situation: True (in the sense that there is a geometric distinction between the two axes), False (in the sense that "imaginary" numbers are physically necessary and fully real in any meaningful sense), and TRALSE (both axes are equally real dimensions of a single complex space, and the distinction between them is a measurement convention — a choice of projection axis — not an ontological fact). This paper argues for the mathematical reform: dissolve the "real/imaginary" binary, adopt new terminology ("manifest" and "phase" components), establish the complex plane as the primitive domain, and formally recognize that any quantity expressed as purely "real" is a special case (phase = 0) rather than the default.